prompt stringlengths 50 973 | response stringlengths 14 4.76k | source stringclasses 7
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Question: A curator is arranging 10 distinct biographies in a row, including one on Grace. If the biographies are randomly ordered, what is the probability that the Grace biography is positioned strictly between the biographies of Bob and Jack (i.e., the Grace biography is neither first nor last among these three, and ... | Consider the relative order of the three specific biographies: Grace, Bob, and Jack.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Grace to be strictly between Bob and Jack.
The favorable orderings are: Bob, Grace, Jack and Jack, Grace, Bob.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Alice. If the biographies are randomly ordered, what is the probability that the Alice biography is positioned strictly between the biographies of David and Bob (i.e., the Alice biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Alice, David, and Bob.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Alice to be strictly between David and Bob.
The favorable orderings are: David, Alice, Bob and Bob, Alice, David.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Ivy. If the biographies are randomly ordered, what is the probability that the Ivy biography is positioned strictly between the biographies of Grace and David (i.e., the Ivy biography is neither first nor last among these three, and the... | Consider the relative order of the three specific biographies: Ivy, Grace, and David.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Ivy to be strictly between Grace and David.
The favorable orderings are: Grace, Ivy, David and David, Ivy, Grace.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Henry. If the biographies are randomly ordered, what is the probability that the Henry biography is positioned strictly between the biographies of Ivy and Frank (i.e., the Henry biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Henry, Ivy, and Frank.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Henry to be strictly between Ivy and Frank.
The favorable orderings are: Ivy, Henry, Frank and Frank, Henry, Ivy.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Grace. If the biographies are randomly ordered, what is the probability that the Grace biography is positioned strictly between the biographies of Bob and David (i.e., the Grace biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Grace, Bob, and David.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Grace to be strictly between Bob and David.
The favorable orderings are: Bob, Grace, David and David, Grace, Bob.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Henry. If the biographies are randomly ordered, what is the probability that the Henry biography is positioned strictly between the biographies of Grace and Ivy (i.e., the Henry biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Henry, Grace, and Ivy.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Henry to be strictly between Grace and Ivy.
The favorable orderings are: Grace, Henry, Ivy and Ivy, Henry, Grace.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Frank. If the biographies are randomly ordered, what is the probability that the Frank biography is positioned strictly between the biographies of Alice and David (i.e., the Frank biography is neither first nor last among these three, a... | Consider the relative order of the three specific biographies: Frank, Alice, and David.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Frank to be strictly between Alice and David.
The favorable orderings are: Alice, Frank, David and David, Frank, Alice.
Thus there are ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Alice. If the biographies are randomly ordered, what is the probability that the Alice biography is positioned strictly between the biographies of Carol and Eve (i.e., the Alice biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Alice, Carol, and Eve.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Alice to be strictly between Carol and Eve.
The favorable orderings are: Carol, Alice, Eve and Eve, Alice, Carol.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Ivy. If the biographies are randomly ordered, what is the probability that the Ivy biography is positioned strictly between the biographies of Henry and Frank (i.e., the Ivy biography is neither first nor last among these three, and the... | Consider the relative order of the three specific biographies: Ivy, Henry, and Frank.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Ivy to be strictly between Henry and Frank.
The favorable orderings are: Henry, Ivy, Frank and Frank, Ivy, Henry.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Carol. If the biographies are randomly ordered, what is the probability that the Carol biography is positioned strictly between the biographies of Alice and Henry (i.e., the Carol biography is neither first nor last among these three, a... | Consider the relative order of the three specific biographies: Carol, Alice, and Henry.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Carol to be strictly between Alice and Henry.
The favorable orderings are: Alice, Carol, Henry and Henry, Carol, Alice.
Thus there are ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Jack. If the biographies are randomly ordered, what is the probability that the Jack biography is positioned strictly between the biographies of David and Bob (i.e., the Jack biography is neither first nor last among these three, and th... | Consider the relative order of the three specific biographies: Jack, David, and Bob.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Jack to be strictly between David and Bob.
The favorable orderings are: David, Jack, Bob and Bob, Jack, David.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Frank. If the biographies are randomly ordered, what is the probability that the Frank biography is positioned strictly between the biographies of Eve and Alice (i.e., the Frank biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Frank, Eve, and Alice.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Frank to be strictly between Eve and Alice.
The favorable orderings are: Eve, Frank, Alice and Alice, Frank, Eve.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Frank. If the biographies are randomly ordered, what is the probability that the Frank biography is positioned strictly between the biographies of Carol and Ivy (i.e., the Frank biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Frank, Carol, and Ivy.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Frank to be strictly between Carol and Ivy.
The favorable orderings are: Carol, Frank, Ivy and Ivy, Frank, Carol.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Henry. If the biographies are randomly ordered, what is the probability that the Henry biography is positioned strictly between the biographies of Eve and Carol (i.e., the Henry biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Henry, Eve, and Carol.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Henry to be strictly between Eve and Carol.
The favorable orderings are: Eve, Henry, Carol and Carol, Henry, Eve.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Ivy. If the biographies are randomly ordered, what is the probability that the Ivy biography is positioned strictly between the biographies of Alice and David (i.e., the Ivy biography is neither first nor last among these three, and the... | Consider the relative order of the three specific biographies: Ivy, Alice, and David.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Ivy to be strictly between Alice and David.
The favorable orderings are: Alice, Ivy, David and David, Ivy, Alice.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Bob. If the biographies are randomly ordered, what is the probability that the Bob biography is positioned strictly between the biographies of Eve and Henry (i.e., the Bob biography is neither first nor last among these three, and the o... | Consider the relative order of the three specific biographies: Bob, Eve, and Henry.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Bob to be strictly between Eve and Henry.
The favorable orderings are: Eve, Bob, Henry and Henry, Bob, Eve.
Thus there are 2 favorable orde... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Frank. If the biographies are randomly ordered, what is the probability that the Frank biography is positioned strictly between the biographies of Grace and Jack (i.e., the Frank biography is neither first nor last among these three, an... | Consider the relative order of the three specific biographies: Frank, Grace, and Jack.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Frank to be strictly between Grace and Jack.
The favorable orderings are: Grace, Frank, Jack and Jack, Frank, Grace.
Thus there are 2 fa... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Henry. If the biographies are randomly ordered, what is the probability that the Henry biography is positioned strictly between the biographies of Grace and David (i.e., the Henry biography is neither first nor last among these three, a... | Consider the relative order of the three specific biographies: Henry, Grace, and David.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Henry to be strictly between Grace and David.
The favorable orderings are: Grace, Henry, David and David, Henry, Grace.
Thus there are ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Grace. If the biographies are randomly ordered, what is the probability that the Grace biography is positioned strictly between the biographies of Jack and Bob (i.e., the Grace biography is neither first nor last among these three, and ... | Consider the relative order of the three specific biographies: Grace, Jack, and Bob.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Grace to be strictly between Jack and Bob.
The favorable orderings are: Jack, Grace, Bob and Bob, Grace, Jack.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Alice. If the biographies are randomly ordered, what is the probability that the Alice biography is positioned strictly between the biographies of Frank and David (i.e., the Alice biography is neither first nor last among these three, a... | Consider the relative order of the three specific biographies: Alice, Frank, and David.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Alice to be strictly between Frank and David.
The favorable orderings are: Frank, Alice, David and David, Alice, Frank.
Thus there are ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Bob. If the biographies are randomly ordered, what is the probability that the Bob biography is positioned strictly between the biographies of Alice and Henry (i.e., the Bob biography is neither first nor last among these three, and the... | Consider the relative order of the three specific biographies: Bob, Alice, and Henry.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Bob to be strictly between Alice and Henry.
The favorable orderings are: Alice, Bob, Henry and Henry, Bob, Alice.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Ivy. If the biographies are randomly ordered, what is the probability that the Ivy biography is positioned strictly between the biographies of Jack and Carol (i.e., the Ivy biography is neither first nor last among these three, and the ... | Consider the relative order of the three specific biographies: Ivy, Jack, and Carol.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Ivy to be strictly between Jack and Carol.
The favorable orderings are: Jack, Ivy, Carol and Carol, Ivy, Jack.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Carol. If the biographies are randomly ordered, what is the probability that the Carol biography is positioned strictly between the biographies of Grace and Frank (i.e., the Carol biography is neither first nor last among these three, a... | Consider the relative order of the three specific biographies: Carol, Grace, and Frank.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Carol to be strictly between Grace and Frank.
The favorable orderings are: Grace, Carol, Frank and Frank, Carol, Grace.
Thus there are ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Henry. If the biographies are randomly ordered, what is the probability that the Henry biography is positioned strictly between the biographies of Jack and Ivy (i.e., the Henry biography is neither first nor last among these three, and ... | Consider the relative order of the three specific biographies: Henry, Jack, and Ivy.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Henry to be strictly between Jack and Ivy.
The favorable orderings are: Jack, Henry, Ivy and Ivy, Henry, Jack.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Alice. If the biographies are randomly ordered, what is the probability that the Alice biography is positioned strictly between the biographies of Henry and Grace (i.e., the Alice biography is neither first nor last among these three, a... | Consider the relative order of the three specific biographies: Alice, Henry, and Grace.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Alice to be strictly between Henry and Grace.
The favorable orderings are: Henry, Alice, Grace and Grace, Alice, Henry.
Thus there are ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on David. If the biographies are randomly ordered, what is the probability that the David biography is positioned strictly between the biographies of Alice and Ivy (i.e., the David biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: David, Alice, and Ivy.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires David to be strictly between Alice and Ivy.
The favorable orderings are: Alice, David, Ivy and Ivy, David, Alice.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Alice. If the biographies are randomly ordered, what is the probability that the Alice biography is positioned strictly between the biographies of Henry and Eve (i.e., the Alice biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Alice, Henry, and Eve.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Alice to be strictly between Henry and Eve.
The favorable orderings are: Henry, Alice, Eve and Eve, Alice, Henry.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Alice. If the biographies are randomly ordered, what is the probability that the Alice biography is positioned strictly between the biographies of Bob and Ivy (i.e., the Alice biography is neither first nor last among these three, and t... | Consider the relative order of the three specific biographies: Alice, Bob, and Ivy.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Alice to be strictly between Bob and Ivy.
The favorable orderings are: Bob, Alice, Ivy and Ivy, Alice, Bob.
Thus there are 2 favorable orde... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Henry. If the biographies are randomly ordered, what is the probability that the Henry biography is positioned strictly between the biographies of Grace and Eve (i.e., the Henry biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Henry, Grace, and Eve.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Henry to be strictly between Grace and Eve.
The favorable orderings are: Grace, Henry, Eve and Eve, Henry, Grace.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Jack. If the biographies are randomly ordered, what is the probability that the Jack biography is positioned strictly between the biographies of Eve and Carol (i.e., the Jack biography is neither first nor last among these three, and th... | Consider the relative order of the three specific biographies: Jack, Eve, and Carol.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Jack to be strictly between Eve and Carol.
The favorable orderings are: Eve, Jack, Carol and Carol, Jack, Eve.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Alice. If the biographies are randomly ordered, what is the probability that the Alice biography is positioned strictly between the biographies of Grace and Carol (i.e., the Alice biography is neither first nor last among these three, a... | Consider the relative order of the three specific biographies: Alice, Grace, and Carol.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Alice to be strictly between Grace and Carol.
The favorable orderings are: Grace, Alice, Carol and Carol, Alice, Grace.
Thus there are ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Jack. If the biographies are randomly ordered, what is the probability that the Jack biography is positioned strictly between the biographies of Ivy and Alice (i.e., the Jack biography is neither first nor last among these three, and th... | Consider the relative order of the three specific biographies: Jack, Ivy, and Alice.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Jack to be strictly between Ivy and Alice.
The favorable orderings are: Ivy, Jack, Alice and Alice, Jack, Ivy.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Grace. If the biographies are randomly ordered, what is the probability that the Grace biography is positioned strictly between the biographies of Ivy and Jack (i.e., the Grace biography is neither first nor last among these three, and ... | Consider the relative order of the three specific biographies: Grace, Ivy, and Jack.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Grace to be strictly between Ivy and Jack.
The favorable orderings are: Ivy, Grace, Jack and Jack, Grace, Ivy.
Thus there are 2 favorable ... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on David. If the biographies are randomly ordered, what is the probability that the David biography is positioned strictly between the biographies of Eve and Henry (i.e., the David biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: David, Eve, and Henry.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires David to be strictly between Eve and Henry.
The favorable orderings are: Eve, David, Henry and Henry, David, Eve.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Henry. If the biographies are randomly ordered, what is the probability that the Henry biography is positioned strictly between the biographies of Carol and Eve (i.e., the Henry biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Henry, Carol, and Eve.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Henry to be strictly between Carol and Eve.
The favorable orderings are: Carol, Henry, Eve and Eve, Henry, Carol.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Grace. If the biographies are randomly ordered, what is the probability that the Grace biography is positioned strictly between the biographies of Bob and Ivy (i.e., the Grace biography is neither first nor last among these three, and t... | Consider the relative order of the three specific biographies: Grace, Bob, and Ivy.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Grace to be strictly between Bob and Ivy.
The favorable orderings are: Bob, Grace, Ivy and Ivy, Grace, Bob.
Thus there are 2 favorable orde... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Bob. If the biographies are randomly ordered, what is the probability that the Bob biography is positioned strictly between the biographies of Henry and Ivy (i.e., the Bob biography is neither first nor last among these three, and the o... | Consider the relative order of the three specific biographies: Bob, Henry, and Ivy.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Bob to be strictly between Henry and Ivy.
The favorable orderings are: Henry, Bob, Ivy and Ivy, Bob, Henry.
Thus there are 2 favorable orde... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Bob. If the biographies are randomly ordered, what is the probability that the Bob biography is positioned strictly between the biographies of Jack and Eve (i.e., the Bob biography is neither first nor last among these three, and the ot... | Consider the relative order of the three specific biographies: Bob, Jack, and Eve.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Bob to be strictly between Jack and Eve.
The favorable orderings are: Jack, Bob, Eve and Eve, Bob, Jack.
Thus there are 2 favorable ordering... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Carol. If the biographies are randomly ordered, what is the probability that the Carol biography is positioned strictly between the biographies of David and Bob (i.e., the Carol biography is neither first nor last among these three, and... | Consider the relative order of the three specific biographies: Carol, David, and Bob.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Carol to be strictly between David and Bob.
The favorable orderings are: David, Carol, Bob and Bob, Carol, David.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: A curator is arranging 10 distinct biographies in a row, including one on Eve. If the biographies are randomly ordered, what is the probability that the Eve biography is positioned strictly between the biographies of Carol and David (i.e., the Eve biography is neither first nor last among these three, and the... | Consider the relative order of the three specific biographies: Eve, Carol, and David.
There are 3! = 6 possible relative orderings of these three biographies.
The condition requires Eve to be strictly between Carol and David.
The favorable orderings are: Carol, Eve, David and David, Eve, Carol.
Thus there are 2 favora... | tp_probability | 67693cfdda | general |
Question: Nova Distribution has a break-even point of 15,974 units per month. The variable cost per unit is $35, and the selling price per unit is $99. If fixed costs increase by $128 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $99 - $35 = $64
Original fixed costs = 15,974 units × $64/unit = $1,022,336
New fixed costs = $1,022,336 + $128 = $1,022,464
New break-even quantity = $1,022,464 / $64 = 15,976 units
#### 15,976 | tp_finance | 5094262438 | general |
Question: Orion Supply has a break-even point of 17,462 units per month. The variable cost per unit is $15, and the selling price per unit is $32. If fixed costs increase by $68 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $32 - $15 = $17
Original fixed costs = 17,462 units × $17/unit = $296,854
New fixed costs = $296,854 + $68 = $296,922
New break-even quantity = $296,922 / $17 = 17,466 units
#### 17,466 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 14,759 units per month. The variable cost per unit is $24, and the selling price per unit is $100. If fixed costs increase by $532 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $100 - $24 = $76
Original fixed costs = 14,759 units × $76/unit = $1,121,684
New fixed costs = $1,121,684 + $532 = $1,122,216
New break-even quantity = $1,122,216 / $76 = 14,766 units
#### 14,766 | tp_finance | 5094262438 | general |
Question: Prime Freight has a break-even point of 14,155 units per month. The variable cost per unit is $24, and the selling price per unit is $97. If fixed costs increase by $438 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $97 - $24 = $73
Original fixed costs = 14,155 units × $73/unit = $1,033,315
New fixed costs = $1,033,315 + $438 = $1,033,753
New break-even quantity = $1,033,753 / $73 = 14,161 units
#### 14,161 | tp_finance | 5094262438 | general |
Question: Orion Supply has a break-even point of 6,742 units per month. The variable cost per unit is $44, and the selling price per unit is $107. If fixed costs increase by $630 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $107 - $44 = $63
Original fixed costs = 6,742 units × $63/unit = $424,746
New fixed costs = $424,746 + $630 = $425,376
New break-even quantity = $425,376 / $63 = 6,752 units
#### 6,752 | tp_finance | 5094262438 | general |
Question: Prime Freight has a break-even point of 17,935 units per month. The variable cost per unit is $44, and the selling price per unit is $115. If fixed costs increase by $497 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $115 - $44 = $71
Original fixed costs = 17,935 units × $71/unit = $1,273,385
New fixed costs = $1,273,385 + $497 = $1,273,882
New break-even quantity = $1,273,882 / $71 = 17,942 units
#### 17,942 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 5,914 units per month. The variable cost per unit is $38, and the selling price per unit is $92. If fixed costs increase by $216 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $92 - $38 = $54
Original fixed costs = 5,914 units × $54/unit = $319,356
New fixed costs = $319,356 + $216 = $319,572
New break-even quantity = $319,572 / $54 = 5,918 units
#### 5,918 | tp_finance | 5094262438 | general |
Question: Nova Distribution has a break-even point of 18,115 units per month. The variable cost per unit is $21, and the selling price per unit is $35. If fixed costs increase by $140 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $35 - $21 = $14
Original fixed costs = 18,115 units × $14/unit = $253,610
New fixed costs = $253,610 + $140 = $253,750
New break-even quantity = $253,750 / $14 = 18,125 units
#### 18,125 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 12,292 units per month. The variable cost per unit is $15, and the selling price per unit is $91. If fixed costs increase by $456 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $91 - $15 = $76
Original fixed costs = 12,292 units × $76/unit = $934,192
New fixed costs = $934,192 + $456 = $934,648
New break-even quantity = $934,648 / $76 = 12,298 units
#### 12,298 | tp_finance | 5094262438 | general |
Question: Orion Supply has a break-even point of 5,195 units per month. The variable cost per unit is $14, and the selling price per unit is $47. If fixed costs increase by $264 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $47 - $14 = $33
Original fixed costs = 5,195 units × $33/unit = $171,435
New fixed costs = $171,435 + $264 = $171,699
New break-even quantity = $171,699 / $33 = 5,203 units
#### 5,203 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 14,895 units per month. The variable cost per unit is $44, and the selling price per unit is $139. If fixed costs increase by $380 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $139 - $44 = $95
Original fixed costs = 14,895 units × $95/unit = $1,415,025
New fixed costs = $1,415,025 + $380 = $1,415,405
New break-even quantity = $1,415,405 / $95 = 14,899 units
#### 14,899 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 9,155 units per month. The variable cost per unit is $36, and the selling price per unit is $92. If fixed costs increase by $56 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $92 - $36 = $56
Original fixed costs = 9,155 units × $56/unit = $512,680
New fixed costs = $512,680 + $56 = $512,736
New break-even quantity = $512,736 / $56 = 9,156 units
#### 9,156 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 7,596 units per month. The variable cost per unit is $35, and the selling price per unit is $88. If fixed costs increase by $159 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $88 - $35 = $53
Original fixed costs = 7,596 units × $53/unit = $402,588
New fixed costs = $402,588 + $159 = $402,747
New break-even quantity = $402,747 / $53 = 7,599 units
#### 7,599 | tp_finance | 5094262438 | general |
Question: Orion Supply has a break-even point of 17,543 units per month. The variable cost per unit is $21, and the selling price per unit is $93. If fixed costs increase by $360 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $93 - $21 = $72
Original fixed costs = 17,543 units × $72/unit = $1,263,096
New fixed costs = $1,263,096 + $360 = $1,263,456
New break-even quantity = $1,263,456 / $72 = 17,548 units
#### 17,548 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 5,093 units per month. The variable cost per unit is $26, and the selling price per unit is $101. If fixed costs increase by $300 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $101 - $26 = $75
Original fixed costs = 5,093 units × $75/unit = $381,975
New fixed costs = $381,975 + $300 = $382,275
New break-even quantity = $382,275 / $75 = 5,097 units
#### 5,097 | tp_finance | 5094262438 | general |
Question: Orion Supply has a break-even point of 17,491 units per month. The variable cost per unit is $41, and the selling price per unit is $64. If fixed costs increase by $115 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $64 - $41 = $23
Original fixed costs = 17,491 units × $23/unit = $402,293
New fixed costs = $402,293 + $115 = $402,408
New break-even quantity = $402,408 / $23 = 17,496 units
#### 17,496 | tp_finance | 5094262438 | general |
Question: Nova Distribution has a break-even point of 16,952 units per month. The variable cost per unit is $44, and the selling price per unit is $100. If fixed costs increase by $392 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $100 - $44 = $56
Original fixed costs = 16,952 units × $56/unit = $949,312
New fixed costs = $949,312 + $392 = $949,704
New break-even quantity = $949,704 / $56 = 16,959 units
#### 16,959 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 19,882 units per month. The variable cost per unit is $22, and the selling price per unit is $93. If fixed costs increase by $497 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $93 - $22 = $71
Original fixed costs = 19,882 units × $71/unit = $1,411,622
New fixed costs = $1,411,622 + $497 = $1,412,119
New break-even quantity = $1,412,119 / $71 = 19,889 units
#### 19,889 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 15,518 units per month. The variable cost per unit is $16, and the selling price per unit is $76. If fixed costs increase by $420 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $76 - $16 = $60
Original fixed costs = 15,518 units × $60/unit = $931,080
New fixed costs = $931,080 + $420 = $931,500
New break-even quantity = $931,500 / $60 = 15,525 units
#### 15,525 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 10,440 units per month. The variable cost per unit is $16, and the selling price per unit is $30. If fixed costs increase by $56 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $30 - $16 = $14
Original fixed costs = 10,440 units × $14/unit = $146,160
New fixed costs = $146,160 + $56 = $146,216
New break-even quantity = $146,216 / $14 = 10,444 units
#### 10,444 | tp_finance | 5094262438 | general |
Question: Orion Supply has a break-even point of 5,403 units per month. The variable cost per unit is $35, and the selling price per unit is $59. If fixed costs increase by $192 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $59 - $35 = $24
Original fixed costs = 5,403 units × $24/unit = $129,672
New fixed costs = $129,672 + $192 = $129,864
New break-even quantity = $129,864 / $24 = 5,411 units
#### 5,411 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 13,320 units per month. The variable cost per unit is $46, and the selling price per unit is $123. If fixed costs increase by $231 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $123 - $46 = $77
Original fixed costs = 13,320 units × $77/unit = $1,025,640
New fixed costs = $1,025,640 + $231 = $1,025,871
New break-even quantity = $1,025,871 / $77 = 13,323 units
#### 13,323 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 11,752 units per month. The variable cost per unit is $33, and the selling price per unit is $59. If fixed costs increase by $260 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $59 - $33 = $26
Original fixed costs = 11,752 units × $26/unit = $305,552
New fixed costs = $305,552 + $260 = $305,812
New break-even quantity = $305,812 / $26 = 11,762 units
#### 11,762 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 16,765 units per month. The variable cost per unit is $40, and the selling price per unit is $112. If fixed costs increase by $576 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $112 - $40 = $72
Original fixed costs = 16,765 units × $72/unit = $1,207,080
New fixed costs = $1,207,080 + $576 = $1,207,656
New break-even quantity = $1,207,656 / $72 = 16,773 units
#### 16,773 | tp_finance | 5094262438 | general |
Question: Orion Supply has a break-even point of 12,921 units per month. The variable cost per unit is $30, and the selling price per unit is $42. If fixed costs increase by $84 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $42 - $30 = $12
Original fixed costs = 12,921 units × $12/unit = $155,052
New fixed costs = $155,052 + $84 = $155,136
New break-even quantity = $155,136 / $12 = 12,928 units
#### 12,928 | tp_finance | 5094262438 | general |
Question: Nova Distribution has a break-even point of 5,938 units per month. The variable cost per unit is $23, and the selling price per unit is $59. If fixed costs increase by $36 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $59 - $23 = $36
Original fixed costs = 5,938 units × $36/unit = $213,768
New fixed costs = $213,768 + $36 = $213,804
New break-even quantity = $213,804 / $36 = 5,939 units
#### 5,939 | tp_finance | 5094262438 | general |
Question: Nova Distribution has a break-even point of 12,765 units per month. The variable cost per unit is $34, and the selling price per unit is $47. If fixed costs increase by $65 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $47 - $34 = $13
Original fixed costs = 12,765 units × $13/unit = $165,945
New fixed costs = $165,945 + $65 = $166,010
New break-even quantity = $166,010 / $13 = 12,770 units
#### 12,770 | tp_finance | 5094262438 | general |
Question: Prime Freight has a break-even point of 6,914 units per month. The variable cost per unit is $44, and the selling price per unit is $56. If fixed costs increase by $24 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $56 - $44 = $12
Original fixed costs = 6,914 units × $12/unit = $82,968
New fixed costs = $82,968 + $24 = $82,992
New break-even quantity = $82,992 / $12 = 6,916 units
#### 6,916 | tp_finance | 5094262438 | general |
Question: Nova Distribution has a break-even point of 14,763 units per month. The variable cost per unit is $50, and the selling price per unit is $119. If fixed costs increase by $483 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $119 - $50 = $69
Original fixed costs = 14,763 units × $69/unit = $1,018,647
New fixed costs = $1,018,647 + $483 = $1,019,130
New break-even quantity = $1,019,130 / $69 = 14,770 units
#### 14,770 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 10,053 units per month. The variable cost per unit is $43, and the selling price per unit is $130. If fixed costs increase by $870 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $130 - $43 = $87
Original fixed costs = 10,053 units × $87/unit = $874,611
New fixed costs = $874,611 + $870 = $875,481
New break-even quantity = $875,481 / $87 = 10,063 units
#### 10,063 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 11,975 units per month. The variable cost per unit is $20, and the selling price per unit is $37. If fixed costs increase by $170 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $37 - $20 = $17
Original fixed costs = 11,975 units × $17/unit = $203,575
New fixed costs = $203,575 + $170 = $203,745
New break-even quantity = $203,745 / $17 = 11,985 units
#### 11,985 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 14,346 units per month. The variable cost per unit is $12, and the selling price per unit is $111. If fixed costs increase by $891 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $111 - $12 = $99
Original fixed costs = 14,346 units × $99/unit = $1,420,254
New fixed costs = $1,420,254 + $891 = $1,421,145
New break-even quantity = $1,421,145 / $99 = 14,355 units
#### 14,355 | tp_finance | 5094262438 | general |
Question: Zenith Shipping has a break-even point of 15,637 units per month. The variable cost per unit is $37, and the selling price per unit is $96. If fixed costs increase by $531 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $96 - $37 = $59
Original fixed costs = 15,637 units × $59/unit = $922,583
New fixed costs = $922,583 + $531 = $923,114
New break-even quantity = $923,114 / $59 = 15,646 units
#### 15,646 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 8,431 units per month. The variable cost per unit is $39, and the selling price per unit is $131. If fixed costs increase by $460 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $131 - $39 = $92
Original fixed costs = 8,431 units × $92/unit = $775,652
New fixed costs = $775,652 + $460 = $776,112
New break-even quantity = $776,112 / $92 = 8,436 units
#### 8,436 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 15,356 units per month. The variable cost per unit is $15, and the selling price per unit is $29. If fixed costs increase by $28 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $29 - $15 = $14
Original fixed costs = 15,356 units × $14/unit = $214,984
New fixed costs = $214,984 + $28 = $215,012
New break-even quantity = $215,012 / $14 = 15,358 units
#### 15,358 | tp_finance | 5094262438 | general |
Question: Nova Distribution has a break-even point of 19,577 units per month. The variable cost per unit is $18, and the selling price per unit is $111. If fixed costs increase by $744 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $111 - $18 = $93
Original fixed costs = 19,577 units × $93/unit = $1,820,661
New fixed costs = $1,820,661 + $744 = $1,821,405
New break-even quantity = $1,821,405 / $93 = 19,585 units
#### 19,585 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 16,397 units per month. The variable cost per unit is $14, and the selling price per unit is $77. If fixed costs increase by $126 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $77 - $14 = $63
Original fixed costs = 16,397 units × $63/unit = $1,033,011
New fixed costs = $1,033,011 + $126 = $1,033,137
New break-even quantity = $1,033,137 / $63 = 16,399 units
#### 16,399 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 12,208 units per month. The variable cost per unit is $16, and the selling price per unit is $36. If fixed costs increase by $160 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $36 - $16 = $20
Original fixed costs = 12,208 units × $20/unit = $244,160
New fixed costs = $244,160 + $160 = $244,320
New break-even quantity = $244,320 / $20 = 12,216 units
#### 12,216 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 6,166 units per month. The variable cost per unit is $19, and the selling price per unit is $43. If fixed costs increase by $120 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $43 - $19 = $24
Original fixed costs = 6,166 units × $24/unit = $147,984
New fixed costs = $147,984 + $120 = $148,104
New break-even quantity = $148,104 / $24 = 6,171 units
#### 6,171 | tp_finance | 5094262438 | general |
Question: Apex Logistics has a break-even point of 15,973 units per month. The variable cost per unit is $22, and the selling price per unit is $118. If fixed costs increase by $288 per month due to a new warehouse lease, what is the new break-even quantity in units?
Answer: | Contribution margin per unit = $118 - $22 = $96
Original fixed costs = 15,973 units × $96/unit = $1,533,408
New fixed costs = $1,533,408 + $288 = $1,533,696
New break-even quantity = $1,533,696 / $96 = 15,976 units
#### 15,976 | tp_finance | 5094262438 | general |
Question: In a office, there are 10 desks placed in 5 rows of 2 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 desks from 10 is C(10,2) = 45.
Each row contains 2 desks.
The number of ways to select 2 desks from a single row is C(2,2) = 1.
There are 5 rows, so the number of favorable pairs is 5 * 1 = 5.
The probability is 5/45.
Simplifying the fraction gives 1/9.
#### 1/9 | tp_probability | a0e773490c | general |
Question: A display in a library contains 6 books in a grid of 2 rows and 3 columns. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 books from 6 is C(6,2) = 15.
Each row contains 3 books.
The number of ways to select 2 books from a single row is C(3,2) = 3.
There are 2 rows, so the number of favorable pairs is 2 * 3 = 6.
The probability is 6/15.
Simplifying the fraction gives 2/5.
#### 2/5 | tp_probability | a0e773490c | general |
Question: A warehouse has 15 identical boxes arranged in a 5x3 matrix. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 boxes from 15 is C(15,2) = 105.
Each row contains 3 boxes.
The number of ways to select 2 boxes from a single row is C(3,2) = 3.
There are 5 rows, so the number of favorable pairs is 5 * 3 = 15.
The probability is 15/105.
Simplifying the fraction gives 1/7.
#### 1/7 | tp_probability | a0e773490c | general |
Question: A garden has 30 identical flowers arranged in a 5x6 matrix. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 flowers from 30 is C(30,2) = 435.
Each row contains 6 flowers.
The number of ways to select 2 flowers from a single row is C(6,2) = 15.
There are 5 rows, so the number of favorable pairs is 5 * 15 = 75.
The probability is 75/435.
Simplifying the fraction gives 5/29.
#### 5/29 | tp_probability | a0e773490c | general |
Question: A display in a school contains 10 students in a grid of 5 rows and 2 columns. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 students from 10 is C(10,2) = 45.
Each row contains 2 students.
The number of ways to select 2 students from a single row is C(2,2) = 1.
There are 5 rows, so the number of favorable pairs is 5 * 1 = 5.
The probability is 5/45.
Simplifying the fraction gives 1/9.
#### 1/9 | tp_probability | a0e773490c | general |
Question: In a school, there are 25 students placed in 5 rows of 5 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 students from 25 is C(25,2) = 300.
Each row contains 5 students.
The number of ways to select 2 students from a single row is C(5,2) = 10.
There are 5 rows, so the number of favorable pairs is 5 * 10 = 50.
The probability is 50/300.
Simplifying the fraction gives 1/6.
#### 1/6 | tp_probability | a0e773490c | general |
Question: In a warehouse, there are 8 boxes placed in 4 racks of 2 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 boxes from 8 is C(8,2) = 28.
Each row contains 2 boxes.
The number of ways to select 2 boxes from a single row is C(2,2) = 1.
There are 4 rows, so the number of favorable pairs is 4 * 1 = 4.
The probability is 4/28.
Simplifying the fraction gives 1/7.
#### 1/7 | tp_probability | a0e773490c | general |
Question: In a warehouse, there are 12 boxes placed in 2 racks of 6 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 boxes from 12 is C(12,2) = 66.
Each row contains 6 boxes.
The number of ways to select 2 boxes from a single row is C(6,2) = 15.
There are 2 rows, so the number of favorable pairs is 2 * 15 = 30.
The probability is 30/66.
Simplifying the fraction gives 5/11.
#### 5/11 | tp_probability | a0e773490c | general |
Question: A display in a library contains 20 books in a grid of 5 rows and 4 columns. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 books from 20 is C(20,2) = 190.
Each row contains 4 books.
The number of ways to select 2 books from a single row is C(4,2) = 6.
There are 5 rows, so the number of favorable pairs is 5 * 6 = 30.
The probability is 30/190.
Simplifying the fraction gives 3/19.
#### 3/19 | tp_probability | a0e773490c | general |
Question: A office has 6 identical desks arranged in a 3x2 matrix. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 desks from 6 is C(6,2) = 15.
Each row contains 2 desks.
The number of ways to select 2 desks from a single row is C(2,2) = 1.
There are 3 rows, so the number of favorable pairs is 3 * 1 = 3.
The probability is 3/15.
Simplifying the fraction gives 1/5.
#### 1/5 | tp_probability | a0e773490c | general |
Question: In a library, there are 18 books placed in 3 shelves of 6 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 books from 18 is C(18,2) = 153.
Each row contains 6 books.
The number of ways to select 2 books from a single row is C(6,2) = 15.
There are 3 rows, so the number of favorable pairs is 3 * 15 = 45.
The probability is 45/153.
Simplifying the fraction gives 5/17.
#### 5/17 | tp_probability | a0e773490c | general |
Question: In a library, there are 16 books placed in 4 shelves of 4 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 books from 16 is C(16,2) = 120.
Each row contains 4 books.
The number of ways to select 2 books from a single row is C(4,2) = 6.
There are 4 rows, so the number of favorable pairs is 4 * 6 = 24.
The probability is 24/120.
Simplifying the fraction gives 1/5.
#### 1/5 | tp_probability | a0e773490c | general |
Question: In a warehouse, there are 12 boxes placed in 4 racks of 3 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 boxes from 12 is C(12,2) = 66.
Each row contains 3 boxes.
The number of ways to select 2 boxes from a single row is C(3,2) = 3.
There are 4 rows, so the number of favorable pairs is 4 * 3 = 12.
The probability is 12/66.
Simplifying the fraction gives 2/11.
#### 2/11 | tp_probability | a0e773490c | general |
Question: A display in a warehouse contains 20 boxes in a grid of 5 rows and 4 columns. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 boxes from 20 is C(20,2) = 190.
Each row contains 4 boxes.
The number of ways to select 2 boxes from a single row is C(4,2) = 6.
There are 5 rows, so the number of favorable pairs is 5 * 6 = 30.
The probability is 30/190.
Simplifying the fraction gives 3/19.
#### 3/19 | tp_probability | a0e773490c | general |
Question: A garden has 6 identical flowers arranged in a 2x3 matrix. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 flowers from 6 is C(6,2) = 15.
Each row contains 3 flowers.
The number of ways to select 2 flowers from a single row is C(3,2) = 3.
There are 2 rows, so the number of favorable pairs is 2 * 3 = 6.
The probability is 6/15.
Simplifying the fraction gives 2/5.
#### 2/5 | tp_probability | a0e773490c | general |
Question: A display in a office contains 8 desks in a grid of 2 rows and 4 columns. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 desks from 8 is C(8,2) = 28.
Each row contains 4 desks.
The number of ways to select 2 desks from a single row is C(4,2) = 6.
There are 2 rows, so the number of favorable pairs is 2 * 6 = 12.
The probability is 12/28.
Simplifying the fraction gives 3/7.
#### 3/7 | tp_probability | a0e773490c | general |
Question: In a school, there are 20 students placed in 4 rows of 5 each. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 students from 20 is C(20,2) = 190.
Each row contains 5 students.
The number of ways to select 2 students from a single row is C(5,2) = 10.
There are 4 rows, so the number of favorable pairs is 4 * 10 = 40.
The probability is 40/190.
Simplifying the fraction gives 4/19.
#### 4/19 | tp_probability | a0e773490c | general |
Question: A warehouse has 25 identical boxes arranged in a 5x5 matrix. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 boxes from 25 is C(25,2) = 300.
Each row contains 5 boxes.
The number of ways to select 2 boxes from a single row is C(5,2) = 10.
There are 5 rows, so the number of favorable pairs is 5 * 10 = 50.
The probability is 50/300.
Simplifying the fraction gives 1/6.
#### 1/6 | tp_probability | a0e773490c | general |
Question: A display in a library contains 25 books in a grid of 5 rows and 5 columns. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 books from 25 is C(25,2) = 300.
Each row contains 5 books.
The number of ways to select 2 books from a single row is C(5,2) = 10.
There are 5 rows, so the number of favorable pairs is 5 * 10 = 50.
The probability is 50/300.
Simplifying the fraction gives 1/6.
#### 1/6 | tp_probability | a0e773490c | general |
Question: A warehouse has 8 identical boxes arranged in a 2x4 matrix. Two items are chosen at random without replacement. What is the probability that they are in the same row? Express your answer as a common fraction in simplest form.
Answer: | Total number of ways to select 2 boxes from 8 is C(8,2) = 28.
Each row contains 4 boxes.
The number of ways to select 2 boxes from a single row is C(4,2) = 6.
There are 2 rows, so the number of favorable pairs is 2 * 6 = 12.
The probability is 12/28.
Simplifying the fraction gives 3/7.
#### 3/7 | tp_probability | a0e773490c | general |
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