prompt stringlengths 50 973 | response stringlengths 14 4.76k | source stringclasses 7
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Question: In a quiz about geography, a player answers 120 questions. The player gains 12 points per correct answer and loses 4 points per incorrect answer. The correct answers made up 85% of all questions. What is the contestant's final score?
Answer: | 0.85 × 120 = 102
120 − 102 = 18
102 × 12 = 1224
18 × 4 = 72
1224 − 72 = 1152
#### 1152 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about science fiction, a player answers 120 questions. Correct answers are worth 10 points and incorrect answers cost 5 points. A total of 85% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.85 × 120 = 102
120 − 102 = 18
102 × 10 = 1020
18 × 5 = 90
1020 − 90 = 930
#### 930 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about music theory, a player answers 120 questions. Each correct answer earns 5 points, while each incorrect answer deducts 6 points. The correct answers made up 25% of all questions. What is the contestant's final score?
Answer: | 0.25 × 120 = 30
120 − 30 = 90
30 × 5 = 150
90 × 6 = 540
150 − 540 = -390
#### -390 | tp_wordproblem | 245393e8ee | general |
Question: A contestant participates in a world history competition with 200 questions. The player gains 20 points per correct answer and loses 4 points per incorrect answer. The correct answers made up 70% of all questions. What is the contestant's final score?
Answer: | 0.7 × 200 = 140
200 − 140 = 60
140 × 20 = 2800
60 × 4 = 240
2800 − 240 = 2560
#### 2560 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about geography, a player answers 220 questions. Correct answers are worth 20 points and incorrect answers cost 6 points. The correct answers made up 55% of all questions. What is the contestant's final score?
Answer: | 0.55 × 220 = 121
220 − 121 = 99
121 × 20 = 2420
99 × 6 = 594
2420 − 594 = 1826
#### 1826 | tp_wordproblem | 245393e8ee | general |
Question: A contestant participates in a world history competition with 120 questions. Correct answers are worth 15 points and incorrect answers cost 3 points. A total of 75% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.75 × 120 = 90
120 − 90 = 30
90 × 15 = 1350
30 × 3 = 90
1350 − 90 = 1260
#### 1260 | tp_wordproblem | 245393e8ee | general |
Question: A contestant participates in a world history competition with 200 questions. The player gains 8 points per correct answer and loses 4 points per incorrect answer. The correct answers made up 75% of all questions. What is the contestant's final score?
Answer: | 0.75 × 200 = 150
200 − 150 = 50
150 × 8 = 1200
50 × 4 = 200
1200 − 200 = 1000
#### 1000 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about music theory, a player answers 250 questions. Correct answers are worth 20 points and incorrect answers cost 4 points. The contestant answered 40% of the questions correctly. What is the contestant's final score?
Answer: | 0.4 × 250 = 100
250 − 100 = 150
100 × 20 = 2000
150 × 4 = 600
2000 − 600 = 1400
#### 1400 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about music theory, a player answers 120 questions. Each correct answer earns 5 points, while each incorrect answer deducts 2 points. A total of 20% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.2 × 120 = 24
120 − 24 = 96
24 × 5 = 120
96 × 2 = 192
120 − 192 = -72
#### -72 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about world history, a player answers 250 questions. Each correct answer earns 8 points, while each incorrect answer deducts 4 points. A total of 80% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.8 × 250 = 200
250 − 200 = 50
200 × 8 = 1600
50 × 4 = 200
1600 − 200 = 1400
#### 1400 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about classic cinema, a player answers 200 questions. The player gains 20 points per correct answer and loses 2 points per incorrect answer. A total of 20% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.2 × 200 = 40
200 − 40 = 160
40 × 20 = 800
160 × 2 = 320
800 − 320 = 480
#### 480 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about classic cinema, a player answers 120 questions. Each correct answer earns 20 points, while each incorrect answer deducts 5 points. A total of 80% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.8 × 120 = 96
120 − 96 = 24
96 × 20 = 1920
24 × 5 = 120
1920 − 120 = 1800
#### 1800 | tp_wordproblem | 245393e8ee | general |
Question: A contestant participates in a classic cinema competition with 120 questions. The player gains 10 points per correct answer and loses 3 points per incorrect answer. The contestant answered 20% of the questions correctly. What is the contestant's final score?
Answer: | 0.2 × 120 = 24
120 − 24 = 96
24 × 10 = 240
96 × 3 = 288
240 − 288 = -48
#### -48 | tp_wordproblem | 245393e8ee | general |
Question: For a world history trivia challenge, 180 questions are presented to a contestant. The player gains 15 points per correct answer and loses 8 points per incorrect answer. A total of 35% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.35 × 180 = 63
180 − 63 = 117
63 × 15 = 945
117 × 8 = 936
945 − 936 = 9
#### 9 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about classic cinema, a player answers 200 questions. Each correct answer earns 12 points, while each incorrect answer deducts 5 points. The contestant answered 35% of the questions correctly. What is the contestant's final score?
Answer: | 0.35 × 200 = 70
200 − 70 = 130
70 × 12 = 840
130 × 5 = 650
840 − 650 = 190
#### 190 | tp_wordproblem | 245393e8ee | general |
Question: A contestant participates in a science fiction competition with 150 questions. The player gains 10 points per correct answer and loses 2 points per incorrect answer. A total of 30% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.3 × 150 = 45
150 − 45 = 105
45 × 10 = 450
105 × 2 = 210
450 − 210 = 240
#### 240 | tp_wordproblem | 245393e8ee | general |
Question: For a world history trivia challenge, 220 questions are presented to a contestant. Each correct answer earns 10 points, while each incorrect answer deducts 5 points. The contestant answered 65% of the questions correctly. What is the contestant's final score?
Answer: | 0.65 × 220 = 143
220 − 143 = 77
143 × 10 = 1430
77 × 5 = 385
1430 − 385 = 1045
#### 1045 | tp_wordproblem | 245393e8ee | general |
Question: In a quiz about science fiction, a player answers 200 questions. Each correct answer earns 5 points, while each incorrect answer deducts 4 points. The contestant answered 85% of the questions correctly. What is the contestant's final score?
Answer: | 0.85 × 200 = 170
200 − 170 = 30
170 × 5 = 850
30 × 4 = 120
850 − 120 = 730
#### 730 | tp_wordproblem | 245393e8ee | general |
Question: A contestant participates in a music theory competition with 120 questions. The player gains 12 points per correct answer and loses 4 points per incorrect answer. The contestant answered 50% of the questions correctly. What is the contestant's final score?
Answer: | 0.5 × 120 = 60
120 − 60 = 60
60 × 12 = 720
60 × 4 = 240
720 − 240 = 480
#### 480 | tp_wordproblem | 245393e8ee | general |
Question: For a classic cinema trivia challenge, 180 questions are presented to a contestant. Each correct answer earns 8 points, while each incorrect answer deducts 3 points. A total of 50% of the questions were answered correctly. What is the contestant's final score?
Answer: | 0.5 × 180 = 90
180 − 90 = 90
90 × 8 = 720
90 × 3 = 270
720 − 270 = 450
#### 450 | tp_wordproblem | 245393e8ee | general |
Question: A library has 6 distinct books about literature, 8 distinct books about biology, and 3 distinct biographies. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction i... | Total books = 6 + 8 + 3 = 17
Total ways to select 3 books = C(17, 3)
C(17, 3) = (17 * 16 * 15) / (3 * 2 * 1) = 680
Ways to select exactly one from each category = 6 * 8 * 3
6 * 8 * 3 = 144
Probability = 144 / 680
Simplify fraction: 144 / 680 = 18 / 85
#### 18/85 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about geography, 4 distinct books about chemistry, and 3 distinct autobiographies. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fract... | Total books = 3 + 4 + 3 = 10
Total ways to select 3 books = C(10, 3)
C(10, 3) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Ways to select exactly one from each category = 3 * 4 * 3
3 * 4 * 3 = 36
Probability = 36 / 120
Simplify fraction: 36 / 120 = 3 / 10
#### 3/10 | tp_probability | 758291e439 | general |
Question: A library has 7 distinct books about science, 7 distinct books about philosophy, and 6 distinct autobiographies. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction... | Total books = 7 + 7 + 6 = 20
Total ways to select 3 books = C(20, 3)
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Ways to select exactly one from each category = 7 * 7 * 6
7 * 7 * 6 = 294
Probability = 294 / 1140
Simplify fraction: 294 / 1140 = 49 / 190
#### 49/190 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about science, 7 distinct books about chemistry, and 5 distinct diaries. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in sim... | Total books = 6 + 7 + 5 = 18
Total ways to select 3 books = C(18, 3)
C(18, 3) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Ways to select exactly one from each category = 6 * 7 * 5
6 * 7 * 5 = 210
Probability = 210 / 816
Simplify fraction: 210 / 816 = 35 / 136
#### 35/136 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about geography, 3 distinct books about economics, and 8 distinct journals. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in si... | Total books = 6 + 3 + 8 = 17
Total ways to select 3 books = C(17, 3)
C(17, 3) = (17 * 16 * 15) / (3 * 2 * 1) = 680
Ways to select exactly one from each category = 6 * 3 * 8
6 * 3 * 8 = 144
Probability = 144 / 680
Simplify fraction: 144 / 680 = 18 / 85
#### 18/85 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about literature, 6 distinct books about economics, and 7 distinct memoirs. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in si... | Total books = 6 + 6 + 7 = 19
Total ways to select 3 books = C(19, 3)
C(19, 3) = (19 * 18 * 17) / (3 * 2 * 1) = 969
Ways to select exactly one from each category = 6 * 6 * 7
6 * 6 * 7 = 252
Probability = 252 / 969
Simplify fraction: 252 / 969 = 84 / 323
#### 84/323 | tp_probability | 758291e439 | general |
Question: A library has 5 distinct books about literature, 3 distinct books about music, and 4 distinct autobiographies. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction i... | Total books = 5 + 3 + 4 = 12
Total ways to select 3 books = C(12, 3)
C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Ways to select exactly one from each category = 5 * 3 * 4
5 * 3 * 4 = 60
Probability = 60 / 220
Simplify fraction: 60 / 220 = 3 / 11
#### 3/11 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about art, 7 distinct books about philosophy, and 4 distinct autobiographies. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in... | Total books = 3 + 7 + 4 = 14
Total ways to select 3 books = C(14, 3)
C(14, 3) = (14 * 13 * 12) / (3 * 2 * 1) = 364
Ways to select exactly one from each category = 3 * 7 * 4
3 * 7 * 4 = 84
Probability = 84 / 364
Simplify fraction: 84 / 364 = 3 / 13
#### 3/13 | tp_probability | 758291e439 | general |
Question: A library has 7 distinct books about history, 6 distinct books about music, and 5 distinct biographies. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simpl... | Total books = 7 + 6 + 5 = 18
Total ways to select 3 books = C(18, 3)
C(18, 3) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Ways to select exactly one from each category = 7 * 6 * 5
7 * 6 * 5 = 210
Probability = 210 / 816
Simplify fraction: 210 / 816 = 35 / 136
#### 35/136 | tp_probability | 758291e439 | general |
Question: A library has 4 distinct books about history, 3 distinct books about economics, and 6 distinct diaries. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simpl... | Total books = 4 + 3 + 6 = 13
Total ways to select 3 books = C(13, 3)
C(13, 3) = (13 * 12 * 11) / (3 * 2 * 1) = 286
Ways to select exactly one from each category = 4 * 3 * 6
4 * 3 * 6 = 72
Probability = 72 / 286
Simplify fraction: 72 / 286 = 36 / 143
#### 36/143 | tp_probability | 758291e439 | general |
Question: A library has 8 distinct books about geography, 7 distinct books about music, and 4 distinct diaries. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simpl... | Total books = 8 + 7 + 4 = 19
Total ways to select 3 books = C(19, 3)
C(19, 3) = (19 * 18 * 17) / (3 * 2 * 1) = 969
Ways to select exactly one from each category = 8 * 7 * 4
8 * 7 * 4 = 224
Probability = 224 / 969
Simplify fraction: 224 / 969 = 224 / 969
#### 224/969 | tp_probability | 758291e439 | general |
Question: A library has 5 distinct books about literature, 5 distinct books about philosophy, and 3 distinct diaries. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in... | Total books = 5 + 5 + 3 = 13
Total ways to select 3 books = C(13, 3)
C(13, 3) = (13 * 12 * 11) / (3 * 2 * 1) = 286
Ways to select exactly one from each category = 5 * 5 * 3
5 * 5 * 3 = 75
Probability = 75 / 286
Simplify fraction: 75 / 286 = 75 / 286
#### 75/286 | tp_probability | 758291e439 | general |
Question: A library has 5 distinct books about literature, 4 distinct books about philosophy, and 4 distinct journals. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in... | Total books = 5 + 4 + 4 = 13
Total ways to select 3 books = C(13, 3)
C(13, 3) = (13 * 12 * 11) / (3 * 2 * 1) = 286
Ways to select exactly one from each category = 5 * 4 * 4
5 * 4 * 4 = 80
Probability = 80 / 286
Simplify fraction: 80 / 286 = 40 / 143
#### 40/143 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about science, 5 distinct books about economics, and 8 distinct journals. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in sim... | Total books = 6 + 5 + 8 = 19
Total ways to select 3 books = C(19, 3)
C(19, 3) = (19 * 18 * 17) / (3 * 2 * 1) = 969
Ways to select exactly one from each category = 6 * 5 * 8
6 * 5 * 8 = 240
Probability = 240 / 969
Simplify fraction: 240 / 969 = 80 / 323
#### 80/323 | tp_probability | 758291e439 | general |
Question: A library has 7 distinct books about art, 3 distinct books about music, and 4 distinct diaries. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simplest fo... | Total books = 7 + 3 + 4 = 14
Total ways to select 3 books = C(14, 3)
C(14, 3) = (14 * 13 * 12) / (3 * 2 * 1) = 364
Ways to select exactly one from each category = 7 * 3 * 4
7 * 3 * 4 = 84
Probability = 84 / 364
Simplify fraction: 84 / 364 = 3 / 13
#### 3/13 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about geography, 5 distinct books about chemistry, and 6 distinct memoirs. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in s... | Total books = 3 + 5 + 6 = 14
Total ways to select 3 books = C(14, 3)
C(14, 3) = (14 * 13 * 12) / (3 * 2 * 1) = 364
Ways to select exactly one from each category = 3 * 5 * 6
3 * 5 * 6 = 90
Probability = 90 / 364
Simplify fraction: 90 / 364 = 45 / 182
#### 45/182 | tp_probability | 758291e439 | general |
Question: A library has 5 distinct books about geography, 8 distinct books about biology, and 6 distinct journals. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simp... | Total books = 5 + 8 + 6 = 19
Total ways to select 3 books = C(19, 3)
C(19, 3) = (19 * 18 * 17) / (3 * 2 * 1) = 969
Ways to select exactly one from each category = 5 * 8 * 6
5 * 8 * 6 = 240
Probability = 240 / 969
Simplify fraction: 240 / 969 = 80 / 323
#### 80/323 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about science, 8 distinct books about music, and 6 distinct memoirs. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simplest ... | Total books = 6 + 8 + 6 = 20
Total ways to select 3 books = C(20, 3)
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Ways to select exactly one from each category = 6 * 8 * 6
6 * 8 * 6 = 288
Probability = 288 / 1140
Simplify fraction: 288 / 1140 = 24 / 95
#### 24/95 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about history, 8 distinct books about philosophy, and 6 distinct journals. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in sim... | Total books = 6 + 8 + 6 = 20
Total ways to select 3 books = C(20, 3)
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Ways to select exactly one from each category = 6 * 8 * 6
6 * 8 * 6 = 288
Probability = 288 / 1140
Simplify fraction: 288 / 1140 = 24 / 95
#### 24/95 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about history, 5 distinct books about philosophy, and 4 distinct diaries. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simp... | Total books = 3 + 5 + 4 = 12
Total ways to select 3 books = C(12, 3)
C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Ways to select exactly one from each category = 3 * 5 * 4
3 * 5 * 4 = 60
Probability = 60 / 220
Simplify fraction: 60 / 220 = 3 / 11
#### 3/11 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about literature, 3 distinct books about economics, and 6 distinct autobiographies. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fracti... | Total books = 3 + 3 + 6 = 12
Total ways to select 3 books = C(12, 3)
C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Ways to select exactly one from each category = 3 * 3 * 6
3 * 3 * 6 = 54
Probability = 54 / 220
Simplify fraction: 54 / 220 = 27 / 110
#### 27/110 | tp_probability | 758291e439 | general |
Question: A library has 7 distinct books about geography, 7 distinct books about philosophy, and 4 distinct memoirs. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in ... | Total books = 7 + 7 + 4 = 18
Total ways to select 3 books = C(18, 3)
C(18, 3) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Ways to select exactly one from each category = 7 * 7 * 4
7 * 7 * 4 = 196
Probability = 196 / 816
Simplify fraction: 196 / 816 = 49 / 204
#### 49/204 | tp_probability | 758291e439 | general |
Question: A library has 4 distinct books about art, 6 distinct books about music, and 7 distinct diaries. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simplest for... | Total books = 4 + 6 + 7 = 17
Total ways to select 3 books = C(17, 3)
C(17, 3) = (17 * 16 * 15) / (3 * 2 * 1) = 680
Ways to select exactly one from each category = 4 * 6 * 7
4 * 6 * 7 = 168
Probability = 168 / 680
Simplify fraction: 168 / 680 = 21 / 85
#### 21/85 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about literature, 8 distinct books about philosophy, and 6 distinct diaries. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in s... | Total books = 6 + 8 + 6 = 20
Total ways to select 3 books = C(20, 3)
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Ways to select exactly one from each category = 6 * 8 * 6
6 * 8 * 6 = 288
Probability = 288 / 1140
Simplify fraction: 288 / 1140 = 24 / 95
#### 24/95 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about art, 6 distinct books about economics, and 6 distinct biographies. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in sim... | Total books = 3 + 6 + 6 = 15
Total ways to select 3 books = C(15, 3)
C(15, 3) = (15 * 14 * 13) / (3 * 2 * 1) = 455
Ways to select exactly one from each category = 3 * 6 * 6
3 * 6 * 6 = 108
Probability = 108 / 455
Simplify fraction: 108 / 455 = 108 / 455
#### 108/455 | tp_probability | 758291e439 | general |
Question: A library has 4 distinct books about science, 3 distinct books about biology, and 3 distinct autobiographies. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in... | Total books = 4 + 3 + 3 = 10
Total ways to select 3 books = C(10, 3)
C(10, 3) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Ways to select exactly one from each category = 4 * 3 * 3
4 * 3 * 3 = 36
Probability = 36 / 120
Simplify fraction: 36 / 120 = 3 / 10
#### 3/10 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about literature, 6 distinct books about biology, and 5 distinct autobiographies. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fracti... | Total books = 3 + 6 + 5 = 14
Total ways to select 3 books = C(14, 3)
C(14, 3) = (14 * 13 * 12) / (3 * 2 * 1) = 364
Ways to select exactly one from each category = 3 * 6 * 5
3 * 6 * 5 = 90
Probability = 90 / 364
Simplify fraction: 90 / 364 = 45 / 182
#### 45/182 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about geography, 3 distinct books about chemistry, and 3 distinct autobiographies. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fracti... | Total books = 3 + 3 + 3 = 9
Total ways to select 3 books = C(9, 3)
C(9, 3) = (9 * 8 * 7) / (3 * 2 * 1) = 84
Ways to select exactly one from each category = 3 * 3 * 3
3 * 3 * 3 = 27
Probability = 27 / 84
Simplify fraction: 27 / 84 = 9 / 28
#### 9/28 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about art, 7 distinct books about philosophy, and 6 distinct diaries. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simplest... | Total books = 6 + 7 + 6 = 19
Total ways to select 3 books = C(19, 3)
C(19, 3) = (19 * 18 * 17) / (3 * 2 * 1) = 969
Ways to select exactly one from each category = 6 * 7 * 6
6 * 7 * 6 = 252
Probability = 252 / 969
Simplify fraction: 252 / 969 = 84 / 323
#### 84/323 | tp_probability | 758291e439 | general |
Question: A library has 7 distinct books about geography, 5 distinct books about economics, and 8 distinct autobiographies. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fract... | Total books = 7 + 5 + 8 = 20
Total ways to select 3 books = C(20, 3)
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Ways to select exactly one from each category = 7 * 5 * 8
7 * 5 * 8 = 280
Probability = 280 / 1140
Simplify fraction: 280 / 1140 = 14 / 57
#### 14/57 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about science, 6 distinct books about philosophy, and 7 distinct diaries. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in si... | Total books = 3 + 6 + 7 = 16
Total ways to select 3 books = C(16, 3)
C(16, 3) = (16 * 15 * 14) / (3 * 2 * 1) = 560
Ways to select exactly one from each category = 3 * 6 * 7
3 * 6 * 7 = 126
Probability = 126 / 560
Simplify fraction: 126 / 560 = 9 / 40
#### 9/40 | tp_probability | 758291e439 | general |
Question: A library has 8 distinct books about history, 7 distinct books about music, and 7 distinct memoirs. If a patron selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simplest ... | Total books = 8 + 7 + 7 = 22
Total ways to select 3 books = C(22, 3)
C(22, 3) = (22 * 21 * 20) / (3 * 2 * 1) = 1540
Ways to select exactly one from each category = 8 * 7 * 7
8 * 7 * 7 = 392
Probability = 392 / 1540
Simplify fraction: 392 / 1540 = 14 / 55
#### 14/55 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about literature, 8 distinct books about philosophy, and 7 distinct memoirs. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in s... | Total books = 6 + 8 + 7 = 21
Total ways to select 3 books = C(21, 3)
C(21, 3) = (21 * 20 * 19) / (3 * 2 * 1) = 1330
Ways to select exactly one from each category = 6 * 8 * 7
6 * 8 * 7 = 336
Probability = 336 / 1330
Simplify fraction: 336 / 1330 = 24 / 95
#### 24/95 | tp_probability | 758291e439 | general |
Question: A library has 8 distinct books about art, 4 distinct books about chemistry, and 8 distinct biographies. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simp... | Total books = 8 + 4 + 8 = 20
Total ways to select 3 books = C(20, 3)
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Ways to select exactly one from each category = 8 * 4 * 8
8 * 4 * 8 = 256
Probability = 256 / 1140
Simplify fraction: 256 / 1140 = 64 / 285
#### 64/285 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about history, 8 distinct books about music, and 3 distinct diaries. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simplest... | Total books = 3 + 8 + 3 = 14
Total ways to select 3 books = C(14, 3)
C(14, 3) = (14 * 13 * 12) / (3 * 2 * 1) = 364
Ways to select exactly one from each category = 3 * 8 * 3
3 * 8 * 3 = 72
Probability = 72 / 364
Simplify fraction: 72 / 364 = 18 / 91
#### 18/91 | tp_probability | 758291e439 | general |
Question: A library has 8 distinct books about art, 6 distinct books about philosophy, and 4 distinct biographies. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in sim... | Total books = 8 + 6 + 4 = 18
Total ways to select 3 books = C(18, 3)
C(18, 3) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Ways to select exactly one from each category = 8 * 6 * 4
8 * 6 * 4 = 192
Probability = 192 / 816
Simplify fraction: 192 / 816 = 4 / 17
#### 4/17 | tp_probability | 758291e439 | general |
Question: A library has 6 distinct books about history, 8 distinct books about music, and 8 distinct biographies. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simp... | Total books = 6 + 8 + 8 = 22
Total ways to select 3 books = C(22, 3)
C(22, 3) = (22 * 21 * 20) / (3 * 2 * 1) = 1540
Ways to select exactly one from each category = 6 * 8 * 8
6 * 8 * 8 = 384
Probability = 384 / 1540
Simplify fraction: 384 / 1540 = 96 / 385
#### 96/385 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about literature, 6 distinct books about music, and 8 distinct biographies. If a student selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in s... | Total books = 3 + 6 + 8 = 17
Total ways to select 3 books = C(17, 3)
C(17, 3) = (17 * 16 * 15) / (3 * 2 * 1) = 680
Ways to select exactly one from each category = 3 * 6 * 8
3 * 6 * 8 = 144
Probability = 144 / 680
Simplify fraction: 144 / 680 = 18 / 85
#### 18/85 | tp_probability | 758291e439 | general |
Question: A library has 3 distinct books about science, 3 distinct books about music, and 5 distinct memoirs. If a borrower selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simples... | Total books = 3 + 3 + 5 = 11
Total ways to select 3 books = C(11, 3)
C(11, 3) = (11 * 10 * 9) / (3 * 2 * 1) = 165
Ways to select exactly one from each category = 3 * 3 * 5
3 * 3 * 5 = 45
Probability = 45 / 165
Simplify fraction: 45 / 165 = 3 / 11
#### 3/11 | tp_probability | 758291e439 | general |
Question: A library has 8 distinct books about science, 8 distinct books about music, and 4 distinct biographies. If a reader selects 3 books at random from this collection, what is the probability that the selection contains exactly one book from each of the three categories? Express your answer as a fraction in simpl... | Total books = 8 + 8 + 4 = 20
Total ways to select 3 books = C(20, 3)
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
Ways to select exactly one from each category = 8 * 8 * 4
8 * 8 * 4 = 256
Probability = 256 / 1140
Simplify fraction: 256 / 1140 = 64 / 285
#### 64/285 | tp_probability | 758291e439 | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 200 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 200 minutes
Number of doubling periods = 200 / 25
Number of doubling periods = 8
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^8
2^8 = 256
Final population = 10 x 256
Final population = 2560
Scientific notation = 2.56 x 10^3
N = 2.56
#### 2.56 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 3 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 180 minutes
Number of doubling periods = 180 / 30
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^6
2^6 = 64
Final population = 10000 x 64
Final population = 640000
Scientific notation = 6.40 x 10^5
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 175 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 175 minutes
Number of doubling periods = 175 / 25
Number of doubling periods = 7
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^7
2^7 = 128
Final population = 1000 x 128
Final population = 128000
Scientific notation = 1.28 x 10^5
N = 1.28
#### 1.28 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 75 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 75 minutes
Number of doubling periods = 75 / 25
Number of doubling periods = 3
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^3
2^3 = 8
Final population = 100 x 8
Final population = 800
Scientific notation = 8.00 x 10^2
N = 8.00
#### 8.00 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 225 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 225 minutes
Number of doubling periods = 225 / 25
Number of doubling periods = 9
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^9
2^9 = 512
Final population = 10000 x 512
Final population = 5120000
Scientific notation = 5.12 x 10^6
N = 5.12
#### 5.12 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 1 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 60 minutes
Number of doubling periods = 60 / 20
Number of doubling periods = 3
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^3
2^3 = 8
Final population = 100 x 8
Final population = 800
Scientific notation = 8.00 x 10^2
N = 8.00
#### 8.00 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 150 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 150 minutes
Number of doubling periods = 150 / 30
Number of doubling periods = 5
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^5
2^5 = 32
Final population = 1000 x 32
Final population = 32000
Scientific notation = 3.20 x 10^4
N = 3.20
#### 3.20 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 15 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 1 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 60 minutes
Number of doubling periods = 60 / 15
Number of doubling periods = 4
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^4
2^4 = 16
Final population = 10000 x 16
Final population = 160000
Scientific notation = 1.60 x 10^5
N = 1.60
#### 1.60 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 4 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 240 minutes
Number of doubling periods = 240 / 30
Number of doubling periods = 8
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^8
2^8 = 256
Final population = 100 x 256
Final population = 25600
Scientific notation = 2.56 x 10^4
N = 2.56
#### 2.56 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 140 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 140 minutes
Number of doubling periods = 140 / 20
Number of doubling periods = 7
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^7
2^7 = 128
Final population = 10 x 128
Final population = 1280
Scientific notation = 1.28 x 10^3
N = 1.28
#### 1.28 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 100 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 100 minutes
Number of doubling periods = 100 / 20
Number of doubling periods = 5
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^5
2^5 = 32
Final population = 100 x 32
Final population = 3200
Scientific notation = 3.20 x 10^3
N = 3.20
#### 3.20 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 225 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 225 minutes
Number of doubling periods = 225 / 25
Number of doubling periods = 9
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^9
2^9 = 512
Final population = 1000 x 512
Final population = 512000
Scientific notation = 5.12 x 10^5
N = 5.12
#### 5.12 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 1 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 60 minutes
Number of doubling periods = 60 / 30
Number of doubling periods = 2
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^2
2^2 = 4
Final population = 100 x 4
Final population = 400
Scientific notation = 4.00 x 10^2
N = 4.00
#### 4.00 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 3 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 180 minutes
Number of doubling periods = 180 / 20
Number of doubling periods = 9
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^9
2^9 = 512
Final population = 1000 x 512
Final population = 512000
Scientific notation = 5.12 x 10^5
N = 5.12
#### 5.12 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 200 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 200 minutes
Number of doubling periods = 200 / 25
Number of doubling periods = 8
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^8
2^8 = 256
Final population = 10000 x 256
Final population = 2560000
Scientific notation = 2.56 x 10^6
N = 2.56
#### 2.56 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 10 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 1 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 60 minutes
Number of doubling periods = 60 / 10
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^6
2^6 = 64
Final population = 10000 x 64
Final population = 640000
Scientific notation = 6.40 x 10^5
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 3 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 180 minutes
Number of doubling periods = 180 / 30
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^6
2^6 = 64
Final population = 100 x 64
Final population = 6400
Scientific notation = 6.40 x 10^3
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 15 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 1 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 60 minutes
Number of doubling periods = 60 / 15
Number of doubling periods = 4
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^4
2^4 = 16
Final population = 10 x 16
Final population = 160
Scientific notation = 1.60 x 10^2
N = 1.60
#### 1.60 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 10 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 90 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 90 minutes
Number of doubling periods = 90 / 10
Number of doubling periods = 9
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^9
2^9 = 512
Final population = 10 x 512
Final population = 5120
Scientific notation = 5.12 x 10^3
N = 5.12
#### 5.12 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 175 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 175 minutes
Number of doubling periods = 175 / 25
Number of doubling periods = 7
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^7
2^7 = 128
Final population = 10000 x 128
Final population = 1280000
Scientific notation = 1.28 x 10^6
N = 1.28
#### 1.28 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 2 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 120 minutes
Number of doubling periods = 120 / 30
Number of doubling periods = 4
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^4
2^4 = 16
Final population = 100 x 16
Final population = 1600
Scientific notation = 1.60 x 10^3
N = 1.60
#### 1.60 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 3 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 180 minutes
Number of doubling periods = 180 / 30
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^6
2^6 = 64
Final population = 10 x 64
Final population = 640
Scientific notation = 6.40 x 10^2
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 10 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 80 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 80 minutes
Number of doubling periods = 80 / 10
Number of doubling periods = 8
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^8
2^8 = 256
Final population = 10 x 256
Final population = 2560
Scientific notation = 2.56 x 10^3
N = 2.56
#### 2.56 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 100 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 100 minutes
Number of doubling periods = 100 / 25
Number of doubling periods = 4
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^4
2^4 = 16
Final population = 1000 x 16
Final population = 16000
Scientific notation = 1.60 x 10^4
N = 1.60
#### 1.60 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 10 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 80 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 80 minutes
Number of doubling periods = 80 / 10
Number of doubling periods = 8
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^8
2^8 = 256
Final population = 1000 x 256
Final population = 256000
Scientific notation = 2.56 x 10^5
N = 2.56
#### 2.56 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 15 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 105 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 105 minutes
Number of doubling periods = 105 / 15
Number of doubling periods = 7
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^7
2^7 = 128
Final population = 10 x 128
Final population = 1280
Scientific notation = 1.28 x 10^3
N = 1.28
#### 1.28 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 100 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 100 minutes
Number of doubling periods = 100 / 25
Number of doubling periods = 4
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^4
2^4 = 16
Final population = 10000 x 16
Final population = 160000
Scientific notation = 1.60 x 10^5
N = 1.60
#### 1.60 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 15 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 90 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 90 minutes
Number of doubling periods = 90 / 15
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^6
2^6 = 64
Final population = 1000 x 64
Final population = 64000
Scientific notation = 6.40 x 10^4
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 2 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 120 minutes
Number of doubling periods = 120 / 30
Number of doubling periods = 4
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^4
2^4 = 16
Final population = 1000 x 16
Final population = 16000
Scientific notation = 1.60 x 10^4
N = 1.60
#### 1.60 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 15 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 135 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 135 minutes
Number of doubling periods = 135 / 15
Number of doubling periods = 9
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^9
2^9 = 512
Final population = 10000 x 512
Final population = 5120000
Scientific notation = 5.12 x 10^6
N = 5.12
#### 5.12 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 140 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 140 minutes
Number of doubling periods = 140 / 20
Number of doubling periods = 7
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^7
2^7 = 128
Final population = 100 x 128
Final population = 12800
Scientific notation = 1.28 x 10^4
N = 1.28
#### 1.28 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 30 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 150 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 150 minutes
Number of doubling periods = 150 / 30
Number of doubling periods = 5
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^5
2^5 = 32
Final population = 10 x 32
Final population = 320
Scientific notation = 3.20 x 10^2
N = 3.20
#### 3.20 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 10 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 90 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 90 minutes
Number of doubling periods = 90 / 10
Number of doubling periods = 9
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^9
2^9 = 512
Final population = 1000 x 512
Final population = 512000
Scientific notation = 5.12 x 10^5
N = 5.12
#### 5.12 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 160 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 160 minutes
Number of doubling periods = 160 / 20
Number of doubling periods = 8
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^8
2^8 = 256
Final population = 1000 x 256
Final population = 256000
Scientific notation = 2.56 x 10^5
N = 2.56
#### 2.56 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 15 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 90 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 90 minutes
Number of doubling periods = 90 / 15
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^6
2^6 = 64
Final population = 10000 x 64
Final population = 640000
Scientific notation = 6.40 x 10^5
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^2$ bacteria, how many bacteria will be present after 150 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 150 minutes
Number of doubling periods = 150 / 25
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^2 x 2^6
2^6 = 64
Final population = 100 x 64
Final population = 6400
Scientific notation = 6.40 x 10^3
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 100 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 100 minutes
Number of doubling periods = 100 / 20
Number of doubling periods = 5
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^5
2^5 = 32
Final population = 10000 x 32
Final population = 320000
Scientific notation = 3.20 x 10^5
N = 3.20
#### 3.20 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^4$ bacteria, how many bacteria will be present after 80 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 80 minutes
Number of doubling periods = 80 / 20
Number of doubling periods = 4
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^4 x 2^4
2^4 = 16
Final population = 10000 x 16
Final population = 160000
Scientific notation = 1.60 x 10^5
N = 1.60
#### 1.60 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 25 minutes. If a culture initially contains $10^1$ bacteria, how many bacteria will be present after 150 minutes? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 150 minutes
Number of doubling periods = 150 / 25
Number of doubling periods = 6
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^1 x 2^6
2^6 = 64
Final population = 10 x 64
Final population = 640
Scientific notation = 6.40 x 10^2
N = 6.40
#### 6.40 | tp_science_calc | 8036b6251a | general |
Question: A bacterial strain in a laboratory has a doubling time of 20 minutes. If a culture initially contains $10^3$ bacteria, how many bacteria will be present after 1 hours? Express your answer in scientific notation as $N \times 10^x$ and provide the value of $N$ (rounded to two decimal places).
Answer: | Total time = 60 minutes
Number of doubling periods = 60 / 20
Number of doubling periods = 3
Final population = Initial population x 2^(Number of doubling periods)
Final population = 10^3 x 2^3
2^3 = 8
Final population = 1000 x 8
Final population = 8000
Scientific notation = 8.00 x 10^3
N = 8.00
#### 8.00 | tp_science_calc | 8036b6251a | general |
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