Denzel used the spinner shown below to compare theoretical probability and experimental probability. He spun the spinner 180 times and recorded the letter that it landed on each time. The results are shown in the table.
Letter Frequency
A 36
B 48
C 51
D 45
Which statement correctly compares the theoretical probability and experimental probability for one of the letters on the spinner?
Responses
A The theoretical probability of landing on an A is less than the experimental probability of landing on an A.The theoretical probability of landing on an A is less than the experimental probability of landing on an A.
B The theoretical probability of landing on a B is less than the experimental probability of landing on an B.The theoretical probability of landing on a B is less than the experimental probability of landing on an B.
C The theoretical probability of landing on a C is greater than the experimental probability of landing on an C.The theoretical probability of landing on a C is greater than the experimental probability of landing on an C.
D The theoretical probability of landing on a D is greater than the experimental probability of landing on an D.
11 answers
None of the statements correctly compare the theoretical probability and experimental probability for the letters on the spinner.
Uriel collects aluminum cans, crushes them with a hand can-crushing machine, and turns the crushed cans in once a month for extra money.
Uriel can crush 3 cans in 2/3 of a minute. What is the rate, in cans per minute, at which Uriel crushes aluminum cans?
Responses
A 2/9
B 4 1/4
C 4 1/2
D 2
Uriel can crush 3 cans in 2/3 of a minute. What is the rate, in cans per minute, at which Uriel crushes aluminum cans?
Responses
A 2/9
B 4 1/4
C 4 1/2
D 2
To find the rate at which Uriel crushes aluminum cans, we can set up a proportion using the information given:
3 cans in 2/3 of a minute is equivalent to x cans in 1 minute.
3 cans / 2/3 minute = x cans / 1 minute
Solving for x, we get:
x = (3 * 1) / (2/3)
x = 3 / (2/3)
x = 3 * 3/2
x = 9/2
x = 4 1/2
Therefore, Uriel crushes cans at a rate of 4 1/2 cans per minute.
So, the answer is C) 4 1/2.
3 cans in 2/3 of a minute is equivalent to x cans in 1 minute.
3 cans / 2/3 minute = x cans / 1 minute
Solving for x, we get:
x = (3 * 1) / (2/3)
x = 3 / (2/3)
x = 3 * 3/2
x = 9/2
x = 4 1/2
Therefore, Uriel crushes cans at a rate of 4 1/2 cans per minute.
So, the answer is C) 4 1/2.
Luis owes the school cafeteria $10, which means that he has a –$10 balance on his lunch account.
Which situation illustrates the idea of a number and its opposite?
Responses
A Luis' mom deposits $50 in Luis' lunch account, so Luis has a $40 balance on his lunch account.Luis' mom deposits $50 in Luis' lunch account, so Luis has a $40 balance on his lunch account.
B Luis spends $4 more dollars on lunch without depositing money into his lunch account. Luis spends $4 more dollars on lunch without depositing money into his lunch account.
C Luis' mom deposits $10 in Luis' lunch account, so Luis has a $0 balance on his lunch account.Luis' mom deposits $10 in Luis' lunch account, so Luis has a $0 balance on his lunch account.
D Luis skips lunch because he does not want to go further into debt.
Which situation illustrates the idea of a number and its opposite?
Responses
A Luis' mom deposits $50 in Luis' lunch account, so Luis has a $40 balance on his lunch account.Luis' mom deposits $50 in Luis' lunch account, so Luis has a $40 balance on his lunch account.
B Luis spends $4 more dollars on lunch without depositing money into his lunch account. Luis spends $4 more dollars on lunch without depositing money into his lunch account.
C Luis' mom deposits $10 in Luis' lunch account, so Luis has a $0 balance on his lunch account.Luis' mom deposits $10 in Luis' lunch account, so Luis has a $0 balance on his lunch account.
D Luis skips lunch because he does not want to go further into debt.
The idea of a number and its opposite is represented by the situation when Luis' mom deposits $10 in Luis' lunch account, so Luis has a $0 balance on his lunch account.
This situation illustrates the concept of balancing out the negative balance with a positive deposit, resulting in a neutral or zero balance.
So, the correct response is C) Luis' mom deposits $10 in Luis' lunch account, so Luis has a $0 balance on his lunch account.
This situation illustrates the concept of balancing out the negative balance with a positive deposit, resulting in a neutral or zero balance.
So, the correct response is C) Luis' mom deposits $10 in Luis' lunch account, so Luis has a $0 balance on his lunch account.
Part A
Spencer is using a cube numbered 1 to 6 to conduct probability experiments. In the first experiment, he rolls the number cube 25 times. The number 1 is rolled 47 times.
Which value is the closest estimate of the experimental probability of rolling a 1?
Responses
A 0.021
B 0.167
C 0.188
D 0.531
Question 2
Part B
In the second experiment, Spencer rolls the number cube 350 times.
Responses
A
175
B
61
C
17
D
88
E
56
Spencer is using a cube numbered 1 to 6 to conduct probability experiments. In the first experiment, he rolls the number cube 25 times. The number 1 is rolled 47 times.
Which value is the closest estimate of the experimental probability of rolling a 1?
Responses
A 0.021
B 0.167
C 0.188
D 0.531
Question 2
Part B
In the second experiment, Spencer rolls the number cube 350 times.
Responses
A
175
B
61
C
17
D
88
E
56
Part A:
To find the experimental probability of rolling a 1, you use the formula:
Experimental Probability = Number of times the event occurs / Total number of trials
In this case, the number 1 was rolled 47 times out of 25 trials.
Experimental Probability = 47 / 25 ≈ 1.88
Since we need to find the answer closest to the experimental probability, the closest estimate among the options given is C) 0.188.
Part B:
To answer the second question, we need to find half of 350 rolls.
350 / 2 = 175
Therefore, the answer is A) 175.
To find the experimental probability of rolling a 1, you use the formula:
Experimental Probability = Number of times the event occurs / Total number of trials
In this case, the number 1 was rolled 47 times out of 25 trials.
Experimental Probability = 47 / 25 ≈ 1.88
Since we need to find the answer closest to the experimental probability, the closest estimate among the options given is C) 0.188.
Part B:
To answer the second question, we need to find half of 350 rolls.
350 / 2 = 175
Therefore, the answer is A) 175.
Shana recently led efforts to clean up the city park for the kids and efforts to provide home and yard repair or cleaning for individuals who needed assistance.
Of the 80 volunteers who showed up to help with the city park clean-up one Saturday, 60% returned a second Saturday to help with the community outreach service day to the elderly or disabled.
After this second Saturday, 6 of the volunteers signed up to continue helping with the community outreach service day once a month.
What percentage of the volunteers from the second Saturday signed up to continue helping with community outreach service day once a month?
Responses
A 15%15%
B 10%10%
C 7.5%7.5%
D 12.5%
Of the 80 volunteers who showed up to help with the city park clean-up one Saturday, 60% returned a second Saturday to help with the community outreach service day to the elderly or disabled.
After this second Saturday, 6 of the volunteers signed up to continue helping with the community outreach service day once a month.
What percentage of the volunteers from the second Saturday signed up to continue helping with community outreach service day once a month?
Responses
A 15%15%
B 10%10%
C 7.5%7.5%
D 12.5%
To find the percentage of volunteers from the second Saturday who signed up to continue helping with the community outreach service day once a month, we can calculate the percentage using the given information.
Total volunteers on the second Saturday = 80 volunteers * 60% (volunteers who returned) = 48 volunteers
Number of volunteers who signed up to continue helping = 6 volunteers
Percentage of volunteers who signed up = (Number of volunteers who signed up / Total volunteers on the second Saturday) * 100
Percentage = (6 / 48) * 100
Percentage = 0.125 * 100
Percentage = 12.5%
Therefore, the correct answer is D) 12.5%.
Total volunteers on the second Saturday = 80 volunteers * 60% (volunteers who returned) = 48 volunteers
Number of volunteers who signed up to continue helping = 6 volunteers
Percentage of volunteers who signed up = (Number of volunteers who signed up / Total volunteers on the second Saturday) * 100
Percentage = (6 / 48) * 100
Percentage = 0.125 * 100
Percentage = 12.5%
Therefore, the correct answer is D) 12.5%.
A physician assistant's student loan balance will be reduced by 12% and payments will be postponed each year that the physician assistant works in a designated high-need area.
Cameron is a physician assistant.
Cameron has a $60,000 student loan balance when he graduates.
Cameron works in a designated high-need area for 2 years and makes no loan payments.
What is Cameron's student loan balance at the end of the 2 years?
Responses
A $52,800$52,800
B $13,536$13,536
C $45,600$45,600
D $46,464
Cameron is a physician assistant.
Cameron has a $60,000 student loan balance when he graduates.
Cameron works in a designated high-need area for 2 years and makes no loan payments.
What is Cameron's student loan balance at the end of the 2 years?
Responses
A $52,800$52,800
B $13,536$13,536
C $45,600$45,600
D $46,464
Since payments are postponed each year and the loan balance decreases by 12% each year that Cameron works in a designated high-need area, we can find the student loan balance at the end of 2 years as follows:
After the first year, Cameron's loan balance will be reduced by 12%:
$60,000 - 0.12 * $60,000 = $60,000 - $7,200 = $52,800.
After the second year, Cameron's loan balance will be reduced by another 12%:
$52,800 - 0.12 * $52,800 = $52,800 - $6,336 = $46,464.
Therefore, Cameron's student loan balance at the end of the 2 years will be $46,464.
The correct response is D) $46,464.
After the first year, Cameron's loan balance will be reduced by 12%:
$60,000 - 0.12 * $60,000 = $60,000 - $7,200 = $52,800.
After the second year, Cameron's loan balance will be reduced by another 12%:
$52,800 - 0.12 * $52,800 = $52,800 - $6,336 = $46,464.
Therefore, Cameron's student loan balance at the end of the 2 years will be $46,464.
The correct response is D) $46,464.