Kiara, Giovanni, and Ebony are triplets and always argue over who can answer basic math facts the fastest. After
completing a few different math fact activities, Kiara, Giovanni, and Ebony record their data, which is shown below.
Kiara: m = 5t, where t represents the time in seconds,
and m represents the number of math facts completed.
Giovanni:
Seconds
Math Facts
5
20
10
40
15
60
1. What is the math fact completion rate for each student?
2. Who would win the argument? How do you know?
Ebony:
Number of Math Facts
56286368
60
30
24
18
Number of Math Facts Per Second
12
6
0
0 1 2 3 4 5 6
Number of Seconds
7 8 9 10
11 12
1. The math fact completion rate for each student is:
Kiara: m = 5t, where t represents the time in seconds, and m represents the number of math facts completed. Therefore, Kiara's math fact completion rate is 5 math facts per second.
Giovanni: Giovanni's math fact completion rate is 4 math facts per second.
Ebony: Ebony's math fact completion rate is 12 math facts per second.
2. Ebony would win the argument, as she has the highest math fact completion rate.
The table shows the drink preferences of 50 shoppers at the mall. What is the probability that one shopper, selected at random from the 50 surveyed, preferred either Drink B or Drink A?
Drink. |. Number of shoppers
A. |. 7
B. | 8
C. |. 10
D. |. 11
E. |. 14
A. 8/25
B. 3/10
C. 11/25
D. 7/25
The probability that one shopper, selected at random from the 50 surveyed, preferred either Drink B or Drink A is:
P(A or B) = P(A) + P(B) - P(A and B)
P(A) = 7/50 (number of shoppers who preferred Drink A divided by the total number of shoppers)
P(B) = 8/50 (number of shoppers who preferred Drink B divided by the total number of shoppers)
P(A and B) = 0 (there are no shoppers who prefer both A and B)
P(A or B) = 7/50 + 8/50 - 0 = 15/50 = 3/10
Therefore, the answer is B. 3/10.
A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling
a number greater than 5.
A. 1/6
B. 1/3
C. 1/4
D. 2/3
There is only one number out of six that is greater than 5, which is 6. Therefore, the probability of rolling a number greater than 5 is 1/6.
So, the answer is A. 1/6.
A number cube is rolled 360 times, and the results are recorded as follows: 61 ones, 26 twos, 36 threes, 76 fours, 73 fives, and 88 sixes. What is the experimental probability of rolling a 2 or a 3?
A. 0.07
B. 0.17
C. 0.26
D. 0.83
The experimental probability of rolling a 2 or a 3 is the number of times a 2 or a 3 is rolled divided by the total number of rolls:
Number of times a 2 or a 3 is rolled = 26 + 36 = 62
Total number of rolls = 360
Experimental probability of rolling a 2 or a 3 = (26 + 36) / 360 = 62 / 360 ≈ 0.17
Therefore, the answer is B. 0.17.
From a barrel of colored marbles, you randomly select 5 blue, 2 yellow, 3 red, 4 green, and 2 purple marbles. Find the experimental probability of randomly selecting a marble that is not yellow.
A. 9/16
B. 7/8
C. 8/9
D. 3/4
The total number of marbles is:
5 blue + 2 yellow + 3 red + 4 green + 2 purple = 16 marbles
The number of marbles that is not yellow is:
5 blue + 3 red + 4 green + 2 purple = 14 marbles
Therefore, the experimental probability of randomly selecting a marble that is not yellow is:
number of marbles that is not yellow / total number of marbles = 14/16 = 7/8
Hence, the answer is B. 7/8.
The probability of winning a game is 25%. How many times should you expect to win if you play 36 times?
A. 3 times
B. 7 times
C. 9 times
D. 11 times
The number of times you should expect to win is equal to the probability of winning multiplied by the number of times you play:
Expected number of wins = probability of winning x number of times played = 0.25 x 36 = 9
Therefore, you should expect to win 9 times if you play 36 times.
The answer is C. 9 times.
A survey showed that 62% of car owners prefer two-door cars, 26% prefer four-door cars, and
12% have no preference. You ask 400 people. How many do you think will prefer the two-door
A. 126 people
B. 152 people
C. 196 people
D. 248 people
To find out how many people will prefer the two-door cars, multiply the total number of people surveyed by the percentage of car owners who prefer two-door cars:
Number of people who prefer two-door cars = 0.62 x 400 = 248
Therefore, you would expect 248 people to prefer two-door cars out of the 400 people surveyed.
So, the answer is D. 248 people.
Tony works in a factory that produces 1,000 computers each day. When 50 computers were sampled, it was found that 7 were defective. Estimate how many defective computers are made each day.
A. 140 computers
B. 7 computers
C. 169 computers
D. 265 computers
If 7 computers are defective out of a sample of 50, we can estimate the proportion of defective computers in the total population to be 7/50. We can then use this proportion to estimate the number of defective computers made each day:
Number of defective computers = (7/50) x 1000 = 140
Therefore, we can estimate that there are 140 defective computers made each day.
The answer is A. 140 computers.
The spinner is divided into equal parts. Use a tree diagram to find the probability that the spinner will land on a vowel both times if the spinner is spun twice.
A. 4/9
B. 2/3
C. 7/9
D. 1/3
To create a tree diagram for this problem, we can start with the first spin and then branch out to show the possible outcomes of the second spin:
The probability of spinning a vowel on the first spin is 2/3, and the probability of spinning a vowel on the second spin after spinning a vowel on the first spin is 1/2 (since there are two vowels left on the spinner out of a total of four equally likely outcomes).
The probability of both events happening (spinning a vowel twice) is the product of the individual probabilities:
Probability of spinning a vowel twice = (2/3) x (1/2) = 1/3
Therefore, the answer is D. 1/3.
A yogurt shop offers 5 different flavors of frozen yogurt and 11 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?
A. 16 choices
B. 53 choices
C. 55 choices
D. 58 choices
To find the total number of choices for a single serving of frozen yogurt with one topping, we can use the multiplication rule, which states that if there are n choices for one event and m choices for another event, then there are n x m choices for both events together. In this case, we can choose one of the 5 flavors of frozen yogurt and one of the 11 toppings, so:
Number of choices = 5 x 11 = 55
Therefore, there are 55 possible choices for a single serving of frozen yogurt with one topping.
The answer is C. 55 choices.
Sammy likes to mix and match her 4 necklaces, 2 bracelets, and 3 hats. The colors are listed in the table. On Monday, she randomly picks a bracelet, a necklace, and a hat. What is the probability of Sammy choosing a red necklace and yellow bracelet?
A. 1/2
B. 1/5
C. 1/9
D. 1/8
Since Sammy has 4 necklaces and 2 bracelets and she chooses one of each, there are 4 x 2 = 8 possible combinations of necklaces and bracelets. However, we want to find the probability of her choosing a red necklace and a yellow bracelet, which is only one combination.
Since Sammy has 3 hats, there are 4 x 2 x 3 = 24 possible combinations of necklaces, bracelets, and hats.
Therefore, the probability of Sammy choosing a red necklace and yellow bracelet with a randomly chosen hat is:
1/24
Since the question does not specify the hat that Sammy chooses, we assume that any of the hats can be chosen with equal probability.
Therefore, the answer is D. 1/8.
Which events are not independent?
A. You draw two colored marbles without replacement and get one red and one blue.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile.
C. You toss two coins and get one head, one tail.
D. You choose two different ice cream flavors for a cone.
The events are not independent if the outcome of one event affects the outcome of the second event.
A. You draw two colored marbles without replacement and get one red and one blue. - The events are not independent, since the probability of drawing a blue marble on the second draw is affected by the fact that a red marble was drawn on the first draw.
B. You pull a green tile from a bag of tiles, return it, and then pull a yellow tile. - The events are independent, since the outcome of the first draw does not affect the outcome of the second draw.
C. You toss two coins and get one head, one tail. - The events are not independent, since the outcome of the first toss affects the probability of getting a head or a tail on the second toss.
D. You choose two different ice cream flavors for a cone. - The events are not independent, since the probability of choosing a second flavor is affected by the fact that a first flavor was already chosen.
Therefore, the answer is A and C.