Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school. a. Predict how many students practice every day. b. What is the sample size?
a. To predict how many students practice every day, we can use the proportion:
7/12 = x/144
To solve for x, we can cross-multiply:
12x = 7 * 144
12x = 1008
x = 84
Therefore, we can predict that 84 martial arts students practice every day.
b. The sample size is 144, which represents the total number of martial arts students at the school.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
a. The theoretical probability of rolling a 3 on a number cube is 1/6, since there is 1 chance of rolling a 3 out of 6 possible outcomes (assuming the number cube is fair).
Therefore, the theoretical probability of rolling a 3 is 1/6.
b. The experimental probability of rolling a 3 is calculated by dividing the number of times a 3 comes up by the total number of rolls:
67/450
To simplify this fraction, we can divide both the numerator and denominator by 3:
(67/3)/(450/3)
= 22.33/150
To write this as a fraction in simplest form, we can round to the nearest whole number and simplify:
22.33/150 ≈ 1/7
Therefore, the experimental probability of rolling a 3 is approximately 1/7.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You mix the letters M, A, T, H, E, M, A, T, I, C, A, and L thoroughly. Without looking, you draw one letter. Find the probability P(A). Write the probability as:
a. a fraction in simplest form
b. a decimal
c. a percent
a. Since there are 12 letters in total and 2 of them are A's, the probability of drawing an A is 2/12. This fraction can be simplified to 1/6 by dividing both the numerator and denominator by 2.
Therefore, P(A) = 1/6.
b. To write this probability as a decimal, we can divide 1 by 6 using a calculator or long division:
1 ÷ 6 = 0.166666...
We can round this decimal to the nearest hundredth:
P(A) ≈ 0.17
c. To write this probability as a percent, we can multiply the decimal by 100:
P(A) = 0.166666... * 100%
P(A) ≈ 16.67%
Rounding to the nearest hundredth, we can also write:
P(A) ≈ 16.67%.
a. To predict how many students practice every day, we can use proportions.
First, we need to find the proportion of martial artists who practice every day. We can calculate this by dividing the number of martial artists who practice every day by the total number of martial artists.
Proportion = Number of martial artists who practice every day / Total number of martial artists
In this case, the number of martial artists who practice every day is 7, and the total number of martial artists is 12.
Proportion = 7/12
Next, we multiply the proportion by the total number of martial arts students at the school to predict how many students practice every day.
Predicted number of students practicing every day = Proportion * Total number of martial arts students
Total number of martial arts students = 144
Predicted number of students practicing every day = (7/12) * 144
b. The sample size refers to the total number of martial arts students at the school, which is given as 144.
a. To predict how many students practice every day, we need to use proportions.
We are given that 7 out of 12 martial artists practice every day.
Let's set up a proportion to solve for the number of students who practice every day:
7/12 = x/144
To solve for x, we can cross multiply:
12 * x = 7 * 144
x = (7 * 144) / 12
x = 84
Therefore, we predict that 84 students practice martial arts every day.
b. The sample size is the total number of martial arts students at the school, which is given as 144. Therefore, the sample size is 144.