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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?
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You roll a number cube twice. Find P (even, then not 2). Write the probability as a fraction in simplest form.
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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.
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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
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Presumably, the sentence is incomplete. Please provide the full sentence.
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A. To predict how many students practice every day, we can set up a proportion:

7/12 = x/144

Solving for x, we get:

x = (7/12) * 144

x = 84

Therefore, we can predict that 84 martial arts students practice every day.

B. The sample size is the number of martial arts students that Marissa researched, which is 12.
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The number cube has six equally likely outcomes: 1, 2, 3, 4, 5, or 6.

To find P(even, then not 2), we need to find the probability of rolling an even number on the first roll and a number that is not 2 on the second roll.

The even numbers on the number cube are 2, 4, and 6. So the probability of rolling an even number on the first roll is 3/6 or 1/2.

After rolling an even number on the first roll, there are five equally likely outcomes remaining: 1, 3, 4, 5, and 6. Only one of these outcomes is a 2, so the probability of not rolling a 2 on the second roll is 4/5.

To find the probability of both events happening, we multiply the probabilities:

P(even, then not 2) = (1/2) * (4/5)

P(even, then not 2) = 2/5

Therefore, the probability of rolling an even number on the first roll and a number that is not 2 on the second roll is 2/5.
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A. The theoretical probability of rolling a 3 on a number cube is 1/6. This is because there are 6 equally likely outcomes (numbers 1 through 6) and only one of them is a 3.

Therefore, the theoretical probability of rolling a 3 is 1/6.

B. The experimental probability of rolling a 3 is found by dividing the number of times a 3 was rolled by the total number of rolls:

Experimental probability of rolling a 3 = number of times 3 was rolled / total number of rolls

Experimental probability of rolling a 3 = 67 / 450

Simplifying the fraction by dividing the numerator and denominator by 5, we get:

Experimental probability of rolling a 3 = 13/90

Therefore, the experimental probability of rolling a 3 is 13/90.
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There are 12 letters in total, including 2 'A's. Therefore:

A. The probability of drawing an 'A' is 2/12, which simplifies to 1/6.

B. The decimal of the probability is 0.166666...

C. Converting the decimal to a percent, we get that the probability of drawing an 'A' is approximately 16.67%.