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 find the number of students who practice every day, we can set up a proportion:
7/12 = x/144
where x is the number of students who practice every day.
To solve for x, we can cross-multiply:
12x = 7 * 144
x = (7 * 144) / 12
x = 84
Therefore, we can predict that 84 students practice every day.
b. The sample size is the total number of martial arts students at the school, which is given to be 144.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
There are six possible outcomes when you roll a number cube: 1, 2, 3, 4, 5, or 6. Out of these, three are even: 2, 4, and 6.
If we roll the number cube twice, there are 6 x 6 = 36 possible outcomes. To find the probability of rolling an even number first and then not rolling a 2, we can use the formula:
P(even, then not 2) = P(even) x P(not 2 | even)
The probability of rolling an even number first is 3/6 since three out of the six possible outcomes are even.
If we roll an even number first, there are five possible outcomes that are not 2: 1, 3, 4, 5, and 6. Out of these, four outcomes are equally likely and lead to our desired event. So the probability of not rolling a 2 given that we rolled an even number is 4/5.
Therefore:
P(even, then not 2) = (3/6) x (4/5)
P(even, then not 2) = (1/2) x (4/5)
P(even, then not 2) = 2/5
So the probability of rolling an even number first and then not rolling a 2 is 2/5.
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
There are 12 letters in the mix, with two of them being 'A'.
a. The probability of drawing an 'A' is the number of 'A's in the mix, divided by the total number of letters. So,
P(A) = number of A's / total number of letters
P(A) = 2 / 12
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
P(A) = 1 / 6
b. To convert this fraction to a decimal, we can divide 1 by 6:
P(A) = 1/6 = 0.166666... (rounded to six decimal places)
c. To convert the decimal to a percent, we can multiply by 100:
P(A) = 0.166666... x 100% = 16.666...% (rounded to three decimal places)
Therefore, the probability of drawing an 'A' is:
a. 1/6
b. 0.166666...
c. 16.666...%
To predict how many students practice every day, we can use proportion to estimate the number based on the given information.
a. To find the number of students who practice every day, we first need to determine the proportion of martial artists who practice every day. The proportion can be calculated by dividing the number of martial artists who practice every day by the total number of martial artists.
Given that 7 out of 12 martial artists practice every day,
Proportion of martial artists who practice every day = 7/12
Now, to predict how many students practice every day, we can multiply the proportion by the total number of martial arts students in the school.
Number of students who practice every day = Proportion * Total number of martial arts students
Number of students who practice every day = (7/12) * 144
Now we can calculate the answer:
Number of students who practice every day = 84
Therefore, we can predict that 84 students practice every day.
b. The sample size refers to the number of individuals or observations in a given sample. In this case, the sample size refers to the total number of martial arts students in the school.
The sample size is given in the question as 144 martial arts students.
Therefore, the sample size is 144.