# A fair number cube with the numbers 1, 2, 3, 4, 5, and 6 is rolled. What is theprobability of getting a multiple of 3?Your answer

2/6

Step-by-step explanation:

There are only 2 multiples of 3, and there are only 6 possible outcomes.

## Related Questions

5Type the correct answer in each box.
50°
60°
709
Х
50°
The value of xis
o, and the value of yis

x = 60°

y = 50°

Step-by-step explanation:

✅x = 180° - (50° + 70°) (sum of interior angles of a triangle theorem)

x = 180° - 120°

x = 60°

✅Based on the exterior angle theorem, the sum of the opposite interior angles of a triangle = the exterior angle.

Therefore,

50° + 60° = x + y

Plug in the value of x

50° + 60° = 60° + y

110° = 60° + y

y = 110° - 60°

y = 50°

Which number(s) below belong to the solution set of the inequality? Check all that apply. 9x 117A.
12

B.
14

C.
19

D.
13

E.
6

F.
8

Question says inequality, but there was no symbol between 9x and 117.

If it were an equation, then it reads 9x=117, in which case the answer is
x=117/9=13.

If it were 9x>=117, then all choices 13 or greater qualify.

If it were 9x<=117, then all choices 13 or less qualify.

The amount of cereal in a box is normal with mean 16.5 ounces. If the packager is required to fill at least 90% of the cereal boxes with 16 or more ounces of cereal, what is the largest standard deviation for the amount of cereal in a box?

The largest standard deviation for the amount of cereal in a box is 0.3906.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

The z-score of X = 16 has a pvalue of 0.1. So it is . Now we have to find the value of .

The largest standard deviation for the amount of cereal in a box is 0.3906.

Is 600​% of 5 less than​ 10, greater than 10 but less than​ 100, or greater than​ 100?

it is greater than ten and less than 100, the answer is 30%

Step-by-step explanation:

600*5=3000

3000/100=30%

The percent of fat calories that a person consumes each day is normally distributed with a mean of 37 and a standard deviation of 10. Suppose that 16 individuals are randomly chosen. Let X = average percent of fat calories. (a) For the group of 16, find the probability that the average percent of fat calories consumed is more than forty. (Round your answer to four decimal places.) 0.382 b) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.) 30.25 percent of fat calories

The probability that the average percent of fat calories is more than 40 for a group of 16 individuals is 0.1151 and the first quartile for the average percent of fat calories is 34.82.

### Explanation:

The problem presented is one of statistics, specifically dealing with the normal distribution. When dealing with the normal distribution, there are a few key facts to know. The mean (μ) is the average value of the data, the standard deviation (σ) measures the spread of the data, and the Z-score measures how many standard deviations an element is from the mean. It appears that you're asked to find the probability that the average percent of fat calories is more than 40 for a group of 16 individuals and the value corresponding to the first quartile.

1. For (a), remember that when dealing with averages, the standard deviation gets divided by the square root of the number of observations. Therefore, the new standard deviation becomes 10/√16 = 2.5. The Z-score can then be calculated by subtracting the mean from the observed value and dividing by the new standard deviation. That is, Z = (40 - 37) / 2.5 = 1.2. You can then refer to a Z-table to find the probability associated with this Z-score. However, since the question is asking for more than 40, you need to subtract the resulting probability from 1. Rounded to four decimal places, the probability that the average percent of fat calories is more than 40 is 0.1151.
2. For (b), the first quartile (Q1) is the value corresponding to the 25th percentile. This corresponds to a Z-score of -0.674 (from the Z-table). You can then use the formula Q1 = μ + Zσ to obtain Q1 = 37 - 0.674*2.5 = 34.815. Therefore, the first quartile for the average percent of fat calories is 34.82 (after rounding to two decimal places).

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The probability that the group consumes more than 40% of fat calories is 0.8849 (or 88.49%). The first quartile for the average percent of fat calories is 34.26%.

### Explanation:

This problem requires the use of normal distributions and the calculation of z-scores, which is a quantitative measure that describes a value's relationship to the mean of a group of values. Knowing the mean (μ) and standard deviation (σ), you can calculate the z-score.

In part a) the problem asks for the probability that a sample of 16 individuals has an average fat calories consumption over 40%. First, we calculate the z-score.

z = (X - μ) / (σ/ √ n ), where n is the sample size. So, z = (40 - 37) / (10 / √ 16) = 1.2. Using a standard normal distribution table, we find that the probability corresponding to this z-value is ~0.1151. However, since the question is asking for more than 40%, we subtract this from 1 (1 - 0.1151 = 0.8849). So, the chance that the average of this sample would have more than 40% fat calories is 0.8849, or 88.49%.

For part b), the first quartile (also known as the 25th percentile) is the point at which 25% of the data fall below it. With a standard normal distribution, this z-value is approximately -0.674. We plug this into our z-score formula to find: X = μ + Zσ = 37 -0.674(10) =34.26%. Therefore, the point where 25% of individual average fat calories fall below it is 34.26%.

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A line passes through the point (2, 7) and has a slope of 4. What is the equation of the line?

y=4x-1

Step-by-step explanation:

Remember the point slope form equation y-y1=m(x-x1) where m is the slope and the given point is (x1,y1)

y-7=4(x-2) . Plug in the numbers for the equation

y-7=4x-8   distributive property

y = 4x-1

y=4x-1 is the equation that passes through (2,7)