If the mean weight of all students in a class is 165 pounds with a variance of 234.09 square pounds, what is the z-value associated with a student whose weight is 140 pounds?

Step-by-step explanation:

The z-score measures how many standard deviation a score X is above or below the mean.

it is given by the following formula:

In which

is the mean, is the standard deviation

In this problem, we have that:

Mean weight of all students in a class is 165 pounds, so

Variance of 234.09 square pounds. The standard deviation is the square root of the variance. So

What is the z-value associated with a student whose weight is 140 pounds?

Z when X = 140. So

28 units

Explanation:

This is an isosceles triangle.  We can tell this by the fact that the base angles, ∠C and ∠B, are marked congruent.

In an isosceles triangle, the two sides adjacent to the two congruent angles are also congruent.  This means that AC ≅ AB; it also gives us the equation

2x+7 = 4x-7

We do not want a variable on both sides, so we can start by subtracting 2x from each side:

2x+7-2x = 4x-7-2x

7 = 2x-7

Add 7 to both sides to cancel it on the right:

7+7 = 2x-7+7

14 = 2x

Divide both sides by 2:

14/2 = 2x/2

7 = x

The length of BC is 4x units; this means it is 4(7) = 28 units.