Answer:
Option 3.
Step-by-step explanation:
It is given that a triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2h) degrees.
The top interior angle of the triangle is 40 degrees.

From the given figure it is clear that
(Supplementary angle)

(Supplementary angle)

According to the angle sum property of triangle, the sum of all interior angles of a triangle is 180 degree.
Combine like terms.
Divide both sides by -4.

The value of h is 55.
Therefore, the correct option is 3.
Answer:
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
Step-by-step explanation:
We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.26.
The standard error of the proportion is:
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 95% confidence interval for the population proportion is (0.192, 0.328).
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
Answer: 30
Step-by-step explanation:
Given :The weight of a bag of golf balls varies directly as the number of golf balls in the bag.
Let x be the number of golf balls in a bag that weighs 1,110 grams.
Then we have the following direct variation equation,

Multiply 1110 both sides , we get

Hence, there are 30 balls in the bag.
Answer:
x=3 meters
Step-by-step explanation:
step 1
Find the area of the rectangular pool

we have

substitute

step 2
Find the area of rectangular pool including the area of the walkway
Let
x ----> the width of the walkway
we have

substitute

step 3
Find the area of the walkway
To find out the area of the walkway subtract the area of the pool from the area of rectangular pool including the area of the walkway
so

step 4
Find the value of x if the area of the walkway equal the area of the pool
so

Solve for x

Solve the quadratic equation by graphing
The solution is x=3 meters
see the attached figure