The tire manufacturer has a 60,000 mile warranty for tread life. To verify the authenticity of its claim, it picks a sample of 250 tires (out of the population of tires) that have been used for 60,000 miles.

Given the hypothesis:

$H_0$ : The proportion of tires that are worn out after 60,000 miles is equal to 0.05.

$H_a$ : The proportion of tires that are worn out after 60,000 miles is less than 0.05.

It is assumed that 5% of the tires in the sample are worn out and the hypothesis is formulated to prove or disprove this assumption.

5 0

4 years ago

Steve is adding wallpaper to a living room wall and he needs to know how much wallpaper to buy. If the wall is 8.5 feet tall and

Bogdan [553]

He needs to buy 106.25 square feet of wallpaper. This is area so you would do length times height. 8.5x12.5

6 0

3 years ago

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i am a decimal number less than 1. the digit in my tenths place is an even prime number. my hundredths digit is twice my tenths

tankabanditka [31]

Answer:

Step-by-step explanation:

7 0

3 years ago

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ol McDonald would like to build a pin for his favorite pig horse and cow he needs to enclose a rectangular plot of land into thr

garri49 [273]

The area of the pen is the products of its dimensions

The dimension of the pen is 300 by 120 feet
The maximum area of the pen is 36000 square feet.

Let the dimension of the fence be x by y.

So, we have:

$\mathbf{2x + 5y = 1200}$ --- perimeter

$\mathbf{Area =xy}$ -- area

Subtract 5y from both sides of $\mathbf{2x + 5y = 1200}$

$\mathbf{2x = 1200 - 5y}$

Divide both sides by 2

$\mathbf{x = \frac{1200 - 5y}{2}}$

Substitute $\mathbf{x = \frac{1200 - 5y}{2}}$ in $\mathbf{Area =xy}$

$\mathbf{Area = \frac{1200 - 5y}{2} \times y}$

$\mathbf{Area = \frac{1200y - 5y^2}{2}}$

Split

$\mathbf{Area = 600y - \frac{5}{2}y^2}$

Differentiate

$\mathbf{A' = 600 -5y}$

Set to 0

$\mathbf{600 -5y = 0}$

Add 5y to both sides

$\mathbf{5y = 600}$

Divide both sides by 5

$\mathbf{y = 120}$

Substitute $\mathbf{y = 120}$ in $\mathbf{x = \frac{1200 - 5y}{2}}$

$\mathbf{x = \frac{1200 - 5 \times 120}{2}}$

$\mathbf{x = \frac{1200 - 600}{2}}$

$\mathbf{x = \frac{600}{2}}$

$\mathbf{x = 300}$

Recall that:

$\mathbf{Area =xy}$

So, we have:

$\mathbf{Area = 300 \times 120}$

$\mathbf{Area = 36000}$

Hence, the maximum area of the pen is 36000 square feet.