Answer: The p-value is 0.154.
Step-by-step explanation:
Since we have given that
We claim that
Null hypothesis :
Alternate hypothesis :
Population mean = 20 hours
Sample mean = 18.5 hours
Sample standard deviation = 4.3 hours
Sample size n = 35
So, test statistic would be
So, the p value would be 0.154.
Hence, the p-value is 0.154.
Given Information:
Area of rectangle = 16 square feet
Required Information:
Least amount of material = ?
Answer:
x = 4 ft and y = 4 ft
Step-by-step explanation:
We know that a rectangle has area = xy and perimeter = 2x + 2y
We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.
So we have
xy = 16
y = 16/x
p = 2x + 2y
put the value of y into the equation of perimeter
p = 2x + 2(16/x)
p = 2x + 32/x
Take derivative with respect to x
d/dt (2x + 32/x)
2 - 32/x²
set the derivative equal to zero to minimize the perimeter
2 - 32/x² = 0
32/x² = 2
x² = 32/2
x² = 16
x = ft
put the value of x into equation xy = 16
(4)y = 16
y = 16/4
y = 4 ft
So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.
Verification:
xy = 16
4*4 = 16
16 = 16 (satisfied)
Greetings!
To start this problem, let's first assign a variable for the missing, consecutive odd numbers. Since they are consecutive and odd, we add two.
<u>Proof:</u> <em>3-1=2, 5-3=2</em>
The first, consecutive, odd number:
The second, consecutive, odd number:
The third, consecutive, odd number:
The fourth, consecutive, odd number:
The sum of the values are equal to 3 times the sum of the first two numbers, of which this is equal to 35 less than the fourth number. Let's create an equation to simplify this:
Complete the operations inside the parenthesis:
Distribute the parenthesis (utilizing the distributive property)
Simplify both sides:
Add -6 and -x to both sides of the equation:
Divide both sides of the equation by 5:
If is equal to -7:
The four numbers are:
I hope this helps!
-Benjamin