So so u would subtract bothe negaitives but two negative equal a positive so then it would then be-3+8
Answer:
Option B) Do not reject null hypothesis, there is not enough evidence to support the claim that the proportion of homes in Oregon heated by natural gas is different from the 48% that the US Department of Energy reported.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 333
p = 48% = 0.48
Alpha, α = 0.01
Number of women belonging to union , x = 149
First, we design the null and the alternate hypothesis
This is a two-tailed test.
Formula:
Putting the values, we get,
Now, we calculate the p-value from the table.
P-value = 0.273079
Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.
Thus, there is not enough evidence to support the claim that proportion of homes in Oregon that were heated by natural gas is different from what was reported.
B. Do not reject null hypothesis, there is not enough evidence to support the claim that the proportion of homes in Oregon heated by natural gas is different from the 48% that the US Department of Energy reported.
Given:
The bases of triangular prism are right triangles with a base of 12 inches and height of 9 inches.
The height of the prism is 11 inches.
To find:
The surface area of the triangular prism.
Solution:
Using the Pythagoras theorem, the hypotenuse of the bases of the triangular prism is:
![Hypotenuse^2=Base^2+Height^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DBase%5E2%2BHeight%5E2)
![Hypotenuse^2=12^2+9^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D12%5E2%2B9%5E2)
![Hypotenuse^2=144+81](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D144%2B81)
![Hypotenuse^2=225](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D225)
Taking square root on both sides.
![Hypotenuse=15](https://tex.z-dn.net/?f=Hypotenuse%3D15)
The surface after of the triangular prism contains 3 rectangles of dimensions 12 inches by 11 inches, 9 inches by 11 inches, 15 inches by 11 inches and two triangles with base 12 inches and height 9 inches.
Area of the rectangle:
![Area=Length \times Width](https://tex.z-dn.net/?f=Area%3DLength%20%5Ctimes%20Width)
So, the area of three rectangles are:
![A_1=12 \times 11](https://tex.z-dn.net/?f=A_1%3D12%20%5Ctimes%2011)
![A_1=132](https://tex.z-dn.net/?f=A_1%3D132)
![A_2=9 \times 11](https://tex.z-dn.net/?f=A_2%3D9%20%5Ctimes%2011)
![A_2=99](https://tex.z-dn.net/?f=A_2%3D99)
![A_3=15 \times 11](https://tex.z-dn.net/?f=A_3%3D15%20%5Ctimes%2011)
![A_3=165](https://tex.z-dn.net/?f=A_3%3D165)
Area of a triangle is:
![Area=\dfrac{1}{2}\times base \times height](https://tex.z-dn.net/?f=Area%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20base%20%5Ctimes%20height)
So, the area of the triangles is:
![A_4=\dfrac{1}{2}\times 12 \times 9](https://tex.z-dn.net/?f=A_4%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2012%20%5Ctimes%209)
![A_4=6 \times 9](https://tex.z-dn.net/?f=A_4%3D6%20%5Ctimes%209)
![A_4=54](https://tex.z-dn.net/?f=A_4%3D54)
And, the triangles have same dimensions so their areas are equal.
![A_4=A_5=54](https://tex.z-dn.net/?f=A_4%3DA_5%3D54)
Now,
![Area=A_1+A_2+A_3+A_4+A_5](https://tex.z-dn.net/?f=Area%3DA_1%2BA_2%2BA_3%2BA_4%2BA_5)
![Area=132+99+165+54+54](https://tex.z-dn.net/?f=Area%3D132%2B99%2B165%2B54%2B54)
![Area=504](https://tex.z-dn.net/?f=Area%3D504)
Therefore, the surface area of the triangular prism is 504 sq. inches.
Answer:
Distributive property
Step-by-step explanation:
Distributive property allows you to multiply a(b+c) as ab + ac.
Answer:
-3,-5
Step-by-step explanation: