Answer:
There is no sufficient evidence to reject the company's claim at the significance level of 0.05
Step-by-step explanation:
Let
be the true mean weight per apple the company ship. We want to test the next hypothesis
vs
(two-tailed test).
Because we have a large sample of size n = 49 apples randomly selected from a shipment, the test statistic is given by
which is normally distributed. The observed value is
. The rejection region for
is given by RR = {z| z < -1.96 or z > 1.96} where the area below -1.96 and under the standard normal density is 0.025; and the area above 1.96 and under the standard normal density is 0.025 as well. Because the observed value 1.4583 does not fall inside the rejection region RR, we fail to reject the null hypothesis.
We need a diagram haha
But just note that the answer can only be A or B because minor arcs are less than 180°
This signifies that 168° and 42° are the only possible choices
Cause it has a slope of -3/2, we could call its equation: y= -3/2x+b
and we have to find out b
In addition, it has a y-intercept of -1, that means this line goes through the point A(0;-1). So we could replace x=0 and y= -1: -1 = -3/2x0+b and we have b= -1
We obtain the equation: y= -3/2x-1
Answer:
If the population has increased by 12% then to ensure a generated maximum capacity must be more than 12% we already have a figure being 100% prior so the answer is 12% population increase =112% and 12%.of 112 =13.44
We add this to 12
12+13.44= 25.44
Step-by-step explanation:
Answer:
![a = -4](https://tex.z-dn.net/?f=a%20%3D%20-4)
Step-by-step explanation:
The equation to solve for "a" is:
![(\frac{1}{9})^{a+1}=81^{a+1}*27^{2-a}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B9%7D%29%5E%7Ba%2B1%7D%3D81%5E%7Ba%2B1%7D%2A27%5E%7B2-a%7D)
The first step is to convert all of them to same bases.
9, 81, and 27, all can be expressed in base 3, lets do this:
![(\frac{1}{9})^{a+1}=81^{a+1}*27^{2-a}\\(3^{-2})^{a+1}=(3^4)^{a+1}*(3^3)^{2-a}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B9%7D%29%5E%7Ba%2B1%7D%3D81%5E%7Ba%2B1%7D%2A27%5E%7B2-a%7D%5C%5C%283%5E%7B-2%7D%29%5E%7Ba%2B1%7D%3D%283%5E4%29%5E%7Ba%2B1%7D%2A%283%5E3%29%5E%7B2-a%7D)
We can use the property:
to simplify further:
![(3^{-2})^{a+1}=(3^4)^{a+1}*(3^3)^{2-a}\\3^{-2a-2}=3^{4a+4}*3^{6-3a}](https://tex.z-dn.net/?f=%283%5E%7B-2%7D%29%5E%7Ba%2B1%7D%3D%283%5E4%29%5E%7Ba%2B1%7D%2A%283%5E3%29%5E%7B2-a%7D%5C%5C3%5E%7B-2a-2%7D%3D3%5E%7B4a%2B4%7D%2A3%5E%7B6-3a%7D)
The right side has 2 same bases multiplied, we can simplify this using the property: ![a^x * a^y = a^{x+y}](https://tex.z-dn.net/?f=a%5Ex%20%2A%20a%5Ey%20%3D%20a%5E%7Bx%2By%7D)
Thus, we have:
![3^{-2a-2}=3^{4a+4}*3^{6-3a}\\3^{-2a-2}=3^{4a+4+6-3a}}\\3^{-2a-2}=3^{a+10}](https://tex.z-dn.net/?f=3%5E%7B-2a-2%7D%3D3%5E%7B4a%2B4%7D%2A3%5E%7B6-3a%7D%5C%5C3%5E%7B-2a-2%7D%3D3%5E%7B4a%2B4%2B6-3a%7D%7D%5C%5C3%5E%7B-2a-2%7D%3D3%5E%7Ba%2B10%7D)
Now, both sides have same base, so exponents would be equal. Now lets equate and solve for "a":
![3^{-2a-2}=3^{a+10}\\-2a-2=a+10\\3a=-12\\a=-4](https://tex.z-dn.net/?f=3%5E%7B-2a-2%7D%3D3%5E%7Ba%2B10%7D%5C%5C-2a-2%3Da%2B10%5C%5C3a%3D-12%5C%5Ca%3D-4)
So,
a = -4