Angle AEB and angle CED are vertical angles, this means they equal each other, therefore we set their values as an equation and solve:
5x-10=3x+40
Subtract 3x to both sides
2x-10=40
Add 10 to both sides
2x=50
Divide both sides by 2
x=25
After we have gotten the value of x we can plug it in into the equation of angle AEB:
5x-10
Substitute x by 25
5(25)-10
Distribute
125-10
Substract
115
The measurement of angle AEB is 115
Hope it helped!, have a great day.
Company B; the ratios of cost to weight are equivalent.
Step-by-step explanation:
Step 1:
In the equation,
k is the constant of proportionality.
If the values are in accordance with
, the values of k will be constant for all the values.
So we determine the values of k for both the companies and see which has a constant k.
If
. In these tables, y is the total cost and x is the weight in lbs.
Step 2:
For company A,
when ![y=10.55, x=1, k = \frac{10.55}{1} = 10.55,](https://tex.z-dn.net/?f=y%3D10.55%2C%20x%3D1%2C%20k%20%3D%20%5Cfrac%7B10.55%7D%7B1%7D%20%3D%2010.55%2C)
when ![y=10.85, x=2, k = \frac{10.85}{2} = 5.425,](https://tex.z-dn.net/?f=y%3D10.85%2C%20x%3D2%2C%20k%20%3D%20%5Cfrac%7B10.85%7D%7B2%7D%20%3D%205.425%2C)
when ![y=11.15, x=3, k = \frac{11.15}{3} = 3.71666.](https://tex.z-dn.net/?f=y%3D11.15%2C%20x%3D3%2C%20k%20%3D%20%5Cfrac%7B11.15%7D%7B3%7D%20%3D%203.71666.)
For company B,
when ![y=2.75, x=1, k = \frac2.75}{1} = 2.75,](https://tex.z-dn.net/?f=y%3D2.75%2C%20x%3D1%2C%20k%20%3D%20%5Cfrac2.75%7D%7B1%7D%20%3D%202.75%2C)
when ![y=5.50, x=2, k = \frac{5.50}{2} = 2.75,](https://tex.z-dn.net/?f=y%3D5.50%2C%20x%3D2%2C%20k%20%3D%20%5Cfrac%7B5.50%7D%7B2%7D%20%3D%202.75%2C)
when ![y=8.25, x=3, k = \frac{8.25}{3} = 2.75.](https://tex.z-dn.net/?f=y%3D8.25%2C%20x%3D3%2C%20k%20%3D%20%5Cfrac%7B8.25%7D%7B3%7D%20%3D%202.75.)
So company B has a constant value of
.
Answer:
Value of the test statistic, ![z_{test} = - 1.17](https://tex.z-dn.net/?f=z_%7Btest%7D%20%20%3D%20-%201.17)
Step-by-step explanation:
Null hypothesis, ![H_{0}: \mu = 53.9](https://tex.z-dn.net/?f=H_%7B0%7D%3A%20%5Cmu%20%3D%2053.9)
Alternative hypothesis, ![H_{a} : \mu \neq 53.9](https://tex.z-dn.net/?f=H_%7Ba%7D%20%3A%20%5Cmu%20%5Cneq%2053.9)
Sample mean, ![\bar{X} = 53.7](https://tex.z-dn.net/?f=%5Cbar%7BX%7D%20%3D%2053.7)
Sample size, n = 110
Standard deviation, ![\sigma = 1.8](https://tex.z-dn.net/?f=%5Csigma%20%3D%201.8)
Significance level, ![\alpha = 0.02](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.02)
The value of the test statistics is given by the formula:
![z_{test} = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n} } } \\z_{test} = \frac{53.7 - 53.9}{\frac{1.8}{\sqrt{110} } } \\z_{test} = - 1.17](https://tex.z-dn.net/?f=z_%7Btest%7D%20%20%3D%20%5Cfrac%7B%5Cbar%7BX%7D%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D%20%5C%5Cz_%7Btest%7D%20%20%3D%20%5Cfrac%7B53.7%20-%2053.9%7D%7B%5Cfrac%7B1.8%7D%7B%5Csqrt%7B110%7D%20%7D%20%7D%20%5C%5Cz_%7Btest%7D%20%20%3D%20-%201.17)
-18.2 + 3.6= -14.6 is the answer to the question