Since
null hypothesis on this data is not rejected.
<h3>Null and Alternative Hypothesis</h3>
Data;
- sample mean x1 = 240993
- population standard deviation σ1 = 25875
- sample size n1 = 35
- sample mean x2 = 249237
- population standard mean σ2 = 27110
- sample size n2 = 35
- significance level α = 0.10
H_o = μ1 = μ2
H_o = μ1 ≠ μ2
This is a two-tailed test and population standard deviation will be used.
<h3>Test Statistic</h3>
The z-stat is
![z = \frac{x_1 - x_2}{\sqrt{\frac{\sigma_1^2}{n_1}+ \frac{\sigma_1 ^2}{n_2} } } \\z=\frac{240993-249237}{\sqrt{\frac{25875^2}{35}+ \frac{27110^2}{35} } } \\z = \frac{-8244}{6334.6388} \\z = -1.301](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7Bx_1%20-%20x_2%7D%7B%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%20%5Cfrac%7B%5Csigma_1%20%5E2%7D%7Bn_2%7D%20%20%7D%20%7D%20%5C%5Cz%3D%5Cfrac%7B240993-249237%7D%7B%5Csqrt%7B%5Cfrac%7B25875%5E2%7D%7B35%7D%2B%20%5Cfrac%7B27110%5E2%7D%7B35%7D%20%20%7D%20%20%7D%20%5C%5Cz%20%3D%20%5Cfrac%7B-8244%7D%7B6334.6388%7D%20%5C%5Cz%20%3D%20-1.301)
The significance level is α = 0.1 and the critical value for a two-tailed test is
![Z_t = Z_1 - _\alpha _/_2 = 1.64](https://tex.z-dn.net/?f=Z_t%20%3D%20Z_1%20-%20_%5Calpha%20_%2F_2%20%3D%201.64)
Since
, we can assume that the null hypothesis is not rejected.
Learn more on null hypothesis here;
brainly.com/question/15980493
6/25 is your answer because you just add them up and take the 6
Step ![1](https://tex.z-dn.net/?f=1)
<u>Find the value of MN</u>
In the right triangle MNL
Applying the Pythagorean Theorem
![ML^{2} =MN^{2} +NL^{2}](https://tex.z-dn.net/?f=ML%5E%7B2%7D%20%3DMN%5E%7B2%7D%20%2BNL%5E%7B2%7D)
Solve for MN
![MN^{2}=ML^{2}-NL^{2}](https://tex.z-dn.net/?f=MN%5E%7B2%7D%3DML%5E%7B2%7D-NL%5E%7B2%7D)
in this problem we have
![ML=25\ units\\NL=15\ units](https://tex.z-dn.net/?f=ML%3D25%5C%20units%5C%5CNL%3D15%5C%20units)
Substitute in the formula above
![MN^{2}=25^{2}-15^{2}](https://tex.z-dn.net/?f=MN%5E%7B2%7D%3D25%5E%7B2%7D-15%5E%7B2%7D)
![MN^{2}=400](https://tex.z-dn.net/?f=MN%5E%7B2%7D%3D400)
![MN=20\ units](https://tex.z-dn.net/?f=MN%3D20%5C%20units)
Step ![2](https://tex.z-dn.net/?f=2)
<u>Find the value of cos (M)</u>
we know that
In the right triangle MNL
![cos(M)=\frac{adjacent\ side\ angle\ M}{hypotenuse}=\frac{MN}{ML}=\frac{MN}{25}](https://tex.z-dn.net/?f=cos%28M%29%3D%5Cfrac%7Badjacent%5C%20side%5C%20angle%5C%20M%7D%7Bhypotenuse%7D%3D%5Cfrac%7BMN%7D%7BML%7D%3D%5Cfrac%7BMN%7D%7B25%7D)
Substitute the value of MN
![cos (M)=\frac{20}{25}=\frac{4}{5}](https://tex.z-dn.net/?f=cos%20%28M%29%3D%5Cfrac%7B20%7D%7B25%7D%3D%5Cfrac%7B4%7D%7B5%7D)
therefore
<u>the answer is</u>
The value of cos(M) is ![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
Answer:
(-4x³ - x²)(8x² - 9) = -32x⁵ - 8x⁴ + 36x³ + 9x²
5x(3x² + 2) = 15x³ + 10x
(3x+ 1)² = 9x² + 6x + 1
(1 + 4x)(1 - 4x) = 1 - 16x²
(3x - 2)(3x - 2) = 9x² - 12x + 4
Step-by-step explanation: