Answer:
Test statistic Z = p diff/std error = 2.3333
p value one tailed = 0.009815
Step-by-step explanation:
Given that in a survey conducted by a website, employers were asked if they had ever sent an employee home because they were dressed inappropriately.
Sample size n = 2755
Sample favourable x = 967
Sample proportion p = ![\frac{967}{2755} \\=0.3510](https://tex.z-dn.net/?f=%5Cfrac%7B967%7D%7B2755%7D%20%5C%5C%3D0.3510)
![H_0: p = 0.3333\\H_a: p >0.3333](https://tex.z-dn.net/?f=H_0%3A%20p%20%3D%200.3333%5C%5CH_a%3A%20p%20%3E0.3333)
(right tailed test at 5% significance level)
p difference = 0.0210
Standard error assuming H0 is true is ![\sqrt{\frac{0.3333*0.6667}{2755} } \\=0.0090](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B0.3333%2A0.6667%7D%7B2755%7D%20%7D%20%5C%5C%3D0.0090)
Test statistic Z = p diff/std error = 2.3333
p value one tailed = 0.009815
Since p <0.05 we reject null hypothesis.
The expression for (r-s)(x) is found by subtracting s from r. That difference is
![3 x^{2} -2x](https://tex.z-dn.net/?f=3%20x%5E%7B2%7D%20-2x)
. The expression for (r+s)(x) is found by adding them, which is
![3 x^{2} +2x](https://tex.z-dn.net/?f=3%20x%5E%7B2%7D%20%2B2x)
. Now we are told to evaluate (r*s)(x) which means they want us to multiply those and state the "new" expression that results.
![(3 x^{2} )(2x)=6x^3](https://tex.z-dn.net/?f=%283%20x%5E%7B2%7D%20%29%282x%29%3D6x%5E3)
. There you go!
<h2>
Explanation:</h2>
The rational expression is given by:
![E=\frac{2x^2-72}{5x^2-245} \\ \\ Factor \ out: \\ \\ E=\frac{2(x^2-36)}{5(x^2-49)} \\ \\ E=\frac{2(x-6)(x+36)}{5(x-7)(x+7)} : \ \ \ \ a^2-b^2=(a-b)(a+b)](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B2x%5E2-72%7D%7B5x%5E2-245%7D%20%5C%5C%20%5C%5C%20Factor%20%5C%20out%3A%20%5C%5C%20%5C%5C%20%20E%3D%5Cfrac%7B2%28x%5E2-36%29%7D%7B5%28x%5E2-49%29%7D%20%5C%5C%20%5C%5C%20E%3D%5Cfrac%7B2%28x-6%29%28x%2B36%29%7D%7B5%28x-7%29%28x%2B7%29%7D%20%3A%20%5C%20%5C%20%5C%20%5C%20a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29)
The denominator can't be zero, therefore:
![(x-7)(x+7)\neq 0 \\ \\ \\ Thus: \\ \\ \boxed{x\neq 7 \ and x \neq -7}](https://tex.z-dn.net/?f=%28x-7%29%28x%2B7%29%5Cneq%200%20%5C%5C%20%5C%5C%20%5C%5C%20Thus%3A%20%5C%5C%20%5C%5C%20%5Cboxed%7Bx%5Cneq%207%20%5C%20and%20x%20%5Cneq%20-7%7D)
Finally,<em> the values of x that make the rational expression undefined are </em>
<em></em>
<em>x = 7 and x = -7</em>
Answer:
Inequalities are,
y ≥ 4x + 2
y ≥ 2
Step-by-step explanation:
Solid yellow line of the graph attached passes through two points (0, -2) and (1, 2).
Let the equation of this line is,
y = mx + b
Slope of the line = ![\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
m = ![\frac{2+2}{1-0}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B2%7D%7B1-0%7D)
m = 4
Y-intercept 'b' = -2
Equation of the line will be,
y = 4x - 2
Since shaded area is on the left side of this solid line so the inequality representing this region will be,
y ≥ 4x - 2
Another line is a solid blue line parallel to the x-axis.
Shaded region (blue) above the line will be represented by,
y ≥ 2
Therefore, the common shaded area of these inequalities will be the solution of the given inequalities.