Use the Pythagorean Theorm for right triangles where the squares of the two legs equal the square of the hypotenuse.
![{a}^{2} + {b}^{2} = {c}^{2}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%20%20%7Bc%7D%5E%7B2%7D%20)
Plug in the known leg and hypotenuse.
![{15.3}^{2} + {b}^{2} = {35.6}^{2}](https://tex.z-dn.net/?f=%7B15.3%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%20%20%7B35.6%7D%5E%7B2%7D%20)
Simplify by squaring.
![234.09 + {b}^{2} = 1267.36](https://tex.z-dn.net/?f=234.09%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%201267.36)
![{b}^{2} = 1033.27](https://tex.z-dn.net/?f=%20%7Bb%7D%5E%7B2%7D%20%20%3D%201033.27)
Isolate b by square rooting both sides.
![b = 32.14](https://tex.z-dn.net/?f=b%20%3D%2032.14)
The result is rounded
Answer:
<h3>In an independent groups experiment, if we must estimate the population standard deviation to determine the significance of the sample results, the appropriate inference test is the<u> t test</u></h3>
Step-by-step explanation:
In an independent groups experiment, if we must estimate the population standard deviation to determine the significance of the sample results, the appropriate inference test is the<u> </u><u>t test</u>
<h3>For :</h3>
- A t-test is one of the methods of a statistic and is used to determine if there is a significant difference between the two groups of their means based on a sample in data.
- The statistical significance is determined by the difference between the averages of group size , the sample size, and standard deviations of the groups.
<h3>Therefore option c) t test is correct</h3>
Answer:
D) ![(\sqrt[4]{2x -8} )^4 = (-\sqrt[4]{2x + 8} )^4](https://tex.z-dn.net/?f=%28%5Csqrt%5B4%5D%7B2x%20-8%7D%20%29%5E4%20%3D%20%28-%5Csqrt%5B4%5D%7B2x%20%2B%208%7D%20%29%5E4)
Step-by-step explanation:
The given equation is ![\sqrt[4]{2x - 8} + \sqrt[4]{2x + 8 } = 0](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2x%20-%208%7D%20%20%2B%20%5Csqrt%5B4%5D%7B2x%20%2B%208%20%7D%20%3D%200)
Before, solve this equation, we have to get rid off the radical sign.
So we move the second term on the other side.
![\sqrt[4]{2x-8} = -\sqrt[4]{2x + 8}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2x-8%7D%20%3D%20-%5Csqrt%5B4%5D%7B2x%20%2B%208%7D)
Since we have to radical of 4, we need to raise the power to 4 on both sides
![(\sqrt[4]{2x - 8)} )^4 = (-\sqrt[4]{2x + 8} )^4\\](https://tex.z-dn.net/?f=%28%5Csqrt%5B4%5D%7B2x%20-%208%29%7D%20%29%5E4%20%3D%20%28-%5Csqrt%5B4%5D%7B2x%20%2B%208%7D%20%29%5E4%5C%5C)
Thank you.
Answer: d) 255 ≤ f(x) ≤ 340
Step-by-step explanation:
The function
f(x)= 8.5x
represents the amount of money that Steve earns given the number of hours, x, he works.
The dependent variable is the total amount that he earns, f(x) while the independent variable is the number if hours, x that he works. The range is the possible values of the dependent variable that satisfies the equation.
Steve works between 30 and 40 hours per week. This means that
the lowest amount that he earns is 8.5×30 = $255
The highest amount that he earns is 8.5× 40 = 340. Therefore, the range is
255 ≤ f(x) ≤ 340
![\frac{5}{3} + \frac{2}{3} = \frac{7}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B3%7D%20%20%2B%20%20%5Cfrac%7B2%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B3%7D%20)
Because the denominators are same, you can just add the numerators.