<span>First calculate the amount of overhead expenses. The selling price was $240. To find 20% of 240, multiply 240 by 0.20, which equals 48. From that, we found that the overhead expenses were $48.
To find the rate of profit, take the selling price and subtract all expenses. We know that Mr Lippman's selling price was $240, he spent $160 to buy the dryer, and he had $48 worth of overhead expenses. 240 - 160 - 48 = 32.
Therefore, the profit was $32.
To find the rate of profit, divide the profit by the total expenses. 32 / (240 + 160) = 0.08.
Therefore, the rate of profit was 8%.</span>
Answer:
33.9 m
Step-by-step explanation:
cos(32) = adjacent/hypotenuse
cos(32) = X/40
X = 40cos(32)
X = 33.92192385 m
Perform indicated multiplications on left side.
8-40x=13 subtract 8 from both sides
-40x=5 divide both sides by -40
x=-5/40
x=-1/8
Note: There are no mixed numbers in this problem.
We have a sample that in fact represents the population.
We have to calculate the standard deviation of this population.
The difference between the standard deviation of a population comparing it to the calculation of the standard deviation of a sample is that we divide by the population side n instead of (n-1).
We have to start by calculating the mean of the population first:
Now, we can calculate the standard deviation as:
![\sigma=\sqrt[]{\dfrac{1}{n}\sum^n_{i=1}\, (x_i-\mu)^2}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%5B%5D%7B%5Cdfrac%7B1%7D%7Bn%7D%5Csum%5En_%7Bi%3D1%7D%5C%2C%20%28x_i-%5Cmu%29%5E2%7D)
![\begin{gathered} \sigma=\sqrt[]{\dfrac{1}{6}((37-34)^2+(38-34)^2+(39-34)^2+(40-34)^2+(39-34)^2+(11-34)^2)} \\ \sigma=\sqrt[]{\frac{1}{6}(3^2+4^2+5^2+6^2+5^2+(-23)^2)} \\ \sigma=\sqrt[]{\frac{1}{6}(9+16+25+36+25+529)} \\ \sigma=\sqrt[]{\frac{1}{6}(640)} \\ \sigma\approx\sqrt[]{106.67} \\ \sigma\approx10.33 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csigma%3D%5Csqrt%5B%5D%7B%5Cdfrac%7B1%7D%7B6%7D%28%2837-34%29%5E2%2B%2838-34%29%5E2%2B%2839-34%29%5E2%2B%2840-34%29%5E2%2B%2839-34%29%5E2%2B%2811-34%29%5E2%29%7D%20%5C%5C%20%5Csigma%3D%5Csqrt%5B%5D%7B%5Cfrac%7B1%7D%7B6%7D%283%5E2%2B4%5E2%2B5%5E2%2B6%5E2%2B5%5E2%2B%28-23%29%5E2%29%7D%20%5C%5C%20%5Csigma%3D%5Csqrt%5B%5D%7B%5Cfrac%7B1%7D%7B6%7D%289%2B16%2B25%2B36%2B25%2B529%29%7D%20%5C%5C%20%5Csigma%3D%5Csqrt%5B%5D%7B%5Cfrac%7B1%7D%7B6%7D%28640%29%7D%20%5C%5C%20%5Csigma%5Capprox%5Csqrt%5B%5D%7B106.67%7D%20%5C%5C%20%5Csigma%5Capprox10.33%20%5Cend%7Bgathered%7D)
Answer: the standard deviation of this population is approximately 10.33
