Let x = mileage
98 >= 35 + .21x
Solving for x:
98 >= 35 + .21x
63 >= .21x
300 >= x
.
This says that if the total mileage is 300 miles or less he will be within his budget.
Answer:
The standard deviation of the data set is
.
Step-by-step explanation:
The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)
To find the standard deviation of the following data set
![\begin{array}{cccccccc}83&87&90&92&93&100&104&111\\115&121&&&&&&\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccccc%7D83%2687%2690%2692%2693%26100%26104%26111%5C%5C115%26121%26%26%26%26%26%26%5Cend%7Barray%7D)
we use the following formula
![\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} }](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%20%5Cfrac%7B%20%5Csum%7B%5Cleft%28x_i%20-%20%5Coverline%7BX%7D%5Cright%29%5E2%20%7D%7D%7Bn-1%7D%20%7D)
Step 1: Find the mean
.
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
![Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cfrac%7BSum%20~%20of%20~%20terms%7D%7BNumber%20~%20of%20~%20terms%7D)
![Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}=\frac{83+87+90+92+93+100+104+111+115+121}{10} \\\\Mean = \frac{996}{10} =\frac{498}{5}=99.6](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cfrac%7BSum%20~%20of%20~%20terms%7D%7BNumber%20~%20of%20~%20terms%7D%3D%5Cfrac%7B83%2B87%2B90%2B92%2B93%2B100%2B104%2B111%2B115%2B121%7D%7B10%7D%20%5C%5C%5C%5CMean%20%3D%20%5Cfrac%7B996%7D%7B10%7D%20%3D%5Cfrac%7B498%7D%7B5%7D%3D99.6)
Step 2: Create the below table.
Step 3: Find the sum of numbers in the last column to get.
![\sum{\left(x_i - \overline{X}\right)^2} = 1472.4](https://tex.z-dn.net/?f=%5Csum%7B%5Cleft%28x_i%20-%20%5Coverline%7BX%7D%5Cright%29%5E2%7D%20%3D%201472.4)
Step 4: Calculate σ using the above formula.
![\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 1472.4 }{ 10 - 1} } \approx 12.7906](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%20%5Cfrac%7B%20%5Csum%7B%5Cleft%28x_i%20-%20%5Coverline%7BX%7D%5Cright%29%5E2%20%7D%7D%7Bn-1%7D%20%7D%09%09%09%09%09%09%20%3D%20%5Csqrt%7B%20%5Cfrac%7B%201472.4%20%7D%7B%2010%20-%201%7D%20%7D%20%5Capprox%2012.7906)
<span>−4.6−(0.4+7.2)
</span><span>−20+(−40)+(−60)
4 and 5 is properties of addition
-80 is your answer
hope this helps</span>