Answer:
Average rate of change: ![-3](https://tex.z-dn.net/?f=-3)
Step-by-step explanation:
<u>Remember:</u>
The average rate of change of a function over an interval
is ![\frac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
<u>Given:</u>
![[a,b]=[1,7]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%3D%5B1%2C7%5D)
![f(b)=f(7)](https://tex.z-dn.net/?f=f%28b%29%3Df%287%29)
![f(a)=f(1)](https://tex.z-dn.net/?f=f%28a%29%3Df%281%29)
<u>Calculation:</u>
![f(b)=f(7)=-(7)^2+5(7)+14=-49+35+14=-49+49=0](https://tex.z-dn.net/?f=f%28b%29%3Df%287%29%3D-%287%29%5E2%2B5%287%29%2B14%3D-49%2B35%2B14%3D-49%2B49%3D0)
![f(a)=f(1)=-(1)^2+5(1)+14=-1+5+14=4+14=18](https://tex.z-dn.net/?f=f%28a%29%3Df%281%29%3D-%281%29%5E2%2B5%281%29%2B14%3D-1%2B5%2B14%3D4%2B14%3D18)
![\frac{f(b)-f(a)}{b-a}=\frac{0-18}{7-1}=\frac{-18}{6}=-3](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%3D%5Cfrac%7B0-18%7D%7B7-1%7D%3D%5Cfrac%7B-18%7D%7B6%7D%3D-3)
Therefore, the average rate of change of the function
over the interval
is
.
Answer:
The 45% off discount saves an additional $10 compared to the 15% discount for a total of $15 off regular price.
Step-by-step explanation:
We can find the original price of the game through a proportion. A proportion is an equation where two ratios or fractions are equal. The ratios or fractions compare like quantities. For example, we will compare percent over percent to an equal ratio of $ to $. Since 15% of 100% is the same ratio as $5 to the unknown original $ price, I write:
![\frac{15}{100} =\frac{5}{y}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B100%7D%20%3D%5Cfrac%7B5%7D%7By%7D)
I can now cross-multiply by multiplying numerator and denominator from each ratio.
![15y=100(5)\\15y=500](https://tex.z-dn.net/?f=15y%3D100%285%29%5C%5C15y%3D500)
I now solve for y by dividing by 15.
![\frac{15y}{15} =\frac{500}{15} \\y= 33.33333....](https://tex.z-dn.net/?f=%5Cfrac%7B15y%7D%7B15%7D%20%3D%5Cfrac%7B500%7D%7B15%7D%20%5C%5Cy%3D%2033.33333....)
The original price was $33.34.
Now, we can find the amount if 45% off and then then compare the two discounts. To find the percent off I can multiply by 0.45(33.34)=15. The 45% off discount saves an additional $10 compared to the 15% discount.
Answer:
21
Step-by-step explanation:
The answer is 8.72.
sqrt(76) = 2sqrt(19)
2sqrt(19) = 8.717797887
Rounded to nearest hundredth ≈ 8.72
From the data shown in the scater plots, the points are scattered apart which means that r is not close to 1.
Also the data points increase to the right which means that r is positive.
Therefore, the estimate for r in the data shown in the scatter plot is 0.55