If there are 10 people in a race how many ways can 1st 2nd 3rd places be awarded

1 answer:

4 0

3 slots
1st slot has 10 possible people
2nd slot has 9 possible people (1 less than previous)
3rd slot has 8 possible people

so there are 10*9*8 ways or 720 ways

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Find the average rate of change for f(x) = x2 − 3x − 10 from x = 4 to x = 6. A) 5 Reactivate B) 7 C) 9 Reactivate D) 11

White raven [17]

Answer:Rate of change is 7

Option B is correct.

Step-by-step explanation:

We need to find the average rate of change for $f(x)=x^2-3x-10$ from x = 4 to x = 6

The formula used to find average rate of change is:

$Rate\,\,of\,\,change=\frac{f(b)-f(a)}{b-a}$

Where b = 6 and x = 4

Finding f(6):

$f(x)=x^2-3x-10\\f(6)=(6)^2-3(6)-10\\f(6)=36-18-10\\f(6)=36-28\\f(6)=8$

Finding f(4):

$f(x)=x^2-3x-10\\f(4)=(4)^2-3(4)-10\\f(4)=16-12-10\\f(4)=16-22\\f(4)=-6$

Now Putting values:

$Rate\,\,of\,\,change=\frac{f(b)-f(a)}{b-a}$

$Rate\,\,of\,\,change=\frac{8-(-6)}{6-4}\\Rate\,\,of\,\,change=\frac{8+6}{2}\\Rate\,\,of\,\,change=\frac{14}{2}\\Rate\,\,of\,\,change=7$

So, Rate of change is 7

Option B is correct.

Keywords: Rate of Change

Learn more about Rate of Change at:

#learnwithBrainly

8 0

3 years ago

Calculate the volume of the right rectangular prism shown. Edulastic Question

Marysya12 [62]

since we have the area of the front side, to get its volume we can simple get the product of the area and the length, let's firstly change the mixed fractions to improper fractions.

$\stackrel{mixed}{23\frac{2}{3}}\implies \cfrac{23\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{71}{3}} ~\hfill \stackrel{mixed}{4\frac{7}{8}}\implies \cfrac{4\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{39}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{3}\cdot \cfrac{39}{8}\implies \cfrac{71}{8}\cdot \cfrac{39}{3}\implies \cfrac{71}{8}\cdot 13\implies \cfrac{923}{8}\implies 115\frac{3}{8}~in^3$