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2 years ago

The fastest human has ever run is 27 mph how many miles per minute did the human run

Mathematics

1 answer:

Phoenix [80]2 years ago

7 0

$\sf \frac{27~ miles}{1 ~hour} \times \frac{1~ hour}{60~ minutes} = \boxed{\frac{9}{20}~miles~per~minute}$

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A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u

Kryger [21]

Given: $f(x) = \frac{1}{x-2}$

$g(x) = \frac{2x+1}{x}$

A.)Consider

$f(g(x))= f(\frac{2x+1}{x} )$

$f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}$

$f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}$

$f(\frac{2x+1}{x} )=\frac{x}{1}$

$f(\frac{2x+1}{x} )=1$

Also,

$g(f(x))= g(\frac{1}{x-2} )$

$g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{x }{1}$

$g(\frac{1}{x-2} )= x$

Since, $f(g(x))=g(f(x))=x$

Therefore, both functions are inverses of each other.

For the Composition function $f(g(x)) = f(\frac{2x+1}{x} )=x$

Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

For the Composition function $g(f(x)) =g(\frac{1}{x-2} )=x$

Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

8 0

3 years ago

Include work pleaseeeee

Angelina_Jolie [31]

Okay so to represent juice we are going to use X, and to represent water we are going to use Y.

We also know that the first two starting equations are:

6x + y = 135

4x + 2y = 110

We can re-arrange the first equation so that it equals y (for now), so it is going to end up looking like this:

y = -6x +135

Now you can take that equation and plug into either one of the starting two equations. I chose the second equation. We just substitute what y equals in for y in the equation, so we have:

4x + 2(135 - 6x) = 110

Now solve

4x + 270 -12x = 110

-8x + 270 = 110

Subtract 270 from both sides

-8x = -160

Now divide by -8 on both sides

x = 20

We can now confirm that juice costs $20

Now lets plug that into the equation where we solved for y, to get the actual value of y.

y = 135 - 6(20)

y = 135 - 120

y = 15

The price of water costs $15

From this we can conclude that the cost of juice is $20 and the price of water is $15

5 0

2 years ago

Help this confusing no matter how any times I do it

3241004551 [841]

Answer:

The variable 8. Equation is 16 + 12x = 112.

Step-by-step explanation:

We know that she spent $16 dollars on magazines, so we can put it in the equation (16 + x= ?). We also know that the total is $112, so we can also add that (16+ x= 112). We don't know how many books she got, but we do know how much they cost (16 + 12x=112. So that makes the books the variable (X).

To find the variable we need to take out the magazines from the price. 112-16=96. Now we're left with 12x=96. Now all we have to do is divide 96 by 12, which equals 8.

Sorry everything is so long, I tried to make it short as possible

8 0

2 years ago

Divide z by 11. Then, add 8.

yulyashka [42]

This may be the answer,hope it helps

8 0

3 years ago

Below are 36 sorted ages of an acting award winner. find the percentile corresponding to age 3838 using the method presented in

horrorfan [7]

Question:

Below are 36 sorted ages of an acting award winner. find the percentile corresponding to age 38 using the method presented in the textbook. 18 19 20 20 21 23 25 31 33 34 35 37 38 47 50 51 55 55 58 59 62 62 64 66 69 70 70 70 71 71 72 74 74 75 77 80 percentile of value 38 = ______ (round to the nearest integer as needed.)

Answer:

33 percentile

Step-by-step explanation:

Given the ages:

18, 19, 20, 20, 21, 23, 25, 31, 33, 34, 35, 37, 38, 47, 50, 51, 55, 55, 58, 59, 62, 62, 64, 66, 69, 70, 70, 70, 71, 71, 72, 74, 74, 75, 77, 80.

We are told to find the percentile corresponding to age 38.

To find the percentile corresponding to age 38 simply means to find the percentage of ages that are less than 38.

From the given values, the number of ages less than 38 are 12. Therefore, the percentile corresponding to age 38 would be:

(Ages less than 38/ total number of ages) * 100

$= \frac{12}{36} * 100 = 33.333$

33.333 ≈ 33

The percentile corresponding to age 38 = 33 percentile

5 0

2 years ago