On average 113,204 aluminum cans are recycled in a minute. Approximately how many cans will be recycled in 16 days?

The demand function for an auto parts manufacturing company is given by f(x)= 100,000-2,500, where x represents price and f(x) r

faust18 [17]

Answer

Part 1) f(x)⁻¹ = 40 - x/2,500

Part 2) quantity

Explanation

f(x)= 100,000-2,500x

In finding the inverse of F(x) we make x the suject of the formula.

f(x)= 100,000-2,500x

2,500x = 100,000 - f(x)

x = 100,000/2,500 - f(x)/2500

x = 40 - f(x)/2,500

Now interchange x with f(x).

f(x)⁻¹ = 40 - x/2,500

4 0

3 years ago

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A grandfather is six times as old as his grandson. If the grandfather was 45 when his grandson was born, how old is the grandson

Semenov [28]

The grandson is 9 years old.

This would mean that the grandpa is 54.

9x6=54
54/6=9

5 0

2 years ago

Verify that f and g are inverses functions using composition , show your steps

pshichka [43]

Answer:

See explanations below

Step-by-step explanation:

Given the functions

f(x) = 12x - 12

g(x) = x/12 - 1

To show they are inverses, we, must show that f(g(x)) = g(f(x))

f(g(x)) = f(x/12 - 1)

Replace x with x/12 - 1 into f(x)

f(g(x)) =12((x-12)/12) - 11

f(g(x)) = x-1 - 1

f(g(x)) =x - 2

Similarly for g(f(x))

g(f(x)) = g(12x-12)

g(f(x)) =(12x-12)/12 - 1

12(x-1)/12 - 1

x-1 - 1

x - 2

Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other

5 0

3 years ago

A probability experiment is conducted in which the sample space of the experiment is upper s equals startset 4 comma 5 comma 6 c

olchik [2.2K]

The correct question statement is:

A probability experiment is conducted in which the sample space of the experiment is S = {4,5,6,7,8,9,10,11,12,13,14,15}. Let event E={7,8,9,10,11,12,13,14,15}. Assume each outcome is equally likely. List the outcomes in $E^{c}$ . Find $P(E^{c})$ .

Solution:

Part 1:

$E^{c}$ means compliment of the set E. A compliment of a set can be obtained by finding the difference of the set from the universal set. The universal set is the set which contains all the possible outcomes of the events which is S in this case.

So, compliment of E will be equal to S - E. S - E will result in all those elements of S which are not present in E. So, we can write:

$E^{c}=S-E \\ \\ 
E^{c}=(4,5,6,7,8,9,10,11,12,13,14,15)-(7,8,9,10,11,12,13,14,15) \\ \\ 
E^{c}=(4,5,6)$

Thus the set compliment of E will contain the elements {4,5,6}.So

$E^{c}$ = {4,5,6}

Part 2)

$P(E^{c})$ means probability that if we select any number from the Sample Space S, it will belong the set E compliment.

$P(E^{c})$ = (Number of Elements in $E^{c}$ )/Number of elements in S

Number of elements in set S = n(S) = 12
Number of elements in set $E^{c}$ = $n(E^{c})$ =3

So,

$P(E^{c})= \frac{n(E^{c}) }{n(S)} \\ \\ 
P(E^{c})= \frac{3}{12} \\ \\ 
P(E^{c})= \frac{1}{4}$

7 0

3 years ago

Keiko started a race at 8:04 AM and finished it at 8:33 AM.

ElenaW [278]

It took her 29 minutes to race. :)

4 0

3 years ago

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