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Svetradugi [14.3K]
3 years ago
13

Courtney works at the local shoe store and receives $150 a week plus 3% of all sales over $1000. This week her sales were $3200.

Find her commission using composition of two functions; then find her total earnings for the week.
f (x) = g (x) =
Will you use f(g(x)) or g(f(x)) to solve for the commission?
Solve for the commission using the composition of two functions below:
The commission of sales will be:
Courtney’s total earnings for the week will be:
Mathematics
1 answer:
schepotkina [342]3 years ago
6 0

The equation you would use to find her earning for the week would be:

y=0.03(x-1000)+150

This would mean she made $66 from commissions and $216 total.

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An account earns simple interest.<br><br> $5200 at 7.36% for 54 months
vovikov84 [41]
A = P(1 +rt)  where A is the total amount(principal and interest), r is the rate, and t is the time invested.

A = 5200[1 + .0736(4.5)]
A = 6922.24

note we had to change the rate to a decimal by dividing by 100 
Also 54 months is equal to 4.5 years...you enter time in years.
6 0
3 years ago
Given: &lt;SPT = &lt;RQT, ST = RT Prove: PR = QS​
andrey2020 [161]

Answer:

See explanation

Step-by-step explanation:

Consider triangles PTS and QTR. In these triangles,

  • ST=RT - given;
  • \angle SPT=\angle RQT - given;
  • \angle STP=\angle RTQ - as vertical angles when lines PR and SQ intersect.

Thus, \triangle PTS\cong \triangle QTR by AAS postulate.

Congruent triangles have congruent corresponding sides, so

PT=QT

Consider segments PR and QS:

PR=PT+TR\ [\text{Segment addition postulate}]\\ \\QS=QT+TS\ [\text{Segment addition postulate}]\\ \\PT=QT\ [\text{Proven}]\\ \\ST=RT\ [\text{Given}]

So,

PR=SQ\ [\text{Substitution property}]

7 0
2 years ago
Consider a series system composed of 4 separate components where each component has a 30% chance of failing. Assume each compone
Marina86 [1]

Answer:

16.15% probability that exactly 3 of them would function

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Probability of each system working:

4 components, which means that n = 4

Each has a 30% probability of failing, so p = 1 - 0.3 = 0.7

For the system to work, all 4 components have to work. This is P(X = 4).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{4,4}.(0.7)^{4}.(0.3)^{0} = 0.2401

0.2401 probability of a system working.

If you have 7 of these systems, what is the probability that exactly 3 of them would function?

Now 7 systems, so n = 7

0.2401 probability of a system working.

We have to find P(X = 3).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{7,3}.(0.2401)^{3}.(0.7599)^{4} = 0.1615

16.15% probability that exactly 3 of them would function

5 0
3 years ago
If the length of a rectangle is 2x + 4 and the width is x - 2. write
Bess [88]

Answer:

  P = 6x +4

Step-by-step explanation:

Use the given values in the formula for the perimeter of a rectangle:

  P = 2(L +W)

__

You have ...

  L = 2x +4

  W = x -2

So, the perimeter is ...

  P = 2((2x +4) +(x -2)) = 2(3x +2)

  P = 6x +4

The perimeter of the rectangle is 6x+4.

3 0
2 years ago
101/25 converted to a mixed number
mamaluj [8]
Hi 
Let me help you out 

101/25 is a in proper fraction. 
To change the in proper fraction to a proper fraction you have to see which number is close to 101 by multiplying numbers to 25. You can also divide 101 by 25 which is 4 remainder 1. 
25*4=100
100 is close to 101

the answer would be 4&<span>1/25</span> 

if you like my answer and think it is helpful then please mark mine as brainliest 
answer thank you 

3 0
3 years ago
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