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Ira Lisetskai [31]
3 years ago
14

(SHOW WORK NEED IT BY TONIGHT! )Write a system of equations to describe the situation below, solve using substitution, and fill

in the blanks.
Nick, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent $47 on equipment and hired a server who makes $15 per hour. Nick is hoping to make up these expense at the next job that is scheduled, which pays a base of $54 in addition to $14 per hour that the server works. In theory, this event could pay enough to cancel out Nick's expenditures. How much would the job pay? How long would the job have to be?



The expenditures and pay would both be $_ if the job lasted for _ hours.
Mathematics
1 answer:
earnstyle [38]3 years ago
8 0

Let X = the number of hours the server works.

The equation for the amount Nick spends is 15x + 47

The next job pays 14x + 54

Set the equations to equal and solve for x:

15x + 47 = 14x +54

Subtract 14x from both sides:

X + 47 = 54

Subtract 47 from both sides:

X = 7

Now replace x with 7 in the second equation:

14x + 54 = 14(7) + 54 = 98 +54 = 152

The job would pay $152 and be 7 hours long.

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6 high school seniors choose from among 20 quotes for their yearbook. What is the probability that at least 2 of them choose the
shusha [124]

Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem, we have that:

  • There are 6 students, hence n = 6.
  • There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.

The probability of one quote being chosen at least two times is given by:

P(X \geq 2) = 1 - P(X < 2)

In which:

P(X < 2) = P(X = 0) + P(X = 1).

Then:

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

P(X = 0) = C_{6,0}.(0.05)^{0}.(0.95)^{6} = 0.7351

P(X = 1) = C_{6,1}.(0.05)^{1}.(0.95)^{5} = 0.2321

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9672 = 0.0328

0.0328 = 3.28% probability that at least 2 of them choose the same quote.

More can be learned about the binomial distribution at brainly.com/question/24863377

6 0
1 year ago
Pedro has twice as many carrots as Martha, who has the same number of carrots as Oliver. If Pedro gives 5 carrots to Oliver, the
choli [55]
"Pedro has twice as many carrots as Martha:"
p = 2m
<span>
"If Pedro gives 5 carrots to Oliver," 
p - 5  (</span>Oliver is irrelevant.)<span>

"then Martha has 3 times as many carrots as Pedro"
</span>
m = 3(p - 5)

We know p in terms of m, so substitute it in:
m = 3(2m - 5)

Distribute the 3:
m = 6m - 15

Subtract 6m from both sides:
m-6m=-15
Combine variable terms:

-5m=-15

Divide out -5

m = -15/-5

m = 3

The answer is c) 3  







3 0
2 years ago
Use the parallelogram below to solve for x x , then find the length of all 4 sides. figure
SVETLANKA909090 [29]
Can u show me what the parallelogram below was
6 0
3 years ago
A shopper bought shoes marked 40$ the sales tax is 8% how much did the shopper pay in all
BlackZzzverrR [31]

Answer:

43.20

Step-by-step explanation:

First we need to find the sales tax

tax = price * tax rate

tax = 40 * 8%

     = 40*.08

      =3.2

We final cost is the price plus the sales tax

final cost = price + tax

                = 40+3.2

                = 43.20

6 0
3 years ago
How to do this does anyone know if u do i will make u brainlist
Studentka2010 [4]

Answer:

Those functions are for a graph.

Step-by-step explanation:

You can compare them by heading to a website like desmos and plugging in each function, I think they even do tables as well.

These are functions that can be graphed, I assume you know what that is, if not, look it up.

good luck

6 0
1 year ago
Read 2 more answers
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