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katrin2010 [14]
3 years ago
12

An advertiser goes to a printer and is charged $73 for 100 copies of one flyer and $82 for 400 copies of a similar flyer. Assumi

ng the cost for a printing job is represented by a linear equation, find the equation (in slope-intercept form) that describes the cost y of a printing job if x is the number of Copies made. Also, write a sentence describing what the slope of the equation represents in this situation.
Mathematics
1 answer:
USPshnik [31]3 years ago
3 0

Answer:

y = 0.03x + 70

Slope here represents the variation in the charges with the change in the number of flyers

Positive slope means that the cost is increasing with increase in number of flyers

Step-by-step explanation:

Given:

for 100 copies advertiser is charged = $73

For 400 copies advertiser is charged = $82

Now,

here the charge is a function of number of flyers

we have the general line equation for a linear relationship as:

y  = mx + c

here m is the slope

c is the constant

for the first case we have

y = $73

x = 100

thus,

73 = 100m + c ...........(1)

for the second case, we have

y = $82

x = 400

thus,

82 = 400m + c ...........(2)

subtracting (1) from (2)

    82 = 400m + c

- ( 73 = 100m + c )

==================

    9 = 300m + 0

or

m = 0.03

substituting the value of slope in equation (1)

73 = 100 × 0.03 + c

73 = 3 + c

or

c = 70

Hence,

the equation is y = 0.03x + 70

here y is amount charged and x are the number of flyers.

Slope here represents the variation in the charges with the change in the number of flyers

Positive slope means that the cost is increasing with increase in number of flyers

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Mrs. Williamson had 18 students in her homeroom at the beginning of the school year and 24 students at the end of the year. What
jarptica [38.1K]

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2 years ago
It is estimated that 0.54 percent of the callers to the Customer Service department of Dell Inc. will receive a busy signal. Wha
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Using the binomial distribution, it is found that there is a 0.8295 = 82.95% probability that at least 5 received a busy signal.

<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:

  • 0.54% of the calls receive a busy signal, hence  p = 0.0054.
  • A sample of 1300 callers is taken, hence n = 1300.

The probability that at least 5 received a busy signal is given by:

P(X \geq 5) = 1 - P(X < 5)

In which:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Then:

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

P(X = 0) = C_{1300,0}.(0.0054)^{0}.(0.9946)^{1300} = 0.0009

P(X = 1) = C_{1300,1}.(0.0054)^{1}.(0.9946)^{1299} = 0.0062

P(X = 2) = C_{1300,2}.(0.0054)^{2}.(0.9946)^{1298} = 0.0218

P(X = 3) = C_{1300,3}.(0.0054)^{3}.(0.9946)^{1297} = 0.0513

P(X = 4) = C_{1300,4}.(0.0054)^{4}.(0.9946)^{1296} = 0.0903

Then:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0009 + 0.0062 + 0.0218 + 0.0513 + 0.0903 = 0.1705.

P(X \geq 5) = 1 - P(X < 5) = 1 - 0.1705 = 0.8295

0.8295 = 82.95% probability that at least 5 received a busy signal.

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

#SPJ1

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