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3 years ago

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The monthly cost in dollars of a long distance phone plan is a linear function of the total calling time in minutes. The monthly

cost for 42 minutes of calls is $18.15 and the monthly cost for 90 minutes is $22.47. What is the monthly cost for 45 minutes of calls

1 answer:

Deffense [45]3 years ago

3 0

Answer:

The monthly cost for 45 minutes is $18.42

Step-by-step explanation:

Let

x -----> the total calling time in minutes

y ----> the monthly cost in dollars

we have the ordered pairs

(42,18.15) and (90,22.47)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{22.47-18.15}{90-42}$

$m=\frac{4.32}{48}$

$m=\$0.09\ per\ minute$

step 2

Find the linear equation in point slope form

$y-y1=m(x-x1)$

we have

$m=0.09\\(x1,y1)=(42,18.15)$

substitute

$y-18.15=0.09(x-42)$

step 3

Find the monthly cost for 45 minutes of calls

For x=45 min

substitute the value of x in the linear equation and solve for y

$y-18.15=0.09(45-42)$

$y-18.15=0.09(3)$

$y-18.15=0.27$

$y=0.27+18.15$

$y=18.42$

therefore

The monthly cost for 45 minutes is $18.42

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

The granola summer buys used to cost $6.00 per pound but it has been marked up %15 A. How much did it cost summer to buy 2.6 pou

Maksim231197 [3]

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3 years ago

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the

EastWind [94]

Answer:

a) $\hat p=\frac{471}{1024}=0.460$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Data given and notation

n=1024 represent the random sample taken

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

$\hat p=\frac{471}{1024}=0.460$ estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The standard error is given by:

$SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156$

And the margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305$

Part b

If we replace the values obtained we got:

$0.460-1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.429$

$0.460+1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.491$

The 99% confidence interval would be given by (0.429;0.491)

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3 years ago

Which of the following is the reciprocal of x2 – 2x – 8?

Ann [662]

Hi again

x² - 2x - 8
Factor
= (x + 2)(x -4)
Answer : A is the correct option.

If you wanna check if A is the right answer, I will solve it for you and it will you give you the exact answer which will be x² - 2x - 8
(x+2)(x-4)
Distribute
(x)(x) + (x)(-4)+(2)(x)+(2)(-4)
= x² - 4x + 2x - 8
= x² - 2x - 8
Here it is, we find the exam answer.

Thus, (x+2)(x-4) is the reciprocal of x² -2x - 8

I hope that's help !

6 0

3 years ago