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2 years ago

14

CyberCafe charges a computer station rental fee of $5 plus $0.20 for each quarter hour spent surfing. Which expression represent

s the total amount Carl will pay to use a computer station for three and a half hours?

1 answer:

ryzh [129]2 years ago

3 0

Answer: x = 0.2y + 5

Step-by-step explanation:

$0.20 * y (number of quarter hours) + an extra $5 = x (the total amount)

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Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.2, n = 200$ . So

$\mu = E(X) = np = 200*0.2 = 40$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66$

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{46 - 40}{5.66}$

$Z = 1.06$

$Z = 1.06$ has a pvalue of 0.8554

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 40}{5.66}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

0.8554 - 0.1446 = 0.7108

71.08% probability that pˆ takes a value between 0.17 and 0.23.

6 0

2 years ago

What is the zero in the quadratic function f(x)= 9x^2-54x-19?

Alex17521 [72]

Answer:

6.33... and 0.333...

Step-by-step explanation:

The quadratic formula is

$x=\frac{-b+\sqrt{b^2-4ac} }{2a}$ .

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}$

We will now solve for the plus and the minus.

The plus,,,

$x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3$

and the minus...

$x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...$

8 0

2 years ago

It shipped traveled for a total of 85 miles over the course of five hours heading west the ship travels and average of 14 mph an

adoni [48]

complete question:

A ship traveled for a total of 85 miles over the course of 5 hours. Heading west, the ship traveled at an average speed of 14 miles per hour, and heading north, it traveled at an average speed of 19 miles per hour. For how many hours was the ship heading north?

Answer:

The ship heading north traveled for 3 hours

Step-by-step explanation:

A ship travels for a total of 85 miles over the course of 5 hours journey. The speed of the journey can be calculated below.

speed = distance/time

total distance = 85

total time = 5 hours

speed = 85/5

speed = 17 miles/hr

West direction

Heading west the ship traveled at an average speed of 14 miles per hour. The speed can be represented for this journey as follows.

speed = distance/time

14 = dist/time

let

a = time traveled west

distance = 14a

North direction

speed = dist/time

19 = dist/time

time travel north = 5 - a

distance = 19(5 - a)

distance = 95 - 19a

Total distance traveled = 85 miles

85 = 14a + 95 - 19a

85 = -5a + 95

-10 = -5a

a = -10/-5

a = 2

The ship heading north will travel for 5 - 2 = 3 hours

5 0

2 years ago

Read 2 more answers

SAT Writing scores are normally distributed with a mean of 491 and a standard deviation of 113.A university plans to send letter

Sholpan [36]

Answer:

$z=1.405$

And if we solve for a we got

$a=491 +1.405*113=649.765$

So the value of height that separates the bottom 92% of data from the top 8% is 649.765.

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(491,113)$

Where $\mu=491$ and $\sigma=113$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.08$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.92 of the area on the left and 0.08 of the area on the right it's z=1.405. On this case P(Z<1.405)=0.92 and P(z>0.92)=0.08

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.405$

And if we solve for a we got

$a=491 +1.405*113=649.765$

So the value of height that separates the bottom 92% of data from the top 8% is 649.765.

6 0

2 years ago

Large flower pots weigh 28 pounds each.

LiRa [457]

Answer:

The correct answer is: 980 pounds

Step-by-step explanation:

1 flower pot = 28 pounds

1 crate = 35 pots

∴ 1 crate = 35 pots × 28 pounds = 980 pounds

5 0

2 years ago

Read 2 more answers