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Eva8 [605]
1 year ago
10

Rita's family is moving to Grand Junction to Dallas. The moving van averages 60 miles each hour. About how many hours does the v

an take to reach Dallas? Explain your work
Mathematics
1 answer:
Eddi Din [679]1 year ago
5 0

Answer:

16 hours and 20 minutes.

Step-by-step explanation:

Please consider the complete question.

Rita's family is moving to Grand Junction to Dallas, which is 980 miles. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas?

To find the time taken by van to reach Dallas, we will divide total distance by speed.

\text{Time}=\frac{\text{Distance}}{\text{Speed}}

\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60\frac{\text{ Miles}}{\text{Hour}}}

\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60}\times \frac{\text{ Hour}}{\text{Miles}}

\text{Time taken to reach Dallas}=\frac{98}{6}\text{ Hour}

\text{Time taken to reach Dallas}=16.3333\text{ Hour}

Let us convert 0.3333 hours into minutes by multiplying 0.3333 by 60.

0.3333\times 60=19.998\approx 20

Therefore, it will take 16 hours and 20 minutes for the van to reach Dallas.

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A double is simply a pair of identical numbers added together. There's a pair of doubles you can <em>subtract </em>1 from to get 6+7, and there's a pair you can <em>add</em> 1 to get the same answer. What are those pairs?

Hint: If you take the example 3+4, you can either <em>subtract 1</em> from the double 4+4 or <em>add 1</em> to the double 3+3 to obtain your answer.
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a contractor needs to purchase 500 bricks. the dimensions of each brick are 5.1 cm by 10.2 by 20.3 cm, and the density of each b
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2 years ago
A hospital finds that 22% of its accounts are at least 1 month in arrears. A random sample of 425 accounts was taken. What is th
GenaCL600 [577]

Answer:

8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears

Step-by-step explanation:

For each account, there are only two possible outcomes. Either they are at least 1 month in arrears, or they are not. The probability of an account being at least 1 month in arrears is independent from other accounts. So the binomial probability distribution is used to solve this question.

However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.

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 = 0.22, n = 425

So

\mu = E(X) = np = 425*0.22 = 93.5

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{425*0.22*0.78} = 8.54

What is the probability that fewer than 82 accounts in the sample were at least 1 month in arrears

This probability is the pvalue of Z when X = 82. So

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

Z = \frac{82 - 93.5}{8.54}

Z = -1.35

Z = -1.35 has a pvalue of 0.0885.

8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears

8 0
1 year ago
=
SOVA2 [1]

Answer:

Tn=13n-18

Step-by-step explanation:

Tn=-5(n-1)13

Simplify

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Answer:

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