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3 years ago

Teresa runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?

Mathematics

2 answers:

Anon25 [30]3 years ago

8 0

Answer:

$\boxed {\tt 5.6 \ miles}$

Step-by-step explanation:

Let's set up a proportion using the following setup:

$\frac{miles}{minutes}= \frac{miles}{minutes}$

We know Teresa can run 7 miles in 80 minutes.

$\frac{7 \ miles}{80 \ minutes}=\frac{miles}{minutes}$

We don't know how many miles she can run in 64 minutes. Therefore, she can run x miles in 64 minutes.

$\frac{7 \ miles}{80 \ minutes}=\frac{x \ miles}{64 \ minutes}$

$\frac{7}{80} =\frac{x}{64}$

We want to solve for x ( miles in 64 minutes). We must isolate x on one side of the proportion. x is being divided by 64 and the inverse of division is multiplication. Multiply both sides of the equation by 64.

$64*\frac{7}{80} =\frac{x}{64}*64$

$64*\frac{7}{80} =x$

$64*0.0875=x$

$5.6=x$

x= 5.6 miles

Teresa can run 5.6 miles in 64 minutes.

sveta [45]3 years ago

4 0

Answer:

She would run about 5.8 miles in 64 min.

Step-by-step explanation:

Let m= miles per minute

7=80m divide 80 on both sides.

0.0875=m Round

0.09 miles per minute

0.09 x 64= 5.76 round or leave it like that

5.8

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2 years ago

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Answer:

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

Step-by-step explanation:

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 distributions 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 case, assume that 104 eligible voters aged 18-24 are randomly selected.

This means that $n = 104$ .

Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

This means that $p = 0.22$

Mean and standard deviation:

$\mu = 104*0.22 = 22.88$

$\sigma = \sqrt{104*0.22*0.78} = 4.2245$

Probability that exactly 27 voted

By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.

X = 27.5

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

$Z = \frac{27.5 - 22.88}{4.2245}$