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3 years ago

Tinley is training to run a half-marathon. She sets a pace so that every mile takes

Mathematics

1 answer:

Lana71 [14]3 years ago

7 0

Answer:

t=7m

Step-by-step explanation:

In this equation, "t" represents time, and "m" represents miles. Each mile is 7 minutes. To find how much time this run will take her, multiple the amount of miles she will run by 7.

For example:

If Tinley runs 13 miles you should do-

7(13)= 91

13 miles would take Tinley 91 minutes

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Answer:

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Step-by-step explanation:

5 is a coefficient of x^0

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3 years ago

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3 years ago

Read 2 more answers

The sum of 5 times one number, x, and 4 times a second number, y, is 75. If the sum of the two numbers is 18, find the two numbe

satela [25.4K]

Answer: $x=3$ and $y=15$

Step-by-step explanation:

First, we are told "sum of 5 times one number, x, and 4 times a second number, y, is 75":

$5x+4y=75$ (1)

Then, we are told "he sum of the two numbers is 18":

$x+y=18$ (2)

At this point we have our system of equations and now we are able to find the values of $x$ and $y$ .

So, let's begin by isolating $x$ from (2):

$x=18-y$ (3)

Substituting (3) in (1):

$5(18-y)+4y=75$ (4)

Finding $y$ :

$90-5y+4y=75$

$y=15$ (5) This is the value of $y$

Substituting (5) in (1):

$5x+4(15)=75$ (6)

Finding $y$ :

$5x+60=75$ (7)

$x=3$ (8) This is the value of $x$

4 0

3 years ago

If the permutations of the letters in the word SURE are numbered 1 through 24 in alphabetical order, what number is RUSE. The an

Lemur [1.5K]

Every possible combination of the letters SURE are going to be listed in alphabetical order. The permutation we want is RUSE which begins with the letter R and will come after every permutation that begins with E since it is the next alphabetically. We can first determine how many permutations begin with E.

Since we start with E, there are only three letters left to form the rest of the permutation. So 3! = 3*2*1 = 6 states that there are 6 permutations that can be made from the remaining three letters. So there will be 6 permutations that begin with E.

Using this same logic, we now know that there are 6 permutations that begin with the letter R. The letters USE are in reverse alphabetical order, which means that the word RUSE will appear as the last permutation that begins with R.

We know there are 6 permutations that begin with E, followed by 6 permutations that begin with R, making 12 total at this point. And since RUSE appears as the last permutation beginning we R, we know that RUSE shows up 12th.

5 0

3 years ago

The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 per

enot [183]

Answer:

The summer interval is wider and has a greater point of estimate

Step-by-step explanation:

Assuming this problem: "An environmental group wanted to estimate the proportion of fresh produce sales indentified as organic in a grocery store. In the winter, the group obtained a random sample of sales from the store and used the data to construct a 95percent z-interval for a proportion (0.087,0.133). Six months later in the summer, the group obtained a second random sample of sales from the store. The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 percent z-interval for a proportion constructed from the summer sample compare to the winter interval? "

Previous concepts

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

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

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.

$z_{\alpha/2}=1.96$

We can find the margin of error from the interval given on this case would be:

$ME= \frac{0.133-0.087}{2}=0.023$

And the point of estimate for the proportion obtained would be:

$\hat p = 0.133-0.023=0.11$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =0.023$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.11(1-0.11)}{(\frac{0.023}{1.96})^2}=710.95$

And rounded up we have that n=711

Now we know that we use the same sample size for the new confidence interval. And replacing into the confidence interval formula we got:

$0.4 - 1.96 \sqrt{\frac{0.4(1-0.4)}{711}}=0.364$

$0.4 + 1.96 \sqrt{\frac{0.4(1-0.4)}{711}}=0.436$

And the new 95% confidence interval would be given (0.364;0.436) has a width of 0.436-0.364=0.072. And the width for the previous confidence interval is 0.133-0.087= 0.046. So then the best answer is:

The summer interval is wider and has a greater point of estimate

7 0

3 years ago