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ololo11 [35]
2 years ago
12

Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town

Hall. Part B The hospital is 3.1 miles west of the fire station. What is the length of a straight line between the school and the hospital? Round to the nearest tenth. Enter your answer in the box.

Mathematics
1 answer:
Maksim231197 [3]2 years ago
4 0

Answer:

2.1 miles

Step-by-step explanation:

you can see a drawing of the situation in the attached picture (you need to draw all the places mentioned and the distance between them),

this way we can form a right triangle  between the school and the hospital with measures of sides: 1.7 and 1.2 miles

and the green line is the straight line between the school and the hospital, so you need pythagoras to find the value:

\sqrt{1.7^2+1.2^2}\\=\sqrt{2.89+1.44}\\=\sqrt{4.33}  \\ =2.081

rounding to the nearest tenth:

2.1 miles

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Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After runni
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For this case, the first thing we must do is define variables.

We have then:

t: the time in minutes

k: the number of kilometers

The relationship between both variables is direct.

Therefore, the function is:

k (t) = c * t

Where, "c" is a constant of proportionality.

To determine "c" we use the following data:

After running for 18 minutes, she completes 2 kilometers.

Substituting values:

2 = c * 18

Clearing c we have:

c = \frac{2}{18}

c = \frac{1}{9}

Then, the equation is given by:

k (t) = \frac{1}{9} * t

Answer:

An equation that can be used to represent k, the number of kilometers Julissa runs in t minutes is:

k (t) = \frac{1}{9} * t

7 0
2 years ago
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A recent survey of 8,000 high school students found that the mean price of a prom dress was $195.00 with a standard deviation of
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To calculate the z-statistic, we must first calculate the standard error.

Standard error is standard deviation divided by the square root of the population. In this case, it is equal to 2.68.

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z = (195 – 208)/2.68 = -4.86

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2 years ago
Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One common ch
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Answer:

y=\frac{-7t^2+22t-7}{7t-22}

Step-by-step explanation:

We are given that

Initial value problem

y'=(t+y)^2-1, y(3)=4

Substitute the value z=t+y

When t=3 and y=4 then

z=3+4=7

y'=z^2-1

Differentiate z w.r.t t

Then, we get

\frac{dz}{dt}=1+y'

z'=1+z^2-1=z^2

z^{-2}dz=dt

Integrate on both sides

-\frac{1}{z}dz=t+C

z=-\frac{1}{t+C}

Substitute t=3 and z=7

Then, we get

7=-\frac{1}{3+C}

21+7C=-1

7C=-1-21=-22

C=-\frac{22}{7}

Substitute the value of C then we get

z=-\frac{1}{t-\frac{22}{7}}

z=\frac{-7}{7t-22}

y=z-t

y=\frac{-7}{7t-22}-t

y=\frac{-7-7t^2+22t}{7t-22}

y=\frac{-7t^2+22t-7}{7t-22}

8 0
2 years ago
A sample of 1714 cultures from individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiot
Damm [24]

Answer:

a) p represent the real population proportion of people who showed partial or complete resistance to the antibiotic

b) \hat p=\frac{973}{1714}=0.568 represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.  

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".

Part a

Description in words of the parameter p

p represent the real population proportion of people who showed partial or complete resistance to the antibiotic

\hat p represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

n=1714 is the sample size required

z_{\alpha/2} represent the critical value for the margin of error

The population proportion have the following distribution  

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

Part b

Numerical estimate for p

In order to estimate a proportion we use this formula:

\hat p =\frac{X}{n} where X represent the number of people with a characteristic and n the total sample size selected.

\hat p=\frac{973}{1714}=0.568 represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

Part c

The confidence interval for a proportion is 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

And replacing into the confidence interval formula we got:

0.568 - 1.96 \sqrt{\frac{0.568(1-0.568)}{1714}}=0.545

0.568 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1714}}=0.591

And the 95% confidence interval would be given (0.545;0.591).

We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.  

5 0
2 years ago
Charlene and Gary want to make trail mix. In order to get the right balance of ingredients for their tastes they bought 3 pounds
AfilCa [17]

Answer:

$2.96

Step-by-step explanation:

3x$2.67=$8.01

3x$2.73=$8.19

5x$3.27=$16.35

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This makes 11 pounds of trail mix.

$32.55 divided by 11 = $2.9590909 = $2.96

7 0
2 years ago
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