All categories

3 years ago

Part B

Mathematics

1 answer:

Troyanec [42]3 years ago

7 0

Answer:

Part A) The length of a straight line between the school and the Fire Station is $4.6\ miles$

Part B) The length of a straight line between the school and the hospital is $2.1\ miles$

Step-by-step explanation:

<u><em>The complete question in the attached figure</em></u>

Let

The positive x-coordinates ----> East

The positive y-coordinates ----> North

The negative x-coordinates ----> West

The negative y-coordinates ----> South

take the point A (0,0) as the Middle School (reference point)

Part A) we have

Town Hall is located 4.3 miles directly east of the Middle School

The coordinates of Town Hall are B(4.3,0)

The Fire Station is located 1.7 miles directly North of Town Hall

The coordinates of Fire Station are C(4.3,1.7)

What is the length of a straight line between the school and the Fire Station?

Remember that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(0,0) and C(4.3,1.7)

substitute

$d=\sqrt{(1.7-0)^{2}+(4.3-0)^{2}}$

$d=\sqrt{(1.7)^{2}+(4.3)^{2}}$

$d=4.6\ miles$

Part B) we have that

The hospital is 3.1 miles west of the fire station

The coordinates of the hospital are D(4.3-3.1,1.7)

D(1.2,1.7)

What is the length of a straight line between the school and the hospital?

Remember that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(0,0) and D(1.2,1.7)

substitute

$d=\sqrt{(1.7-0)^{2}+(1.2-0)^{2}}$

$d=\sqrt{(1.7)^{2}+(1.2)^{2}}$

$d=2.1\ miles$

You might be interested in

Suppose that 20% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable com

riadik2000 [5.3K]

Answer:

4.01% probability that the cable company will keep the shopping channel.

Step-by-step explanation:

For each subscriber, there are only two possible outcomes. Either they watch the shopping channel at least once a week, or they do not. This means that we can solve this problem using the binomial probability distribution.

However, we are working with samples that are considerably big. 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:

$n = 100, p = 0.20$

$E(X) = 100*0.20 = 20$

$\sqrt{V(X)} = \sqrt{100*0.20*0.80} = 4$

The cable company has decided to keep the shopping channel if the sample proportion is greater than 0.27. What is the approximate probability that the cable company will keep the shopping channel, even though the true proportion who watch it is only 0.20?

This probability is 1 subtracted by the pvalue of Z when $X = 0.27*100 = 27$ . So