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2 years ago

14

Is a triangle with the side lengths 4 feet, 7. 5 feet, and 8. 5 feet a right triangle? Why or why not?

1 answer:

Doss [256]2 years ago

5 0

Answer:

Yes

Step-by-step explanation:

You can test if a triangle is right-angled by using Pythagoras' Theorem.

So:

$4^2 + 7.5^2 = 8.5^2$

16 + 56.25 = 72.25

They do in fact add up so this triangle is right angled.

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An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0

zmey [24]

Answer:

96.33% probability that everyone who appears for the flight will get a seat

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

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:

$n = 105, p = 0.9$

So

$\mu = E(X) = np = 105*0.9 = 94.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{105*0.9*0.1} = 3.07$

What is the probability that everyone who appears for the flight will get a seat

100 or less people appearing to the flight, which is the pvalue of Z when X = 100. So

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

$Z = \frac{100 - 94.5}{3.07}$

$Z = 1.79$

$Z = 1.79$ has a pvalue of 0.9633

96.33% probability that everyone who appears for the flight will get a seat

7 0

3 years ago

The length of a rectangle is 4 times its width and the perimeter is 150

grandymaker [24]

Answer:

Y = W = 15 ft.

X= L = 60 ft.

So width is 15 and the length is 60.

6 0

3 years ago

Read 2 more answers

Determine which equation is belongs to the graph of the limacon curve below.

JulsSmile [24]

Answer: Option C.

Step-by-step explanation:

We have functions of r(θ)

In our graph, we can see that the minimum value of r is when θ = 0°, and the maximum value is when θ = 180°.

We also know that the graph is in the square (-5, 5)x(-5, 5) and you can see that the maximum radius is almost less than 5.

Then let's analyze the options:

A) r = 3 - 2*cos(θ)

the maximum is at the right angle, but the maximum is:

r = 3 -2*(-1) = 5, so this maximum value is bigger than the one in the graph.

B) r = 3 - sin(θ)

For the sin functions, the maximum and minimum do not correspond with the values i write earlier, so we can discard this option.

C) r = 3 - cos(θ)

The maximum is: r = 3 - (-1) = 4, so this may be the correct answer.

the minimum is r = 3 - 1 = 2,

this is a possible equation for our circle.

D) r = 2 - 2*cos(θ)

Here, when θ = 0, we have: r = 2 - 2*1 = 0, but in the graph we can see that the radius is not 0 when θ = 0, so we can discard this option.

So the only option that makes sense is option C.

8 0

3 years ago

Sarah received a gift in a rectangular box with a volume of 240 in3. If the base of the box was 20 in2, how tall was the box?

Murrr4er [49]

V = l * w * h
240 = 20* h
divide both sides by 20
12 = h
height = 12 inches

8 0

3 years ago

Read 2 more answers

Find the value of x.

posledela

Answer:

<u>x = 50°</u>

Step-by-step explanation:

2x = 140 - 40

2x = 100

x = 100/2

<u>x = 50°</u>

8 0

2 years ago

Read 2 more answers