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MatroZZZ [7]
3 years ago
13

If your friend Doug is on a balcony and asks you to throw him a donut, how many stories up can he be and you would still feel co

nfident in your ability to get the donut to doug?
Mathematics
1 answer:
Katena32 [7]3 years ago
8 0
The building that I would imagine would be 40 stories, about 404 feet tall perhaps. If he were to throw the donut from that distance until the ground, catching it would be impossible. So no, I am not confident in catching the donut all the way there. 
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Given points A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1), which of the following proves that
damaskus [11]

Similar triangles may or may not have equal side lengths

Triangles ABC and DEF are similar by SSS theorem

<h3>How to determine the similarity statement</h3>

The coordinates of the two triangles are:

A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1)

Calculate the lengths of both triangles using the following distance formula

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

For triangle ABC, we have:

AB = \sqrt{(0 -4)^2 + (0 -0)^2} = 4

BC = \sqrt{(4 -0)^2 + (0 -2)^2} = 2\sqrt 5

CA = \sqrt{(0 -0)^2 + (0 -2)^2} = 2

For triangle DEF, we have:

DE = \sqrt{(0 -2)^2 + (0 -0)^2} = 2

EF = \sqrt{(2 -0)^2 + (0 -1)^2} = \sqrt 5

FD = \sqrt{(0 -0)^2 + (1 -0)^2} = 1

Divide corresponding sides of the triangles to calculate the scale factor k

k = \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}

This gives

k = \frac{4}{2} = \frac{2\sqrt 5}{\sqrt 5} = \frac{2}{1}

Evaluate the quotients

k = 2 = 2 = 2

Since the quotients are equal, then the triangles are similar

Hence, triangles ABC and DEF are similar by SSS theorem

Read more about similar triangles at:

brainly.com/question/14285697

3 0
2 years ago
Suppose that an airline uses a seat width of 16.5 in. Assume men have hip breadths that are normally distributed with a mean of
Alexxx [7]

Answer:

a) 0.018

b) 0            

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  14.4 in

Standard Deviation, σ = 1 in

We are given that the distribution of breadths is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(breadth will be greater than 16.5 in)

P(x > 16.5)

P( x > 16.5) = P( z > \displaystyle\frac{16.5 - 14.4}{1}) = P(z > 2.1)

= 1 - P(z \leq 2.1)

Calculation the value from standard normal z table, we have,  

P(x > 16.5) = 1 - 0.982 = 0.018 = 1.8\%

0.018 is the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.5 in.

b) P( with 123 randomly selected​ men, these men have a mean hip breadth greater than 16.5 in)

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}  

P(x > 16.5)  

P( x > 16.5) = P( z > \displaystyle\frac{16.5-14.4}{\frac{1}{\sqrt{123}}}) = P(z > 23.29)  

= 1 - P(z \leq 23.29)

Calculation the value from standard normal z table, we have,  

P(x > 16.5) = 1 - 1 = 0

There is 0 probability that 123 randomly selected men have a mean hip breadth greater than 16.5 in

4 0
3 years ago
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