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3 years ago

Which set of side lengths form a right triangle?

Mathematics

2 answers:

ivolga24 [154]3 years ago

8 0

Answer: Option 'B' is correct.

Explanation:

We need to find the side lengths that form a right triangle ,

To find the pythagorean triplet ,we will use "Pythagorus theorem", which states that

$H^2=B^2+P^2$

As we have given that

A) 7 cm, 8 cm, 10 cm

We'll check for this

$7^2+8^2\neq 10^2\\\\49+64\neq 100$

so, it can't be the side of right triangle.

B) 15 m, 20 m, 25 m

We'll check for this

$15^2+20^2=25^2\\\\225+400=625\\\\625=625$

Hence, it is correct set of side lengths that form a right triangle.

On the other hand, C) and D) are not satisfying the pythagorus theorem,

because,

$41^2\neq 40^2+10^2\\\\1681\neq 1600+100\\\\1681\neq 1700\\\\Similarly,\\\\3^2+5^2\neq 6^2\\\\9+25\neq 36\\\\34\neq 36$

Hence, Option 'B' is correct.

OLga [1]3 years ago

4 0

I have taken the test and I can confirm that the answer is

B. 15 m, 20 m, and 25 m.

Have a fantastic day!

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Help me please with my math questions

klio [65]

Answer:

Step-by-step explanation:

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3 years ago

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To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

nexus9112 [7]

Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

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

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

This Zscore is how many standard deviations the value of the measure X 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.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

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

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$

The standard deviation of a sample of n young man is given by the following formula

$s = \frac{\sigma}{\sqrt{n}}$

We want to have $s = 0.167$

$0.167 = \frac{2.8}{\sqrt{n}}$

$0.167\sqrt{n} = 2.8$

$\sqrt{n} = \frac{2.8}{0.167}$

$\sqrt{n} = 16.77$

$\sqrt{n}^{2} = 16.77^{2}$

$n = 281.23$

We need a sample of at least 282 young men.

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4 years ago

Simplify: squareroot 64r^8 8r2 8r4 32r2 32r4

Sav [38]

Answer:

8r^4

Step-by-step explanation:

√(64r^8) = √((8r^4)^2) = 8r^4

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You can make use of either or both of these rules of exponents:

(a^b)^c = a^(b·c) . . . . . used above

$\sqrt[n]{a}=a^{\frac{1}{n}}$

Using the second rule, you can write the expression as ...

$\sqrt{64r^8}=\sqrt{64}\cdot r^{8\cdot\frac{1}{2}}=8r^4$

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4 years ago

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I solved 4, the answer is 11, seconds: 5x+4(x-3)=87 = x=11, but I don't know how to solve number 5, please anyone explain how to

liq [111]

The answer x = 11 is correct for problem 4. Nice work.

Use this x value to find the answer in problem 5. From problem 4, we're told that Romeo runs at a speed of 5 m/s. If he runs for x = 11 seconds,then he runs a total distance of:

5*x =(5 m/s)*(x meters) = (5 m/s)*(11 seconds) = 5*11 = 55 meters

The answer to problem five is 55 meters

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3 years ago

A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee ca

vladimir2022 [97]

Answer:

There are 8 ways.

Step-by-step explanation:

For each employee there are two possibilities: first office and second office.

Therefore,

the number of ways the company can assign 3 employees to 2 different offices will be :

$2^{3}$ = 8

We can also look at this problem like suppose ABC are employees.

We can arrange them like -

0 ABC

ABC 0

AB C

BC A

CA B

A BC

B CA

C AB

So, there are total 8 WAYS.

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3 years ago