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4 years ago

Best estimate of 20% 516

Mathematics

2 answers:

tensa zangetsu [6.8K]4 years ago

8 0

Since it's an estimate, probably 103

drek231 [11]4 years ago

3 0

Around 103 (approximately 103.2) :)

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What is the perimeter of the figure? A. 144 cm B. 76 cm C. 74 cm D. 45 cm

tatiyna

76 cm would be your answer, so B.

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3 years ago

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Find x and y Please, need help quick. Lines and Angles

kaheart [24]

Answer:

100 degrees

Step-by-step explanation:

angle x and y are 100 degrees

angle x and y are the same because of the angle marks the question gives

next if we think of this mathematically, we know that all the angle degrees must = 360 so,

360=60+2x+x

x=100

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3 years ago

Find the degree measure of the missing angle, b, in the diagram below by setting up (writing) and solving a correct linear equat

Georgia [21]

Check the picture below

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3 years ago

Pls someone help me with this question

telo118 [61]

Step-by-step explanation:

remember, i = sqrt(-1)

you know what an exponent means, right ?

it means you multiply the enclosed term that many times with itself.

when you envision this as a long chain of (1+i)/(1-i) multiplications, you can see you can group them into pairs, and then multiply these pairs - just half the times than for the single terms.

so,

((1+i)/(1-i))²⁰²⁰ = ((1+i)/(1-i))² ^ 1010

to get an idea what the result of the long chain of multiplications might be, let's start with the square and see, if we can find a pattern, that we then can use to come to a conclusion about the total result.

((1+i)/(1-i))² = (1+i)²/(1-i)²

(1+i)² = 1×1 + 1×i + 1×i + i² = 1 + 2i - 1 = 2i

(1-i)² = 1×1 - 1×i - 1×i + i² = 1 - 2i - 1 = -2i

so,

((1+i)/(1-i))² = 2i/-2i = -1

aha !

so,

((1+i)/(1-i))² ^ 1010 = (-1)¹⁰¹⁰

just to be sure you understand, we use the same trick again

(-1)¹⁰¹⁰ = (-1)² ^ 505 = 1⁵⁰⁵ = 1

as 1 to any power is always 1.

so, the right answer is A.

remember, a negative number to an even power results always in a positive number. and to an uneven/odd power in a negative number.

again, because such an exponent is only the summary of many multiplications.

5 0

3 years ago

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines

storchak [24]

Answer:

The null hypothesis is $H_o: \mu = 4$ .

The alternate hypothesis is $H_a: \mu \neq 4$

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

$H_o: \mu = 4$

At the alternate hypothesis we test if it is different. So

$H_a: \mu \neq 4$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

4 is tested at the null hypothesis:

This means that $\mu = 4$

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that $n = 196, X = 4.14$

He knows that the population standard deviation is 0.83 cm.

This means that $\sigma = 0.83$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}$

$z = 2.36$

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

5 0

3 years ago