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3 years ago

The angles measures x and 4x are complementary angles. Which is the value of x?

Mathematics

2 answers:

defon3 years ago

7 0

Answer: 36

Step-by-step explanation:

Hitman42 [59]3 years ago

3 0

Answer:

The angles measures x and 4x are complementary angles. The value of x is 36 degrees

Solution:

Given, two angles are x and 4x

We have to find the value of above given x

We are also given that, given two angles are complementary angles for each other

So, we know that, sum of any two complementary angles will always be equal to 180 degrees

Then, in the problem given,

$x+4 x=180 \rightarrow 5 x=180 \rightarrow x=\frac{180}{5} \rightarrow x=36$

Hence the angles measures x and 4x are complementary angles. The value of x is 36 degrees

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andrew-mc [135]

Answer: A. one real solution

This solution is a double root (it repeats itself). An example would be x^2-8x+16 = 0 has the only solution x = 4.

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3 years ago

When an angle is reflected across a line, what happens to its measure

Vlad1618 [11]

It remains the same. if the shape is the same then so is it's angle measure.

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3 years ago

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In 2010, the Census Bureau estimated the proportion of all Americans who own their homes to be 0.669. An urban economist wants t

Alexxandr [17]

Answer:

Sample size making use of the Census Bureau: 1,499 American adults.

Sample size without making use of the Census Bureau: 1,692 American adults

ii)

Step-by-step explanation:

The sample size n in Simple Random Sampling is given by

$\bf n=\frac{z^2p(1-p)}{e^2}$

where

z = 1.645 is the critical value for a 90% confidence level (*) 

p= 0.669 is the population proportion given by the Census

e = 0.02 is the margin of error

$\bf n=\frac{(1.645)^2*0.669*0.331}{0.02^2}=1,498.05\approx 1,499$

rounded up to the nearest integer.

(*)This is a point z such that the area under the Normal curve N(0,1) 1nside the interval [-z, z] equals 90% = 0.9

It can be obtained with tables or in Excel or OpenOffice Calc with

NORMSINV(0.95)

If she ignores the Census estimate, the she has to take the largest sample possible that meets the requirements.

Let's show it is obtained when p = 0.5

As we said, the sample size n is

$\bf n=\frac{z^2p(1-p)}{e^2}$

where

e = 0.02 is the error proportion

z = 1.645

hence

$\bf n=\frac{(1.645)^2p(1-p)}{(0.02)^2}=6765.0625p(1-p)=6765.0625p-6765.0625p^2$

taking the derivative with respect to p, we get

n'(p)=6765.0625-2*6765.0625p

and

n'(p) = 0 when p=0.5

By taking the second derivative we see n''(p)<0, so p=0.5 is a maximum of n

This means that if we set p=0.5, we get the maximum sample size for the confidence level required for the proportion error 0.02

Replacing p with 0.5 in the formula for the sample size we get

$\bf n=6765.0625*0.5-6765.0625(0.5)^2=1691.27\approx 1,692$

rounded to the nearest integer.

ii)

When we do not have a proportion but a variable whose approximate standard deviation s is known, then the sample size n in Simple Random Sampling is given by

$\bf n=\frac{z^2s^2}{e^2}$

where

z = 2.241 is the critical value for a 95% confidence level (*) 

s = 7.5 is the estimated population standard deviation

e = 2 hours is the margin of error

$\bf n=\frac{z^2s^2}{e^2}=\frac{(2.241)^2(7.5)^2}{(2)^2}=70.62\approx 71$

(*)This is a point z such that the area under the Normal curve N(0,1) inside the interval [-z, z] equals 95% = 0.95

It can be obtained in Excel or OpenOffice Calc with

NORMSINV(0.9875)

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4 years ago

What is 2 1/4 times 2/3?

love history [14]

Answer:

Hello! :) have a good day!

Exact Form:

3/2

Decimal Form:

1.5

Mixed Number Form:

1 1/2

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3 years ago

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HELP ASAP!!!!! What is the value of X? Enter your answer in the box

andre [41]

ANSWER:

48°

STEP BY STEP EXPLAINATION:

The opposite side of the angle X is 48° and with angles the opposite sides are equal

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3 years ago