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3 years ago

An angle measures 32° more than the measure of its complementary angle. What is the measure of each angle?

Mathematics

1 answer:

Leviafan [203]3 years ago

3 0

Answer:

29° ; 61°

Step-by-step explanation:

Let one angle = x°

Other angle = (x + 32)°

x + x + 32 = 90 {given they are complementary}

2x + 32 = 90

2x = 90 -32

2x = 58

x = 58/2

x = 29

One angle = 29°

Other angle = 29 + 32 = 61°

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3 years ago

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You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you w

Margaret [11]

Answer:

The null hypothesis is

$H_o : \mu = 21$

The Alternative hypothesis is

$H_a : \mu< 21$

$\sigma_{\= x} = 0.8944$

$t = -2.236$

Yes the mean population is significantly less than 21.

Step-by-step explanation:

From the question we are given

a set of data

20 18 17 22 18

The confidence level is 90%

The sample size is n = 5

Generally the mean of the sample is mathematically evaluated as

$\= x = \frac{20 + 18 + 17 + 22 + 18}{5}$

$\= x = 19$

The standard deviation is evaluated as

$\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }$

$\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }$

$\sigma = 2$

Now the confidence level is given as 90 % hence the level of significance can be evaluated as

$\alpha = 100 - 90$

$\alpha = 10$ %

$\alpha =0.10$

Now the null hypothesis is

$H_o : \mu = 21$

the Alternative hypothesis is

$H_a : \mu< 21$

The standard error of mean is mathematically evaluated as

$\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }$

substituting values

$\sigma_{\= x} = \frac{2}{ \sqrt{5 } }$

$\sigma_{\= x} = 0.8944$

The test statistic is evaluated as

$t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }$

substituting values

$t = \frac{ 19 - 21 }{ 0.8944 }$

$t = -2.236$

The critical value of the level of significance is obtained from the critical value table for z values as

$z_{0.10} = 1.28$

Looking at the obtained value we see that $z_{0.10}$ is greater than the test statistics value so the null hypothesis is rejected

6 0

3 years ago

(05.02)

MaRussiya [10]

Answer:

Answer choice a.

Step-by-step explanation:

Let's do part of the work of solving the given system:

6x + 2y = −6

3x − 4y = −18

Multiply the first equation by 2 so as to make the coefficient of y = to 4:

12x + 4y = -12

Combine this result with the second equation:

12x + 4y = -12

3x − 4y = −18

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15x = -30

Note that these results are precisely the same as the equations in Answer Choice a.

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3 years ago

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Genrish500 [490]

Answer:

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Step-by-step explanation:

Well Lila ate 1/4 already and his freind ate 1/3

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