The measures of the acute angles of a right triangle are in the ratio 5:7

T/5=2.9

iVinArrow [24]

Answer:

multiply by 5

Step-by-step explanation:

in order to get t by itself, you must do the incerverse operation of division, which is multiplication

5(t/5)=5(2.9)

the 5 crosses out and you get

t=14.5

4 0

3 years ago

Read 2 more answers

R 2x-6+3=6x-5 please help

frozen [14]

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$2x - 6 + 3 = 6x - 5$

$2x - 3 = 6x - 5$

$6x - 5 = 2x - 3$

Add sides 5

$6x - 5 + 5 = 2x - 3 + 5$

$6x = 2x + 2$

Subtract sides 2x

$- 2x + 6x = - 2x + 2x + 2$

$4x = 2$

Divide sides by 4

$\frac{4x}{4} = \frac{2}{4} \\$

$x = \frac{1}{2} \\$

_________________________________

CHECK :

$2( \frac{1}{2} ) - 3 = 6( \frac{1}{2} ) - 5 \\$

$1 - 3 = 3 - 5$

$- 2 = - 2$

Thus the solution is correct....

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3 0

3 years ago

Read 2 more answers

The measure of the supplement of an angle is three times the measure of the

gtnhenbr [62]

<h2>Answer:</h2>

<h3><em>x=45degrees</em></h3>

<h2>Step-by-step explanation:</h2>

Let the angle to be solved be x

Let the supplement/compliment by y

x+y=90 Complimentary angles add up to 90 degrees.

x+3y=180 Supplementary angles add up to 180 degrees, the other angle is thrice the other compliment.

Evaluating this as a system:

x+y=90 Isolate x:

x=90−y Input into the other equation:

(90−y)+3y=180 Combine like terms, isolate y and its coefficients:

2y=90 Isolate y

y=45 Input into the first equation:

x+45=90 Isolate x:

x=45degrees

5 0

3 years ago

In a random sample of 75 American women age 18 to 30, 26 agreed with the statement that a woman should have the right to a legal

ddd [48]

Answer:

a) $z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236$

$p_v =2*P(Z>0.236)=0.813$

If we compare the p value and using any significance level for example $\alpha=0.01$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.

b) We are confident at 99% that the difference between the two proportions is between $-0.188 \leq p_B -p_A \leq 0.226$

Step-by-step explanation:

Previous concepts and data given

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion of women age 18 to 30 agreed with the statement that a woman should have the right to a legal abortion for any reason

$\hat p_A =\frac{26}{75}=0.347$ represent the estimated proportion of women age 18 to 30 agreed with the statement that a woman should have the right to a legal abortion for any reason

$n_A=75$ is the sample size for A

$p_B$ represent the real population proportion for women age 58 to 70 agreed with the statement that a woman should have the right to a legal abortion for any reason

$\hat p_B =\frac{21}{64}=0.328$ represent the estimated proportion of women age 58 to 70 agreed with the statement that a woman should have the right to a legal abortion for any reason

$n_B=64$ is the sample size required for B

$z$ represent the critical value for the margin of error and for the statisitc

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

We need to conduct a hypothesis in order to check if the proportion are equal, the system of hypothesis would be:

Null hypothesis: $p_{A} = p_{B}$

Alternative hypothesis: $p_{A} \neq p_{B}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{A}-p_{B}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{A}}+\frac{1}{n_{B}})}}$ (1)

Where $\hat p=\frac{X_{A}+X_{B}}{n_{A}+n_{B}}=\frac{26+21}{75+64}=0.338$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>0.236)=0.813$

If we compare the p value and using any significance level for example $\alpha=0.01$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.

Part b

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$(0.347-0.328) - 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=-0.188$

$(0.347-0.328) + 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=0.226$

And the 99% confidence interval for the difference of proportions would be given (-0.188;0.226).

We are confident at 99% that the difference between the two proportions is between $-0.188 \leq p_B -p_A \leq 0.226$

5 0

3 years ago

Find the measure of.. (Image included) <br> I'll take all the help I can get please :)

sergey [27]

Answer:

$\sf\Huge\boxed{C.40}$

Step-by-step explanation:

Hello There!

Remember: sum of interior angles of a triangle = 180

so to find x we use this equation

180 = 90 + 7x + 5 + 9x + 5 ( the little square in the triangle indicates that the angle is a right angle. right angles have a measure of 90 so that's where the 90 came from.)

now we solve for x

step 1 combine like terms

90 + 5 + 5 = 100

7x + 9x = 16x

now we have 180 = 16x + 100

step 2 subtract 100 from each side

180 - 100 = 80

100 - 100 cancels out

now we have 80 = 16x

step 3 divide each side by 16

80/16 = 5

16x/16=x

we're left with x = 5

Finally we plug in 5 into x for angle a

7(5)+5

7*5=35

35+5=40

so we can conclude that the measure of angle A is 40 degrees

4 0

3 years ago