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3 years ago

The comeplement of 99

1 answer:

3 0

1. the complement is when two angles add up to 99 degrees and the supplement is when the two angles add up to 180 degrees.

2. Let x be the measure of the unknown angle .

3. Let 90 -x be it's complement and 180- x be the supplement of the angle .

4. Given 90-x=3x+9 the measure of the complement of an angle is 3x+9. Solve using the following steps.

99-x=3x+9
Add x-9 to both sides to isolate x-terms on right side and numbers on left
90-x+x-9=3x+9+x-9

90-x+x-9=3x+9+x-9

91=4x
divide by 4 to both sides yields
91/4=x

5. Given 3x+99=180-x. The measure of the supplement of an angle is 3x+99. So
3x+99=180-x

Add x+99 to both sides of equations to isolate x on right side and number on left
3x+99+x-99=180-x+x-99

4x=91

X=91/4

6. The angle is x=91/4

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The 95% confidence interval would be given (0.0109;0.1651).

We are confident at 95% that the difference between the two proportions is between $0.0109 \leq p_{elementary} -p_{High school} \leq 0.1651$

Step-by-step explanation:

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 for elementary school

$\hat p_A =\frac{226}{397}=0.569$ represent the estimated proportion for elementary school

$n_A=397$ is the sample size required for Brand A

$p_B$ represent the real population proportion for high school teachers

$\hat p_B =\frac{129}{268}=0.481$ represent the estimated proportion for high school teachers

$n_B=268$ is the sample size required for Brand B

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

The population proportion have the following distribution

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

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 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.