Find the value of x and y

Mathematics

1 answer:

Alexeev081 [22]4 years ago

6 0

Answer:

x = 36 and y = 72

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an external angle to the triangle on the right, thus

y = 2x

The sum of the 3 angles in a triangle = 180

Consider the triangle on the left. then

x + 2y = 180 ← substitute y = 2x

x + 4x = 180

5x = 180 ( divide both sides by 5 )

x = 36 and y = 2x = 2 × 36 = 72

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Gardeners on the west coast of the United States are investigating the difference in survival rates of two flowering plants in d

Travka [436]

Answer:

$ME=z_{\alpha/2} SE= 2.58*0.082=0.21156$

The 99% confidence interval would be given (0.09844;0.5216).

We are confident at 99% that the difference between the two proportions is between $0.09844 \leq p_B -p_A \leq 0.5216$

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 plant A

$\hat p_A =0.75$ represent the estimated proportion for plant A

$n_A$ is the sample size required for plant A

$p_B$ represent the real population proportion for plant b

$\hat p_B =0.44$ represent the estimated proportion for plant B

$n_B$ is the sample size required for plant 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 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.