Safety regulations state that roller coasters cannot operate safely in heavy rains. Throughout the day, ride operators measure the rainfall at several random locations along the track to verify that the rainfall is below an established threshold value. allowing the ride to operate safely. The collected data is used to conduct a one-sample 2-test of the null hypothesis that the mean rainfall is minimal against the alternative that the mean rainfall is too heavy. If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions. Choose the correct description of a type I error and a type II crror in this context. Type I error: a. The rainfall is minimal enough to operate safely, and the ride is shut down. b. The rainfall is minimal enough to operate safely, and the ride continues to operate. c. The rainfall is too heavy to operate safely, and the ride continues to operate, d. The rainfall is too heavy to operate safely, and the ride is shut down. Type II error: a. The rainfall is minimal enough to operate safely, and the ride is shut down. b. The rainfall is minimal enough to operate safely, and the ride continues to operate. c. The rainfall is too heavy to operate safely, and the ride is shut down. d. The rainfall is too heavy to operate safely, and the ride continues to operate.

Type I error:

a. The rainfall is minimal enough to operate safely, and the ride is shut down.

Type II error:

d. The rainfall is too heavy to operate safely, and the ride continues to operate.

Step-by-step explanation:

In this case:

The null hypothesis (H0) states that mean rainfall is minimal

The alternative hypothesis (H1) states that mean rainfall is heavy.

A type I error occurs if one rejects the null hypothesis when it is actually true.

In this case; if the rainfall is minimal enough to operate safely and the ride is shut down is an example of Type I error because the null hypothesis is true and it is rejected.

A type II error occurs if one does not reject the null hypothesis when it is false, that is one accept the null hypothesis when it is false.

In this case; the null hypothesis is false and it is accepted is an example of type II error. So, the rainfall is too heavy to operate safely (means null hypothesis is false) and the ride continues to operate (means the null hypothesis is accepted when it is false).

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)