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Nana76
15 days ago
8

According to a report from the United States Environmental Protection Agency, burning one gallon of gasoline typically emits abo

ut 8.9 kg of CO2. A fuel company wants to test a new type of gasoline designed to have lower CO2 emissions. Here are their hypotheses:
H0: μ = 8.9 kg
Ha: μ < 8.9 kg (where μ is the mean amount of CO2 emitted by burning one gallon of this new gasoline).

Which of the following would be a Type II error in this setting?

A. The mean amount of CO2 emitted by the new fuel is actually 89 kg but they conclude it is lower than 89 kg
B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg
C. The mean amount of CO2 emitted by the new fuel is actual 89 kg and they alto conclude it is lower than 89 kg and they conclude it is lower than 9 kg
D. The mean amount of CO2 emitted by the new fuels actually lower than 8.9
Mathematics
1 answer:
tester [12.3K]15 days ago
8 0

Answer:

B. The average amount of CO_2 emitted by the new fuel is indeed beneath 89 kg, yet they fail to determine it is less than 89 kg

Step-by-step explanation:

A Type II error refers to the lack of rejection of a false null hypothesis.

Considering the null and alternative hypotheses of a gasoline company that seeks to evaluate a new gasoline type intended to have lower CO_2 emissions.:

H_0: \mu = 8.9 kg\\H_a: \mu < 8.9 kg \\\text{ (where \mu is the mean amount of CO_2 emitted by burning one gallon of this new gasoline)}

where \mu signifies the mean amount of CO_2 emitted from burning one gallon of this novel gasoline.

If the null hypothesis is not correct, then:

H_a: \mu < 8.9 kg

Not asserting the alternative hypothesis will represent a Type II error.

Hence:

The Type II error can be described as: (B) The mean amount of CO_2 emitted by the new fuel is actually less than 89 kg but they mistakenly conclude it is greater than 89 kg.

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Answer:

The solution to the equation is 40

This indicates the max number of wedding invitations they can afford to send within their budget.

Step-by-step explanation:

To find the zero of the function, we set the dependent variable (here, m) to zero.

So we have;

0 = 50-1.25w

1.25w = 50

w = 50/1.25

w = 40

What implication does this have in this context?

Essentially, it means that the couple can send out invitations to a total of 40 people based on their budget.

7 0
1 month ago
A flat circular plate has the shape of the region x2 + y2≤1. The plate, including the boundary where x2 + y2 = 1, is heated such
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Setting both partial derivatives to zero results in a single critical point at (x,y)=\left(\dfrac12,0\right), located within the unit disk.

At this given point, the derivative value of the Hessian matrix is

|H|=\begin{vmatrix}T_{xx}&T_{xy}\\T_{yx}&T_{yy}\end{vmatrix}=\begin{vmatrix}2&0\\0&4\end{vmatrix}=8>0

and the second-order partial derivative with respect to x yields

T_{xx}\bigg|_{(x,y)=(1/2,0)}=2>0

This suggests that the critical point represents a local minimum, marking it as the coldest area on the plate with a temperature of T\left(\dfrac12,0\right)=-\dfrac14.

To find the hottest area on the plate, it must be located along the boundary. Let x=\cos\theta and y=\sin\theta, so that

T(x,y)=T(\theta)=\cos^2\theta+2\sin^2\theta-\cos\theta
T(\theta)=\dfrac32-\cos\theta-\dfrac12\cos2\theta

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T'(\theta)=\sin\theta+\sin2\theta=0
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You will discover that T(\theta) achieves three extrema on the interval (0,2\pi), with relative maxima occurring at \theta=\dfrac{2\pi}3 and \theta=\dfrac{4\pi}3, and a relative minimum at \theta=\pi (and \theta=0, if you wish to include that).

Our minimum has already been identified inside the plate - which you can check to have a lower temperature than at the points noted by T(\theta) - and we identify two maxima at \theta=\dfrac{2\pi}3 and \theta=\dfrac{4\pi}3, both showing a maximum temperature of T=\dfrac94.

Reverting to Cartesian coordinates, these points match up with \left(-\dfrac12,\pm\dfrac{\sqrt3}2\right).
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18 days ago
A merry-go-round has a radius of 18 feet. If a passenger gets on a
Zina [12379]

Answer:

The rotation angle measures 2.11 °

Step-by-step explanation:

Stated as follows:

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The distance rolled by the wheel = l = 38 feet

Let us denote the angle of rotation as Ф

Now, according to the problem:

∵ the length of an arc at the center corresponds to an angle Ф

Thus,

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As 180° represents π radians

And π approximates to 3.14

Thus, distance rolled by the wheel = 180 °× radius × \frac{\Theta }{180^{\circ}}

That is l = r × Ф

So, Ф = \frac{l}{r}

Consequently, Ф = \frac{38 feet}{18 feet}

Therefore, Ф = 2.11 °

Thus, the rotation angle is Ф = 2.11 °

Hence, the rotation angle is 2.11 ° Answer

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Answer:

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Then, simplify to solve:

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