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Colt1911 [192]
3 years ago
15

The shape of a dome can be modeled by the equation h=2dsquared +100 when h issue height (in feet) of the dome from the floor d f

eet from its center. How far from the center of the domes is the height 50 feet?
Mathematics
1 answer:
Law Incorporation [45]3 years ago
6 0

Given that,

The shape of a dome can be modeled by the equation :

h=2d^2+100 ....(1)

h is the height of the dome

d is distance from its center

We need to find the distance from the center of the dome if the height is 50 feet. Put h = 50 in equation (1)

50=2d^2+100\\\\2d^2=100-50\\\\2d^2=50\\\\d^2=25\\\\d=5\ \text{feet}, neglecting d = -5 feet (as height can't be negative)

So, at a distance of 5 feet from the center of domes the height is 50 feet.

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Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobil
o-na [289]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $120 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1.

State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.

At a 0.01 level of significance, what is your conclusion? What is the p-value?

Answer:

Null hypotheses = H₀ = σ₁² ≤ σ₂²

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic = 1.44

p-value = 0.1954

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

Step-by-step explanation:

Let σ₁² denotes the variance of 4 years old automobiles

Let σ₂² denotes the variance of 2 years old automobiles

State the null and alternative hypotheses:

The null hypothesis assumes that the variance in annual repair costs is smaller for older automobiles.

Null hypotheses = H₀ = σ₁² ≤ σ₂²

The alternate hypothesis assumes that the variance in annual repair costs is larger for older automobiles.

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic:

The test statistic is given by

Test statistic = σ₁²/σ₂²

Test statistic = 120²/100²

Test statistic = 1.44

p-value:

The degree of freedom corresponding to 4 years old automobiles is given by

df₁ = n - 1  

df₁ = 26 - 1  

df₁ = 25

The degree of freedom corresponding to 2 years old automobiles is given by

df₂ = n - 1  

df₂ = 23 - 1  

df₂ = 22

Using Excel to find out the p-value,  

p-value = FDIST(F-value, df₁, df₂)

p-value = FDIST(1.44, 25, 22)

p-value = 0.1954

Conclusion:

When the p-value is less than the significance level then we reject the Null hypotheses

p-value < α   (reject H₀)

But for the given case,

p-value > α

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

8 0
3 years ago
Which quadrant will (30,-45) fall into?
Varvara68 [4.7K]

Answer:

Quadrant 4

Step-by-step explanation:

The x value is positive so it is either in 1 or 4

The y value is negative so it is either 3 or 4

To meet both conditions, it must be 4

6 0
2 years ago
Read 2 more answers
Write the equations of the lines on the grid.
klasskru [66]
Answer;
red line: y = x
green line: y = -x
6 0
3 years ago
14.4% of a voters in middleville voted for rocky rufus for mayor. if 2500 people voted, how many votes did rocky get?
il63 [147K]

Answer:

360 votes

Step-by-step explanation:

Move the decimal to the left 2 times and you'll get .144. Multiply that by 2500, and you have your answer.

3 0
3 years ago
Please help with the following question
Alex17521 [72]
P1=(0,0)=(x1,y1)→x1=0, y1=0
P2=(3,-2)=(x2,y2)→x2=3, y2=-2

Slope: m=(y2-y1)/(x2-x1)
m=(-2-0)/(3-0)
m=(-2)/3
m=-2/3

Point-slope equation:
y-y1=m(x-x1)
y-0=(-2/3)(x-0)
y=-(2/3)x

Answer: The equation of the line is: y=-(2/3)x
5 0
3 years ago
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