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liubo4ka [24]
3 years ago
8

The circular opening of an ice cream cone has a diameter of 7 centimeters. The height of the cone is 10 centimeters. What is the

volume of the ice cream cone in cubic centimeters
Mathematics
1 answer:
Nataly [62]3 years ago
8 0

We have been given that the circular opening of an ice cream cone has a diameter of 7 centimeters. The height of the cone is 10 centimeters. We are asked to find the volume of the ice cream cone in cubic centimeters.

We will use volume of cone formula to solve our given problem.

V=\frac{1}{3}\pi r^2h, where,

r = Radius

h = Height.

We know that diameter is two times the radius, so radius of cone would be half the diameter that is \frac{7}{2} cm.

V=\frac{1}{3}\pi\cdot (\frac{7}{2}\text{ cm})^2\cdot 10\text{ cm}

V=\frac{1}{3}\pi\cdot \frac{49}{4}\text{ cm}^2\cdot 10\text{ cm}

V=\frac{490\pi }{12}\text{ cm}^3

V=128.2817\text{ cm}^3

Upon rounding to nearest tenth, we will get:

V\approx 128.3\text{ cm}^3

Therefore, the volume of the cone would be approximately 128.3 cubic cm.

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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
Kindly solve this question
Dmitry_Shevchenko [17]

Answer:

x=-1/7

Step-by-step explanation:

\frac{3x-1}{3} -\frac{2x}{x-1} =x

\frac{(3x-1)(x-1)}{3x-3} -\frac{2x(3)}{3x-3} =x

\frac{3x^2-4x+1}{3x-3} -\frac{6x}{3x-3} =x

\frac{3x^2-10x+1}{3x-3} =x

\frac{3x^2-10x+1}{3x-3} =\frac{x(3x-3)}{3x-3}

\frac{3x^2-10x+1}{3x-3} =\frac{3x^2-3x}{3x-3}

3x^2-10x+1=3x^2-3x

-10x+1=-3x

-7x=1

x=-1/7

3 0
2 years ago
What is the lcm of 1 and 5
Temka [501]

Answer:

5

Step-by-step explanation:

6 0
3 years ago
Round 8,624 to the nearest thousand
Shtirlitz [24]

8,624 rounded to the nearest thousand is 9,000

Hope this helps

-AaronWiseIsBae

8 0
3 years ago
Read 2 more answers
1651 rounded to the nearest thousand
geniusboy [140]

Answer:

2000

nearest thousandth

if the last 3 digits are over 500 then it's rounding up

7 0
2 years ago
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