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3 years ago

The volume of a cylinder is 675π cm3. The radius of the base of the cylinder is 5 cm. What is the height of the cylinder?

Mathematics

1 answer:

frosja888 [35]3 years ago

4 0

Answer: 27 cm

Step-by-step explanation:

We know that the volume of a cylinder is $V=\pi r^2h$ . Since we were given the volume and radius, we can plug them in and solve for height.

$675\pi =\pi (5^2)h$ [divide both sides by π]

$675 = (5^2)h$ [exponent]

$675=25h$ [divide both sides by 25]

$h=27$

Now, we know that the height is 27 cm.

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How to subtract a negative fraction from a positive fraction?

ikadub [295]

Let's take an example to illustrate this case:

positive fraction = 2/7

negative fraction = - 3/5

Now we need to subtract - 3/5 from 2/7

Right?

2/7 - (-3/5) = 2/7 + 3/5

here we need to unify the denominators as follows:

the lowest common factor between 7 and 5 is 35
2/7 = 10/35
3/5 = 21/35

Now back to 2/7 + 3/5:

2/7 + 3/5 = 10/35 + 21/35 = (10+21)/35 = 31/35

That's it

Hope that helps you

8 0

3 years ago

Please help with 13 14 15 16

Vikentia [17]

The domain and the range for the relations are given as follows:

13. Domain x ∈ R, range y ∈ R.

14. Domain {x ∈ Z| -4 ≤ x ≤ 4 and x is even} , range y ∈ {y ∈ Z| -1 ≤ y ≤ 4}.

15. Domain {x ∈ Z| -4 ≤ x ≤ 1} , range y ∈ {y ∈ Z| -4 ≤ y ≤ 1}.

16. Domain x ∈ R, range y ∈ R.

<h3>What are the domain and range of a function?</h3>

The domain of a function is the set that contains all possible input values. Hence, in a graph, the domain is given by the values of x.

The range of a function is the set that contains all possible output values. Hence, in a graph, the domain is given by the values of y.

For items 13 and 16, the functions are continuous, hence it is over the real numbers, and both the domain and range are all real values.

For items 14 and 15, the functions are discrete, hence it is over the integer numbers, and the domain is composed by the values assumed by x and the range is composed by the values assumed by y.

More can be learned about domain and range at brainly.com/question/10197594

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5 0

1 year ago

If a child weighs 83 pounds, how many ounces does she weigh? 664 oz. 664 oz. 830 oz. 830 oz. 966 oz. 966 oz. 1328 oz.

NikAS [45]

Answer:

The answer is 1,328

Step-by-step explanation:

8 0

2 years ago

A quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain bra

tensa zangetsu [6.8K]

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

Let $\mu$ = average calorie content of a 12-ounce can.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 120 calories {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, $H_A$ : $\mu$ > 120 calories {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average calories per can = 124 calories

s = sample standard deviation = 6 calories

n = sample of cans = 10

So, test statistics = $\frac{124-120}{\frac{6}{\sqrt{10} } }$ ~ $t_9$

= 2.108

The value of t test statistics is 2.108.

Now, at 0.05 significance level the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

7 0

3 years ago

In a random sample of 100 registered voters who were considered likely to vote, 63% favored the Democratic candidate. In last we

weqwewe [10]

Answer:

C. I hope this helps!

Step-by-step explanation:

6 0

3 years ago

The volume of a cylinder is 675π cm3. The radius of the base of the cylinder is 5 cm. What is the height of the​ cylinder?

The volume of a cylinder is 675π cm3. The radius of the base of the cylinder is 5 cm. What is the height of the cylinder?