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Ratling [72]
2 years ago
11

The volume of the cylindrical water tank shown below is 490π feet^3. If the tank is 10 feet high, what does its radius r equal?

Mathematics
1 answer:
luda_lava [24]2 years ago
5 0

The cylindrical water tank with a volume of 490π feet³, and a height of 10 feet, has a radius of <u>7 feet</u>.

The volume of a cylinder having a radius of r units, and a height of h units, is given by the formula, V = πr²h.

In the question, we are asked to find the radius (r), of a cylindrical water tank, with a volume of 490π feet³, and a height of 10 feet.

Substituting the value of V = 490π feet³, and h = 10 feet, in the formula for the volume of a cylinder, V = πr²h, we get:

490π feet³ = π.(r²)(10 feet).

Rearranging this, we can write:

r² = (490π)/(10π) feet²,

or, r² = 49 feet²,

or, r = √49 feet,

or, r = 7 feet.

Thus, the cylindrical water tank with a volume of 490π feet³, and a height of 10 feet, has a radius of <u>7 feet</u>.

Learn more about the volume of a cylinder at

brainly.com/question/9554871

#SPJ1

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Colt1911 [192]

Hello!

Step-by-step explanation:

Slope: \frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}

\frac{9-3=6}{2-(-1)=2+1=3}=\frac{6}{3}=2

<em><u>Therefore, the slope is 2.</u></em>

<em><u>Answer is 2.</u></em>

Hope this helps!

Thank you!

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Have a great day!


7 0
4 years ago
5. Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.
HACTEHA [7]

Carla can babysit for 5 hours and tutor for 7 hours or babysit for 8 hours and tutor for 5.5 hours

<h3>How to graph the inequality?</h3>

Let x represents hours babysitting and y represents hours tutoring

So, we have:

Earnings = Rate of babysitting * x + Rate of tutoring* y

This gives

Earnings = 5x + 10y

He wants to earn at least $95.

This means that:

5x + 10y ≥ 95

See attachment for the graph of the inequality

From the attached graph, two possible solutions are: (5, 7) and (8, 5.5)

This means that Carla can babysit for 5 hours and tutor for 7 hours or babysit for 8 hours and tutor for 5.5 hours

Read more about inequalities at:

brainly.com/question/25275758

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5 0
2 years ago
Find ? in each case.
user100 [1]

Answer:

a) For this case we have that n = 30 and p =1/6

X \sim Binom(n=30, p=1/6)

b)  For this case we have that n = 10 and p =1/100

X \sim Binom(n=10, p=1/100)

c)  For this case we have that n = 20 and p =0.3

X \sim Binom(n=20, p=0.3)      

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

Assuming the following question : "For each of the following binomial random variables specify n and p"  

Solution to the problem

a. A fair die is rolled 30 times. X = number of times a 6 is rolled.

For this case we have that n = 30 and p =1/6

X \sim Binom(n=30, p=1/6)

b. A company puts a game card in each box of cereal and 1/100 of them are winners. You buy ten boxes of cereal, and X = number of times you win.

For this case we have that n = 10 and p =1/100

X \sim Binom(n=10, p=1/100)

c. Jack likes to play computer solitaire and wins about 30% of the time. X = number of games he wins out of his next 20 games.

For this case we have that n = 20 and p =0.3

X \sim Binom(n=20, p=0.3)

6 0
4 years ago
Help please. (12 points)
Sphinxa [80]
 because the symbol is a less than sign < the blue area needs to be below the red line and does not include the solution to Y ( if it included Y it would be a ≤ symbol.
 When the solution isn't included, it is a dashed line.
 so the answer would be D



6 0
3 years ago
1/x=y-z/a solve for x
const2013 [10]

\frac{1}{x}=y-\frac{z}{a}

x=\frac{1}{y-\frac{z}{a} },                ( y-\frac{z}{a} = \frac{y}{1}- \frac{z}{a} = \frac{ya-z}{a} )

x=\frac{1}{y-\frac{z}{a} }

x=\frac{1}{\frac{ya-z}{a} },               (        \frac{1}{\frac{ya-z}{a} } =\frac{a*1}{ya-z }        )

x=\frac{a}{ya-z }

3 0
4 years ago
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