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alexdok [17]
2 years ago
12

A cone-shaped water tank is completely filled. The tank has a depth of 12 feet and a radius of 29 feet. A pump removes water fro

m the tank at a rate of 1000 cubic feet per hour.
What is the volume of water in the tank before the water is pumped out?
Use 3.14 to approximate π and express your final answer to the nearest hundredth.
How many hours will it take to drain all the water?
Mathematics
1 answer:
Sauron [17]2 years ago
7 0

Answer:

Volume = 10562.96  cu ft

10.56 hr. to drain all the water

Step-by-step explanation:

V = 1/3Bh        B = area of the base           h = height

The base is a circle, so B = \pi r^{2}

V = \frac{1}{3} (3.14) (29^{2})(12) = 10562.96  cu ft

10562.96/1000  = 10.56 hr.

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In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean
Otrada [13]

Answer:

a=1050 -0.126*218=1022.532

So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.  

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Solution to the problem

Let X the random variable that represent the consumption levels of a population, and for this case we know the distribution for X is given by:

X \sim N(1050,218)  

Where \mu=1050 kWh and \sigma=218kWh

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.55   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.45 of the area on the left and 0.55 of the area on the right it's z=-0.26. On this case P(Z<-0.126)=0.45 and P(z>-0.126)=0.55

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.126=\frac{a-1050}{218}

And if we solve for a we got

a=1050 -0.126*218=1022.532

So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.  

8 0
3 years ago
Savannah is buying a $1,200.00 Iphone 12 on an installment plan. She makes a down payment of $200.00. She makes monthly payments
natita [175]

Answer:

1.5789... is the interest rate

Step-by-step explanation:

200 down payment

1320. = 55 times 24 monrhs

----------

1520.00 total paid in 2 years

-1200. original price

---------

320. interest paid to finance company

7 0
3 years ago
Pleasee Help!11! Pts 13
klemol [59]

Answer:

They are all 23 because all the sides are equal.

Step-by-step explanation:

8 0
2 years ago
. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the
FromTheMoon [43]

Answer:

The smaller bottle holds 12.5 ml of perfume.

====================

<h2>Given</h2>

  • Two bottles of similar shape;
  • Larger bottle has volume of 100 ml;
  • The length of larger bottle is 10 cm;
  • The length of smaller bottle is 5 cm.

<h2>To find </h2>

  • The volume of smaller bottle.

<h2>Solution</h2>

Find the scale factor, the ratio of corresponding dimensions:

  • k = 5/10 = 1/2

We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:

  • V_{small}/V_{large} = k^3\\

Substitute the known values and find the volume of small bottle:

  • V_{small}/100= (1/2)^3\\
  • V_{small}/100= 1/8
  • V_{small}= 1/8*100=12.5

The smaller bottle holds 12.5 ml of perfume.

4 0
1 year ago
Read 2 more answers
Find the slope in (-2,8) and (1,6)
Salsk061 [2.6K]

Formula for slope: \frac{y2 - y1}{x2 - x1}

y₂: 6

y₁: 8

x₂: 1

x₁: -2

Plug them into the slope equation:

\frac{6 - 8}{1 - (-2)}

--> \frac{-2}{1 + 2}

---> -\frac{2}{3}

The slope is -\frac{2}{3}.

8 0
3 years ago
Read 2 more answers
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