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A rectangular resort pool has a length of 45 feet and a width of 30 feet. A sitting area is attached to the pool and is in the shape of a semicircle with a diameter of 20 feet, as shown below. If the pool is filled to a depth of 5 feet and the sitting area is filled to a depth of 2.5 feet, approximately how much water is contained in both the sitting area and the pool?

Athletic Outfitters packs tennis balls into a cylinder with a diameter of 9.6 centimeters and a height of 39.5 centimeters. Each tennis ball has a diameter of 9.5 centimeters and there are 4tennis balls in each container. Approximately how much extra space is in the container?

Answers

Answer 1

Answer:

1 7142.699082ft³  (C)

2 1063.420642cm³ (A)

Step-by-step explanation:

Hey There!

1. So for the first one we want to find the volume of the rectangular pool and the volume of the semi cylinder

The dimension given are

length - 45

width - 30

height - 5

to find the volume we use

[tex]V=lwh[/tex]

[tex]45*30=1350\\1350x5=6750[/tex]

so the volume of the rectangular pool is 6750ft³

now we need to find the volume of the semi cylinder

the dimensions given are

diameter - 20

height - 2.5

so we find the volume by using the volume for a cylinder then dividing by 2

the volume for a cylinder formula is

[tex]V=\pi r^2h[/tex]

r = radius

h = height

to find the radius given the diameter we just divide by 2

20/2=10 so the radius is 10

now we just plug in the values and get

[tex]V=\frac{1}{2} \pi 10^22.5[/tex]

Note: the 1/2 is added because were finding the volume of a semi cylinder

[tex]10^2=100\\100(2.5)=250\\250\pi =785.3981634\\\frac{785.3981634}{2} =392.6990817[/tex]

So the volume of the sitting area is 392.6990817

Now that we have found the volume of each part we add them together to get the answer

[tex]392.6990817+6750=7142.699082[/tex]

2. For the second one we need to find the volume of the cylinder and subtract it by the volume of the tennis ball..s times 4 ( because there are 4 of them)

For the cylinder we are given the dimensions

height - 39.5

diameter - 9.5

Remember this is the formula of the volume of a cylinder

[tex]V=\pi r^2h[/tex]

r =radius

h = height

to convert diameter to radius we divide by 2

9.5/2=4.75

now we plug in the values

[tex]V=\pi 4.75^239.5\\4.75^2=22.5625\\22.565(39.5)=891.21875\\891.21875\pi =2859.100642[/tex]

so the volume of the container is 2859.100642cm³

now we need to find the volume of the tennis ball

to do this we use the formula

[tex]V=\frac{4}{3} \pi r^3[/tex]

we are given the dimensions of

diameter - 9.5

once again to convert to radius we divide by 2

9.5/2=4.75

now we plug in the values

[tex]V=\frac{4}{3} \pi 4.75^3\\4.75^3=107.171875\\107.171875\frac{4}{3} =142.8958333\\142.8958333\pi =448.9205002\\448.9205002(4)=1795.682001[/tex]

So the volume of the tennis bal...ls is 1795.682001

note: i multiplied by 4 because there are 4 tennis bal...ls

our final step is to subtract the volume of the bal...ls from the container

2859.100642-1795.682001=1063.420642

hope this helps :)


Related Questions

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1 yard=3 feet so 100 yard=300 feet

Answer:

Step-by-step explanation:

Gallon is more

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A.
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the answer is 95 degrees. the 50 degree angle is the same on the opposite side, so that means that angle ms is 35 degrees. 50 plus 35 is 85, subtract that from 180 and you have 95

I need help PlEaSeEe
Bethany has a sticker book with 200 pages.
Each sticker takes up 1/8 page. How many stickers can she put in the book?

A.
250 stickers

B.
25 stickers

C.
1,600 stickers

D.
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Answers

Answer:

25 stickers.

Step-by-step explanation:

I hope this helps! Maybe you can mark this brainly? Hope you have a amazing day! <3

The population of a town can be modeled by the function P= 16,512(1.03)' where t'is
the number of years after 2006. What is the significance of the value 16,512?

Answers

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The answer is C

Step-by-step explanation:

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Answers

Answer:

(+2)(+8)

Step-by-step explanation:


7) A container is 1/3 full of water and 1/4 full of oil. What fraction of the container is empưy?​

Answers

Answer:

[tex]Empty = \frac{5}{12}[/tex]

Step-by-step explanation:

Given

[tex]Water = \frac{1}{3}[/tex]

[tex]Oil = \frac{1}{4}[/tex]

Required

The fraction that is empty

The constituent of the water can be represented as:

[tex]Water + Oil + Empty = 1[/tex]

Make Empty the subject

[tex]Empty = 1 - Water - Oil[/tex]

Substitute values for Water and Oil

[tex]Empty = 1 - \frac{1}{3} - \frac{1}{4}[/tex]

Take LCM

[tex]Empty = \frac{12 - 4 - 3}{12}[/tex]

[tex]Empty = \frac{5}{12}[/tex]

in a classroom of 1/6 of the students were wearing blue and 2/3 are wearing white there are thirty six students in the class how many students are wearing a shirt other than blue or white

Answers

Answer:

6

Step-by-step explanation:

1/6 of 36=6

2/3 of 36= 24

24+6=30

36-30=6

Find the measurement of Angle SPQ

Answers

Answer:

146 °

Step-by-step explanation:

sum of angles in circle = 360°

360 - 154-60-86 = 60

60 = UPS

SPQ = UPS + QUP = 60 + 86 = 146°

the answer is 146 degrees

In a deck of 52 cards there are 2 jokers and 4 each of the number cards 1-10. The probability of picking a joker is 2 out of 52 or 2/52. Write as a fraction, the probability of drawing a number 7 card.​

Answers

Answer:

1/13

Step-by-step explanation:

The number 7 cards= 4 of them

Total number of cards= 52

4/52 are 7's

Simplify 4/52>>>>2/26>>>>1/13

Hope this helped! Please give a brainly if you can <33

help pleasee!!!!!!!!!!!!!!!!!!

Answers

Answer:

76 because if the two lines are parallel then x = 76

hope this helps and brainliest please

Identify the domain of the function pictured below.

Answers

Can you attach the picture of the function please?

PLEASE HELP NOW I NEED TO KNOW THIS OR ILL HAVE TO GO TO SUMMER SCHOOL!!!!!!!

Answers

Answer:

BXZ= 75

AYX=44

B= 61

Step-by-step explanation:

B=180-(75+44)

=61

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Please help! It’s due soon!

Answers

Answer:

0.083

Step-by-step explanation:

151 divided by 1800 is 0.083

might be wrong WARNING

Find the perimeter and area of the triangle. Show all work.
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Answers

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Carlos' grandmother will give him $20 plus $5 for every hour that he completes yard work. This situation can be described by an equation of the form y = mx + b, where x = the time in hours and y = the total amount of money earned. What is the value of b in this equation?

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Which set of ordered pairs (x,y) could represent a linear function x?

Mrs. Egan is saving money for a new television. She already has $110 in the bank. She is going to save $65 per week. Write an equation that represents Mrs. Egan's savings account​

Answers

110+65x so if she already has 110 that means you’ll add 65 every week it’s not clear on how many weeks so that’s why the x is there for x amount of weeks

. The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If she is willing to replace 3% of the motors that fail, how long a guarantee (in years) should she offer

Answers

Answer:

She should offer a guarantee of 13.76 years.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The average life of a certain type of small motor is 10 years with a standard deviation of 2 years.

This means that [tex]\mu = 10, \sigma = 2[/tex]

If she is willing to replace 3% of the motors that fail, how long a guarantee (in years) should she offer?

She should offer the 100 - 3 = 97th percentile as a guarantee, so X when Z has a pvalue of 0.97, that is, X when Z = 1.88.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.88 = \frac{X - 10}{2}[/tex]

[tex]X - 10 = 2*1.88[/tex]

[tex]X = 13.76[/tex]

She should offer a guarantee of 13.76 years.

solve for X

please answer will give brainliest!!

Answers

Answer:

x=19.55

hope it help you..

Answer:

19.55

Step-by-step explanation:

x/8.5 = 2.3

x = 8.5 × 2.3

x = 85 × ⅒ × 23 × ⅒

x = 85 × 23 × ⅒ × ⅒

x = 1955 × 1/100

x = 1955/100

x = 19.55

4. Find the percent of increase from 56 to 70. Round your answer
to the nearest tenth of a percent.

Answers

Answer:

25%

Step-by-step explanation:

PLEASE HELP WILL MARK BRAINLIEST!!!!
The measure of an angle is 37.1º, What is the measure of its complementary angle?

Answers

Answer:

52.9º

Step-by-step explanation:

complementary is when the sum of two angles is 90 degrees

to solve, simply take 37.1 and subtract it from 90:

⇒ 90 - 37.1

⇒ 52.9

what the heck guys please help me

Answers

Answer:

10, 12, 13, 20

Step-by-step explanation:

Please help ...........

Answers

Answer:

B

Step-by-step explanation:

What is 3 to the power of 9 ?​

Answers

Answer:

3 to the power of 9 = 19,683

Step-by-step explanation:

3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3= 19,683

hope this is helped

if it did let me know if it was right

and mark brainlest  

13. You are buying plants and soil for your garden. The soil costs $4.00 per bag and the plants cost $10.00 each. You want to buy at least 5 plants and can spend no more than $100.00 total

Answers

Answer:

Part a) The system of linear inequalities is

y\geq 5y≥5

4x+10y\leq 1004x+10y≤100

Part b) The graph in the attached figure

Part c) A solution could be (5,7) (see the explanation)

Step-by-step explanation:

The complete question is

You are buying plants and soil for your garden. The soil cost 4.00 dollars per bag and the plants cost 10.00 each. You want to buy at least 5 plants and can spend no more than10.00each.Youwanttobuyatleast5plantsandcanspendnomorethan100

a) write a system of linear inequalities to model the situation

b) Graph the system of linear inequalities

c) Identify and interpret a solution to the system

Part a) write a system of linear inequalities to model the situation

Let

x -----> the number of bags of soil

y ----> number of plants

we know that

The word "at least" means "greater than or equal"

y\geq 5y≥5 ----> inequality A

The word "no more" means "less than or equal"

4x+10y\leq 1004x+10y≤100 ----> inequality B

Part b) Graph the system of linear inequalities

we have

y\geq 5y≥5 ----> inequality A

4x+10y\leq 1004x+10y≤100 ----> inequality B

using a graphing tool

the solution is the triangular shaded area

see the attached figure

Part c) Identify and interpret a solution to the system

we know that

If a ordered pair is a solution to the system, then the ordered pair must lie on the shaded area of the solution

i take the point (5,7)

the point (5,7) lie on the shaded area of the solution

so

is a solution of the system

That means ----> You are buying 5 bags of soil and 7 plants for your garden

Verify the solution

Remember

If a ordered pair is a solution to the system, then the ordered pair must satisfy both inequalities

Verify inequality A

7\geq 57≥5  ----> is true

so

The ordered pair (5,7) satisfy inequality A

Verify inequality B

4(5)+10(7)\leq 1004(5)+10(7)≤100

90\leq 10090≤100 ---> is true

so

The ordered pair (5,7) satisfy inequality B

therefore

The ordered pair (5,7) is a solution to the system

A record with a diameter of 12 inches rotates at 33 revolution per minute find the angular speed of the record in radians per second

Answers

9514 1404 393

Answer:

  1.1π radians/second

Step-by-step explanation:

Each revolution is 2π radians, and there are 60 seconds in a minute. The rotation rate is ...

  (33 rev/min)×(2π rad/rev)×(1 min)/(60 sec) = 66π/60 rad/sec

  = 1.1π rad/sec

The angular speed is 1.1π radians per second.

Monica has a cylindrical container full of marbles. The container is shown below.
10 cm
The height of the container is approximately 12 centimeters. Which is closest to
the volume of Monica's container, in cubic centimeters?

Answers

Answer:

Area of a circle is  pi * [tex]r^{2}[/tex]

then multiply that by the height

Step-by-step explanation:

diameter = 10

radius is   diameter / 2

r = 10/2 = 5

A = pi * [tex]5^{2}[/tex]

A = 78.5398

height * A = volume

12 * 78.5398 = 942.477

So about 942  , answer 3 looks right  :)   sorry I got to your question late, send me a note , when you have a question, so I'll see  :)

help me please!!! thank you!!!

Answers

Answer:

254.47 inches squared

Step-by-step explanation:

Area of a circle is

[tex]\pi {r}^{2} [/tex]

so to find the radius we half the diameter( which here is 18 inches) which equals to 9

we replace r to 9 because that's the radius

[tex]\pi \times {9}^{2} [/tex]

which is 254.47 inches squared

PLS HELP I WILL MARK BRAINLIST!!

Answers

Answer:

C, 105

Step-by-step explanation:

45 divided by 3 is 15 so 15 x 7 = 105 minutes.

Write a quadratic function that reflects the x axis, stretches by a factor of 5, and shifts left 6 and up 3

Answers

Answer:

y=(x+6)^5+3

Step-by-step explanation:

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