The tank shown is a cylinder with diameter equal to 4 feet and height equal to 12 feet. the tank holds 1130 gallons of rainwater when full. how many gallons of water are in the tank when the depth of the water is 9 feet?

Answers

Answer 1

we know that
volume of the tank=1130 gal

step 1
find the volume of the tank with deep 9 ft
volume of the tank with deep 9 ft=pi*r²*h
r=4/2-----> 2 ft
h=9 ft
volume of the tank with deep 9 ft=pi*2²*9-----> 113.04 ft³

step 2
convert to gal
1 ft³------------------> 7.48052 gal
113.04 ft³--------> x
x=113.04*7.48052-----> x=845.60 gal

the answer is
845.60 gal

alternative method

if the volume of the tank is 1130 gal for ----------> a height of 12 ft
X volume-----------------------------------> 9 ft
x=9*1130/12-----> 847.5 gal

Related Questions

Please help !!

Question posted below

Answers

4 (6) - 3 (4)
24 - 12 = 12

angle 0 is in quadrant 1 with sin0 = 2/5. Use the Pythagorean identity, sin^2 0 + cos^2 0 = 1, to calculate the value of cos0 as a radical.

Answers

we know that
sin²x+cos²x=1
so
clear cos x
cos x=(+/-)√[1-sin²x]

in this problem
Angle 0 is in quadrant 1 -----> cos o and sin o are positive
sin o=2/5
cos x=√[1-(2/5)²]----> cos o=√[1-4/25]----> cos o=√[21/25]---> cos o=√21/5

the answer is
cos o=√21/5

Michael, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Michael also gives a 5% discount if the entire amount is paid up front. A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2.20 dollars, Basic Proofreading 2.80 dollars, Extended Proofreading 3.90 dollars, and Deep Editing 12 dollars Maria has a 25-page manuscript. The equation below shows the relationship between the total cost of editing 25 pages, T, and the cost per page, c, if she gets the 5% discount: 25c − 0.05(25c) = T Using the equation, what is the best quality of editing that Maria can get done for a maximum of $66.50?

Answers

Using the equation, the cost per page Maria can afford is
25c -.05(25c) = 66.50
0.95*25*c = 66.50
c = 66.50/(0.95*25) = 2.80

The best quality of editing that Maria can afford is ...
Basic Proofreading

Need help on this as soon as possible!

Answers

Volume of the prism: V= Ab*h
Area of the base of the prism: Ab=Area of the equilateral triangle
Height of the prism: h=6

Ab=A triangle= sqrt(3)/4*s^2
Ab=sqrt(3)/4*3^2
Ab=sqrt(3)/4*9
Ab=9 sqrt(3)/4

V=Ab*h
V=[9 sqrt(3)/4](6)
V=54 sqrt(3) /4
V=27 sqrt(3) / 2
V=27/2 sqrt(3)

Which of the following equations could be used to solve the given equation?

9x + 26 + 7x - 17 = 2x + (-3x) + 5x

16x + 9 = 0
16x + 9 = 4x
16x + 11 = 4x

Answers

If we simplify like terms on left and right sides we gwt

16x + 9 = 4x

Its B

Answer: The correct option is (B) [tex]16x+9=4x.[/tex]

Step-by-step explanation: We are given to select the correct equation that could be used to solve the following equation :

[tex]9x+26+7x-17=2x+(-3x)+5x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the correct equation, we need to simplify the given equation (i).

From equation (i), we get

[tex]9x+26+7x-17=2x+(-3x)+5x\\\\\Rightarrow (9+7)x+(26-17)=2x-3x+5x\\\\\Rightarrow 16x+9=(2-3+5)x\\\\\Rightarrow 16x+9=4x.[/tex]

Thus, the required equation is [tex]16x+9=4x.[/tex]

Option (B) is CORRECT.

One of the angles of a parallelogram is equal to 40°. Find the rest of the angles.

Answers

angles a and b must add up to 180 degrees. So the angles are 40, 140, 40, 140

The angles of parallelogram are 40°, 140°, 40°, 140°.

What is parallelogram?

A parallelogram is a type of quadrilateral. It is a two-dimensional figure with four sides. The most important properties of a parallelogram are that the opposite sides are parallel and congruent and the opposite angles are also equal.

For the given situation,

One angle of parallelogram = 40°

Let the unknown angle be 'x'

The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.

⇒ [tex]40+x=180[/tex]

⇒ [tex]x=140[/tex]

The opposite interior angles are equal.

Hence we can conclude that the angles of parallelogram are 40°, 140°, 40°, 140°.

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neil tried to simplify an expression step by step 5^-6/5^-4

Answers

The simplified form of the given expression is 1/25.

The given expression is [tex]\frac{5^{-6} }{5^{-4} }[/tex].

We need to simplify the given expression.

What are exponents and how do solve exponents questions?

The exponent of a number shows how many times the number is multiplied by itself. The properties of exponents or laws of exponents are used to solve problems involving exponents. These properties are also considered major exponents rules to be followed while solving exponents.

Using quotient law [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex].

Now, [tex]\frac{5^{-6} }{5^{-4} }[/tex] can be written as [tex]\frac{5^{4} }{5^{6} }[/tex]

By using the quotient rule, we get [tex]\frac{5^{4} }{5^{6} }=5^{4-6}[/tex]

[tex]=5^{-2}=\frac{1}{5^{2}}[/tex]

=1/5×5=1/25

Therefore, the simplified form of the given expression is 1/25.

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Find the surface area of the equilateral triangular pyramid.

Answers

C is the correct answer

good luck

Answer:

i think the answer is C.

GOOD LUCK!!!

Assuming the cost of cement blocks is $75 per 1,000, how much will it cost for the blocks to build a wall 7ft. tall by 20 ft. long if the block is 6 inches thick and 10 blocks are needed for 1 cubic foot.

Answers

First, we are going to convert the thick of the block from inches to feet. To do that we are going to take advantage of the fact that 1 foot=12 inches to create a multiplier:
[tex]6in* \frac{1ft}{12in} =0.5ft[/tex]

Since the thickens of the wall will be equal to the thickness of each block, the thick of the all is 0.5 feet.
Now, to find the volume of the wall, we are going to use the formula:
[tex]V_{w}=hlt[/tex]
where
[tex]V_{w}[/tex] is the volume of the wall
[tex]h[/tex] is the height of the wall
[tex]l[/tex] is the length of the wall
[tex]t[/tex] is the thickness of the wall
We know for our problem that the wall is 7ft. tall by 20 ft. long, so [tex]h=7ft[/tex] and [tex]l=20ft[/tex]. We also know from our previous calculation that the thickness of the wall is 0.5ft, so [tex]t=0.5ft[/tex]. Lets replace those values in our formula:
[tex]V_{w}=hlt[/tex]
[tex]V_{w}=(7ft)(20ft)(0.5ft)=70ft^3[/tex]

Now we know that the volume of the wall is 70 cubic feet. We also know that 10 blocks are needed for 1 cubic foot, so to find the total numbers of blocks needed, we are going to multiply the volume of the wall by the number of blocks needed for 1 cubic foot:
[tex]TotalBlocks=70ft^3* \frac{10blocks}{1ft^3 } =700 blocks [/tex]

Finally, to find the total cost, we are going to multiply the number of blocks needed by the cost of 1000 blocks:
[tex]TotalCost=700blocks* \frac{75}{1000} =52.5[/tex]

We can conclude that the cost of the wall will be $52.5

Danielle ran 3 1/8 miles on Tuesday and 4 and 1/2 miles on Wednesday and 5 1/4 miles on Thursday how far did Danielle run all together this

Answers

well you would figure out a common denominator for all fractions.

3 1/8

4 1/2

5 1/4

the common denominator would be 8. so multiply all the fractions by the number that would give you 8 on the bottom of the fraction

1/8 x 1 = 1/8

1/2 x 4 = 4/8

1/4 x 2 = 2/8

now you would set up your problem

3 1/8 + 4 4/8 + 5 2/8

first add the fractions

1/8 + 4/8 + 2/8 = 7/8

then add the whole numbers

3 + 4 + 5 = 12

now put the number and fractions together and you have your answer

12 and 7/8

How do you find the inverse of y=2x-3

Answers

Subtract 3 from each side

y - 3 = 2x

Divide through by 2

y/2 - 3/2 = x

or x = y/2 - 3/2

Now simply switch labels: x↔y

y = x/2 - 3/2

A wise man once said, "500 reduced by 3 times my age is 200." What is his age?

Answers

The answer is: " 100 " .
_________________________________________________________

Explanation:
_________________________________________________________

Let "x" represent the numerical value of [the man's age].

500 - 3x = 200 ; Solve for "x" ;

Subtract "500" from each side of the equation:

500 - 3x - 500 = 200 - 500 ;

to get:

- 3x = -300 ;

Now, divide each side of the equation by "-3" ; to isolate "x" on one side of the equation; & to solve for "x" ;

- 3x / -3 = -300 / -3 ;

x = 100 .
_______________________________________________________
The answer is: " 100 " .
_______________________________________________________

What is the surface area of the cylinder in terms of pi? The diagram is not drawn to scale.

Answers

Surface Area = 2πr² + 2πrh

Surface Area = 2π(7)² + 2π(7)(15) = 308π in²²

Answer: 308π in²

The solution is, 308π in² is the surface area of the cylinder in terms of pi.

What is surface area?

Surface area is the amount of space covering the outside of a three-dimensional shape. The surface area of a solid object is a measure of the total area that the surface of the object occupies.

here, we have,

from the given diagram , we get,

the cylinder has,

radius = r = 7

height = h = 15

we know that,

Surface Area = 2πr² + 2πrh

so, we get,

r = 7

h = 15

substituting the values, we get,

Surface Area

= 2π(7)² + 2π(7)(15)

= 308π in²²

Answer: 308π in²

Hence, The solution is, 308π in² is the surface area of the cylinder in terms of pi.

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A sum of money is divided among peter paul and jane in ratio 13:12:7 calculate how much paul gets if amount peter gets more than jane is 78$

Answers

First we define variables:
x: Money Peter receives
y: Money Paul receives
z: Money Jane receives
We write the system of equations:
x / y = 13/12
x / z = 13/7
x = z + 78
Solving the system we have:
x = $ 169
y = 156 $
z = 91 $
Answer:
Paul gets 156 $

Two similar cones have volumes of 8pi and 64pi find the ratios of the radio

Answers

we have that
volume larger cone=64*pi unit³
volume smaller cone=8*pi unit³

we know that
volume larger cone=[scale factor]³*volume smaller cone
[scale factor]³=volume larger cone/volume smaller cone
[scale factor]³=64*pi/(8*pi)-----> 8
[scale factor]=∛8------> [scale factor]=2

Find the ratios of the radio
[radio larger cone/radio smaller cone] is equal to the scale factor
so
[radio larger cone/radio smaller cone]=2
or
[radio smaller cone/radio larger cone]=1/2

In spherical geometry, what is the term used for the shortest distance between two points?

Answers

The correct answer for the question shown above is: Geodesic.

The explanation of is shown below:
1. You have that ,by definition, the spherical geometry studies figures on the surface of the spheres.
2. And the termn known as "Geodesic" is define as the shortest distance between two points on the surface of a sphere or a curved surface.

Tracy solved the system of equations by making a substitution for x in the second equation.

What equation did she get as a result of that substitution?

x = –2y – 2
2x + 3y = –6

–2y – 2 = –6
–2y + 1 = –6
–4y – 2 + 3y = –6
–4y – 4 + 3y = –6

Answers

Tracy put (-2y-2) where x is in the second equation. This resulted in
2(-2y-2) +3y = -6
After eliminating parentheses, Tracy had
-4y -4 +3y = -6

The 4th selection is appropriate:
-4y - 4 + 3y = -6

Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? millimeters

Answers

Answer:

6 millimeters

Explanation:

The standard deviation is the square root of the variance.

Since the variance is 36, the standard deviation would be

√36 = 6

Answer:6

Step-by-step explanation:

What would “x” be ?

Thanks you

Answers

cos x = 16/21

So x would equal to 40.37 degrees

Step-by-step explanation:

[tex]cos \: x = \frac{a}{h} \\ cos \: x = \frac{16}{21} = 0.76 \\ cos \: x = 40.36degrees[/tex]

Suppose you want to build a rectangular sandbox where the width is 5 feet less than the length and the diagonal is 5 feet longer than the length. what are the dimensions of the sandbox?

Answers

Let L = length
W = L - 5 ←5 feet less than (reverse order - ) the length (L)
D = L + 5
These 3 lengths form a right triangle with D being the hypotenuse, c.
Using the Pythagorean Theorem, a² + b² = c²
L² + (L - 5)² = (L + 5)²
L² + L² - 10L + 25 = L² + 10L + 25
L² - 20L = 0
L = 0 (can't use this answer) or L = 20 (this is a usable answer)
Dimensions of the sandbox 20 ft by 15 ft
Length = 20 ft
Width = 15 ft
Diagonal = 25 ft

triangle ABC is similar to Triangle XYZ. AB=5x+25, BC=7x+44, YZ=29, XZ=45, XY=14 Find x

Answers

Answer: The fraction -109/47 (see note below)

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

Explanation:

Triangle ABC is similar to Triangle XYZ. This means that
AB/BC = XY/YZ
is one proportion we can form

Plug in the given expressions and then isolate x
AB/BC = XY/YZ
(5x+25)/(7x+44) = 14/29
29(5x+25) = 14(7x+44)
29(5x)+29(25) = 14(7x)+14(44)
145x+725 = 98x+616
145x-98x = 616-725
47x = -109
x = -109/47

note: its possible your teacher made a typo since we got a negative fraction here. I would ask your teacher to double check.

WILL MARK BRAINLIEST!!

Given: x - 5 > -10.

Choose the solution set.

{x | x R, x < -15}

{x | x R, x > -5}

{x | x R, x < 5}

{x | x R, x > 15}

Answers

Answer:

{x | x R, x > −5}

Step-by-step explanation:

x - 5 > -10

+ 5 + 5

__________

x > −5

I am joyous to assist you anytime.

What is the value of x?

132√ cm

526√3 cm

262√ cm

263√ cm

Answers

30 60 90 right triangle on the right
ratio of short leg: long leg :hypo = a: a√3: 2a
So if hypo = 52 cm then short leg = 52/2 = 26 cm

The other right triangle on the left is 45 45 90 because it has 2 equal sides
ratio of leg: leg :hypo = a: a: a√2

the leg = 26 cm
so hypo x = 26√2

Answer
26√2 cm

[tex]\huge \boxed{\sf 26\sqrt{2}\ cm } \\\\\\\sf Using\ trigonometric\ functions \\\\\displaystyle cos \theta = \frac{adj}{hyp} \\\\cos(60)=\frac{adj}{52} \\\\adj=cos(60) \times 52=26 \\\\Using\ the\ Pythagorean\ theorem \\\\x=\sqrt{26^2+26^2} =26\sqrt{2}[/tex]

To find the length ab of a small lake, a surrounding veyor measured angle acb to 96, ac to be 91 yards, and bc to be 71 yards. what is the approximate length of the lake?

Answers

Using the law of Cosins that states: For any triangle, a, b and c are sides and C is the angle opposite side c
c² = a² + b² − 2ab cos(C)

Applying this in our problem, we get:
AB²= 71²+91²- 2x91x71 cos96
AB²=14627.7 yard²
AB=121 yard

The pyramid shown below has a square base, a height of 7, and a volume of 84. what is the length of the side of the base?

Answers

Volume of a pyramid is (length * width * height) / 3

So we plug in the given information and solve. Let x = length and width since it's a square their measurements are the same.

84 = (x * x * 7) or 84 = 7x²

Divide both sides by 7 to isolate the squared variable.

x² = 12

Now square root both sides to isolate the variable

x = √12 which simplifies to x = 2√3

The measurements for the length and width of the base are 2√3 units or approximately 3.464 units.

The length of the side of the base is 6 units.

What is the volume of the pyramid?

The volume of the pyramid is;

[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base[/tex]

The pyramid shown below has a square base, a height of 7, and a volume of 84.

Substitute all the values in the formula

[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base\\\\\rm84 =\dfrac{1}{3}\times height \times 7\\\\Height = \dfrac{84\times 3}{7}\\\\ Height = \dfrac{252}{7}\\\\Height =36[/tex]

The length of the side of the base is;

[tex]\rm Side\ length^2=height\\\\ Side\ length^2=36\\\\Side\ length^2=6^2\\\\Side\ length=6[/tex]

Hence, the length of the side of the base is 6 units.

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HIGH AMOUNT OF POINTS! MATH QUESTION! IF YOU DON'T KNOW IT, DON'T ANSWER!

Answers

Solving the equations by graphing requires plotting the given functions.
y=x^2-3
x-y=1
thus the plot will be as shown in the picture. The solutions are:
(-2,-1) and (2,1)

classify 4x^5+2x^4-5x^3+12 by number of terms

Answers

That is 4 terms long.

The polynomial 4x⁵ + 2x⁴ - 5x³ + 13 has a degree of five and a quadrinomial (four terms).

What is a polynomial?

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials can be classified based on degree as linear, quadratic, cubic and so on. Polynomials can also be classified based on number of terms.

The polynomial 4x⁵ + 2x⁴ - 5x³ + 13 has a degree of five and a quadrinomial (four terms).

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In the figure, what is the value of x?

Answers

1. C 2. B 3. D 4. B 5. C

Answer:x=90 °

Step-by-step explanation:

In any circle the exterior angle formed is half of the major arc - minor arc .

Angle formed by tangents or secants = [tex]\frac{1}{2}(Major arc - minor arc )[/tex]

The sum of measure of arcs inany circle is 360°.

Minor arc is given as x°.So Major arc = 360-x.

Substituting the given values in the formula :

[tex]x=\frac{1}{2}(360-x-x)[/tex]

[tex]x=\frac{1}{2}(360-2x)[/tex]

x=180-x

Adding x both sides we have:

2x=180.

Dividing both sides by 2.x= 90.

The domain of this graph is {x | x≥−2}.

True.
False.

Answers

The correct answer is: [B]: " True ".
_____________________________________________________
Note: From visual inspecton of the graph shown — [Note: all images attached refer to the same graph.] :

→ We can see that when "x = -2" ; there is only one value for "y" ; and then the "line" of the graph stops for any coordinate corresponding to any "x-value" LESS THAN "-2" ;

→ and that there are corresponding "y-coordinates" corresponding to any "x-value that is equal to "-2" and "GREAT THAN "-2" .
_________________________________________________________

The domain of the graph is {x|x>= - 2}

So the answer is TRUE

Find the quotient. Write your answer USING A DECIMAL and ROUNF TO THE NEAREST HUNDREDTH.

8,426÷82

Answers

This is my work hope it is correct. Do not add 0 at the end. Hope this helps!

the quotient is 102.76

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