An 80-foot diameter reservoir currently holds 825,000 gallons of water. What is the depth of water in this reservoir, measured in feet?
Answer:
Step-by-step explanation:
d=80 ft
r=80/2=40 ft
volume of cylinder=π r²h,where h is height or depth of cylinder.
π×40²×h=825,000
πh=825,000/40²=4125/8
h=4125/(8π)≈164.1285≈164.13 ft
The depth of water in the reservoir is approximately 21.92 feet.
To find the depth of water in the reservoir, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Where:
Volume is the total volume of water in the reservoir (in gallons),
π (pi) is a mathematical constant approximately equal to 3.14159,
r is the radius of the reservoir (half of the diameter), and
h is the depth of water in the reservoir (in feet).
Given:
Diameter = 80 feet
Volume = 825,000 gallons
We first need to calculate the radius (r) of the reservoir:
Radius (r) = Diameter / 2 = 80 feet / 2 = 40 feet
Now, we can convert the volume from gallons to cubic feet because we need the measurements to b²e in consistent units:
1 gallon ≈ 0.13368 cubic feet
Volume (in cubic feet) = 825,000 gallons * 0.13368 cubic feet/gallon ≈ 110,127 cubic feet
Now, we can find the depth (h) using the formula:
110,127 cubic feet = π * (40 feet)² * h
Solving for h:
h = 110,127 cubic feet / (π * 40 feet)² ≈ 110,127 cubic feet / 5026.5482 square feet ≈ 21.92 feet
Therefore, the depth of water in the reservoir is approximately 21.92 feet.
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Kevin and Randy Muise have a jar containing 81 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $10.45. How many of each type of coin do they have?
Answer:
Number of nickels is 49 and the number of quarters is 32
Step-by-step explanation:
Factor the expression.
25a + 15 =
Geno invested $2,000 into an account that earns 8.5% interest compounded annually. How
much interest will Geno earn after 3 years?
HELP
what’s the area
4x+2
6x
Who can give me this answer
Determine the cubic function obtained from the parent function y=x^3 after each sequence of transformations.
a reflection across the x-axis; a translation 1 unit up; and a translation 2 units right
Answer:
-(y+3)=(x-2)^3
Step-by-step explanation:
Transformed function B is f' ( x ) = - ( x - 2 )³ + 1
The transformed function is given by y = - ( x - 2 )³ + 1
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be denoted as A
Now , the value of A is
y = x³
Let the transformed function be denoted as B
Now , the value of B is calculated by
Step 1 :
A reflection across the x-axis
So , the function changes to g ( x ) = -x³
Step 2 :
A translation 1 unit up
Up by d units: y = f(x) + d
So , the function changes to h ( x ) = -x³ + 1
Step 3 :
A translation of 2 units right
Right shift by c units: y=f(x-c)
So , the function changes to f' ( x ) = - ( x - 2 )³ + 1
Therefore , the value of B is f' ( x ) = - ( x - 2 )³ + 1
Hence , the transformed function B is f' ( x ) = - ( x - 2 )³ + 1
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PLEASE HELP (will give brainiest) (please dont steal it would mean Alot)
Answer:
87, if it were 45 degrees, it would be 90, closest to 90 is 87
Answer:
87 feet
Step-by-step explanation:
We have an angle that's 44 degrees and we know that Susan is 90 feet from the base of the tree. We need to know the height of the tree, which is the value opposite from the angle we know.
Use tangent to find height.
tan (44) = x / 90 then multiply both sides by 90
x = tan (44) * 90 evaluate tan(44) and substitute into the equation
x = 86.911
round to nearest whole foot: 87 feet
Emily has 5 packs of gum. Each pack has 50 pieces of gum. If Emily eats 9 pieces of gum, how many pieces of gum are left in all? Emily that’s a lot of gum...
Annisa wrote an expression that represents
“the product of 6.2 and the sum of 3c and 8.”
What are the factors of the expression?
Answer:
“the product of 6.2 and the sum of 3c and 8'' will be algebraically represented as:
⇒ (6.2) (3c + 8)
We know that the numbers that we multiply are the factors of the product.
Here, (6.2) and (3c+8) are the factors of the expression.
Step-by-step explanation:
Let us breakdown and translate the word expression into an algebraic expression.
The sum of 3c and 8 is algebraically represented as:
⇒ 3c + 8
Thus, “the product of 6.2 and the sum of 3c and 8'' will be algebraically represented as:
⇒ (6.2) (3c + 8)
We know that the numbers that we multiply are the factors of the product.
Here, (6.2) and (3c+8) are the factors of the expression.
The bakery sells each cake for $120. Last year, the bakery sold 98 cakes. How much money did the bakery earn selling cakes?
Answer:
The bakery earned $11760 by selling cakes
Step-by-step explanation:
Cost of 1 cake = $120
Bakery sold cakes = 98
We need to find how much money did the bakery earn selling cakes?
We are given cost of 1 cake, if we multiply cost of 1 cake by 98 we can get cost of 98 cakes. Solving:
Cost of 1 cake = 120
Cost of 98 cakes = 120 x 98
= 11760
So, The bakery earned $11760 by selling cakes
GUYS PLEASE HELPPPP (and dont take the points pls)
Answer:
12.9
Step-by-step explanation:
Let's understand this,
Angle of elevation is 30° and the is standing perpendicularly, we have to find the distance from the branch to the mouse.
According to question,
cosine or cos thita = Base/Hypotenuse
Cos 30° = 15/H
0.86 = 15/H
H = 0.86 × 15
H = 12.9 (Round off 13)
Hope it helps!
A
woman has
ten
skirts and
four
blouses. Assuming that they all match, how many different
skirt-and-
blouse combinations can
she wear?
Question content area bottom
Part 1
The
woman can wear
enter your response here
different
skirt-and-
blouse combinations.
can someone pls answer this? (the dots at the beginning of each sentence is a A,B,C type of thing)
Answer: dude take a deep breath and answer the question it’s very easy
Step-by-step explanation:
What is the area of a rectangle with side lenghts of 5/12 foot and 2/3 foot
Answer:
0.277 ft^2
Step-by-step explanation:
5/12 * 2/3 = 0.277
Answer:
5/18
Step-by-step explanation:
5/12 * 2/3 = 5/6 * 1/3 = 5/18
(WILL MARK BRAINLIEST) answer the question in image below please follow the directions on the paper about answer as improper fraction in simplest form, Many thanks!
Answer:
43/24
Step-by-step explanation:
The solving steps are as follows:
rearrange the fractionsthen figure out the LCM of the denominator , that is 24 in this casedivide 24 by the the denominator of the first fraction and multiply the result with the numerator. Follow the same process as (3) for the latter fractionSubstract the result of (4) from (3) And we're done!![tex] - \dfrac{3}{8} + \dfrac{13}{6} \\ = \dfrac{13}{6} - \dfrac{3}{8} \\ = \dfrac{13 \times 4 - 3 \times 3}{24} \\ = \dfrac{52-9}{24} \\ = \boxed{\frac{43}{24} }[/tex]
Answer:
43/24
Step-by-step explanation:
Fraction addition: First find the LCM of the denominators 8 and 6.Using the LCM find equivalent fractions.Now, the denominators are same and so add the numerators.Simplify.LCM of 6 and 8 = 24
[tex]\sf \dfrac{-3}{8}=\dfrac{-3*3}{8*3}=\dfrac{-9}{24}\\\\\\\dfrac{13}{6}=\dfrac{13*4}{6*4}=\dfrac{52}{24}\\\\\\\dfrac{-3}{8}+\dfrac{13}{6}=\dfrac{-9}{24}+\dfrac{52}{24}[/tex]
[tex]\sf = \dfrac{-9+52}{24}\\\\= \dfrac{43}{24}\\\\[/tex]
A 16 oz bottle of a new soda costs $3.59. What is the unit rate, rounded to the nearest tenth of a cent?
The unit rate is __ cents per oz.
The unit rate is 22.5 cents per oz .
The unit rate of any quantity is calculated by dividing (total cost) with (total units purchased).
For Example : If 12 bananas cost $120 then 1 banana will cost 120/12=$10.
In the given question
16oz bottle costs $3.59.
As we have to find the unit rate in cents per oz , we first convert $3.59 to cents.
We know that
$1=100cents
$3.59=100*3.59
=359cents
So the price of 16 oz bottle = 359 cents
Unit rate = (total price ) / (units purchased)
Substituting the total price as 359 cents and units purchased as 16oz.
Unit rate = 359/16
=22.4375
≅22.5
Therefore , the unit rate is 22.5 cents per oz.
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please help i need the answer asap
Answer:
thanks for the free points! anways but i think it s c
Step-by-step explanation:
its c
Chad plans to spin the spinner below 40 times. Predict and explain the number of times the spinner will land on 3.
Answer:B
Step-by-step explanation:2/8*40=10
The perimeter of a rectangular garden is 294 feet. If the length of the garden is81 feet, what is its width?
Step-by-step explanation:
hope this helps you out some
Max has $17 in a fund he is creating to save for a bike. He adds $6 per week of his babysitting
earnings to the fund. If his weekly fund balance is represented by an arithmetic sequence, find
the 27th term.
The 27th term is $173.
In an arithmetic progression the difference between the two consecutive terms is same.
Here it is given that the first term of the AP which is represented by a is $17.
And Max adds $6 after every week in his fund so the common difference d is $6.
We know the general expression to find the nth term of an AP is
= a+(n-1)d
Here we have to find the 27th term. so the value of n will be 27.
Now the 27th term of the AP = 17+(27-1)6
= 17+156
= $ 173
The balance in the fund after 27th week will be $173.
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Help plz Translate this sentence into an equation.
The product of Jenny's savings and 2 is 36.
Use the variableſ to represent Jenny's savings.
Answer:
2j = 36
Step-by-step explanation:
First, look for keywords.
"Product" means you multiply, and when you multiply a number by a variable you set it up by putting them together as demonstrated. 36 is the product so it's your total.
Alexa is making a recipe that requires 1 cup of water and 4 cups of flour. Which of the following combinations shows the same ratio of water to flour?
A. 2 cups of water to 3 cups of water
B. 2 cups of water to 4 cups of flour
C. 2 cups of water to 8 cups of flour
D. 3 cups of water to 6 cups of flour
Answer: c
Step-by-step explanation: 1:4 is 4 times the flour to water and 2:8 is also 4 times the flour
To determine the number of trout in a lake, a conservationist catches 94 trout, tags them and throws them back into the lake. Later, 30 trout are caught; 10 of them are tagged. How many trout would the conservationist expect to be in the lake?
Find the value of each variable.
A=?
B=?
C=?
Answer:
a:3.5
b:0.2
c:.3
Step-by-step explanation:
Solve the problem below
8 ÷ 2(2+2)=
Answer: 16
Step-by-step explanation:
do the parentheses first.
8 / 2 x 4
then calculate.
4 x 4 = 16
Can you please help me with this math problem question five
Answer:
Both calculated the slope as 2/9
Step-by-step explanation:
The area of the rectangle is
(18x - 12) square inches.
Write an expression that represents the
length of the rectangle (in inches).
Answer:
L = 3x - 2
P = 6x - 10
Step-by-step explanation:
Area = length * width
A = l*w
so if the width is 6 inches we can say w = 6
and we can say that l = to the length of the rectangle
if we substitute this:
(18x - 12) = l * 6
we get the answer l = 3x - 2 since we divide both sides by 6.
the expression for length of the rectangle is -> l = 3x - 2
for the perimeter:
P = 2(l + w)
if we substitute this:
P = 2(3x - 2) + 6
distributive property:
P = 2(3x) - 2(2) + 6
then would be:
P = 6x - 4 + 6
(combine like terms) -> P = 6x - (4 + 6)
then you would get: P = 6x - 10
which can also be writtern as -> P = 6x + (-10)
but this is not simplified so you would just write it as 6x - 10
Hope this helps, and hope this was the answer you were looking for. Thank you. Sorry if this does not help
SOMEONE HELPPP I CANT DO IT
Answer:
???????
Step-by-step explanation:
what values of a,b,c make this equation true? (2x-5)(x+2)+(ax^2+bx+c)=6x^2-4x-7
Answer:
A - a = 4, b = -3, c = 3
Step-by-step explanation:
When you substitute in a, b, and c you get
(2x - 5) (x + 2) + (4x^2 + -3x + 3)
collect like terms
(2x)(x) + (2x)(2) + (−5)(x) + (−5)(2) + 4x^2 + −3x + 3
combine like terms
2x^2 + 4x + −5x + −10 + 4x^2 + −3x + 3
(2x^2 + 4x^2) + (4x + −5x + −3x) + (−10 + 3)
6x^2 + −4x + −7
6x^2 + −4x −7