1. Main Show Tank Calculation:
The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number.
2. Holding Tank Calculations:
The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 30 feet and the height of tank #2 is 110 feet?
3. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made ⅛ of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
4. Using the information from #4, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answers
So the volume of the tank would be = (1/4)(4/3)π(60)³
= (1/3)π(60)³
= 72,000π ft³
2. The holding tanks are half cylinders. Combined they make a whole cylinder. volume of a cylinder is area of circle times length.
volume tank 1&2 = (110)π(30)²
= 99,000π ft³
3. radius of main show tank goes from 60 real tank to 60/8 = 7.5 mock-up tank
= (1/3)π(7.5)³
= 140.625 ft³
4. 72,000/140.625 * 100 = 51,200%
essentially 8³ * 100
very high since you are looking at % real tank to model tank
Related Questions
find the x and y intercepts -3x-6y=12
Answers
Answer:
x-intercept: -4y-intercept -2Step-by-step explanation:
The x-intercept is found where the graph crosses the x-axis, at y=0. Substituting that into the equation and solving for x, we get ...
-3x = 12
x = 12/-3 = -4 . . . . . x-intercept = -4
The y-intercept is found where the graph crosses the y-axis, at x=0. Substituting that into the equation and solving for y, we get ...
-6y = 12
y = 12/-6 = -2 . . . . . y-intercept = -2
_____
A graphing calculator confirms these values.
When the federal reserve wants more money to be printed, which agency will be in charge of printing it?
Answers
Answer:
The U.S. Treasury.
Step-by-step explanation:
Kendall is stacking boxes that are 7.5inches tall. Explain how to find the height (in inches)
Answers
Final answer:
To find the height of stacked boxes, multiply the height of one box (7.5 inches) by the total number of boxes stacked.
Explanation:
Kendall is stacking boxes that are each 7.5 inches tall. To find the total height in inches of the stacked boxes, you would need to multiply the height of one box by the total number of boxes stacked. For example, if Kendall stacks 10 boxes, the calculation would be 7.5 inches x 10, which equals 75 inches. Therefore, the total height of the 10 stacked boxes would be 75 inches.
Use the information about sports in the photo to explain how inequalities can be used to describe school sports. Include an inequality describing the number of schools needed to add girls’ track and field so that the number is greater than the number of schools currently participating in girls’ basketball.
Answers
Simplify this problem: X3 / X.
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It would be x².
The question is x³/x.
X with no power is x to the power of one.
When dividing powers you subtract them.
3 - 1 = 2,
Therefore, making your answer x²
Hope This Helps You!
Good Luck :)
- Hannah ❤
6 ( y + 8 ) = 3 ( 2y - 7 )
Answers
6 ( y + 8 ) = 3 ( 2y - 7 )
6y + 48 = 6y - 21
-48 -48
6y = 6y - 27
+27 +27
33y÷33 = 6y÷33
y=2/11 or 0.18
Hope this helps!
Joel earns $1,700 per month. If he spends $425 on rent each month, what percent of his income does he spend on rent? A. 20% B. 331/3% C. 40% D. 25%
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425 / 1700 = 0.25
0.25 x 100 = 25.
25% is your answer, letter D.
Solomon is taking out a 5,320 two year loan with an APR of 10.25%. What will the finance charge be for this loan to the nearest dollar?
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What could the answer be?
Answers
Which statements are true the ordered pair (1, 2) and the system of equations?
y=−2x+4
7x−2y=3
Select each correct answer.
When (1, 2) is substituted into the first equation, the equation is true.
When (1, 2) is substituted into the first equation, the equation is false.
When (1, 2) is substituted into the second equation, the equation is true.
When (1, 2) is substituted into the second equation, the equation is false.
The ordered pair (1, 2) is not a solution to the system of linear equations.
The ordered pair (1, 2) is a solution to the system of linear equations.
Answers
(1,2)...x = 1 and y = 2
y = -2x + 4 7x - 2y = 3
2 = -2(1) + 4 7(1) - 2(2) = 3
2 = -2 + 4 7 - 4 = 3
2 = 2 (correct) 3 = 3 (correct)
when (1,2) is subbed into the first equation, the equation is true
when (1,2) is subbed into the 2nd equation, the equation is true
the ordered pair (1,2) is a solution to the system of equations...and it is a solution to the system because it satisfies both equations...if it would have only satisfied one of them, it would not be a solution to the system of equations
Anna has 10 to the 2nd power quarters. Jazmin has 10 to the second power dimes Who has more money, Anna or Jasmine? How much more? Explain
Answers
A quarter is 25 cents, while a dime is only 10 cents. Since they both have the same amounts of coins, the one with 100 quarters has more money, so Anna has more money than Jasmine.
Now, we need to figure put by how much! 100 quarters is one hundred 25 cent coins. 100*25 = 2500. That is 25 dollars. Whereas, Jasmine has one hundred times 10 cents, which is 1000 cents. This is 10 dollars.
So, Anna has 15 more dollars than Jasmine.
This question is based on the concept of logical reasoning.Therefore,they both have the same amounts of coins, the one with 100 quarters has more money.Thus, Anna has more money than Jasmine.
Given:
Anna has 10 to the 2nd power quarters. Jazmin has 10 to the second power dimes.
We need to calculate the who has more money, Anna or Jasmine.
According to the question,
Anna has 10 to the 2nd power quarters.
In mathematically expressed as,
[tex]\bold{10^2 = 100}[/tex] quarters
Now, Jazmin has 10 to the second power dimes.
In mathematically expressed as,
[tex]\bold{10^2 = 100}[/tex] dimes
So,they both have 100 coins. But, we know that quarter is 25 cents, while a dime is only 10 cents.
Anna has 100 quarters = [tex]\bold{100 \times 25 = 2500}[/tex]. That is 25 dollars.
Jasmine has 100 dimes = [tex]\bold{100 \times 10 = 1000}[/tex]. This is 10 dollars.
Therefore,they both have the same amounts of coins, the one with 100 quarters has more money.Thus, Anna has more money than Jasmine.
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Solve. 5t<-15
A) t > 3
B) t < 3
C) t > -3
D) t < -3
Answers
Hope this helps!!
When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [(1 × 102) + (2 × 101) + (3 × 100)] + [(4 × 102) + (2 × 101) + (3 × 100)] make the operation more like a polynomial addition problem?
Answers
When you add polynomials, you can only combine like terms.
When you add expanded numbers, you can only combine like powers of 10.
123 + 423 =
= (100 + 20 + 3) + (400 + 20 + 3)
= (1 * 10^2 + 2 * 10^1 + 3 * 10^0) + (4 * 10^2 + 2 * 10^1 + 3 * 10^0)
= (1 * 10^2 + 4 * 10^2) + (2 * 10^1 + 2 * 10^1) + (3 * 10^0 + 3 * 10^0)
= 5 * 10^2 + 4 * 10^1 + 6 * 10^0
= 500 + 40 + 6
= 546
Rules for Plotting Points:
1) Start at the origin: _________
2) If your x-value is ___________, move right; if it is ___________, move left;
if it is _____, don’t move.
3) If your y-value is ___________, move up; if it is ___________, move down;
if it is _____, don’t move.
Answers
2. Positive, Negative, 0
3. Positive, Negative, 0
I hope this helps.
2) positive, negative, 0
3) positive, negative, 0
The coordinates of point D are (7, 4) and the coordinates of point E are (1, −3) .
What is the slope of the line that is perpendicular to DE¯¯¯¯¯?
Enter your answer as a simplified fraction in the box.
Answers
[tex]- \frac{6}{7} [/tex]
EXPLANATION
The given points are
[tex](x_1,y_1)=(7,4)[/tex]
and
[tex](x_2,y_2)=(1,-3)[/tex]
The formula for finding the slope is given by,
[tex]slope = \frac{y_1-y_1}{x_1-x_1} [/tex]
We substitute the points to obtain,
[tex]slope = \frac{ - 3 - 4}{1 - 7} = \frac{7}{6} [/tex]
The slope of the line that is perpendicular to DE is the negative reciprocal of
[tex]\frac{7}{6} [/tex]
Thus, the line perpendicular to DE has slope,
[tex] \frac{ - 1}{ \frac{ 7}{6} } =-\frac{6}{7} [/tex]
The solution to -5m = -20 is negative.
True or false
Answers
False
a negative number times a negative number would have a positive answer
Given: M is the midpoint of LN; LM =8 prove:LN=16
Answers
If LM = 8, then MN = 8.
Adding both together, you would get 16 for the length of LN.
The proof of LN= 16 is shown below:
What is midpoint?The midpoint formula is applied when one is required to find the exact center point between two defined points. So for a line segment, use this formula to calculate the point that bisects a line segment defined by the two points.
Given:
LM= 8
and M is the midpoint of LN
So, the line LN will be break into two equal parts LM and MN
then we can write
LM= MN= 8
Now,
LN= LM+ MN
LN= 8+8
L=16
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HELP PLEASE ASAP!
BRAINLIESTTTTTTTTTTTTT
Answers
Solve the equation. How old is Sam?
Sam's age doubled plus 5 is the same as Sam's age tripled minus 1.
Question 5 options:
Sam is 6yrs old.
Sam is 4 yrs old.
Sam is 12 yrs old.
Sam is 5 yrs old.
\\
@Mochimin
Answers
6x3=18-1=17
Of the birds in Monica's pet shop, 1/5 are pigeons. Of the pigeons, 1/3 are white. Look at each expression. Can it be used to find the fraction of birds in Monica's pet shop that are white pigeons?
Answers
1/15.
The expression that can be used to find the fraction of birds in Monica's pet shop that are white pigeons is:
1/5 x 1/3 = 1/15
This calculation is derived by multiplying the fraction of pigeons in the pet shop (1/5) by the fraction of white pigeons among pigeons (1/3).
The length of a rectangle is 4.2 cm more than 2 times the width. If the perimeter of the rectangle is 42.6 cm, what are its dimensions?
Answers
42.6 = 6w + 8.4
34.2 = 6w
w = 5.7
L= 15.6
You have a rectangular vegetable garden in your backyard that measures 15 feet by 10 feet. You want to double the area of the garden by adding the same distance x to the length and width of the garden. Find the value of x and the new dimensions of the garden.
Answers
To double the area of the rectangular vegetable garden, we need to add the same distance, x, to the length and width. The value of x is 10 feet, and the new dimensions of the garden are 25 feet by 20 feet.
Explanation:To double the area of the garden, we need to add the same distance, x, to both the length and width of the garden. The original dimensions of the garden are 15 feet by 10 feet, with an area of 150 square feet. To double the area, we set up the equation 2(15+x)(10+x) = 2(15)(10). Solving this equation gives us the value of x and the new dimensions of the garden.
Expanding the equation, we have 30x + x² + 300 = 300. This simplifies to x² + 30x - 300 = 0. Factoring this quadratic equation, we get (x - 10)(x + 30) = 0. So x = -30 or x = 10. We discard the negative value since distance cannot be negative, so x = 10 feet.
The new dimensions of the garden are 15+10 = 25 feet and 10+10 = 20 feet.
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Factor the four-term polynomial.
xz + x + yz + y
A. (z - y)(x + 1)
B.(x - y)(z + 1)
C.(x + y)(z + 1)
Answers
(xz+x) + (yz+y)
x(z+1) + y(z+1)
factor out (z+1)
= (z+1)(x+y)
= solution C.
PLEASE HELP ME, I NEED IT.
Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 < 33?
A. a number line with open circles at negative 2 and 5 with shading in between.
B. number line with open dot at negative 2 with shading to the left and an open dot at 5 with shading to the right
C. number line with shading everywhere.
D. number line with open dot at negative 2 and a closed dot at 5 with shading in between.
Answers
The answer is B :)
I hope this helped
what are the steps for using a compass and a straightedge to construct the bisector of
Answers
ANSWER:
How to construct a Line Segment Bisector AND a Right Angle
using just a compass and a straightedge.
STEP-BY-STEP EXPLANATION:
Steps:
1)Place the compass at one end of line segment.
2)Adjust the compass to slightly longer than half the line segment length
3)Draw arcs above and below the line.
4)Keeping the same compass width, draw arcs from other end of line.
5)Place ruler where the arcs cross, and draw the line segment.
The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −7 0 −1 1 5 g(x) g(x) = 5x − 4 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
Answers
Rewriting the table for f(x):
x -1 0 1
f(x) -7 -1 5
Notice that for every increase of one unit in 'x', there are an increase 6 units on f(x). Hence, the gradient of the slope of f(x) is 6.
g(x) = 5x - 4 ⇒ This function follows the general form of the straight line equation, y = mx + c, where 'm' is the gradient and 'c' is the y-intercept.
Hence, the gradient of the slope of g(x) is 5.
The slope of f(x) is steeper than the slope of g(x).
---------------------------------------------------------------------------------------------------------------
Question B:
The y-intercept is the value of y where a straight line crosses the y-axis (or when x is zero).
From the table of f(x), the y-intercept is -1 (this is the value of 'y' when 'x' is zero)
From the given function g(x) = 5x - 4, the y-intercept is -4.
f(x) has a greater y-intercept.
A rectangle has one side on the xx-axis and two vertices on the curve y=74+x2. y=74+x2. find the vertices of the rectangle with maximum area.
Answers
We find the vertices of the rectangle with maximum area as follows:
Because of the symmetry of the given curve, the base of the retangle is 2x and the height of the rectangle is y.
Thus, the area of the required rectangle is 2xy where [tex]y= \frac{7}{4+x^2} [/tex]
Thus, [tex]Area=\frac{14x}{4+x^2}[/tex]
For maximum area, we find value of x for which the derivative of the function for the area is equal to zero.
The derivative of the function for the area is given by:
[tex](Area)'= \frac{14(4-x^2)}{(4+x^2)^2} =0 \\ \\ \Rightarrow4-x^2=0 \\ \\ \Rightarrow x^2=4 \\ \\ \Rightarrow x=\sqrt{4}=2[/tex]
Thus, the area is maximum when x = -2 and x = 2
When x = -2,
[tex]y= \frac{7}{4+(-2)^2}= \frac{7}{4+4} = \frac{7}{8} [/tex]
Similarly, when x = 2,
[tex]y= \frac{7}{4+(2)^2}= \frac{7}{4+4} = \frac{7}{8} [/tex]
Therefore, the required vertices are: [tex](-2,0),\ \left(-2, \frac{7}{8} \right), \ \left(2, \frac{7}{8}\right), \ (2, 0)[/tex]
The rectangle with maximum area does not exist as the curve y = 74 + x^2 does not intersect the x-axis.
Explanation:To find the vertices of the rectangle with maximum area, we need to find the points of intersection between the curve y = 74 + x^2 and the x-axis.
Setting y = 0, we can solve the equation 74 + x^2 = 0 to find the x-coordinates of the vertices.
Since the curve is a parabola facing upwards, there are no points of intersection with the x-axis.
Therefore, the rectangle does not exist.
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What is the parents function of f(x)=3x-5
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
now, that said, A and D are just transformations of it.
[tex]\bf f(x)=\stackrel{A}{3}x\stackrel{D}{-5}\qquad \qquad \stackrel{parent~function}{f(x)=x}[/tex]
jasmine has $15 dollars and save $2.50 every month . radha has $0 and save $3.50 every month. jasmines savings after x months can be represented by the function f(x)=2.5x+15. radahs savings after x months can be represented by the function g(x)=3.5x after how any moths will they both have the same amount in savings? find the value of x which f(x)=g(x)
Answers
2.5x+15 = 3.5x
subtract 2.5x from each side
15 = x
they will have the same amount after 15 months
The linear pair postulate states that if two angles form a linear pair, then they are __________ angles.
Answers
________________________________________________
Answer:
supplementary
Step-by-step explanation: