Answer:
The deep of the sand will be 3.5 feet
Step-by-step explanation:
step 1
Find out the area of the court plus a 10-foot boundary around the court for safety
[tex]A=(30+10+10)(60+10+10)\\A=(50)(80)\\A=4,000\ ft^2[/tex]
step 2
Find the deep of the sand
we know that
The volume of the sand is equal to
[tex]V=Ah[/tex]
where
A is the area of the base
h is the height or deep of the sand
substitute the given values
[tex]14,000=(4,000)h[/tex]
Solve for h
[tex]h=14,000/4,000=3.5\ ft[/tex]
Jerry's indoor beach volleyball court, including a 10-foot boundary, would have an area of 4,000 square feet, and with 14,000 cubic feet of sand, it would result in the sand being 3.5 feet deep.
Explanation:Since Jerry wants to build an indoor beach volleyball court with a 10-foot boundary around it and has ordered 14,000 cubic feet of sand, we need to calculate the volume of the sand to determine how deep it will be when spread evenly over the entire area, including the boundary. The dimensions of the volleyball court are 30 feet by 60 feet, and adding a 10-foot boundary around it increases each dimension by 20 feet (10 feet on each side), resulting in a total area dimension of 50 feet by 80 feet.
To calculate the depth of the sand, we first calculate the area of the court including the boundary: Area = length × width = 50 feet × 80 feet = 4,000 square feet. Next, we divide the total amount of sand by the area to find the depth: Depth = volume / area = 14,000 cubic feet / 4,000 square feet = 3.5 feet deep. Therefore, if Jerry uses all the sand, it will be 3.5 feet deep.
Find the pattern, then write the next two numbers.
0, 2, 6, 12, 20,
Answer:
30, 42
Step-by-step explanation:
You add 2 to the additional 2 you started with
0+2=2
2+(2x2)=6
6+(2x3)=12
The required next two-term of the sequence is 30 and 42.
Given that,
To determine the pattern and next two-term of numbers 0, 2, 6, 12, 20.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The given sequence is,
0, 2, 6, 12, 20,
a0 = 0,
a1 = 2
nth term an = a(n - 1) + 2(n - 1)
For 6th term
n = 6
6th term = a(6 - 1) + 2(6 - 1)
a6 = a5 + 10
a6 = 20 + 10
a6 = 30
7th term,
an = a(n -1) + 2 (n - 1)
a7 = a6 + 2*6
a7 = 30 + 12
a7 = 42
Thus, the required next two-term of the sequence is 30 and 42.
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11. The perimeter of a rectangle is 60 cm. The length is four times the width. What
are the length and the width of the rectangle?
Answer:
Length = 24 cm
Width = 6 cm.
Step-by-step explanation:
The formula to compute the perimeter of a rectangle is,
[tex]Perimeter=2(length+width)[/tex]
Given:
Perimeter = 60 cm
width = w
length = 4w
Determine the value of width as follows:
[tex]Perimeter=2(length+width)\\60=2\times(4w+w)\\60=10w\\w=6[/tex]
The value of length is:
[tex]length(l)=4\times w\\l=4\times6\\l=24[/tex]
Thus, the length and the width of the rectangle are 24 cm and 6 cm respectively.
How do you solve X+10y=-9 X=5y+21
Answer:
Step-by-step explanation:
Please help with question number three. Only first and third. I appreciate your help, I am lost!
I'll do the first part to get you started.
--------------------
Area = 1/2
Length = 7/8
Width = W
Area of rectangle = Length*Width
A = L*W
1/2 = (7/8)*W
(8/7)*(1/2) = (8/7)*(7/8)*W .... see note1 below
(8*1)/(7*2) = (8*7)/(7*8)*W .... see note2
8/14 = (56/56)*W
4/7 = 1*W .... see note3 and note4
W = 4/7Final Answer: 4/7--------------------
Foot notes
note1: I multiplied both sides by the reciprocal of 7/8, that way the "7/8" on the right side cancels out (as you'll see in a few steps later)note2: I used the rule (a/b)*(c/d) = (a*c)/(b*d)note3: the 56/56 turns into 1, and later on 1*W becomes just Wnote4: 8/14 reduces to 4/7 after dividing both parts by 2Draw 2 supplementary angles. One angle is x-15 degrees and one is 2x degrees. What is the value of x in degrees?
Answer:
Step-by-step explanation:
Since they are supplementary, it means the addition of both angles gives 180 degree.
[tex]x - 15 + 2x = 180\\3x = 180 + 15\\3x = 195\\x = \frac{195}{3} \\x = 65[/tex]
GIVING BRAINLIEST. Write a proportion that could be used to solve for each variable. Then solve. 12 balls in 2 boxes 78 balls in x boxes a. 12/2 = 78/x; x = 13 c. 12/2 = 78/x; x = 12 b. 2/12 = 78/x; x = 468 d. 12/2 = x/78; x = 458
Answer:
B. 2/12 = 78/x ; x = 468
Step-by-step explanation:
12/2 = 78/x
6 = 78/x
6 x 78 = x
468
A store sells cantaloupes at a price of 6 for $9.00. Henry wants to send 24 cantaloupes to his grandmother. How much will Henry spend if he buys the cantaloupes at the store?
Answer: $36
Step-by-step explanation:
Each cantaloupe is $1.5.
Answer:
he will spend 36 dollars because 24 ÷ 6 = 4 and 9$ times 4 = 36$
f(x) = 4x + 6, g(x) = 2x2
Find (fg)(x).
We know x in f(x) is g(x) which is 2x^2 because we are to find (fg)(x)
f(x)=4(2x^2)+6
f(x)=8x^2+6
So (fg)(x) is 8x^2+6
Hope this helped!
(4x+6)(2x^2) = 8x3 + 12x2
This should be easy I hope
Answer:
two to the power of one multiply by two hundred twenty seven to the power of one.
Step-by-step explanation:
456÷2=227
227 can not be divided any further so it would be two to the power of one multiply by two hundred twenty seven to the power of one.
You are supposed to find prime factorization by dividing the number by prime numbers.
A circle and a square each have a perimeter of 160 feet. Which has the greater area and by how much
Answer:
[tex]The \: circle \: has \: a \: bigger \: area \: by \approx 438 \: {ft}^{2} [/tex]
Explanation:
[tex]Diameter \: of \: circle:160 \div 3.14 \approx 51 \: ft \\ Area \: of \: circle : \frac{3.14 \times {51}^{2} }{4} \approx 2038 \: {ft}^{2} \\ Sides \: of \: square:160 \div 4 = 40 \: ft \\
Area \: of \: square: \: {40}^{2} = 1600 \: {ft}^{2} \\ 2038 - 1600\approx 438 \: {ft}^{2} [/tex]
Final answer:
Comparing the areas of a circle and a square with the same perimeter of 160 feet, the circle has a greater area by approximately 435.75 square feet.
Explanation:
We are comparing the areas of a circle and a square which both have a perimeter of 160 feet. For the square, since the perimeter (P) is 160 feet, each side (s) will be P/4, which gives us s = 40 feet. The area of the square (Asquare) is s², so Asquare = 40² = 1600 square feet.
For the circle, the perimeter is the circumference (C), which is 160 feet. The formula for the circumference of a circle is C = 2πr, where r is the radius. So, 160 = 2πr, giving us r = 160/(2π). The area of the circle (Acircle) is πr², so Acircle = π(160/(2π))². After calculation, we find that Acircle ≈ 2035.75 square feet.
Comparing the two areas, the circle has a greater area than the square by Acircle - Asquare ≈ 2035.75 - 1600 ≈ 435.75 square feet.
9 pounds for $1.50 how many pounds for $1.00
1. Find how much one pound is.
- to do this, divide 1.50 by 9. This will give you one pound.
2. Figure out how many times 1 pound can go in a dollar.
proportion
[tex]\frac{9}{1,5} = \frac{x}{1} \\[/tex]
1.5x=9*1
1.5x=9
x=[tex]\frac{9}{1.5}[/tex]
x=6
5. The measures of the angles of a triangle are in the extended ratio 17:16:12. What is the measure of the (1 point)
largest angle?
O 34
O45
O48
068
Solve for x.
3x = 6x – 2
Answer:
x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
3x = 6x - 2 ( subtract 6x from both sides )
- 3x = - 2 ( divide both sides by - 3 )
x = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]
Answer:
x=2/3
Step-by-step explanation:
Its just right
use limits to find the area of the region bounded by the graph f(x)=4-2x^3 , the x-axis , and the vertical lines x=0 and x=1
A) 7
B) infinity
C) 7/2
D) 7/4
Answer:
[tex]\frac{7}{2}[/tex] square units.
Step-by-step explanation:
We have to use limits to find the area of the region bounded by the graph [tex]f(x) = 4 - 2x^{3}[/tex] , the x-axis, and the vertical lines x=0 and x=1.
So, the area will be
A = [tex]\int\limits^1_0 {(4 - 2x^{3})} \, dx[/tex]
= [tex][4x - \frac{x^{4}}{2} ]^{1} _{0}[/tex]
= [tex]4 - \frac{1}{2}[/tex]
= [tex]\frac{7}{2}[/tex] square units. (Answer)
Find the equation of a line that is parallel to line g that contains (P, Q).
the coordinate plane has a line g that passes through the points (-3,2) and (0,5).
3x − y = 3P − Q
3x + y = Q − 3P
x − y = P − Q
x + y = Q − P
Correct option:
[tex]\boxed{x-y=P-Q}[/tex]
Explanation:
Given that the line we are looking for is parallel to g, then the slope of that line and g is the same, therefore:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ (x_{1},y_{1})=(-3,2) \\ \\ (x_{2},y_{2})=(0,5) \\ \\ \\ m=\frac{5-2}{0-(-3)}=1[/tex]
So we can write the point-slope form of the equation of the line as follows:
[tex]y-y_{0}=m(x-x_{0}) \\ \\ (x_{0},y_{0})=(P,Q) \\ \\ \\ y-Q=1(x-P) \\ \\ y-Q=x-P \\ \\ \\ Arranging: \\ \\ P-Q=x-y \\ \\ \boxed{x-y=P-Q}[/tex]
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A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope and b is the y intercept.
Line g passes through (-3,2) and (0,5). hence:
[tex]Slope\ of\ line\ g=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{0-(-3)}=1[/tex]Two lines are parallel if they have the same slope. Hence:
Line parallel to line g has a slope of 1. Since it passes through (P, Q), hence:
[tex]y-y_1=m(x-x_1)\\\\y-Q=1(x-P)\\\\y-Q=x-P\\\\x-y=P-Q[/tex]
The equation of a line that is parallel to line g that contains (P, Q) is x - y = P - Q
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Which statement proves that quadrilateral UWXY is a parallelogram? A. Diagonals UX and WY bisect each other B. Diagonals UX and WY are perpendicular C. Sides UW and XY are congruent D. Sides UW and XY are parallel (there was no given figure just this)
Answer: It’s D, i got it right!!
Step-by-step explanation:
There are 14 books on a shelf. 9 of these books are new.
(a) What is the ratio of all books to used books?
(b) What is the ratio of used books to new books?
Answer:
all books to new books- 14:5
used books to new books- 5:9
Step-by-step explanation:
Answer: a. 14:5 b. 5:9
Step-by-step explanation:
There are 14 books and 9 are new so subtract 9 from 14 and get 5 and your ration would be 14:5. Once you have the answer to a you know how many new books there are and how many old books there are, so you can easily figure out the ratio would be 5:9.
Which equation represents the line of best fit for the scatter plot?
A. y=x+10
B. y=2x+10
C. y=-x+10
D. y=-2x+10
the equation line of the scatter plot is y = ×+10
2 to the 3rd power times 4 divided by 2 plus 2
Answer: 18
Step-by-step explanation: 2 x 2 x 2= 8
8 x 4 = 32
32 / 2 = 16
16 + 2 = 18
In right triangle PQR PR=17 RQ=15 PQ =8 What is tan P
What is the answer
Answer:
The value of tan P = 1.875
Step-by-step explanation:
Given:
PR=17
RQ=15
PQ =8
To find:
tan P = ?
Solution:
In trigonometric ratio
tan = [tex]\frac{opposite}{adjacent}[/tex]
Now on substituting the given values(refer the figure)
tan (P) =[tex]\frac{15}{8}[/tex]
tan (P) = 1.875
Find the value of the expression:
a
p^2q^2+pq–q^3–p^3 for p=1 and q=−1
Answer:
0
Step-by-step explanation:
Put the numbers where the letters are and do the arithmetic.
(1)^2(-1)^2 +(1)(-1) -(-1)^3 -(1)^3
= 1·1 -1 -(-1) -1
= 1 - 1 + 1 - 1 = 0
The value of the expression is 0.
at dinner jermey and his friend spent $24. They left a 20% tip and then slpit the cost? How much did eacj person pay
Answer: They each paid $2.40.
If there are 21 chickens on the farm and 10 die, how many are still left on the farm?
Answer:
11 live chickens and 10 dead chickens
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
21-10=11
RIP chickens
Rectangle 25 feet long. It has a perimeter of 130 feet. What is the area of the basement?
Final answer:
To find the area of the basement, we started with the given perimeter of 130 feet and the known length of 25 feet and solved for the missing width. Once we determined the width was 40 feet, we used the formula for the area of a rectangle (Area = length × width) to calculate that the basement's area is 1000 square feet.
Explanation:
To solve the question regarding the area of a rectangle where the length is 25 feet and the perimeter is 130 feet, we must first deduce the width of the rectangle using the perimeter formula: P = 2l + 2w (where P is the perimeter, l is the length, and w is the width). Since we know the perimeter (P) and the length (l), we can rearrange this formula to solve for the width (w).
The perimeter formula is expressed as:
130 = 2(25) + 2w
130 = 50 + 2w
2w = 130 - 50
2w = 80
w = 40 feet
Now that we have both the length and the width, we can calculate the area of the rectangle using the formula Area = length × width.
Therefore, the area of the rectangle is:
Area = 25 feet × 40 feet
Area = 1000 square feet
The sum of two numbers is 39 and their difference is 5. Which is the larger number?
Answer:
22
Step-by-step explanation:
Let x be a number
Other number = 39 -x
x - (39 - x) =5
x - 39 + x = 5
2x = 5 + 39 = 44
x = 44/2
x = 22
Other number = 39 - 22 = 17
Answer:
The larger number = 22
Step-by-step explanation:
Let the two number x and y
The sum of two numbers is 39 can be represented as:
x + y = 39----------------1
The difference of two numbers is 5 can be represented as:
x - y = 5------------------2
x + y = 39----------------1
x - y = 5------------------2
Using Elimination Method and subtracting 2 from 1
x-x + y-(-y) = 39 - 5
0+y+y=34
2y=34
y=34/2
y=17
substituting y=17 in 1
x+17=39
x=39-17
x=22
∴ The larger number = 22
An arc of a circle of radius 7cm subtends an eagle of 120degree at the centre. Find its perimeter.
Answer:
[tex]\dfrac{14\pi }{3}\ cm[/tex]
Step-by-step explanation:
The circumference of the circle with radius of 7 cm is
[tex]C=2\pi r\\ \\C=2\pi \cdot 7=14\pi \ cm[/tex]
An arc of a circle o subtends an angle of [tex]120^{\circ}[/tex] at the centre.
The circle has the full angle of [tex]360^{\circ},[/tex] then
[tex]14\pi \ cm - 360^{\circ}\\ \\x\ cm - 120^{\circ}[/tex]
Write a proportion:
[tex]\dfrac{14\pi }{x}=\dfrac{360}{120}\\ \\\dfrac{14\pi }{x}=\dfrac{3}{1}\\ \\14\pi =3x\\ \\x=\dfrac{14\pi }{3}\ cm[/tex]
Alice is planning her next vacation. She budgeted 110 for travel expenses, and she expects to spend 120 each day for food and lodging. Her total budget for the trip is 710 . How many days can Alice have for her vacation without exceeding her budget?
Answer:
5 days to spend exactly $710
Step-by-step explanation:
Answer:
5 days
Step-by-step explanation:
5 x 120 = 600
600 + 110 = 710
what is the area of the composite figure ? enter your answer in the box . use 3.14 for pi
Answer:
The area of the composite figure = 12.785 square units
Step-by-step explanation:
The figure composite of :
A ⇒ Rectangle with coordinates (0,0) , (0,5) , (2,5) and (2,0)
B ⇒ Rectangle with coordinates (2,0) , (2,1) , (4,1) and (4.0)
C ⇒ Quarter of a circle with coordinates (2,1) , (2,2) and (3,1)
Area of A: Length = 5 and Width =2
Area of A = Length times the width = 5*2 = 10 square units
Area of B: Length = 2 and Width =1
Area of B = Length times the width = 2*1 = 2 square units
Area of C: radius = 1
Area of C = 0.25 * pi * r² = 0.25 * 3.14 * 1² = 0.785 square units
Total Area = 10 + 2 + 0.785 = 12.785 square units
Answer:
the answer is 12.785
Step-by-step explanation:
i took the test
How many cubic feet of concrete are needed to pour 4 cylindrical pillars 5 feet high with a diameter of 4 inches?
Answer: 1.75 cubic feet concrete is needed.
Step-by-step explanation:
Alright, lets get started.
The volume of the pillar is : [tex]\pi r^2h[/tex]
We have given the height is 5 feet.
We have given the diameter is 4 inches.
So the radius will be : [tex]\frac{4}{2}=2 \ inches[/tex]
Converting inches into feet.
The radius will be : [tex]\frac{2}{12} \ feet[/tex] [tex]= 0.167 feet[/tex]
So the volume of the cylinder will be : [tex]\pi * 0.167^2*5[/tex]
So the volume of the cylinder will be : [tex]0.4380 \ cubic \ feet[/tex]
As there are 4 pillars, so total volume will be : [tex]4*0.4380[/tex]
So, total volume will be : [tex]1.75 \ cubic \ feet[/tex]
Hence 1.75 cubic feet concrete is needed. : Answer
Hope it will help :)
Answer:
1.75 cubic feet
Step-by-step explanation:
Measure the diameter of the cylinder. ...
Hope this helps
What is the value of -36÷(-4/9)
The value of -36 divided by (-4/9) is 81, which is found by multiplying -36 with the reciprocal of (-4/9), giving the result 324/4, which simplifies to 81.
To find the value of -36 divided by (-4/9), you can think of division by a fraction as multiplication by its reciprocal. So, the problem changes from division to multiplication: -36 * (-9/4). To solve this:
First, multiply the numerators: -36 * -9 = 324.
Then, multiply the denominators: 1 * 4 = 4.
Now, divide 324 by 4 to get 81.
Therefore, the value of -36 divided by (-4/9) is 81.