The volume of a tennis ball is about 8.65 cubic inches
The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
Calculating volumeFrom the question, we are to determine the volume of a tennis ball
From the given information,
The circumference of a tennis ball is 8 inches
That is,
C = 2πr (C is circumference)
8 = 2πr
∴ r = 8/2π
r = 4/π inches
This the radius of a tennis ball
Now, for the volume of a tennis ball
Using the formula for calculating the volume of a sphere
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
Then, the volume of a tennis is
[tex]V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}[/tex]
[tex]V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}[/tex]
[tex]V = \frac{256}{3\pi^{2}}[/tex]
V = 8.64607 cubic inches
V ≅ 8.65 cubic inches
Hence, the volume of a tennis ball is about 8.65 cubic inches
b. To find the amount of space within the cylinder not taken up by the tennis balls
First, we will calculate the volume of the cylinder
Using the formula for calculating the volume of a cylinder
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
r = 1.43 inches
h = 8 inches
Putting the parameters into the formula, we get
V = π × 1.43² × 8
V = 16.3592π
V = 51.39 cubic inches
This is the volume of the cylinder
Now, for the amount of space within the cylinder not taken up by the tennis balls
Since there are three tennis balls,
The amount of space not taken up will be
51.39 cubic inches - 3(8.65 cubic inches)
51.39 cubic inches - 25.95 cubic inches
= 25.44 cubic inches
Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
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Rectangular prism A measures 2 inches by 7 inches by 8 inches. Rectangular prism B measures 1 inches by 5 inches by 10 inches.
Rectangular Prism A:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
Rectangular Prism B:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³
Surface Area to Volume Ratio = 43/28
Mensuration of SolidsGiven Data
Rectangular prism A
Length = 2 inches
Width = 7 inches
Height = 8 inches
Surface Area
A=2(wl+hl+hw)
A=2(7*2+8*2+8*7)
A=2(14+16+56)
A= 172 inches²
Volume
Volume = L*W*H
Volume = 2*7*8
Volume = 112 inches³
Surface Area to Volume Ratio
= 172/112
= 43/28
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What is it help pleaseee
Answer:
25.13cm
Step-by-step explanation:
formula for circumference of a circle is (2r)π with r being the radius
since the problem gave us the diameter already we can change the formula to 8π (2r is equal to the diameter since diameter is twice as long as the radius)
this gives us the circumference of 25.13
Which is the solution set of the compound inequality 3.5 x minus 10 greater-than negative 3 and 8 x minus 9 less-than 39 negative 2 less-than x less-than 3 and three-quarters negative 2 less-than x less-than 6 2 less-than x less-than 6 2 less-than x less-than 3 and three-quarters
Answer:
The solution for the compound inequality is x \in(2,6)
Step-by-step explanation:
To find the solution set for these compound inequalities, we need to solve the inequality.
First, we shall solve the inequality
Adding both sides of the equation by 10, we have,
Dividing both sides by 3.5, we get,
Now, we shall solve the inequality ,
Adding both sides of the equation by 9, we have,
Dividing both sides by 8, we get,
The solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.
What is the general equation of a Straight line inequality?
The general equation of a straight line inequalities are -
[y] < [m]x + [c]
[y] > [m]x + [c]
[y] ≥ [m]x + [c]
[y] ≤ [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the following compound inequality -
3.5x - 10 > - 3
8x - 9 < 39
We have -
3.5x - 10 > - 3
8x - 9 < 39
3.5x - 10 > - 3
3.5x > 7
x > 2
AND
8x - 9 < 39
8x < 48
x < 6
Solution inequality -
2 < x < 6
Therefore, the solution inequality for the given set of compound inequality 3.5x - 10 > - 3 & 8x - 9 < 39 is 2 < x < 6.
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Please help me with this question, it says:
Solve the equation
x to the power of 3, take away x equals to 120
Using a trial and improvement method.
You must show working out.
Answer:
x = 5.
Step-by-step explanation:
x^3 - x = 120
We first guess the value of x and calculate the left side.
Take x = 4:-
4^3 - 4 = 64-4 = 60
This is < 120 so try x = 5:
5^3 - 5 = 125 - 5 = 120.
So one solution is x = 5.
A keypad has only the letters A−D. What is the total number of possible outcomes if the code has 3 letters?
Answer:
9
Step-by-step explanation:
Because 3 letter to find that just do 3 times 3 which = 9
Hope This Helped
Answer:
64
Step-by-step explanation:
There are 4 options to choose from:
ABCDEach has a 1/4 chance of being picked.
For 3 times in a row, we would multiply the chance of being picked for one option, by whatever the other option's chance is.
As they all have the same chance, and it is 3 times in a row, we would do the following:
1/4 x 1/4 x 1/4
This is:
1/16 x 1/4
Which is:
1/64
Therefore, any possible combination has a 1/64 chance of occurring, meaning that there are 64 possible combinations that could be created.
Which of the following situations can be defined using an exponential function?
A The value of the stocks decreased by $100 last year.
B The number of bacteria decreases by 7% each hour.
C The number of bacteria increases by 700 each hours.
D The value of the stocks increases by $10 every year you own them.
The situation which can be defined using an exponential function is "The number of bacteria decreases by 7% each hour".
What is an exponential function?An exponential function is used to represent a situation in which values of an event do not increase at a constant or linear rate.
From the above,
The value of the stocks decreased by $100 last year is a linear function.The number of bacteria increases by 700 each hour is a linear function.The value of the stocks increases by $10 every year you own them is a linear function.Learn more about exponential function:
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Of the following three statements, choose the best option and write a viable argument showing how it is reflected by the cost function for wichita's factory
A viable argument showing how it is reflected by the Cost Function for Wichita’s factory is; The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.
How to Interpret Cost Functions?
From the given options, the best statement is;
The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
A cost function is a formula used to predict the cost that will be experienced at a certain activity level. Thus, the cost function for the best option is;
The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.
The missing options are;
___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.
___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
___ Overtime wages were required to produce at levels above 25,000 units.
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Solve 2x+6 ≤ 10 or 2x + 8 > 20.
A. x ≤2 or x>6
OB. x < 1 or x > 2
OC. x ≤ 1 or x > 6
OD.
2 and x > 2
Answer:
A. x ≤2 or x>6Step-by-step explanation:
2x+6 ≤ 10 or 2x + 8 > 20
⇔ 2x ≤ 4 or 2x > 12
⇔ x ≤ 2 or x > 6
−6×(−8)= what is the answers
Answer:
48
Step-by-step explanation:
when you multiply a negative times a negative (or divide a negative by a negative), it equals a positive!
-6 times -8 will equal 48!
let me know if you have any questions :)
Ida's ice-cream stand has increasing profits each week during the hot summer months. Ida finds that each week during the summer her profits increase by 15% over what they were the previous week. In her first week of business, her profits were $600.How much money will she make in all over 5 weeks
Answer:
4045.43
Step-by-step explanation:
triangle png What is the angle measure of angle B?
Answer:
[tex]m\angle B = 28^{\circ}[/tex]
Step-by-step explanation:
All angles in a triangle must add up to [tex]180^{\circ}[/tex]
We can solve for [tex]\angle B[/tex] using this knowledge
[tex]\angle B + 40 + 112 = 180\\\angle B + 152 = 180\\\boxed{\angle B = 28}[/tex]
That is the answer
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Need Help ASAP
Consider the circles A, B, C, and D.
Four circles A, B, C, and D are shown. Circle A has a diameter of 8 feet. Circle B has a diameter of 10 inches. Circle C has a diameter of 2 feet. Circle D has a radius of 50 inches.
a. Without calculating, circle
has the greatest circumference.
Question 2
Explain.
Answer:
Circle D
Step-by-step explanation:
The circumference of a circle can be calculated by multiplying the diameter by π. Therefore, the circle with the greatest circumference will be the circle with the greatest diameter.
The only circle for which we have been told the radius is Circle D. The diameter of a circle is twice the radius, therefore the diameter of Circle D is 50 in × 2 = 100 in
There are 12 inches in 1 ft.
Therefore, the circumferences of the circles in order from smallest to largest is: B < C < A < D
Proof
Diameters
Circle A = 8 ft = 96 inCircle B = 10 inCircle C = 2 ft = 24 inCircle D = 2 × 50 in = 100 inCalculate the mean of 1,2,3,4,5,6
Answer:
mean = 3.5
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{1+2+3+4+5+6}{6}[/tex] = [tex]\frac{21}{6}[/tex] = 3.5
Answer:
The mean of 1 , 2 , 3 , 4 , 5 , 6 is 3.5
Given :
The observations 1 , 2 , 3 , 4 , 5 , 6
To find :
The mean of 1 , 2 , 3 , 4 , 5 , 6
Solution :
Step 1 of 2 :
Calculate sum of the observations
Here the given observations are 1 , 2 , 3 , 4 , 5 , 6
Number of observations = 6
Sum of the observations
= 1 + 2 + 3 + 4 + 5 + 6
= 21
Step 2 of 2 :
Find the mean
The required mean
can someone help me with this problem? Thank you!
Answer:
152
Step-by-step explanation:
If you substitute the 6, the expression will look like this-
8( 3(6) + 1 )
You can then times 3 by 6, this makes 18. You then add the one, this equals 19.
19 times 8 = 152.
I hope this helps, have a lovely day.
how many Years are in 1,000
The number of years in 1000 days is = 2 . 74 years .
How many Years are in 1,000 day?Division is the arithmetic operation that is used to determine the quotient of a number. Division parts a number into equal parts with another number.
Number of years in 100 days = 1000 / 365
= 2 . 74 years
Here is the complete question:
how many Years are in 1,000 days
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show your working please.
Offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
2 bags for £35
2 bags means 50 kg (2×25)
Each kg cost = 35/50 = £0.7 per kg
3 bags for £92.50
3 bags means 150 kg
Each kg cost = 92.50/150 = £0.61 per kg
As we can see, offer B has a low cost per kg
Thus, offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
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Evaluate
4(x+5)(x+1)
(x+3)(x-3)
for x = 5.
Answer:
3840
Step-by-step explanation:
Given expression:
4(x+5)(x+1)(x+3)(x - 3)
To:
Evaluate the expression ; for x = 5.
Solution:
4(x+5)(x+1)(x+3)(x - 3)Evaluate x = 5 :
4(5+5)(5+1)(5+3)(5 - 3)Simplify using PEMDAS rule:
P : Parentheses
E : Exponents
M : Multiplication
D : Division
A : Addition
S : Subtraction
(4)(10)(5+1)(5+3)(5−3)40(5+1)(5+3)(5−3)(40)(6)(5+3)(5−3)(240(5+3)(5−3)(240)(8)(5−3)1920(5−3)(1920)(2)3840Hence, after evaluating the given expression for x = 5 , the answer'll be 3840.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to evaluate
[tex]\large\pmb{4(x+5)(x+1)(x+3)(x-3)}[/tex] for x=5.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Use PEMDAS. With the help of this acronym, we will not make any mistakes in the Order of Operations!Here's what PEMDAS stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
So, let's start computing...
///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\//\\\///\\\///\\\///\\\\///\\\\///\\\///\\\///\
Evaluating the expression
First, substitute 5 for x:
[tex]\star~\large\pmb{4(5+5)(5+1)(5+3)(5-3)}[/tex]
Now, use the Order of Operations.
The first operation here is:
[tex]\dag[/tex] P=Parentheses
So we need to perform the operations inside the parentheses first:
[tex]\star~\large\pmb{4(10)(6)(8)(2)}[/tex]
The next operation is multiplication, since we don't have any exponents here:
[tex]\star~\large\pmb{40\times6\times8\times2}[/tex]
Multiply!
[tex]\star~\Large\pmb{3840}~~\square\!\!\!\!\!\checkmark[/tex]
That's the value of the expression 4(x+5)(x+1)(x+3)(x-3) for x=5.
Hope it helps you out! :D
Ask in comments if any queries arise.
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if three times a certain number is increased by 4 the result is 28
Answer:
The number is 8
Step-by-step explanation:
Let x be the number
3x+4 = 28
Subtract4 from each side
3x+4-4 = 28-4
3x= 24
Divide by 3
3x/3 =24/3
x = 8
Fill out the chart please!
The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
What is the Mean, Median, and Interquartile Range of a Data?Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
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Find the area of the following rhombus: A m? 52m 8m A=?m2
The area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have given a rhombus with diagonals.
The length of the long diagonal p = 2×52 = 104 m
The length of the short diagonal q = 2×8 = 16 m
Area = pq/2 = (104×16)/2 = 832 square m
Thus, the area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.
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If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 2 ones?
[tex]\displaystyle|\Omega|=6^3=216\\A=\binom{3}{2}\cdot5=3\cdot5=15\\|A|=\dfrac{15}{216}=\dfrac{5}{72}\approx0.069[/tex]
A mosquito has a mass of about 0.00000225 kilograms. Which of these is the measure of the mass in scientific notation?
Answer:
2.25x 10^-6
Step-by-step explanation:
In order to find out which is the scientific notation you would want to count how many zeros are in front of the number in this case it has 6 zeros before the series of numbers meaning that it would be 10^-6
Hello Brainly, The Question is Find the Area of this Parallelogram. Please Help! Thank You!
Answer:
24 ft sq
Step-by-step explanation:
find area of triangles
6×4=24
24/2=12
add areas together
12+12=24
he triangles below are similar. Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters. Which similarity statement expresses the relationship between the two triangles? Triangle Z Y X is similar to triangle C A B Triangle Z Y X is similar to triangle A C B Triangle Z Y X is similar to triangle C B A Triangle Z Y X is similar to triangle A B C
And
AB=12BC=6AC=14Check
AB/YX=BC/ZY=AC/XZ12/6=6/3=14/72=2=2Hence
ABC=XYZOr
ZYX≈CBAOption C
wyatt has a square garden. he adds 3 feet to one side and 1 foot to the other and now it is a rectangle with an area of 24 ft^2 what are the new dimensions of the garden
The new dimension of the rectangle are as follows;
6 ft4 ftHow to find the new dimension of the rectangle?The new dimension of the rectangle can be found as follows;
The sides of a square are equal.
Therefore,
let the side of the square = x
Hence,
length = x + 3
width = x + 1
area of rectangle = lw
where
l = lengthw = widthTherefore,
24 = (x + 3)(x + 1)
24 = x² + x + 3x + 3
24 = x² + 4x + 3
x² + 4x + 3 - 24
x² + 4x - 21 = 0
(x - 3)(x + 7)
Therefore,
x = 3 or -7
It can't be negative. Hence, x = 3 ft
Therefore, the new dimension of the rectangle are as follows;
x + 3 = 3 + 3 = 6 ftx + 1 = 3 + 1 = 4 ftlearn more on rectangles here: https://brainly.com/question/17562456
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Fawzia randomly selected 50 plants at a nursery to test for aphids. she discovered 7 plants that had the pests. if the nursery has 780 plants. what could be the predicted number of plants with aphids?
The predicted number of plants with aphids is 109.
What is the predicted number of plants with aphids?The predicted number of plants with aphids is the ratio of the random plants with aphids to total number of random plants selected multiplied by the number of plants in the nursery.
Predicted number = (7/50) x 780 = 109.
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The speed of light is roughly 186,000 miles per second. How many minutes does it take for light to arrive from the sun, which is 93,000,000 miles away?
Answer:
8.3 minutes
Step-by-step explanation:
93,000,000 m/186,000 m/s = 500 s
500/60 = 8.333333
Question Help
Reasoning A cone with radius 6 and height 9 has its radius quadrupled. How many times greater is the
volume of the larger cone than the smaller cone?l
Let's see
For initial cone
r=6h=9Volume
1/3πr²h1/3π(6)²(9)3(36)π108π units³For new cone
r=4(6)=24h=9Volume
1/3π(24)²(9)3(576)π1728πSo
1728π/108π16timesAnswer:
16 times
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h[/tex]
Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.
ProofGiven:
radius = 6height = 9Substituting the given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units[/tex]
If the radius is quadrupled:
radius = 6 × 4 = 24height = 9Substituting the new given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units[/tex]
To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:
[tex]\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16[/tex]
So the volume of the larger cone is 16 times greater than the volume of the smaller cone.
B
5 in.
a.
(6.257 25) in.
-
b. (6.25π – 12.5√2)in.²
d.
Find the value of x and y rounded to the nearest tenth.
C.
(6.25π- 12.5) in.2
none of these
Answer:
Step-by-step explanation:
5 in.
a.
(6.257 25) in.
-
b. (6.25π – 12.5√2)in.²
d.
Find the value of x and y rounded to the nearest tenth.
C.
(6.25π- 12.5) in.2
what is the slope of the line through the points (-3,3) and (6,-8)
Answer:
[tex]\displaystyle \frac{-11}{9}[/tex]
Step-by-step explanation:
We will use the equation of change in y over change in x to solve for the slope of the line. Then, we will simplify.
[tex]\displaystyle \frac{y_{2}-y_1 }{x_2-x_1}[/tex]
[tex]\displaystyle \frac{-8-3}{6--3}[/tex]
[tex]\displaystyle \frac{-8-3}{6+3}[/tex]
[tex]\displaystyle \frac{-11}{9}[/tex]