a sphere is inscribed in a cube with a volume of 125 cubic inches what is the volume of the sphere

Answers

Answer 1

Answer:

using [tex]\pi[/tex]:   65.45 in³ (nearest hundredth)

using [tex]\pi =3.14[/tex]:   65.42 in³ (nearest hundredth)

Step-by-step explanation:

The radius of the sphere is half the side length of the cube (see attached diagram).  Therefore, the side length of the cube = 2r

Given:

volume of the cube = 125 in³side length of cube = 2r

[tex]\textsf{Volume of a cube}=x^3\quad \textsf{(where}\:x\:\textsf{is the side length)}[/tex]

[tex]\implies 125=(2r)^3[/tex]

[tex]\implies \sqrt[3]{125}=2r[/tex]

[tex]\implies 5=2r[/tex]

[tex]\implies r=\dfrac52[/tex]

Substitute the found value of r into the volume of a sphere equation:

[tex]\begin{aligned}\textsf{Volume of a sphere} & =\dfrac43 \pi r^3\\\\ & =\dfrac43 \pi \left(\dfrac52\right)^3\\\\ & =\dfrac43 \pi \left(\dfrac{125}{8}\right)\\\\ & =\dfrac{500}{24} \pi\\\\ & =\dfrac{125}{6} \pi\\\\ & =65.45\:\sf in^3\:(nearest\:hundredth) \end{aligned}[/tex]

A Sphere Is Inscribed In A Cube With A Volume Of 125 Cubic Inches What Is The Volume Of The Sphere

Related Questions

Please help me answer this! Thank you! No links!

Answers

Answer:

139

Step-by-step explanation:

100 POINTS ANSWER ASAP

George's living room is a square that is 33 ft long on each side. He knows the diagonal of the ceiling from corner to corner must be longer than 33 ft.

(a) He thinks that because a square cut in half forms a special right triangle with the diagonal as the hypotense, so he multiples the side length by two to get 66 feet.
What is George's mistake?

(b) What is the correct length of the diagonal of George's ceiling using the correct special right triangle shortcut? (give exact answer, do not round)

(c) Use either the pythagorean theorem OR the correct trigonometry ratios to solve for the length of the diagonal (round to the nearest tenth of a foot)

Make sure to show all your work.

Answers

Answer:

47

Step-by-step explanation:

a)

a^2 + b^2 = c^2

33^2+33^2=c^2

2178=c^2

c=(nearest is 47)

b)

If you cut the square in half diagonally, it forms two right triangles with angle measures 90-45-45. You can use sin (opposite over hypotenuse) to find the length of the hypotenuse.  sin (45) would be 33/(hypotenuse length). From a trig chart, you can find that sin (45) is 1/sqrt(2), meaning that 33/x = 1/sqrt(2). This means that x=33sqrt(2), which is around 47.

47. Hope that this helps!

what is the greatest prime number less than 50?

Answers

Answer:

The greatest prime number less than 50 is 47

Use ABC to find the value of tan B 41/9 40/9 41/40 9/41

Answers

Answer:

tanB =40/9

Step-by-step explanation:

tan B = opposite/adjacent

where the opposite is 40 and the adjacent is 9

therefore, tanB =40/9

Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.

Answers

Answer:

the answer is in the picture

Which equation does NOT represent a linear function? A. y = 5 B. 4 y = 2 x − 8 C. y = x + 2 x 2 D. y = − 2 3 x − 1

Answers

The answer is C
A, B, and D are all linear

What is z in the context of the problem that’s at hand?

Answers

Answer:

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean

Step-by-step explanation:

i dont know if i am correct tho, please like if i am correct

What is a rewritten form of the radical?
A.
-8816
B.
C.
D.
-90.75
-98616
-2.904

Answers

the only the answer is D

Write an equation in slope-intercept form of the line shown.
An equation is

Answers

Answer:

y = -x - 4

hope this helped :)

some one help me solve this asap pls and thx!!

Answers

Answer:

x = 14

Step-by-step explanation:

Knowing that this figure is a vertical angle.

Define vertical angles ⇒ a pair of opposite angles formed by intersecting lines

Thus, if the left side = 122

then the other side must equal 122

The equation is:

8x + 10 = 122

Subtract 10 from both sides

8x + 10 - 10 = 122 -10

8x = 122

Divide both sides by the same factor

8x/8 = 122/8

Simplify

x = 14

Thus, x = 14.

Kavinsky

8. The expression below is evaluated when x = 9, y = 3,
and z = 2. What is the value of the expression?
8x - 72 + 2y

Answers

Answer:

64

Step-by-step explanation:

First of all substitute the values to where ever you see their corresponding variables to make them multiply.

x = 9

y = 3

z = 2

so we get

8x as 8(9),

7z as 7(2)

2y as 2(3)

then the it's will be

8(9) - 7(2) + 2(3)

which is

72 - 14 + 6

finally we get

64

write an inequality for this situation
Embiid scored at least 31 points
A, E > 31
B, E < 31

Answers

Answer:  [tex]E \ge 31[/tex]

Reason:

"at least 31 points" means "31 or more".

So either E = 31 or E > 31 (meaning Embiid scored 31 points or he scored more than 31 points).

Choice A looks like the closest match assuming the inequality sign is [tex]\ge[/tex]

Saying E > 31 instead of [tex]E \ge 31[/tex] would be false because it leaves out the case E = 31.

help me with this pls​

Answers

Answer:

sure I'll help u with this as this question required to have a and asuch a being used to review with an associate with you in the comment of the item that you used in the comment is the only one that was a good one to review the product and details about the refund

why does thsi always happen

Answers

Answer:

It always happens because you asked the question

Step-by-step explanation:

Solve for x=?
a. 1.5(x+t)=9

Answers

Answer:

1.5x1.5t=9

Step-by-step explanation:

because i am learning this topic

Please help me with this math question. Thank you.

Answers

Answer:

D

Step-by-step explanation:

We want to find the values of x such that:

[tex]\displaystyle -x^2 + 7x + 5 = 0[/tex]

We can use the quadratic formula. Recall that:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = -1, b = 7, and c = 5. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} x & = \frac{-(7)\pm\sqrt{(7)^2-4(-1)(5)}}{2(-1)}\\ \\ & = \frac{-7\pm\sqrt{49+20}}{-2} \\ \\ & = \frac{-7\pm\sqrt{69}}{-2}\end{aligned}[/tex]

In conclusion, the answer is D.

A rectangular dance floor has an area of 96 square feet and a length of 8 feet. What is the width of the dance floor?

Answers

Answer:

The answer is 12ft

Step-by-step explanation:

96/8 = 12

Area = length x width

I need help solving this math problem. The teacher wants us to fill in three things using this math equation: 2x - 3√x + 1 = 0

(1) u=_

(2) u^2=_

(3) _u^2+_u+1=0

The teacher wants us to accomplish this using the U-Substitution method.

Answers

I'm not sure for my awnser but I thing 30

Please help on math.​

Answers

Answer:

The median is 45

Step-by-step explanation:

The median is also referred to as "the middle" value, so you want to take all the values in order and find the middle number. that will be the median. It's the same either box plots.

A quicker way to find it with box plot is to look at the line inside the of the box (line is not always in center of box) on the plot. that is where you'll find the median on questions like these.

hope this helps! :)

Two angles are supplementary. The larger angle is
150

larger than the smaller angle. Find the measure of both angles, and separate your answers with a comma.

Answers

Answer:

x = 165, y = 15

Step-by-step explanation:

1. Well, what does supplementary mean? - The angles add up to 180°.

2. Let's form an equation: x + y = 180°

3. Let's say x is the larger angle and y is the smaller angle.

4. Let's form another equation: x = 150 + y

5. Put the two equations next to each other:

x + y = 180

x = 150 + y

6. We know what x is equaled to, so let's plug it into the first equation!

150 + y + y = 180

150 + 2y = 180

-150           -150

2y = 30

y = 15

7. Now, we know what y is, let's find x!

x + 15 = 180

   -15     -15

x = 165

The measure of both angles are  15 degrees and 165 degrees.

What is Angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle

Given that the two angles are supplementary.

we know that supplementary angles are the angles whose sum is added to 180 degrees.

Let the smaller angle is x.

The larger angle is 150∘ larger than the smaller angle.

y=x+150

Now add both the angles which makes 180 degrees

x+x+150=180

2x+150=180

Subtract 150 on both sides

2x=30

Divide both sides by 2

x=15

So the smaller angle is 15 and the larger angle is 165 degrees

Hence,  the measure of both angles are  15 degrees and 165 degrees.

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What is the answer to3/8 + 3/4=?

Answers

9/8 or 9 1/8

You multiply 3/4 with 2/2 to give you 6/8. You then add 3 to 6 and you get 9.

Find the missing dimension of the triangle.
Area = 30 mm squared
6 mm = height
b = mm

Answers

Answer:

b = 10 mm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex]bh ( b is the base and h the height )

given A = 30 and h = 6 , then

[tex]\frac{1}{2}[/tex]b × 6 = 30 , that is

3b = 30 ( divide both sides by 3 )

b = 10

henry had charged 847 dollars to his credit card. the cost of his next purchase caused him to exceed his credit limit of 1000

Answers

Answer:

The purchase is greater than $153

Step-by-step explanation:

Suppose you play a game in which 5 dice (6-sided) are rolled simultaneously.
If a "4" is rolled, then you win $2 for each "4" showing.
If all the dice are showing "4", you win $1000.
If none of the dice are showing "4", then you lose $5.

What is the expected value of this game. (Show work)
If you want to you can take a photo of the work and upload it.

Answers

The expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.

How to find the mean (expectation) and variance of a random variable?

Supposing that the considered random variable is discrete, we get:

Mean =  [tex]E(X) =[/tex] [tex]\sum_{\forall x_i} f(x_i)x_i[/tex]

Here,   [tex]x_i; \: \: i = 1,2, ... ,[/tex] n is its n data values and [tex]f(x_i)[/tex]is the probability of  [tex]X = x_i[/tex]

Suppose you play a game in which 5 dice (6-sided) are rolled simultaneously.

If a "4" is rolled, then you win $2 for each "4" showing.If all the dice are showing "4", you win $1000.If none of the dice are showing "4", then you lose $5.

Let Y is the amount of money player won. The value of X can be,

[tex]Y=2,4,6,8,1000,-5[/tex]

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consists of n independent Bernoulli trials. Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]

Put the values as 5 trials for each time 4 appears.

[tex]P(X =0) = \: ^5C_1(\dfrac{1}{6})^0(1-\dfrac{1}{6})^{5-0}=0.4018 \:\\P(X =1) = \: ^5C_1(\dfrac{1}{6})^1(1-\dfrac{1}{6})^{5-1}=0.402\\P(X =2) = \: ^5C_2(\dfrac{1}{6})^2(1-\dfrac{1}{6})^{5-2}=0.162\\P(X =3) = \: ^5C_3(\dfrac{1}{6})^3(1-\dfrac{1}{6})^{5-3}=0.032\\P(X =4) = \: ^5C_4(\dfrac{1}{6})^4(1-\dfrac{1}{6})^{5-4}=0.0032\\P(X =5) = \: ^5C_5(\dfrac{1}{6})^5(1-\dfrac{1}{6})^{5-5}=0.00013\\[/tex]

The probability of loosing $5 equal probability of 0 success.

[tex]P(Y=-5)=P(x=0)[/tex]

Similarly, for probability of getting profit are,

[tex]P(Y=2)=P(x=1)\\P(Y=4)=P(x=2)\\P(Y=6)=P(x=3)\\P(Y=8)=P(x=4)\\P(Y=1000)=P(x=5)[/tex]

Expected value of game,

[tex]E(Y)=\sum y .P(Y=y)\\E(Y)=-5.P(X=0)+2.P(X=1)+4.P(X=2)+6.P(X=3)+8.P(X=4)+1000.P(X=5)\\E(Y)=-0.2094[/tex]

Thus, the expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.

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1. Find the volume of the figure.
4 cm
2 cm
10 cm
10 cm
1 cm
3 cm
1 cm 1 cm

Answers

Put an attachment so we can help you, please.

What are all possible values of x if 10x + 7 ≥ 67

Answers

[tex]~~~~10x+7\geq 67\\\\\implies 10x \geq 67 -7\\\\\implies 10x \geq 60\\\\\implies x \geq \dfrac{60}{10}\\\\\implies x \geq 6[/tex]

Please help and explain this to me!! I am confused and would like to know how to solve!!

Answers

Answer:

13. C) The sum of the numerators is incorrect.

14. B) [tex]-\frac{5}{8}+\frac{1}{8}=\frac{-5+1}{8}=\frac{-4}{8} =-\frac{1}{2}[/tex]

Step-by-step explanation:

13. The reason why it's incorrect.

When dealing with the sum of fractions, denominators must be the same. So allows us to do the sum of the numerator. The image displayed is the incorrect sum of the numerator.

14. [tex]-\frac{5}{8}+\frac{1}{8}=\frac{-5+1}{8}=\frac{-4}{8} =-\frac{1}{2}[/tex]

where can I get study guide help for algebra 2 thank you ​

Answers

Answer:

Stay after school more often with your math teacher or come early to school to practice math or to see what your stuggling at.

A table of values for the quadratic function f is shown below. If 3 is one solution to f(x) = 0, what is the value of the other solution?
Record your answer and fill in the bubbles on your answer document.

Answers

Answer:The answer to this oroblem would be -7

Step-by-step explanation:We can see this by when f(x) is 0 right next to it is -7

The value of the other solution for f(x)=0 is -7. This is obtained by taking the general form of the quadratic equation f(x)=y.

Quadratic function:A function is represented by an equation f(x)=ax²+bx+c where a≠0 and b, c are any real numbers.This can be generalized into f(x)=y where x is an independent variable and y is a dependent variable.

Given data:

In the table, x values range from -8 to 1

So, we can write using the general form f(x)=y for these values

For x=-8, f(-8)=-2.75

x=-7, f(-7)=0

x=-6, f(-6)=2.25

x=-5, f(-5)=4

x=-4, f(-4)=5.25

x=-3, f(-3)=6

x=-2, f(-2)=6.25

x=-1, f(-1)=6

x=0, f(0)=5.25

x=1, f(1)=4

And 3 is one of the solution to f(x)=0.

Calculating solution for f(x)=0:

It is given that f(x)=0 when x=3

Thus,

f(3)=0

From the table,

f(-7)=0

So, the other solution for the function f(x)=0 is -7.

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The angle of elevation to the top of a Building in New York is found to be 3 degrees from the ground at a
distance of 2 miles from the base of the building. Using this information, find the height of the building.
Your answer is in feet

Answers

Answer:

The height of the building is about 553.4 feet.

Step-by-step explanation:

tan (3°) = h/2

h = 2 tan (3°) = .10481 miles = 553.4 feet

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