A ball inside of a cube has a volume of 113 cubic inches. If each side of the cube measures 12.6 inches, what is the volume of air inside the cube? (Round to the nearest tenth.)


1357.1 cubic inches
1244.1 cubic inches
1887.4 cubic inches
1226.0 cubic inches

Answer:

The equation is

y=1/4x-3

Answer:

y = 1/4x - 5

Step-by-step explanation:

If gradient or slope (m) equal to 1/4

then y - y¹ = m( x - x¹) ..........(1)

where the line happen to be passing through the point given above

therefore let x¹ be 8.........(2)

and y¹ be -3...............(3)

substitute (3) and (2) into (1)

we have y -(-3) = 1/4 (x - 8)

so 4(y+3)= (x-8)

4y = x - 8 - 12

therefore y = 1/4x - 5

Answer:

x = y² + 12x

y² = x - 12

y² = -11x.

Step-by-step explanation:

We need to find the inverse of the given function , which is ,

[tex]\rm\implies y = x^2 + 12x [/tex]

Step 1 : Interchange x and y :-

[tex]\rm\implies x = y^2 + 12y [/tex]

But according to the steps given in the Question , in very first step in 12x , x is not replaced by y . After which , the steps go wrong in the question .

The 3 errors :-

Answer:

f(x)= -2[x+1]

this is the answer of the question

Answer:

-6

Step-by-step explanation:

Parallel lines have the same slope

If a line has a slope of -6, all lines parallel to this will have a slope of -6

Answer:

7/24

Step-by-step explanation:

11/12 - 5/8

Get a common denominator of 24

11/12 * 2/2 = 22/24

5/8 *3/3 = 15/24

22/24 -15/24 = 7/24

Answer:

A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 27.8 minutes and a standard deviation of 11.4 minutes.

This means that [tex]\mu = 27.8, \sigma = 11.4[/tex]

How long must a visit be to put a shopper in the longest 10 percent?

The 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 27.8}{11.4}[/tex]

[tex]X - 27.8 = 1.28*11.4[/tex]

[tex]X = 42.39[/tex]

A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.

Answer:

10

Step-by-step explanation:

1. [tex]6^{2} + 8^{2} = c^{2}[/tex]

2 [tex]100 = c^{2}[/tex]

3. c = 10

9514 1404 393

Answer:

  D.  4 hours

Step-by-step explanation:

The tiger will run (5 mi/h)(2 h) = 10 mi in 2 hours. That will put it 2+10 = 12 miles from Sampson's starting location.

Samson can run 12 miles in time ...

  time = distance/speed = (12 mi)/(3 mi/h) = 4 h

Sampson will get to the tiger's location after 4 hours, just as the tiger is ending its rest period.

__

The graph shows the position of Sampson (red) and the tiger (blue) x hours after the chase starts. The distance (y miles) is measured from Sampson's starting point, assuming the tiger is running away.

Answer:

y = mx + b

Step-by-step explanation:

This is the basic equation for a line where m is the slope and b is the y intercept.

Answer:0.824

Step-by-step explanation:

The coefficient of determination is approximately 0.885 or 88.5%.

A correlation coefficient (r) is a number between -1 and 1 that measures the strength and direction of a linear relationship between two variables.

The coefficient of determination (R-squared) is equal to the square of the correlation coefficient (r).

Therefore, to find the coefficient of determination with an r-value of 0.941, we can simply square it:

R-squared = r² = 0.941² = 0.885481

Thus, the coefficient of determination is approximately 0.885 or 88.5%.

This means that 88.5% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.

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Answer:

[tex]\text{A. }39/50[/tex]

Step-by-step explanation:

The probability that a randomly selected cap will not be green is equal to the number of non-green caps divided by the total number of caps.

Since there are 100 caps total and 22 are green, there must be [tex]100-22=78[/tex] non-green caps.

Divide this by the total number of caps (100) to get the probability that a randomly selected cap will not be green:

[tex]\frac{78}{100}[/tex]

Simplify by dividing both the numerator and denominator by 2:

[tex]\frac{78}{100}=\boxed{39/50}[/tex]

Answer:

y=x-5/2

Step-by-step explanation:

Swap y and x

x=2y+5

since a function has to be in the form y=mx+c

take 5 to the other side in order to remain with 2y then divide both sides by 2

x-5/2=y

y=x-5/2

Answer:

Duke is a very good team and

Answer:

24 premium tickets were sold.

Step-by-step explanation:

Let :

Deluxe ticket = x

Regular tickets = x + 78

Premium tickets = y

x + (x + 78) + y = 208

4x + 2(x+78) + 10y = 714

2x + y = 208 - 78

4x + 2x + 156 + 10y = 714

2x + y = 130 - - - - - (1)

6x + 10y = 558 - - - - (2)

Now we can solve the simultaneous equation using elimination method :

From (1)

y = 130 - 2x

Put y = 130 - 2x in (2)

6x + 10(130 - 2x) = 558

6x + 1300 - 20x = 558

- 14x = 558 - 1300

-14x = - 742

x = 742 / 14

x = 53

Put x = 53 in y = 130 - 2x

y = 130 - 2(53)

y = 130 - 106

y = 24

Answer:

17cm

Step-by-step explanation:

Given that the Volume of a cone is 4,000 cm³. And we need to determine the height of the cone , if the diameter is 30cm .

Diagram :-

[tex]\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(17.5,1.6){\sf{15cm }}\put(9.5,10){\sf{17\ cm }}\end{picture} [/tex]

Step 1: Using the formula of cone :-

The volume of cone is ,

[tex]\rm\implies Volume_{(cone)}=\dfrac{1}{3}\pi r^2h [/tex]

Step 2: Substitute the respective value :-

[tex]\rm\implies 4000cm^3 =\dfrac{1}{3}(3.14) ( h ) \bigg(\dfrac{30cm}{2}\bigg)^2 [/tex]

As Radius is half of diameter , therefore here r = 30cm/2 = 15cm .

Step 3: Simplify the RHS :-

[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) (15cm)^2\\ [/tex]

[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) 225cm^2\\ [/tex]

Step 4: Move all the constant nos. to one side

[tex]\rm\implies h =\dfrac{ 4000 \times 3}{ (3.14 )(225 )} cm \\[/tex]

[tex]\implies \boxed{\blue{\rm Height_{(cone)}= 16.98 \approx 17 cm }}[/tex]

Hence the height of the cone is 17cm .

9514 1404 393

Answer:

Step-by-step explanation:

I find it convenient to draw the graph first when looking for relative extrema.

The function can be differentiated to get ...

  f'(x) = -3x^2 +9

This is zero when ...

  -3x^2 +9 = 0

  x^2 = 3

  x = ±√3 . . . . . x-values of relative extrema

Then the extreme values are ...

  f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3

The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...

 (x, y) = (-√3, -6√3) and (√3, 6√3)

__

Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of  x between the minimum and the maximum.

  decreasing: x < -√3, and √3 < x

  increasing: -√3 < x < √3

Answer:

Following are the solution to the given points:

Step-by-step explanation:

When the two-tailed were testing then:

Null and alternative hypothesis:

[tex]H_0 : p = 0.611\\\\H_a : p \neq 0.611[/tex]

Testing the statistics:

[tex]\to z = 2.08\\\\P-value = 0.0375\\\\\alpha = 0.01\\\\0.0375> 0.01\\\\P-value < \alpha\\\\[/tex]

therefore, it fails to reject the null hypothesis.

Answer:

Sydney's age = 42

Step-by-step explanation:

104 divided by 2 = 52

52 - 10 = 42

I am sorry if this is wrong. But this is what I learned at my school.

Answer: move each corner (where you see the right triangles) 2 units to the left and three units up. Then, draw the quadrilateral.

Step-by-step explanation:

Answer:

480

Step-by-step explanation:

(10)3- (2)3- (8)3

1000- 8- 512

= 480

Please mark mee brainlist....

Answer: A

Step-by-step explanation:

Answer:

12 lb   1 oz

Step-by-step explanation:

Add the amounts together

4lb 3oz ,

3 lb 9oz

4 lb 5 oz

-------------------

11 lb  17 oz

But 16 oz is 1 lb so subtract 16 oz and add 1 lb

11 lb 17 oz

+1lb - 16 oz

--------------------

12 lb   1 oz

Answer:y - y1 = m(x + x1)

m = (y2 - y1)/(x2 - x1) = (-6 - 2)/(-1 - 5) = -8/(-6) = 4/3

y - 2 = 4/3(x - 5) is a possible answer

y + 6 = 4/3(x + 1) is also a possible answer

Step-by-step explanation:

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Answer: 40.16

Step-by-step explanation:

The length of the side AC will be 12.28 units. The correct option is C.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Given that the hypotenuse of the triangle is 42 and the angle B is 17 degrees.

The side AC will be calculated as below:-

sin(47) = P / 42

AC = 42 x sin42

AC = 12.27

Therefore, the length of the side AC will be 12.28 units. The correct option is C.

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Answer:

[tex]\int _{\left(-1\right)}^1\frac{x^3+1}{2}dx[/tex]

[tex]=\frac{1}{2}\cdot \int _{\left(-1\right)}^1x^3+1dx \Leftarrow(take \: constant\: out)[/tex]

[tex]=\frac{1}{2}\left(\int _{\left(-1\right)}^1x^3dx+\int _{\left(-1\right)}^11dx\right) \Longleftarrow (Sum\:Rule)[/tex]

[tex]\int _{\left(-1\right)}^1x^3dx=0[/tex]

[tex]\int _{\left(-1\right)}^11dx=2[/tex]

[tex]=\frac{1}{2}\left(0+2\right)[/tex]

[tex]=1[/tex]

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Answer:

a  = d+c - r

Step-by-step explanation:

a - c = d - r

Add c to each side

a - c+c = d - r+c

a  = d+c - r

Its A trapezium

For Calculations Refer to the attachment

Answer:

Step-by-step explanation:

Plot the points.

See the attached.

It is easy to calculate the length of sides and diagonals using the coordinates and the distance formula.

The sides are all equal to [tex]\sqrt{5}[/tex] units and the diagonals are both equal to [tex]\sqrt{10}[/tex] units.

This is a property of a square.

Answer:

option d.opposite / adjacent

Step-by-step explanation:

opposite /adjacent ratio represents the tangent of an angle .

hope it is helpful to you ☺️

Answer:

D.

Step-by-step explanation:

From the trigonometry shortcuts we can use the acronyms:

SOH  CAH  TOA

for an arbitrary angle Ф, plug in the length of the sides:

sin(Ф) = opposite/hypotenuse

cos(Ф) = adjacent/hypotenuse

tan(Ф) = opposite/adjacent

Answer:

This spinner can be designed in 5040 ways.

Step-by-step explanation:

Number of possible arrangements:

The number of possible arrangements of n elements is given by:

[tex]A_{n} = n![/tex]

In this question:

7 colors, so:

[tex]A_{7} = 7! = 5040[/tex]

This spinner can be designed in 5040 ways.