the volume of a volleyball is 288 cubic inches. What is the radius of the volleyball, to the nearest tenth of an inch?

Volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.

As given,

Volume of solid of revolution formed by rotating about the x-axis region between the graph of f(x)= x /2:

Volume = π∫[f(x)]²dx  

⇒Volume =π∫(x/2)²dx

⇒Volume =(π/4)∫x²dx

⇒Volume =(π/4) (x³/3)

                 =(π/12)(x³)

x axis between x=2 and x=5

Volume =(π/12)(125-8)

             =117π/12 unit³

Therefore, volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.

The complete question is:

Find the volume of the solid of revolution formed by rotating about the x axis the region between the graph of

f(x)= x /2

and the x axis between x=2 and x=5.

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Answer:

The rate at which the surface area is changing with respect to time when r = 40 cm is 22400π cm²/min

Not sure if you want it in absolute values since the question says use symbolic notation but if so, multiplying by π gives 70371.675 cm²/min

Step-by-step explanation:

[tex]\text {Volume of a sphere of radius r is given by }\\\\ \text {$V = \dfrac{3}{4}\pi r^3$}[/tex]

The surface area of a sphere of radius r is given by:

[tex]\\S = 4\pi r^2\\[/tex]

The rate of change of surface area is given by
[tex]\dfrac{dS}{dt} = \dfrac{d}{dt}\left(4\pi r^2\right)}\\\\\dfrac{dS}{dt} = 4 \pi \dfrac{d}{dt}\left( r^2\right)}\\\\\\\dfrac{d}{dt}(r^2) = 2r\dfrac{dr}{dt}\\\\\\[/tex]

[tex]\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}[/tex]

We are given that [tex]\text{$\dfrac{dr}{dt}$}[/tex] = 70 cm/min and asked to find rate of change of S when r = 40 cm

Substituting these values into the equation for [tex]\dfrac{dS}{dt}[/tex]
[tex]\dfrac{dS}{dt} = 8 \pi \cdot 40 \cdot 70\\\\\\\\\dfrac{dS}{dt} = 22400 \pi \;cm^2/min[/tex]

In absolute values

Answer:

15 + m = 60; m = 45 minutes

Step-by-step explanation:

Hello!

According to the question He had a total of 60 minutes to complete the entire exam. He spent 15 minutes on Part 1 of the exam. how much time he had left to complete Part 2.

Let's make an equation where the time spent on part 1 which is 15 + m which is minutes remaining for part 2 is equal to Total minutes which is 60 minutes

So, if we put it together;

15 + m = 60

So, let's solve for m

15 + m = 60

Substract 15 from both sides

15 - 15 + m= 60 - 15

m = 45

So, the equation is 15 + m = 60 and he had 45 minutes of time remaining to complete part 2.

If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its  possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.

Percent error = 1%

Kilogram of iron ore = 500 kilograms

First step is to find the 1% of 500 kilograms

= .01 × 500 kilograms

= 5

Second step is to find the possible reading

Possible reading :

500 - 5

=495

500 + 5

= 505

Therefore we can conclude that  based on the above analysis the possible reading can be between 495 and 505.

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The most appropriate choice for perimeter of rectangle will be given by-

Mr Smith must buy 61 m of fencing.

What is perimeter of rectangle?

It is equal to the total distance of the boundary of the rectangle.

If length of rectangle is l m and breadth of rectangle is b m, perimeter of rectangle is 2 x (l + b) [tex]m^2[/tex]

Here,

Length of yard = 61 ft

Breadth of yard = 39 ft

Perimeter of yard = 2 x (61 + 39)

                             = 2 x 100

                             = 200 ft

1 ft = 0.305 m

200 ft = 0.305 x 200 m

          = 61 m

Mr Smith must buy 61 m of fencing.

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The factorised form of the algebraic expression 16cd − 56c²d as given in the task content is; 8cd (2 - 7c).

It follows from the task content that the factorised form of the expression; 16cd − 56c²d as given is to be determined.

Since the given expression is;

16cd − 56c²d

First, each of the terms can be factored as follows;

16cd = 2 × 2 × 2 × 2 × c × d

56c²d = 2 × 2 × 2 × 2 × 7 × c × c × d

Therefore, since the factors which are common to both terms as follows; 2 × 2 × 2 × c × d = 8cd.

Therefore the factorised form of the expression is;

8cd (2 - 7c).

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The probability that at least 75 students arrive at the library is 0.1440.

From the information, the undergraduate library at State U tends to have 33.4 students enter every hour during normal operation.

The expected number of students for the two hours will be:

= 2 × 33.4

= 66.8

The probability that at least 75 students arrive at the library will be:

P(x >= 75) = 1 - P(x <= 74)

This will be looked at in the distribution table

= 1 - 0.8560

= 1.440

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To convert the number given in base 7 to a bse 10 number we follow the procedure shown, that is, we need to multiply each number by the appropiate power of seven (given by their position) and then add them, then we have that:

Therefore:

The width of the rectangle DOGS is 119cm

To solve this, since is a ratio problem, we know that the two ratios must add to the total. This is, for a ratio of 5:7, 5 + 7 = 12 is the total "divisions" for the ratio.

This means that if 12 of 12 parts add to the perimeter (408cm):

12/12 represents the perimeter 408cm.

The, we can divide the perimeter by 12 and get:

Since the width is 7/12 of the perimeter:

But, we are taking the perimeter of a rectangle, which is twice the width plus twice the length, thus we need to divide this number by 2:

And we get the final answer of 119cm

Notice that the values for w are multiples of 9, and their respective factor is expressed on the values of z. Therefore, the equation to describe the relationship between w and z is w=9z

Expected value:

For the given scenario:

Answer:

2:3

Step-by-step explanation:

Answer:

Step-by-step explanation:

x-84/6

Answer:

Step-by-step explanation:

The distance expression of the number of units between points A and B is √[(-2 - 3)^2 + (5 - 5)^2]

From the question, we have the following parameters:

This means that

A = (-2, 5)

B = (3, 5)

The distance between the points is calculated as

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Where

A = (x1, y1) = (-2, 5)

B = (x2, y2) = (3, 5)

Substitute the known values in the above equation

So, we have

Distance = √[(-2 - 3)^2 + (5 - 5)^2]

The question does not imply that the we simplify the above expression

So, we leave the expression unsimplified

Hence, the expression of the distance between A and B is √[(-2 - 3)^2 + (5 - 5)^2]

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Answer:

i think it is 7 but not sure

Step-by-step explanation:

GCF of 28 and 35 is the largest possible number that divides 28 and 35 exactly without any remainder. The factors of 28 and 35 are 1, 2, 4, 7, 14, 28 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 28 and 35 - prime factorization, Euclidean algorithm, and long division.

Answer:

He raised 51 dollars

Step-by-step explanation:

If for every 5 points he raised 3 dollars he would have raised 51 dollars because he had 85 points.

As we can see in the card, on Monday the worker clocked in at 08:15 and clocked out at 12:15. This means they worked 4 hours.

They then clocked in at 13:00 and clocked out at 17:30. This means they worked for 4 and a half hours.

Since they earn a wage of $14.50/h, they earned:

So that day they earned $123.25

.

Answer:

C). Or SAS~with 3/2 proportionate sides.

Step-by-step explanation:

You can tell because the similar angle shows which sides should be proportional to the other on the corresponding triangle, and of those sides, 6/4 = 10.5/7

Easily simplifying to 3/2 both times to find the rate at which the side lengths where changed.

Hope this helps.

Using transformations, the functions that could represent the one graphed are given as follows:

A transformation is when a function undergoes a change in it's definition. Depending on the type of the transformation, the function can keep the same orientation, same side lengths, and so on.

In the context of this problem, the function kept the same orientation, it just changed it's position, hence the type of transformation that the function underwent was a translation.

The possible translations are given as follows:

The domain of the graphed function is given by:

x ≥ 0.

Which is the same domain as the parent square root function, given as follows:

y = sqrt(x).

From the graph, the function was translated down a units, changing it's range, hence the function has the following format:

y = sqrt(x) - a.

Hence the first two options can be correct, either with a = 1 or with a = 3. The last two options change the range but not the domain, hence they are incorrect.

The image at the end of the answer gives the complete problem.

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The domain of f⁻¹(x) is (9,∞).

The function we have is

f(x) = 4x² + 9 for x ≤ 0

Now, let us find the inverse of the function f(x),

To find the inverse of f(x),

Replacing f(x) with f(y)

f(y) = 4y² + 9

Now the equation is,

x = 4y² + 9

y² = (x-9)/4

y = √(x-9)/2

The inverse of f(x) is,

f⁻¹(x) = √(x-9)/2

The domain of √(x-9)/2 can be found as,

(x-9)>0

x>9

The domain of f⁻¹(x) is (9,∞).

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Answer: 1049

Step-by-step explanation:

As given by the question

There are given that the expression

Now,

Multiply by 5 on both side of the equation

So,

Hence, the value of a is 110.

If Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

Here Nolan is dividing 2 by 11.

Division is one of  the basic arithmetic operation. Division is operation of splitting a specific number into equal parts

The quotient is the result from dividing a number from another number.

Divide the given terms and the result will be

2/11 = 0.1818...

The result will be a repeating quotient . Here the pattern is repeating endlessly

Hence, if Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...

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Answer:

4826.166666km

Step-by-step explanation:

d=distance

  [tex]\frac{1259km}{1h} =\frac{d}{23/6h}[/tex]

= [tex]\frac{1259km}{1h}= \frac{6d}{23}[/tex]

= [tex]1259=\frac{6d}{23}[/tex]

= [tex]1259*23=6d[/tex]

= [tex]28,957=6d[/tex]

= [tex]\frac{28,957}{6}=d[/tex] ≈4826.166666

(a) 291/2020

Divide the total for the 10-14 year column by the total.

(b) 77/465

There are 465 people from the east, 77 of which were loyal for 10 to 14 years

(c) 437/1010

There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.

(d) 145/376

376 people are from the West, (45+100)=145 of which are at least 10.

(e) 32/157

157 people were loyal for less than a year, 32 of which were from the East.

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

Answer:

6 is the awnswer

Step-by-step explanation: