MODELING WITH MATHEMATICS Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches. Round your answers to the nearest hundredth.
I just need help with part b
A picture shows three tennis balls placed one above another in a cylindrical container.

a. Find the volume of a tennis ball. Round your answer to the nearest hundredth.
The volume of a tennis ball is about
cubic inches.
Answer is about 8.65
b. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.
The volume of the space within the cylinder not taken up by the tennis balls is about
cubic inches.

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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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:

Evaluate x = 5 :

Simplify using PEMDAS rule:

P : Parentheses

E : Exponents

M : Multiplication

D : Division

A : Addition

S : Subtraction

Hence, after evaluating the given expression for x = 5 , the answer'll be 3840.

Hi student, let me help you out! :)

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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]

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

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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.

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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Answer:

4045.43

Step-by-step explanation:

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.

Answer:

Step-by-step explanation:

2x+6 ≤ 10  or  2x + 8 > 20

⇔ 2x ≤ 4  or  2x > 12

⇔ x ≤ 2  or  x > 6

The area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.

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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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 :)

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

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

The predicted number of plants with aphids is 109.

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 situation which can be defined using an exponential function is "The number of bacteria decreases by 7% each hour".

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,

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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

And

Check

Hence

Or

Option C

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.

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

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

The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³

Surface Area to Volume Ratio = 43/28

Given 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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Let's see

For initial cone

Volume

For new cone

Volume

So

Answer:

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.

Given:

Substituting 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:

Substituting 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.

[tex]\displaystyle|\Omega|=6^3=216\\A=\binom{3}{2}\cdot5=3\cdot5=15\\|A|=\dfrac{15}{216}=\dfrac{5}{72}\approx0.069[/tex]

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:

Each 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.

Answer:

24 ft sq

Step-by-step explanation:

find area of triangles

6×4=24

24/2=12

add areas together

12+12=24

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.

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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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

The new dimension of the rectangle are as follows;

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

Therefore,

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;

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Answer:

8.3 minutes

Step-by-step explanation:

93,000,000 m/186,000 m/s = 500 s

500/60 = 8.333333

The number of years in 1000 days is = 2 . 74 years .

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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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.

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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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]

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.

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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