A cylindrical container of three rubber balls has a height of 27 centimeters and a diameter of 9 centimeters. Each ball in the container has a radius of 4.5
centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number.

Given :

A Straight line passes through A(-2,1) and B(2,-k).

The  line is perpendicular to a line 3y+2x=5 .

To Find :

The value of k.

Solution :

Let, slope of line is m.

We know, product of slope of in straight line is -1.

[tex]m \times \dfrac{-2}{3} = -1\\\\m = \dfrac{3}{2}[/tex]

We know, slope is given by :

[tex]\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{3}{2}\\\\\dfrac{1-(-k)}{-2 - 2} = \dfrac{3}{2}\\\\\dfrac{1+k}{-4} = \dfrac{3}{2}\\\\k = -7[/tex]

Therefore, the value of k is -7.

36 minutes

Going through the question in bits:

i. Two people together can do a certain job in 20 minutes.

This implies that the time taken to finish the job is 20 minutes.

This also means that in 1 minute, they will do [tex]\frac{1}{20}[/tex] of the job i.e the rate at which the job is done by the two of them is [tex]\frac{1}{20}[/tex]

ii. If one of them can do the job in 45 minutes.

This implies that the time taken by one of them to finish the job is 45 minutes.

This also means that in 1 minute, he will do [tex]\frac{1}{45}[/tex]  of the job. i.e the rate at which the job is done by one of them is [tex]\frac{1}{45}[/tex]

iii. let the other person do the job in x minutes.

This implies that the time take by the other person to finish the job is x minutes.

This also means that in 1 minute, he will do [tex]\frac{1}{x}[/tex] of the job. i.e the rate at which the job is done by the other person is [tex]\frac{1}{x}[/tex]

Now,

The rate by which the job will be done by the two of them combined is the sum of the individual rates.

i.e

[tex]\frac{1}{20}[/tex] = [tex]\frac{1}{45}[/tex] + [tex]\frac{1}{x}[/tex]

Multiply through by 90x and solve

(90x * [tex]\frac{1}{20}[/tex]) = (90x *  [tex]\frac{1}{45}[/tex]) + (90x *  [tex]\frac{1}{x}[/tex])

4.5x  = 2x + 90

4.5x - 2x = 90

2.5x = 90

x = [tex]\frac{90}{2.5}[/tex]

x = 36

Therefore it will take the other person 36 minutes to finish the job.

Answer:

Hello! answer: 105

Step-by-step explanation:

When doing these for squares you have to do base × height and for triangles you do base × height ÷ 2 So Lets do the triangles sense there more complex so we can get them out of the way. The base for the triangles our 5 and the height is 8 so we will do 5 × 8 = 40 now we will just divide that by 2 so 40 ÷ 2 = 20 now sense we have four identical triangles we will just multiply 20 by 4 so 20 × 4 = 80 now for the 1 in the middle its nice and simple just 5 × 5 so 5 × 5 = 25 now we just add 80 + 25 and 80 + 25 = 105 So 105 is the area! Hope that helps!

Answer:

[tex]Pr = \frac{9}{49}[/tex]

Step-by-step explanation:

Given

[tex]d = 28[/tex] --- big circle

[tex]A_2 = 36 \pi[/tex] --- area of small circle

Required

Probability that a point selected lands on the small circle

Calculate the area of the big circle using;

[tex]A_1 = \pi r^2[/tex]

Where

[tex]r = d/2[/tex]

So, we have:

[tex]r = 28/2 = 14[/tex]

This gives:

[tex]A_1 = \pi * 14^2[/tex]

[tex]A_1 = \pi * 196[/tex]

[tex]A_1 = 196\pi[/tex]

The probability that a point selected lands on the small circle is calculated by dividing the area of the small cicle by the big circle

This gives:

[tex]Pr = \frac{36\pi}{196\pi}[/tex]

[tex]Pr = \frac{36}{196}[/tex]

Simplify

[tex]Pr = \frac{9}{49}[/tex]

Answer:

Here we want to graph the equations:

f(x) = y =(8/3)*x

and

g(x) = y = -(8/3)*x

To graph these you need to find some coordinate points of each one, and then connect them, such that the graph of these two equations can be seen below.

Where the blue one is f(x) and the green one is g(x)

We now want to look at the graph and find the point of intersection p.

By looking at the graph below, we can see that the intersection is at the origin, then p = (0,0)

Also remember that an intersection of two functions means that:

f(x) = g(x)

for that particular x value, then we can solve this for our functions and get:

(8/3)*x = -(8/3)*x

That equation is only true when x = 0

Then we have the intersection at x = 0, and the correspondent y value is given by f(0) or g(0) (will be the same value)

y = f(0) = (8/3)*0 = 0 = -(8/3)*0 = g(0)

Then we also found analytically that the intersection is in the point (0, 0)

Answer:

b

Step-by-step explanation:

expense is usually done everywhere.

Answer:

A

Step-by-step explanation:

Cash

Answer:

the answer is C

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Based on the attached picture we can say that function representing these values would be exponential because the Y values for successive Integer values of X have a common ratio of 16. This can be proven by multiplying each one of the y values by 16, which would give us the next y value in the successive set. For example,

2.5 * 16 = 40

40 * 16 = 640

640 * 16 = 10,240

Meaning that the values have a common ratio of 16, and are increasing exponentially.

Answer:

e) 20

Step-by-step explanation:

Segment lengths:

|(2, 7) -> (8, 7)| = |(8-2, 7-7)| = |(6, 0)| = 6

|(8, 7) -? (8, 11)| = |(8-8, 11-7)| = |(0, 4)| = 4

because we know it's a rectangle, we can infer that the other two sides also have lengths 4 and 6, so the perimeter is 4+4+6+6=20

Answer:

5

Step-by-step explanation:

f(n)=3n^2-7

f(-2)=3(-2)^2-7

f(-2)=3(-2)(-2)-7

f(-2)=3(4)-7

f(-2)=12-7

f(-2)=5

Answer:

2.85125 is the answer.

Step-by-step explanation:

according to the calculator

Answer:

2.75124851367

Step-by-step explanation:

8/8.41=951248513674+1.8=2.75124851367 so its 2.75124851367

Answer:

Step 1:

Subtract $19 from total

366.50 - 19 = 347.5

Step 2:

Divide this total by the ticket price

347.50 / 34.75 = 10

Step 3:

You have your answer

10 people can go to the amusement park

Answer:

as many as 11 people

Step-by-step explanation:

n = # of people

5.50 + 34.75n ≤ 387.75

subtract 5.5 from each side to get:

34.75n ≤ 382.25

divide each side by 34.75

n ≤ 11

Answer:

Step-by-step explanation:

It's 10 since it's a whole number.

Answer:

{1/2 (b)(h) = Area of a triangle}

1/2(b)(4) < 14

2b<14

B<7 in

Answer:

top left

Step-by-step explanation:

a function is if there is only one number that isnt the same as the other x

Answer:

15%

Step-by-step explanation:

You kind of have two ways to do this:

Way 1:

Find how many 60 cents fit into $4. To do that, divide $4 by $0.60 or 400 by 60. You get 6.66666667.

You can divide 100 by 6.66666667, and get 15%,

Way 2:

Knowing that 400 cents is 100%, you can divide 60 by the same number that you divide 400 by to get to 100. To get from 400 to 100, you divide by 4, so divide 60 by 4 and get the same answer, 15%

Hope that helps :)

Answer:

29 3/4 cups

Step-by-step explanation:

total amount of tanner in the 3 containers = sum of tanners in each container

total cups in containers b and c = 2/3 x 12 3/4

2/3 x 51/4 = 17/2 cups or 8 1/2 cups

total capacity = 8 1/2 + 8 1/2 + 12 3/4 = 17 + 12 3/4 = 29 3/4

Answer:

The equation of a line in point-slope form is.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣aay−y1=m(x−x1)aa∣∣−−−−−−−−−−−−−−−−−−−−−−

where m represents the slope and (x1,y1) a point on the line.

To calculate the slope use the gradient formula

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣∣aam=y2−y1x2−x1aa∣∣∣−−−−−−−−−−−−−−−−−

where (x1,y1) and (x2,y2) are 2 coordinate points.

here the 2 points are (-3 ,4) and (0 ,3)

let (x1,y1)=(−3,4) and (x2,y2)=(0,3)

⇒m=3−40+3

Step-by-step explanation:

this is guid to answer that hope it help to you mahar

Answer:

5 days.

Step-by-step explanation:

Jasmine has two options:

Rent skis at the resort for $30 per day.

Then if she rents the skis for N days, the cost will be:

C(N) = N*$30

Buy skis for $150

Now we can ignore the lift pass because she will pay that in both cases.

Now we want to find the number of days N such that the cost of renting is the same as the cost of buying.

Then we need to solve:

C(N) = $150

N*$30 = $150

N = $150/$30 = 5

So if you rent the skis for 5 days, you will pay the same as if you bought the skis.

Answer:

1/8 and 2/1 or 1:8 and 2:1

Step-by-step explanation:

Answer:

[tex]B' = (-2,-3)[/tex]

Step-by-step explanation:

Given

[tex]A = (1,-4)[/tex]

[tex]B = (4,-6)[/tex]

[tex]C = (2,-1)[/tex]

reflection across y

[tex]d = \frac{1}{2}[/tex]

Required

New coordinate of B

When reflected across the y-axis.

The rule is:

[tex](x,y) \to (-x,y)[/tex]

So:

[tex](4,-6) \to (-4,-6)[/tex]

Next is a dilation by 1/2

To do this, we multiply the new point by 1/2

So:

[tex]B' = (-4,-6) * \frac{1}{2}[/tex]

[tex]B' = (-4* \frac{1}{2},-6* \frac{1}{2})[/tex]

[tex]B' = (-2,-3)[/tex]

Answer:x=57

Step-by-step explanation:

isolate x by subtracting 17 from both sides, you should get x = 74-17, which is 57.

Answer:

Step-by-step explanation:

taylor is building doghouses to sell. each doghouse requires 3 full sheets of plywood which taylor cuts into new shapes. the plywood is shipped in bundles of 14 full sheets. how many doghouses can taylor make from 12 bundles of plywood?

Answer:

The mode is 75

Step-by-step explanation: It is the one that appears most often

Answer:

216in

Step-by-step explanation:

6 + 8 + 10 = 24

24 * 9 = 216

Answer:

each lb of jellybeans = $1.50

each lb of almonds = $2.75

Step-by-step explanation:

let j = jellybean cost for each pound

let a = almond cost for each pound

3j + 2a = 10

5j + 6a = 24

Using elimination method:

15j + 10a =50

15j + 18a = 72

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

-8a = -22

a = 2.75

using 3j + 2a = 10

3j + 2(2.75) = 10

3j + 5.5 = 10

3j = 4.5

j = 1.5

Answer:

Ana  spent $17  per book on average.

Juan  spent $14.78  per book on average.

y = $15 + 17x--------- equation 1

y= $10 + 14.78 x------------- equation 2

Step-by-step explanation:

Ana has to pay a yearly fee of $15 to join.

She spends a total of $525 for 30 books.

The amount spent on books = Total amount - yearly fee

                                                 = $525- $15= $510

Price per book on the average = $510/30= $ 17

Ana  spent $17  per book on average.

Juan has to pay a yearly fee of $10 to join.

He spends a total of $350 for 23 books.

The amount spent on books = Total amount - yearly fee

                                                 = $350- $10= $340

Price per book on the average = $340/23= $ 14.78≅ $15

Juan  spent $14.78  per book on average.

The function can be established if y gives the total cost and x gives the number of books

y = $15 + 17x--------- equation 1

y= $10 + 14.78 x------------- equation 2

Juan has a better deal because the yearly fee is less also the price per book is less.

Answer:

Yes

Step-by-step explanation:

-1 < 6 + 2  True

-1 > 3 - 2(6)  

-1 > 3 - 12

-1 > -9   True