Mai has a dome paperweight that she can use as a magnifier. The paperweight is
shaped like a hemisphere made of solid glass, so she wants to design a box to keep it in
so it won't get broken. Her paperweight has a radius of 3 cm.
What should the dimensions of
the inside of box be so the box is
as small as possible?
What is the volume of the box?
If the radius is 3, what's the diameter?

Answer:

Step-by-step explanation:

The point-slope form of equation where m is the slope and passing the point (x₀,y₀) is:  y - y₀ = m(x - x₀)  

m = -2

(7, 10)     ⇒    x₀ = 7,    y₀ = 10

y - 10 = -2(x - 7)

Step-by-step explanation:

Set M = {20,22,24,26,28,30,32,34}

n(M) = no. of elements in set M

i.e.

n(M) = 8

Answer:

7

Step-by-step explanation:

Even numbers between 20 and 35 are 22, 24, 26, 28, 30, 32, 34.

M = { 22, 24, 26, 28, 30, 32, 34}

There are 7 elements in the set M.

Thus, n(M) = 7

Answer:       0.3

Step-by-step explanation:        I took the test

Answer:

Step-by-step explanation:

Answer:

10.110 km

Step-by-step explanation:

1000 meter = 1 kilometre

Since we are to provide the answer in kilometres, we have to convert the meters to kilometres

1685 m = 1685/1000 = 1.685km

Total kilometres swan by the 6 members =  1.685km x 6 = 10.110 km

Method 2

1.685km +  1.685km +  1.685km +  1.685km +  1.685km +  1.685km = 10.110km

Answer:

27 pages in 1 hour

Step-by-step explanation:

9*3 = 27

[tex]x(x-1)-y(y-1)=0\\x^2-x-y^2+y=0\\[/tex]

The graph is a x.

Hi, I believe this should be correct. The way the boxes are phrased is very misleading.

Answer:

3. PR=51

4. FE=28

Step-by-step explanation:

3. since the two triangles are similar, set up a proportion:

x+8/3x-9=24/28

*cross multiply*:

28(x+8)=24(3x-9)

28x+224=72x-216

44x=440

x=20

to find PR:

PR=3x-9

PR=3(20)-9

PR=51

4. same here:

39/4x+2=42/5x-2

39(5x-2)=42(4x+2)

195x-78=168x+84

27x=162

x=6

to find FE:

FE=5x-2

FE=5(6)-2

FE=28

Answer:

In the first rectangle,

one side =15*1=15

other side = 15* 3=45

in the second rectangle,

one side = 25*1=25

other side= 25*3=75

Step-by-step explanation:

Answer:

1550 mL

Step-by-step explanation:

Total capacity of water = 4 Litre

4 L = 4 * 1000 mL = 4000 mL

200mL cups filled = 1 ; 200 mL

750mL cups filled = 3 ; 750 * 3 = 2250 mL

Total = (200 + 2250) mL = 2450 mL

Water left in filter :

(4000 - 2450) mL = 1550 mL

Answer:

A for the first one, B for the second one, and i think B for the third.

Step-by-step explanation:

Answer:

$900

Step-by-step explanation:

the steps are above

Step-by-step explanation:

step 1. 10x/y - x when x = 4, y = 8

step 2. 10(4)/8 - 4

step 3. 40/8- 4

step 4. 5 - 4

step 5. answer: 1

Answer:

22) 20000000

23) 0.034

24) 0.0000000015

25) 59000000000

26) 0.0048

27) 625000

Step-by-step explanation:

Answer

KK

Step-by-step explanation:

1/3+2/3 so first u do 1+2=3 and u dont add 3+3 so there for it would be 3/3 or 1.

Answer:

The four cats ate 1 cup of food all together.

Step-by-step explanation:

1/3 + 2/3 = 3/3

3/3 as a simplified fraction is 1.

Answer:

y=0.1(3)^x

Step-by-step explanation:

hope it helps you..

have a great day!!

Answer:

x=45

Step-by-step explanation:

First, this figure takes place half of the circle. So we are dealing with a semi circle.

Angle C is inscribed angle in the semi circle. A semi circle measure 180 degrees. Since Angle C is inscribed, It measures 90 degrees.

This theorem proves this

If an angle is inscribed in a semicircle, it will be half the measure of a semicircle (180 degrees), therefore measuring 90 degrees.

Solve for x

[tex]2x = 90[/tex]

[tex]x = 45[/tex]

Answer:

A

Step-by-step explanation:

We have to determine the future value of the annuity to determine which account has a greater value

Future value = Amount x annuity factor

annuity factor = Annuity factor = {[(1+r)^n] - 1} / r

Account A = 300 x[ (1.042)^15 - 1 ] / 0.042 = $6097.14

Account B = 250  x[ (1.051)^15 - 1 ] / 0.051 = $5435,42

Account A will be greater

[tex]\sqrt[6]{5}[/tex]

Hope This Helps You!

Good Luck Studying ^-^

Answer:

[tex]\frac{(x -7)(x-1)}{y}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex] / x - 1 - 6x - 7/ x - 1

(it's the equation shown in the picture, you might have typed it wrong on your question)

The equation has the same denominator so, it will become:

[tex]\frac{x^{2} - 6x - 7}{y}[/tex]

Which factors into:

[tex]\frac{(x -7)(x-1)}{y}[/tex]

Answer:

3rd on 6 feet

Step-by-step explanation:

Answer:

x = -11

Step-by-step explanation:

Hello There!

create an equation

x + 51 + 60 + 80 = 180

combine like terms

51 + 60 + 80 = 191

x + 191 = 180

subtract 191 from each side

180 - 191 = -11

we're left with

x = -11

Answer:

1) (x + 12)²+(y+6)²= 28

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√28

h=-12

k=-6

;.centre=(-12,-6)

radius =√28 units

2) x²+(y+7)²=15

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√15

h=0

k=-7

;.centre=(0,-7)

radius=√15 units

3) (x + 4)²+(y - 1)² = 4

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√4=2units

h=-4

k=1

;.centre=(-4,1)

radius=√2units

4) (x+3)²+(y-1)²= 8

comparing above equation with(x-h)²+(y-k)²=r²

we get

r=√8=2√2units

h=-3

k=1

;.centre=(-3,1)

radius=2√2units

Answer:

63

Step-by-step explanation:

if 2 inches = 7 feet and the model plane is 1.5 feet, and that is 18 inches 18/2*7=63

1 inch is =12.

Answer:

18

Step-by-step explanation:

Take the 54. The cake reduces her size by 1/3 so you multiply 54*1/3 to get 18 inches or 1.5 feet tall. :)

Answer:

$11.5

Step-by-step explanation:

Subtract 30 from 64.50 to get rid of the cost of shirts. (3 shirts costing 10 dollars) to get 34.50. DIvide 34.50 by 3 for the number of shorts. Your final answer is 11.5