What is it pls help !

18 POINTS! At the AoPS office, mice vary inversely with cats, that is, mice=k/cats, for some value of k. When there are 3r-19 ca

Blizzard [7]

Answer:

k=30

Step-by-step explanation:

The number of mice vary inversely with cats. This is written as:

$Mice \propto \dfrac{1}{Cat} \\Mice = \dfrac{k}{Cat}$

When there are 3r-19 cats, there are 2r+1 mice

$2r+1 = \dfrac{k}{3r-19}\\$Cross multiply$\\k=(3r-19)(2r+1)$

When there are 6r-27 mice, there are r-5 cats.

$6r-27 = \dfrac{k}{r-5}\\$Cross multiply$\\k=(6r-27)(r-5)$

Taking the values of k above, we have:

$k=(3r-19)(2r+1) =(6r-27)(r-5)\\(3r-19)(2r+1) =(6r-27)(r-5)\\6r^2+3r-38r-19=6r^2-30r-27r+135\\$Collect like terms\\6r^2-6r^2+3r+30r-38r+27r-19-135=0\\22r-154=0\\22r=154\\$Divide both sides by 22\\r=7$

Therefore:

$k=(3r-19)(2r+1) \\=(3*7-19)(2*7+1)\\=(21-19)(14+1)\\=2*15\\k=30$

8 0

2 years ago

In forming a confidence interval for μ1 - μ2, only two assumptions are required: independent samples and sample sizes of at leas

AysviL [449]

I’m not sure but I guess it’s false

6 0

2 years ago

A coffee franchise is opening a new store. The company estimates that there is an 80% chance the store will have a profit of $10

natta225 [31]

Answer:

$70,750

Step-by-step explanation:

The expected gain/loss is found by adding the products of all of the profits/losses by their probability. So,

(0.8 * 100000) + (0.1 * 0) + (0.1 * -2500) =

80000 + 0 + -250 =

$70750

5 0

2 years ago

A room 9m long,6m broad and 3.6 m high has one door 1.4m by 2m and two windows,each 1.6m by 75cm find: the cost of white-washing

Tcecarenko [31]

Answer:

The cost of white-washing the walls from inside at the rate of 22.50 per m² is 1098

Step-by-step explanation:

Step 1: Finding the area of the room

Area of the room = Length X breadth

Length = 9m long

Breadth = 6m broad

Area of the room = 9 x 6 =54 square metres

Step 2: Finding the area of the door

Area of the door = Length x breadth

Breadth = 1.4m

Length = 2m

Area of the door = 1.4 x 2 = 2.8 square metres

Step 3: Finding the area of the Window

Area of the window= Length x breadth

Length = 1.6 m

Breadth = 75 cm

Converting cm to m

we have

75 cm =0.75 m

Area of the 1 window= 1.6 x 0.75 = 1.2 square metres

Step 4: Finding the area to be painted

Area to be painted = Total area of the room - area of the door - 2(area of the window)

Area to be painted = 54 - 2.8 - 2(1.2)

Area to be painted = 54 - 2.8 - 2.4

Area to be painted = 48.8 square metres

Step 5: Finding the cost for painting

For painting one square metre = $22.50

For painting 48.8 square metres = 22.50 x 48.8 = 1098

5 0

3 years ago

A 13 and one fourth inch board is cut from a 38 and three fourths inch board. The saw cut takes three eighths inch. How much of

gogolik [260]

Answer:

There is 25 1/8 inches left

Step-by-step explanation:

We have a board that is 38 3/4 inches

We cut away 13 1/4

38 3/4

-13 1/4

-----------

25 2/4

The saw takes 3/8

25 2/4

- 3/8

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

Get a common denominator of 8 2/4 * 2/2 = 4/8

25 4/8

- 3/8

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

25 1/8

There is 25 1/8 inches left

7 0

3 years ago

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