How can I divide greater numbers using a standard procedure

There are 72 boys and 90 girls on the math team for the next math competition Mr. Johnson would like to arrange all the students

yawa3891 [41]

Answer:

Mr. Johnson can arrange 18 students in each row, that is 4 rows of boys and 5 rows of girls.

Step-by-step explanation:

Given:

Number of boys = 72

number of girls = 90

We need to arrange students in rows with equal number of only boys and only girls.

To find the maximum number (x) of boys or girls in each row, we will find the GCF (Greatest Common Factor) of the numbers 72 and 90, such that 'x' divides both numbers evenly without a remainder.

Now to find GCF we will factorize both numbers.

$72 = 2\times2\times2\times3\times3$

$90= 2\times 3\times 3\times 5$

from above we can say that;

GCF = $2\times 3\times 3 = 18$

Hence Mr. Johnson can arrange 18 students in each row, that is 4 rows of boys and 5 rows of girls.

5 0

3 years ago

How do you draw the probabilities for this tree diagram?

Likurg_2 [28]

Step-by-step explanation:

The prize is equally likely to have been placed behind doors 1, 2, and 3, so the probabilities of D₁, D₂, and D₃ are equal.

P(D₁) = P(D₂) = P(D₃) = 1/3

The contestant initially chooses door 1, so the host will not open it.

P(H₁|D₁) = P(H₁|D₂) = P(H₁|D₃) = 0

The host will not open the door with the prize.

P(H₂|D₂) = P(H₃|D₃) = 0

The remaining probabilities for each door are equal.

P(H₂|D₁) = P(H₃|D₁) = 1/2

P(H₃|D₂) = 1

P(H₂|D₃) = 1

4 0

3 years ago

A print shop makes bumper stickers for election campaigns. If x stickers are ordered (where x < 10,000), then the price per s

Sergeu [11.5K]

Answer:

P(x) = (0.049x - 0.0000015x²)

Step-by-step explanation:

price per sticker is 0.14 − 0.000002x dollars

total cost of producing the order is 0.091x − 0.0000005x² dollars.

P(x) = profit = Revenue - Cost

Let the number of units of stickers made be x

Revenue = (price per sticker) × (total units sold) = (0.14 − 0.000002x) × (x)

= (0.14x - 0.000002x²) dollars.

Cost of producing x units in the order = (0.091x − 0.0000005x²)

P(x) = 0.14x - 0.000002x² - (0.091x − 0.0000005x²) = 0.14x - 0.091x - 0.000002x² + 0.0000005x²

= (0.049x - 0.0000015x²)

P(x) = (0.049x - 0.0000015x²)

Hope this Helps!!!

3 0

4 years ago

Malliki Williams earned a $48,000 from royalties on her cookbook.She paid a 28% income tax on these royalties. The balance wasin

Nikitich [7]

Answer:

$20000 and $14560

Step-by-step explanation:

First, we need to get the total tax paid by Malliki Williams

To get that, we have to multiply her income tax (28%) by total royalties ($48000)

28% of $48000 = $13440

Balance after tax = $48000 - $13440

Balance = $34560

She invested some of the balance ($34560) at the rate of

3.25% ---- First investment

1.75% --- Second investment

Assume her first investment is x dollars

Definitely, her second investment would be $34560 - x

3.25% of x + 1.75% (34560 - x ) = 904.8

0.0325x + 0.0175(34560-x) = 904.8 ----- Open the bracket

0.0325x + 604.8x - 0.0175x = 904.8 ------ Collect like terms

0.0325x -0.0175x =904.8 - 604.8

0.015x = 300 ------ Divide both sides by 0.015

x = 300/0.015

x = 20000

Remember that x represents her first investment

Her second investment is $34560 - $20000 =$14560

4 0

3 years ago

Solve by substitution, elimination, or graphing. Show your work.

Flura [38]

1. 3t + 2b = 16....multiply by -3
5t + 3b = 25...multiply by 2
----------------
-9t - 6b = -48 (result of multiplying by -3)
10t + 6b = 50 (result of multiplying by 2)
---------------- add
t = 2

3t + 2b = 16
3(2) + 2b = 16
2b = 10
b = 5

so tacos (t) cost $ 2 and burritos (b) cost $ 5
===================
d + q = 75......d = 75 - q
0.10d + 0.25q = 10.95

0.10(75 - q) + 0.25q = 10.95
7.50 - 0.10q + 0.25q = 10.95
0.15q = 3.45
q = 23....so there are 23 quarters
=====================
x = 2 point shots, y = 3 point shots
x + y = 24.....multiply by -2
2x + 3y = 54
----------------
-2x - 2y = -48 (result of multiplying by -2)
2x + 3y = 54
----------------add
y = 6.......so there was 6 three point shots

x + y = 24
x + 6 = 24
x = 18......and 18 two point shots
======================
5.50g + 5 = 2.50g + 17
5.50g - 2.50g = 17 - 5
3g = 12
g = 4......they will cost the same with 4 game rentals
less then 4 rentals, use Fun Guys....more then 4, use Game Bank
=======================
(2,5)(4,9)
slope = (9 - 5) / (4 - 2) = 4/2 = 2

y = mx + b
slope(m) = 2
(2,5)...x = 2 and y = 5
now sub and find b, the y int
5 = 2(2) + b
5 = 4 + b
5 - 4 = b
1 = b
so ur equation is : y = 2x + 1 (line A)

(0,5)(3,8)
slope = (8 - 5) / (3 - 0) = 3/3 = 1

y = mx + b
slope(m) = 1
(0,5)...x = 0 and y = 5
now sub
5 = 1(0) + b
5 = b
so ur equation is : y = x + 5 (line B)

y = 2x + 1
y = x + 5

2x + 1 = x + 5
2x - x = 5 - 1
x = 4

y = 2x + 1
y = 2(4) + 1
y = 8 + 1
y = 9
so they will meet at (4,9)
=====================
sorry..not 100% sure about the bonus

4 0

3 years ago