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Evgen [1.6K]
3 years ago
5

Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 2 yell

ow disks numbered 7 through 8, find the probability of selecting a red disk, given that an odd-numbered disk is selected.
Mathematics
1 answer:
Tatiana [17]3 years ago
6 0

Answer:

\frac{3}{4}

Step-by-step explanation:

Total number of red disk=6

Total number  of yellow disk=2

Total disk=6+2=8

Odd number=1,3,5,7=4

Odd number on red disk=1,3,5=3

Probability,P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}

Using the formula

The probability of getting odd number disk=\frac{4}{8}=\frac{1}{2}

The probability of getting odd numbered  red disk=\frac{3}{8}

The probability of selecting a red disk,given that an odd numbered disk is selected=\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{8}\times 2=\frac{3}{4}

Using conditional probability

P(A/B)=\frac{P(A\cap B)}{P(B)}

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The area of a triangle is given by the formula A= \frac{1}{2}Bh, where B is the base and h is the height. We can rearrange this formula to solve for B.

\dfrac{A}{ \frac{1}{2}h} = B\\ \\\\\dfrac{2A}{h} = B.

We plug in the given area, 640 square millimeters, and the given height, 32 millimeters.

B= \dfrac{2(640)\ mm^2}{32 \ mm} = 40 \ mm.

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5 0
2 years ago
A paint company mixes it's paint with water to create more paint per gallon. They currently have ten gallon jugs which contain 1
Karo-lina-s [1.5K]
<h3>Answer:  1.25 gallons</h3>

==================================

Explanation:

They currently have ten gallon jugs that contain 10% water, so this means 0.10*10 = 1 gallon of the jug is water and the other 10-1 = 9 gallons is paint. This is assuming the cans are just paint and water.

The ratio of paint to water is 90:10 which reduces to 9:1

Often it helps to reduce as much as possible, but it's actually more handy in this case to keep it at 90:10 so you can see the two parts add back up to 100%

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

Let x be the amount of water we add. This amount is in gallons.

We start off with 1 gallon of water and it bumps up to 1+x gallons of water.

The overall amount of 10 gallons also bumps up to 10+x gallons.

We want a ratio of 80:20 this time, so we want 20 parts water and 80 parts paint. In other words, we want 20/(20+80) = 20/100 = 20% water

Divide (1+x) over (10+x) to get (1+x)/(10+x). This represents the fraction of water. We want this fraction to be equal to 0.20, which is the 20% water amount. It is also equal to 20/100.

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

(1+x)/(10+x) = 20/100

100(1+x) = 20(10+x) ... cross multiply

100+100x = 200+20x ... distribute

100x-20x = 200-100

80x = 100

x = 100/80 ... divide both sides by 80

x = 1.25

You need to add 1.25 gallons of water

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

If you add 1.25 gallons of water, then,

amount of water = 1+x = 1+1.25 = 2.25

amount of paint&water = 10+x = 10+1.25 = 11.25

So you'll have 2.25 gallons of water out of 11.25 gallons of water&paint mix

2.25/11.25 = 0.2 = 20% water

This confirms our answer.

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

Extra info:

1.25 gallons = 1 gallon + 1/4 gallon

1.25 gallons = 1 gallon + 1 quart

This is because 1 gallon = 4 quarts, so 1 quart = 1/4 gallon.

5 0
3 years ago
The distributive property can be applied to which expression to factor 12x3 – 9x2 4x – 3?
fomenos
3x2(4x<span> – 3) + 1(4</span>x<span> – 3) </span>
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3 years ago
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Step-by-step explanation:

Please refer to the attachment

8 0
2 years ago
Katie feeds her cat, Elmer, 2/3 of a cup of food each day. She buys a bag of cat food that contains 18 cups of dry
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Answer:

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Step-by-step explanation:

Set up a proportion.

1 day / (2/3 cup) = x/ 18 cups            Cross Multiply

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1 day * 18 cups * 3 = 2x

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54 day cups/2 cups = x

27 days (The cups cancel)

8 0
2 years ago
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