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Zielflug [23.3K]
2 years ago
5

Two cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find P(X = 1).

Mathematics
1 answer:
svetlana [45]2 years ago
3 0

Answer:

0.14479638

Step-by-step explanation:

Because 2 cards out of 52 are drawn without replacement, hypergeometric probability distribution should be used. Hence,

Combination of drawing 1 ace of 4 total aces C(4,1)

Combination of drawing 1 non-ace of 48 total non aces C(48,1)

Combination of drawing 2 cards of total 52 cards C(52.2)

C(4,1) = 4, C(48,1) = 48, C(52,2) = 1326

4*48/1326 = 0.14479638

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How many gallons of pure water should be evaporated from 160 gallons of a solution containing 12% salt
AfilCa [17]

Answer:

66 gallons

Step-by-step explanation:

Given that initially 160 gallons of a solution containing 12% salt.

So, the initial amount of salt = 12% of 160 = 12/100 x 160 = 19.2 gallons.

Let x gallons of water get evaporated so that the remaining solution contains 20% salt.

The remaining amount of solution = 160-x gallons.

As the initial amount of salt is still in the solution which is equal to 20% of the remaining solution, so

19.2 = 20% of (160-x)

\Rightarrow 19.2 = \frac {20}{100}\times (160-x) \\\\\Rightarrow 19.2 = \frac {1}{5}\times (160-x) \\\\\Rightarrow 19.2 \times 5= 160-x \\\\\Rightarrow 96= 160-x \\\\\Rightarrow x= 160-96 \\\\

\Rightarrow x= 66 gallons

Hence, 66 gallons of water must be evaporated to get a 20% salt solution.

6 0
3 years ago
Read 2 more answers
The original blueprint of a concrete patio has a scale ofmath2inches=3feet. Victoria wants to make a new blueprint of the patio
DedPeter [7]

Complete question :

the original blueprint of a concrete patio has a scale of 2 inches=3 feet. victoria wants to make a new blueprint of the patio with a length of 16.8 inches. original blueprints length is 14 inches and original blueprints width is 12 inches. what is the scale for the new blueprint and what is the width of the blueprint with the new scale?

Answer:

2.5 fts, 14.4 fts

Step-by-step explanation:

Given that:

Scale of original blueprint : 2inches = 3 feets

To make a new blueprint with a length of 16.8 inches, the scale for the new blueprint will be :

Original scale : 2 inches = 3 feets

Original blueprint length = 14 inches

Then,

2 inches = 3 feets

14 inches = d

Cross multiply :

2d = 42

d = 21 feets

Hence, new scale for blueprint :

16.8 inches = 21 feets

2 inches = d

16.8d = 42

d = 2. 5 feets

For the width :

14 inches = 16.8 feets

12 inches = w

14w = 201.6

w = 201.6/14

Width = 14.4feets

3 0
3 years ago
What are the common factors for 88 and 112
SCORPION-xisa [38]
Hello!

Common factors are numbers that both numbers can be divided by

The common factors are 2, 4 and 8

The answers are 2, 4 and 8

Hope this helps!
4 0
3 years ago
Read 2 more answers
For which method of data collection is it most important to select a representative sample so that the information may be genera
dalvyx [7]

ANSWER:

INFERENTIAL STATISTICS

STEP-STEP-BY EXPLANATION:

Inferential statistics are mathematical tools for estimating how likely it is that a statistical result based on data from a random sample is representative of the population from which the sample is assumed to have been selected.

It can make inferences from data to more general conditions like

* estimate the degree of confidence that can be placed in generalizations from a sample to the population from which the sample was drawn. (generalize your sample to a larger population)

5 0
4 years ago
4x - 5y = 15<br> find the slope and y-intercept
Mazyrski [523]

Answer:

slope=4/5

y-intercept = -3

Step-by-step explanation:

first we need to rewrite the expression to

y=mx+b

were b is the y-intercept and m the slope

4x-5y=15\\\\4x-5y+5y=15+5y\\\\4x+0=15+5y\\\\4x=5(3)+5(y)\\\\4x=5(3+y)\\\\\frac{1}{5}*4x= \frac{1}{5}*5(3+y) \\\\\frac{4x}{5}=3+y\\\\\frac{4x}{5} -3=3+y-3\\\\\frac{4x}{5} -3=y+0\\\\y=\frac{4x}{5} -3\\\\y=\frac{4}{5}x-3

so there we have it

m=\frac{4}{5} \\\\b=-3

6 0
3 years ago
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