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svetoff [14.1K]
3 years ago
10

Solve this multi step equation: 8a + 2(1 - 5a) < 20 (dash under <)

Mathematics
2 answers:
Delicious77 [7]3 years ago
6 0
Distribute 2(1-5a)
8a+2-10a<20
Combine like terms
-2a+2<20
Subtract 2 from both sides
-2a<18
Divide both sides by -2, when dividing by a negative number flip the sign
So the answer is a>-9
Citrus2011 [14]3 years ago
5 0
Okay. Basically, a is greater than or equal to 9.
First, you do distribute the 2.
8a+2-10a(< or =)20
Subtract two on both sides.
8a-10a(< or =)18
Then subtract 10a from 8a
-2a(< or =)18
Divide by two on both sides
and switch around the greater than sign since you divided by a <span>-2
</span>a(> or =)-9
<span>And if you check, -9 works, -8 works, and -10 doesn't work.</span>
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5y-21=14

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A stack of cards consists of seven red and four blue cards. A second stack of cards consists of eleven red cards. A stack is sel
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Answer:

0.1733 = 17.33% probability the first stack was selected.

Step-by-step explanation:

To solve this question, it is needed to understand conditional probability, and the hypergeometric distribution.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Conditional probability:

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

Probability of all red cards for the first stack:

For this, we use the hypergeometric distribution, as the cards all chosen without replacement.

7 + 4 = 11 cards, which means that N = 11.

7 red, which means that k = 7

3 are chosen, which means that n = 3

We want all red, so we find P(X = 3).

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 3) = h(3,11,3,7) = \frac{C_{7,3}*C_{4,0}}{C_{11,3}} = 0.2121

Conditional probability:

Event A: All red

Event B: From the first stack.

Probability of all red cards:

0.2121 of 50%(first stack)

1 of 50%(second stack). So

P(A) = 0.2121*0.5 + 1*0.5 = 0.60605

Probability of all red cards and from the first stack:

0.21 of 0.5. So

P(A \cap B) = 0.21*0.5 = 0.105

What is the probability the first stack was selected?

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.105}{0.60605} = 0.1733

0.1733 = 17.33% probability the first stack was selected.

4 0
3 years ago
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