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larisa86 [58]
2 years ago
14

13. For what value of b would the following system of equations have an infinite number of solutions?

Mathematics
1 answer:
tiny-mole [99]2 years ago
5 0

Answer:

b=2

Step-by-step explanation:

we have

9x+12y=21 -----> equation A

6x+8y=7b ----> equation B

we know that

If the system of equations have an infinite number of solutions then the equation A must be equal to the equation B

Multiply equation B by 1.5 both sides

1.5*[6x+8y[=7b*1.5

9x+12y=10.5b ----> equation C

Compare equation A and equation C

9x+12y=21 -----> equation A

9x+12y=10.5b ----> equation C

For the equations to be equal it must be fulfilled that

21=10.5b

solve for b

b=21/10.5

b=2

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Answer:

280 people

Step-by-step explanation:

Given that 65% of people surveyed were pleased with condition of the park.

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1 year ago
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Answer:

Step-by-step explanation:

Sample size = 95

X=cash carried by the persons

x bar = 8.00

s = sample std dev = 2.50

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Hence Z score would be

\frac{x-8}{0.2565}

a) P(X

-0.00

b) P(9

c) 95% conf interval margin of error = ±1.96*0.2565

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1 year ago
On the island of liars each inhabitant lies with probability 2/3. You overhear an inhabitant making a statement. Next you ask an
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Answer:

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

Step-by-step explanation:

Let A be the event 'the first inhabitant speaks the truth' and B the event the person you asked speaks the truth'

We have that

P(A) = P(B) = 1/3

The second person will say that the first person speaks the truth if:

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The probability that both inhabitants lies is 2/3 * 2/3 = 4/9

The probability that both inhabitants speaks the truth is 1/3² = 1/9

Therefore, in this problem, we want to know P(A ∩ B | (A∩ B) ∪ (A^c ∩ B^c) )

(note that, since the second persons says that A didnt lie, then in order for it to be true then the second person have to also say the truth).

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P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) ) = P((A∩ B) ∪ (A^c ∩ B^c) | A ∩ B) * P(A∩ B)/ P((A∩ B) ∪ (A^c ∩ B^c))

Note that P((A∩ B) ∪ (A^c ∩ B^c) | A∩B) = 1 because the condition is more restrictive than the probability we are asking for, therefore

P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) )  = P(A∩ B)/P((A∩ B) ∪ (A^c ∩ B^c))  = (1/9) / (4/9) = 1/4.

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

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