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Dafna11 [192]
3 years ago
6

Please answer this X+2y=6 3x-y= -10

Mathematics
1 answer:
valentina_108 [34]3 years ago
4 0
3x-y=-10
y=3x+10
so the equation “x+2y=6” is “x+2(3x+10)=6” so we have:
x+6x+20=6
7x=6-20
7x=-14
x=-14/7=-2
to get y we can replace x with its value “-2” in the equation”y=3x+10” so we have:
y=3(-2)+10=-6+10=4
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$25.98

Step-by-step explanation:

Add the items Sara buys to find the total:

17.50 + 6.50 = 24

Convert 8.25% into a decimal:

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Multiply 0.0825 by 24:

0.0825 x 24 = 1.98

1.98 is the amount of tax, then add the tax to the total amount you got before tax.

24 + 1.98 = 25.98

Your answer would be 25 dollars and 98 cents!

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Answer:

a) There is a 18.75% probability that the first question that she gets right is the second question.

b) There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

c) There is a 10.35% probability that she gets the majority of the questions right.

Step-by-step explanation:

Each question can have two outcomes. Either it is right, or it is wrong. So, for b) and c), we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

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

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

And \pi is the probability of X happening.

In this problem we have that:

Each question has 4 choices. So for each question, Robin has a \frac{1}{4} = 0.25 probability of getting ir right. So \pi = 0.25. There are five questions, so n = 5.

(a) What is the probability that the first question she gets right is the second question?

There is a 75% probability of getting the first question wrong and there is a 25% probability of getting the second question right. These probabilities are independent.

So

P = 0.75(0.25) = 0.1875

There is a 18.75% probability that the first question that she gets right is the second question.

(b) What is the probability that she gets exactly 1 or exactly 2 questions right?

This is: P = P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955

P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637

P = P(X = 1) + P(X = 2) = 0.3955 + 0.2637 = 0.6592

There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

(c) What is the probability that she gets the majority of the questions right?

That is the probability that she gets 3, 4 or 5 questions right.

P = P(X = 3) + P(X = 4) + P(X = 5)

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

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There is a 10.35% probability that she gets the majority of the questions right.

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