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swat32
3 years ago
10

How do i solve the following question 2x + 3 = 9

Mathematics
1 answer:
Mademuasel [1]3 years ago
6 0

Answer: x = 3

Step-by-step explanation: To solve for <em>x</em> in the equation you see here, our goal is to get <em>x</em> by itself.

Our first step will be to isolate the term containing <em>x</em> which in this case is 2x. To isolate 2x, we have to get rid of this +3 by subtracting from both sides of the equation.

On the left, +3 -3 cancels and we're left with 2x. On the right, 9 - 3 simplifies to 6.

So now we have the equation 2x = 6.

To get <em>x</em> by itself since it's being multiplied by 2, we just to divide by 2 on both sides of the equation. On the left, the 2's cancel and we're left with <em>x</em>. On the right, \frac{6}{2} simplifies to 3 so our answer is <em>x = 3</em>.

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(a) The probability that a randomly selected parcel arrived late is 0.026.

(b) The probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.

(c) The probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.

(d) The probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

Step-by-step explanation:

Consider the tree diagram below.

(a)

The law of total probability sates that: P(A)=P(A|B)P(B)+P(A|B')P(B')

Use the law of total probability to determine the probability of a parcel being late.

P(L)=P(L|A_{1})P(A_{1})+P(L|A_{2})P(A_{2})+P(L|A_{3})P(A_{3})\\=(0.04\times0.40)+(0.01\times0.50)+(0.05\times0.10)\\=0.026

Thus, the probability that a randomly selected parcel arrived late is 0.026.

(b)

The conditional probability of an event A provided that another event B has already occurred is:

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

Compute the probability that a parcel was late was being shipped through the overnight mail service A₁ as follows:

P(A_{1}|L)=\frac{P(L|A_{1})P(A_{1})}{P(L)} \\=\frac{0.04\times 0.40}{0.026} \\=0.615

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.

(c)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

P(A_{2}|L)=\frac{P(L|A_{2})P(A_{2})}{P(L)} \\=\frac{0.01\times 0.50}{0.026} \\=0.192

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.

(d)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

P(A_{3}|L)=\frac{P(L|A_{3})P(A_{3})}{P(L)} \\=\frac{0.05\times 0.10}{0.026} \\=0.192

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

4 0
3 years ago
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