Consider the system of equations. y = 3x + 2 y = − 2 3 x − 4 Explain why these particular equations can be graphed immediately.

Answer:

a.  P(x = 3) = 0.061313

b. The anticipated number of radio blackouts = 4

c.  It's unclear when the next radio blackout will occur.

d. P(x = 4) = 0.19537

Step-by-step explanation:

Based on the provided details:

A Poisson process is utilized to model the occurrence of this event:

Minor radio blackouts occur, on average, two times annually.

Therefore:

For question (a)

time t = 1/2 (i.e., six months)

Let x represent the likelihood of 3 incidents during the remaining months of the year.

Then:

P(x = 3) = 0.061313

b).

The expected number of radio blackouts over two years is calculated as follows:

We start with:

t = 2 years

E(x) = λ × t

E(x) = 2 × 2

E(x) = 4

Thus, the predicted number of radio blackouts = 4

c).

The time we must wait until the probability of witnessing the next radio blackout reaches at least 0.5 is as follows:

In this case, time (t) =???

Thus:

P(x =1) = 0.5

Consequently, we are unable to ascertain the probability (50%) of the next radio blackout.

d)

We can compute the probability that the time until the fourth blackout is at most 2 years as follows:

Here;

x =4, t = 2

Thus:

P(x = 4) = 0.19537

The correct answer is option D. Detailed explanation: As per the attached image. Observing the image, the coordinates are outlined. To determine the reflection of a point across a line, the distances from the points to the line must be equal. Point A(1,1) sits on the line x = 1, meaning its reflection A' remains at A'(1,1). Point C(2,5) is a distance of 1 from x = 1 on the right, hence its reflected position C' shifts left by the same distance — subtracting 1 from its x-coordinate places it at C'(1 - 1, 5) or C'(0, 5). Point B(4,1) is positioned 3 from x = 1 on the right; therefore, its reflection B' would also move left by 3 – leading to B'(1 - 3, 1) or B'(-2, 1). Plotting A', B', and C' confirms option D as the correct choice.