Question

1. (l134) for the function $f(x)=6x - 8$, what is the matching value for $x$ when $f(x)=8$?

a) $\frac{11}{2}$
b) $\frac{8}{3}$
c) $\frac{2}{11}$
d) $\frac{7}{3}$
e) none of the above

1. (l139) what is the probability of rolling a 6 - sided die and getting a 1 or 2?

a) $\frac{1}{2}$
b) $\frac{1}{3}$
c) $\frac{1}{4}$
d) $\frac{1}{5}$
e) $\frac{1}{6}$

Explanation:

Step1: Solve for x in the function

Set \(f(x)=8\) in \(f(x) = 6x - 8\), so we have the equation \(6x-8 = 8\).

Step2: Add 8 to both sides

Adding 8 to both sides of \(6x - 8=8\) gives \(6x=8 + 8\), which simplifies to \(6x=16\).

Step3: Solve for x

Dividing both sides of \(6x = 16\) by 6, we get \(x=\frac{16}{6}=\frac{8}{3}\).

Step4: Calculate probability of die - roll

A 6 - sided die has 6 possible outcomes. The event of getting a 1 or 2 has 2 favorable outcomes.
The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{2}{6}=\frac{1}{3}\).

Answer:

1. b) \(\frac{8}{3}\)
2. b) \(\frac{1}{3}\)