Question

1. marcuss favorite casserole recipe requires 3 eggs and makes 6 servings. marcus will modify the recipe by using 5 eggs and increasing all other ingredients in the recipe proportionally. what is the total number of servings the modified recipe will make?

a. 6
b. 8
c. 10
d. 12
e. 15

1. the 35 - member history club is meeting to choose a student government representative. the members decide that the representative, who will be chosen at random, cannot be any of the 3 officers of the club. what is the probability that hiroko, who is a member of the club but not an officer, will be chosen?

f. 0
g. \\( \frac { 4 } { 35 } \\)
h. \\( \frac { 1 } { 35 } \\)
j. \\( \frac { 1 } { 3 } \\)
k. \\( \frac { 1 } { 32 } \\)

1. for what value of \\( x \\) is the equation \\( 2 ^ { 2 x + 7 } = 2 ^ { 15 } \\) true?

a. 2
b. 4
c. 11
d. 16
e. 44

1. let the function \\( f \\) be defined as \\( f ( x ) = 5 x ^ { 2 } - 7 ( 4 x + 3 ) \\). what is the value of \\( f ( 3 ) \\)?

f. \\( - 18 \\)
g. \\( - 26 \\)
h. \\( - 33 \\)
j. \\( - 60 \\)
k. \\( - 75 \\)

Explanation:

Step1: Substitute \(x = 3\) into the function

Given \(f(x)=5x^{2}-7(4x + 3)\), when \(x = 3\), we first calculate \(5x^{2}\) and \(7(4x + 3)\) separately.
For \(5x^{2}\), substitute \(x = 3\): \(5\times3^{2}=5\times9 = 45\).
For \(7(4x + 3)\), substitute \(x = 3\): \(7\times(4\times3+ 3)=7\times(12 + 3)=7\times15=105\).

Step2: Calculate \(f(3)\)

Now, \(f(3)=5x^{2}-7(4x + 3)\), substituting the values we found: \(f(3)=45-105=-60\).

Answer:

J. \(-60\)