Question

question 10 (multiple choice worth 1 points) (04.03r mc) a students course grades and their corresponding weights are given in the table

what is the minimum grade needed on the final exam to earn an overall grade of 83% in the class? 30% 57% 75% 90%

Explanation:

Step1: Set up the weighted - average formula

Let \(x\) be the grade on the final exam. The weighted - average formula is \(\text{Overall Grade}=\sum(\text{Grade}\times\text{Weight})\). So, \(83=(100\times0.1)+(80\times0.3)+(95\times0.2)+(x\times0.4)\).

Step2: Simplify the left - hand side of the equation

First, calculate the known products:
\(100\times0.1 = 10\), \(80\times0.3=24\), \(95\times0.2 = 19\).
The equation becomes \(83=10 + 24+19+0.4x\).

Step3: Combine the constant terms

\(10 + 24+19=53\). So the equation is \(83=53+0.4x\).

Step4: Solve for \(x\)

Subtract 53 from both sides: \(83 - 53=0.4x\), which gives \(30 = 0.4x\).
Then divide both sides by 0.4: \(x=\frac{30}{0.4}=75\).

Answer:

75%