Solve the problem using matrices.The final grade for an algebra course is determined by grades on the midterm and final exam. The grades for four students and two possible grading systems are modeled by the following matrices.  

src="https://sciemce.com/media/4/ppg__tttt0518191431__f1q86g6.jpg" style="vertical-align: -15.0px;" />Find the final course score for Student 3 for both grading System 1 and System 2.

A. System 1: 44.2; System 2: 53
B. System 1: 85; System 2: 83
C. System 1: 77.2; System 2: 76
D. System 1: 67.4; System 2: 98.6

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Answer: B

Mathematics

Solve the problem.Find the volume that remains after a hole of radius 1 is bored through the center of a solid sphere of radius 2. Round to the nearest tenth.

A. 21.8 B. 65.3 C. 6.9 D. 5.4

Solve the problem.Suppose that the dollar cost of producing x radios is  Find the marginal cost when 50 radios are produced.

A. $60 B. $20 C. $2,300 D. -$2,300

Find the particular solution to the given differential equation that satisfies the given conditions.3y" + 16y' - 12y = 0; y' = 0 and y = 2 when x = 0

A. y = e^6x + e^(-2/3)x
B. y = e^-6x + e^(2/3)x
C. y = e^-6x + e^(2/3)x
D. y = - e^-6x - e^(2/3)x

How many terms of the series would you need to add to find its sum to within 0.02?

What will be an ideal response?