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kolbaska11 [484]
3 years ago
6

A​ student's course grade is based on one midterm that counts as 20​% of his final​ grade, one class project that counts as 20​%

of his final​ grade, a set of homework assignments that counts as 30​% of his final​ grade, and a final exam that counts as 30​% of his final grade. His midterm score is 64​, his project score is 80​, his homework score is 94​, and his final exam score is 77. What is his overall final​ score? What letter grade did he earn​ (A, B,​ C, D, or​ F)? Assume that a mean of 90 or above is an​ A, a mean of at least 80 but less than 90 is a​ B, and so on.
Mathematics
1 answer:
Rus_ich [418]3 years ago
5 0

Answer:

His overall final​ score is 80.1.

His letter grade is a B.

Step-by-step explanation:

To find his grade, we multiply each grade by it's weight.

Grades and weights:

His midterm score is 64​. The midterm counts 20% = 0.2.

His project score is 80​. The project score counts 20% = 0.2.

His homework score is 94. The homework score counts 30%.

His final exam score is 77. It counts 30%.

What is his overall final​ score?

64*0.2 + 80*0.2 + 94*0.3 + 77*0.3 = 80.1

His overall final​ score is 80.1.

What letter grade did he earn​ (A, B,​ C, D, or​ F)?

At least 80 but less than 90 is a​ B. He scored 80.1, so his letter grade is a B.

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Then, we have to check that identity is true for n = k+1, under the assumption that n = k is true:

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(2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)

k\cdot (2\cdot k - 1)+3\cdot (2\cdot k +1) = (k + 1)\cdot (2\cdot k +3)

2\cdot k^{2}+5\cdot k +3 = (k+1)\cdot (2\cdot k + 3)

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