A student's course grade is based on one midterm that counts as 5% of his final grade, one class project that counts as 25% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 72, his project score is 83, his homework score is 91, and his final exam score is 74. 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. His overall final score is nothing.

His overal final score is 81.2. His letter grade is a B.

Step-by-step explanation:

Weighed average:

The sum of all values multiplied by it's weight. The weight is a proportion(a value between 0 and 1).

So.

Score of 72 on the midterm, which counts 5%.

Score of 83 on the project score, which counts 25%.

Score of 91 on homework assignments, which counts 35%.

Score of 74 on the final exam, which counts 35%.

His grade is:

G = 72*0.05 + 83*0.25 + 91*0.35 + 74*0.35 = 82.1.

His overal final score is 81.2.

At least 80 but less than 90 is a B

So his letter grade is a B.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.