In a given course a student receives preliminary examination grades of 81, 85, and 95. the final examination is weighed for one-third and the average of the preliminary grades is weighed as 2/3 of the final grade. what should the final examination grade be for a semester average of 90?

The average of the 3 grades = (81+85+95) /3 =87

This counts as 2/3 of the final grade:

87 * 2/3 = 58 points

For a grade of 90, they still need 90 -58 = 32 points

Let x = final exam score

The final exam is worth 1/3, so we get:

1/3x = 32

To get x, multiply both sides by 3:

x = 32 *3

x = 96

They need a 96 on the final exam.

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

=  √(225 +64)

=  √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.