Answer:
The mean for the combined sample = 6.
Step-by-step explanation:
We have been given that one sample of n = 10 scores has a mean of M = 8.
So the sum of 10 scores for 1st sample will be: 
We are also told that second sample of n = 5 scores has a mean of M = 2.
So the sum of 5 scores for 2nd sample will be: 
When the both samples are combined, so total points will be:
and total scores will be
.



Therefore, the mean for the combined sample will be 6.
Answer:
8, 6.
x=8 y=6
Step-by-step explanation:
-3 + 11 = +8
-5 + 11 = +6
This problem can be completed in 2 ways. Both are acceptable.
Option 1:This is an isosceles trapezoid that can be divided into a rectangle and two congruent triangles.
The area of the rectangle is the base times the height.

The area of one of the triangles is half the base times the height.

The other triangle must have that area too.

The area is 56 square centimeters.
Option 2:We can use the area formula for the trapezoid.

Where

is the length of the shorter base
and

is the length of the longer base
and

is the height.
The length of the shorter base is 9.
The length of the longer base is 9+5+5, or 19.
The height is 4.


Same answer. The area is 56 square centimeters.
Both options are two acceptable ways the problem can be tackled.
Answer:
The ball reached its maximum height of (
) in (
).
Step-by-step explanation:
This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.
The first step in completing the square is to group the quadratic and linear term:

Now factor out the coefficient of the quadratic term:

After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:

Now take the balancing term out of the parenthesis:

Simplify:

The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is:
