Will give brainliest! , you! the data is attached. 5)the table shows the test scores and the sleep averages of several students. a. write the least squares regression equation that models the data. let x = hours of sleep and y = test score. b. use the equation to determine the approximate test score of a student who sleeps an average of 8 h a night. show your work.

a. To find the least squares regression equation for a group of (x,y) points:

Step 1: For each point(x,y), we need to calculate x² and xy first.

Step 2:Sum all x, y, x² and xy, which gives us Σx, Σy, Σx² and Σxy

Step 3:Calculate Slope m: m = (NΣxy − Σx Σy)/ N(Σx²) − (Σx)² , here N is the number of data.

Step 4:Calculate Intercept b: b = Σy − m(Σx)/ N

Step 5: Assemble the equation as y= mx+b

Here, we have ∑x = 120, ∑y= 1379, ∑x²= 919.5, ∑xy= 10466 and N= 16

So, m= (NΣxy − Σx Σy)/ N(Σx²) − (Σx)²

=

=

=

= 6.33

and b = Σy − m(Σx)/ N

=

=

=

= 38.71

So, the least squares regression equation is : y= mx+b ⇒ y= 6.33x +38.71

b. When x= 8, then y= (6.33×8)+38.71 = 50.64 + 38.71 =89.35

The approximate test score of a student who sleeps an average of 8 h a night is 89.35%

a) 0.25x times 3. (could be wrong on equation.)

b) 2.25 pound of dark chocolate. (can i eat all the chocolate? plz? anyway, again, could be wrong, but i hope im right. all the chocolate together should be 5.25 pounds)

have a good day!

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc