Some students in a school were surveyed to determine how many hours they study per night and their grade-point averages. the results are shown in the table. hours studying per night vs. grade-point average hours studying per night, x grade-point average, y 0.4 2.0 0.9 2.4 1.5 2.6 2.2 3.1 2.6 3.5 3.3 3.8 if the data are entered into a regression calculator, what is the approximate y-intercept of the resulting regression line?

1.75927

Step-by-step explanation:

Refer the attached figure

x                  y                  

0.4               2

0.9               2.4

1.5                2.6

2.2               3.1

2.6               3.5

3.3                3.8

Mean =

Mean of x values :

Mean of y values :

-1.4167

-0.9167

-0.3167

0.3833

0.7833

1.4833

-0.9

-0.5

-0.3

0.2

0.6

0.9

2.0069

0.8403

0.1003

0.1469

0.6136

2.2003

SS: 5.9083

1.275

0.4583

0.095

0.0767

0.47

1.335  

SP: 3.71

Sum of X = 10.9

Sum of Y = 17.4

Mean X = 1.8167

Mean Y = 2.9

Sum of squares (SS) = 5.9083

Sum of products (SP) = 3.71

Regression Equation = ŷ = bX + a

b = SP/SS = 3.71/5.91 = 0.62793

a = = 2.9 - (0.63*1.82) = 1.75927

Thus ŷ = 0.62793X + 1.75927

Equation of line : y =mx+c

Where m = slope

c = y-intercept

Comparing regression equation with equation of line

ŷ = 0.62793X + 1.75927

m= 0.62793

y-intercept =1.75927

Hence the approximate y-intercept of the resulting regression line is 1.75927

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

there are 25 people coming to the party

step-by-step explanation:

the text says that there will be 22 children at this party, 1 teacher, and 2 parents. so if you add them all together (22+1+2) it will equal 25. (=25)