3. Given the following GPA for 4 students: 2, 3, 3, 4. Age of students are: 10, 11, 12, 15. There are 10,000 total students. Average GPA: Unknown, Standard Deviation of GPA: 0.02 and it’s Normal. d. Find Regression Line Equation. (5 points) e. If a student’s age is 13, what is the corresponding GPA? (5 points) Please show the work, thanks

Part A: Compute the derivative of ?(?)=(4?^4 + 2?)(?+9)(?−6)

Part B: Compute the derivative of ?(?)= (9x^2 + 8x +8)(4x^4 + (6/x^2))/x^3 + 8

Part C: Compute the derivative of ?(?)=(15?+3)(17?+13)/(6?+8)(3?+11).

Prove that for every n ∈ N:

a) (10^n + 3 * 4^(n+2)) ≡ 4 mod 19, [note that 4^3 ≡ 1 mod 9]

b) 24 | (2*7^(n) + 3*5^(n) - 5),

c) 14 | (3^(4n+2) + 5^(2n+1) [Note that 3^(4n+2) + 5^(2n+1) = 9^(2n)*9 + 5^(2n)*5 ≡ (-5)^(2n) * 9 + 5^(2n) *5 ≡ 0 mod 14]

A = [4, 5, 9]
B = [-4, 5, -7]
C = [2, -7, -8, 5]
D = [1, -9, 5, -3]
E = [3, 3, -1]

Uz = 1/|z| ^z
d(X,Y) = (Rθ) d = diameter R = Radius θ = Theta

Find

a. Uc
b. d (D, C)
c. Let P = B + 3E, UP =
d. A x B
e. 3B x E
f. C x D

JAVA LANGUAGE

Write a program that declares a 2-Dimensional Array with 4 rows and 4 columns to store integer values, and then:
fill elements with values as the sum of its column index and row index, e.g., the element at row index 0 and column index 0 is (0+0=0), the element at row index 0 and column index 1 is (0+1=1).
compute the sum of elements at the second row.
compute the sum of elements at the third column.
compute the sum of all elements.
print the array in tabular form.

Write a program that declares an array list to store integers and fills the elements with users’ inputs from keyboards. Then prints the following outputs (each in one line):
Every element at an even index.
Every even element (using enhanced for loop).
Every odd element (using common loop, not enhanced for loop).
All elements in reverse order.
Only the first, the middle and the last element.
The largest and smallest element.
The alternating sum of all elements. For example, if your program reads the values from users: 1 4 9 16 10 7 4 9 11 5, then it computes 1-4+9-16+10-7+4-9+11-5=-6.

a = [4, −9, 4] b = [7, 2, 3] c = [5, −8, 9] d = [1, −3, 2] e = [6, −2, −5, 9] f = [4, −3, 7, 5] g = [1, 3, −1, 5]
h = [7, −5, 5] i = [5, 13, −7, 11]
Express the hyperplane implicitly or explicitly given the following
a) a and h
b) f and i
c) e, f, and g
d) The hyperplane containing b, c and d can be expresses both implicitly and explicitly. Express in both forms and show they are equivalent

evaluate the indefinite integral

sqrt(4-x^2)

George who is the General Director of the Research Institute for Tourism in Greece, believes that the percentage composition of 5 Stars hotels is not the same in Crete and elsewhere (Southern Aegean Islands and Ionian Islands). In order to test this statement, create two additional binary variables as follows:
5STARS: Yes (Code 1) when STARS = 5; No (Code 0) when STARS ≠ 5.
CRETE: Yes (Code 1) when Region_ID = 1; No (Code 0) when Region_ID ≠ 1.
3.1 State the null and the alternative hypotheses.
3.2 Test the null hypothesis at α = 5%.
3.3 What is your conclusion?

Calculate the Chi Square ..the critical value ..the p -value and the margin error!

REGION ID

1= Crete
2=Southern Aegean Islands
3=Ionian Islands

3.4 Let π1 denote the population proportion of 5 stars hotels in Crete and π2 the population proportion of 5 stars hotels elsewhere. Set up a symmetric 95% confidence interval estimate of the difference (π1 - π2). What is your main conclusion?