4. .) Three professors taught three different sections of a course last semester. The table below shows the grade distribution for each of the three professors. Grade Professor 1 Professor 2 Professor 3 Total A 12 11 27 B 16 29 25 C 35 30 15 OTHER 27 40 23 TOTAL Using a .01 significance level, test the null hypothesis that the grade and professor taken are independent.

Q: dy dx 23 X + 24 2メ+ツ

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Q: Find mZVUZ if mZZUT= 16x + 2, | MLVUZ = 24x – 1, and mZVUT = 16

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Q: Solve for the following: a) Var(2X−5) when X ∼ U {1,2,…,20}. b) Var(3X−4) when X ∼ U {1,2,…,30}.

A: Given,X~U(1,2,.....20)minimum value=1maximum value=20f(x)=120-1f(x)=119         ; 1≤X≤20

Q: Solve for x :C+Vz + m = A

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Q: So lue ty'= (2x -1)

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Q: x² y² + (y²) ² y" = = U C

A: We are going to solve this by substitution method

Q: е 0.32+ j0.56

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Q: d?y Determine if: 2x2 – xy + 5y2 = 7 dx2

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Q: 2. Solve for x. A. В. С. D. A 8A 12 24

A: Since, lines are parallel and the transversals are cutting the parallel lines, which are not…

Q: Show that fu,, u,) is an orthogonal basis for R?. Then express x as a linear combination of the u's.…

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Q: 6. Sš(vtny - (ylny - )dy 9-у?

A: Solving the following integral in two parts and then combining the results gives the solution.

Q: 2. (-2, 3) and (2, -1) m%3D X,- X, 1- 2 -

A: Given that (-2,3) and (2,-1)

Q: What are parts h-j?

A: The complete table is              R         L         S        TotalH        140     240     400…

Q: tim D1R (++)) + om 1 Im te i ned d

A: limn→∞((n1+n)α+sin(1n)),foralln∈Qnow ,We recall some…

Q: / esx+3 dx = %3D

A: To evaluate the integral :- I = ∫e5x+3 dx Substitute    u = 5x+3du = 5 dxdx = du5

Q: IPIAI Evaluate p²^z^¸¶= J=

A: The given integral is;

Q: 1 = 4y-24 ア-6 9.

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Q: 16 C 73° 12 61 20

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Q: R =  C − S t ; S

A: R=C-St

Q: Solve the Coout's linear wsuation by method. 2n, t0 x + X3 = 4 -3n, +4Xz -213 6.

A: To Determine :-  The linear equation by Crout's method . 2x1 + 0x2 + x3 =4-3x1 + 4x2 -2x3 =-3x1 +7x2…

Q: r4 3 +1 d y? 1

A: We will solve the problem

Q: Which is the depem expression given th How long did Gabr 15.75 miles?

A: Given Gabriel went running in the park. he ran 6.3 miles per hour. The equation that shows the total…

Q: Fuid x;on [o,360) 2"(-2)

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Q: flx). a/2)=6x+6.and hlx) -alA 88

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Q: dx 19. S 16+9x² A. tan- () + B습tan-' () + ccot- () + c -1 В. + C 16 16

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Q: Reduce (1+j)?/(1-j) to the form a+jb. a. others b. -1-j С. 1+] d. 1-j е. -1+j

A: 1+j21-j×1+j1+j=(1+j)31+1=j3+3j2+3j+12=-j-3+3j+12=2j-22=j-1=-1+j

Q: integrate show full solution

A: To Integrate: ∫x26e-x/2dx

Q: A hot pizza (25 degree Celsius) is taken directly from an oven and placed in a table where the air…

A: Given that, A hot pizza (250 degree Celsius) is taken directly from an oven and placed in a table…

Q: Evaluate the product of C and ET in order CET if possible. Evaluate matrix K if K=ED.

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Q: 24. Find the first approximate solutions for -2x? + 4x + 2 = 0. 1 - and x = 3- 3 3 x = and x = 3- 3…

A: -2x2+4x +2 = 0Dividing Both the Sides by -2x2-2x-1 = 0Since the coefficient of x2 is 1Move the…

Q: If = , where b + 0 and d # 0, then a · d = b•c.

A: Given: ab=cd, b≠0, d≠0 For prove given expression, we do cross multiplication and simplify it as…

Q: a2z If z = In(x² + y²), find a²z + dx2 ду?

A: Given, z=lnx2+y2

Q: Solve Lc = b to find c. Then solve Ux= c to find x. What was A? L C= X = A = [100] 110 1 1 1 U = [1…

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Q: 6 15 10 /3х - 2 12 D C

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Q: Find A ) A= [ ' for A -3 -2 3.

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Q: 11. The diagonal of a square is 2 times the length of one side. True False

A: We consider the square and check for the given condition

Q: 27 4х + 2 24 4х A) 4 С) 3 В) 0 D) 12

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Q: What is the magnitude of a=?

A: a=<−1,0,2>To find its magnitude