38. An operation A is defined on the real numbers x and y by the equation xAy = |x|– y². Which of the following is true for all real numbers x and y ? (A) xAy = yA X (B) xAy = (-x)Ay (C) If xAy = 0, then y = 0. (D) If xA y = 0, then y = -x. (E) If xAy = 1, then y = 0.

Q: Suppose that y= 2(1- e *). Compute y' and show that y' =2-y. y' =] 2-y%3D Does y' = 2-y? O Yes O No

A:

Q: Write out explicitly and simplity possible as h= 5 n!

A: ∑n=0n=5 n2n!=?

Q: 7 --y2 Then 2 5 Q2: If z = –x² az + 5x ду az 7y ||

A:

Q: 4 z+9 (z – 2) + 2 (9 – 2) < 18 (x + 1) Enter the exact answer in interval notation. -To enter 00,…

A:

Q: 5. Find the on the interval [0, 4]

A:

Q: if f(x1,x2) = e-*-*2, 0 < x1 < o, 0 < x2 < o, F(x1, x2) = e-Xie-x2 + e-X2 True False

A:

Q: 2.1 Without using a calculator, rationalise the denominator and simpny. 3-J2 3+2 (3) 2.2 Solve for…

A:

Q: 11 Compute x2+ where x =i- 1. Answer: 2.

A: We have to find the value

Q: 6. Evaluate In (x - In (r-...))dr in terms of some new variable t (do not simplify).

A: Given :- ∫lnx-lnx-...dx To find the given integral in terms of some new variables t

Q: Suppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible…

A:

Q: 11. If AJKL - AMKN, find the value of x. 12 N 20 x+1 Зх - 2 J

A: It is known that in a pair of similar triangles, the corresponding sides are proportional. It is…

Q: : 2 < x < 4} and B = {x € R : –4 < x < 1}. Prove

A:

Q: 22. Differentiate the following with respect to the variable x, giving your answer in a implified…

A:

Q: Verify that 2. 1 Hint: Consider x 0, x 0 separately

A: To verify

Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: Let x = (3,-1,0) and y = (0,1,5). a) Show that no choice of numbers a and b can make ax + by =…

A:

Q: If X is a positive number such that : X² – 10X = 9VX Then X – VX = ?

A: given:x2-10x=9xsquaring both the sides:x4-20x3+100x2=81xwe get x=0, x=1, x=19±372.but for the…

Q: NEED ASAP PLS!! Use exact values whenever possible! 1. 3z^2-(5-j4)z+(2-j3)=0

A: The given equation is: 3z2-5-j4z+2-j3=0 We have to solve this equation for z. Required formula:…

Q: 2 is > 2 of x, the

A:

Q: 6. Find f'(1) if Ax) = nx

A:

Q: 9. Find the general solutions of X' = AX with A =

A:

Q: Find positive integers that satisfy x + y + z = 6 x + 5y + 8z = 35 x = i ! y = i

A:

Q: 4. Which relation between x and u yields 16+x² = 4/1+u?

A: Given:

Q: Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined as f: R ->…

A:

Q: Given: 3(x + 2) = 15 Prove: x = 3

A:

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: create 3 equations of the form ax + by + cz = d where a, b, c, and d are constants (integers between…

A: Integers between -5 and 5 are -4, -3, -2, -1, 0, 1, 2, 3 &amp; 4. Let us choose a=1, b=2, c=3 &amp;…

Q: Express (2ry+ 2x- 1)-i (x2 - y-2y) as polynomial in the binomial argument z = x+ iy. O iz? + 2z + 1…

A:

Q: evaluate x2 -(xy-y) for x satisfying x/9 -7 = x/2 and satisfying -3y -5=4y+23

A: See the details solution in below

Q: 2. Σ--1)k , k%3D k+1

A: The given sequence is ∑k=0∞-1kkk+1

Q: 11| Q1) If A--2 -1,B 3 3 4 -5 -1 -1 13 -1 Find (–1 x A) + (B + C)

A:

Q: What is the domain of { (z,3z2- 5) Iz ER except 0}? All real numbers All negative numbers {x\x€R>0}…

A:

Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A:

Q: Q2-Prove tut- va" - r* ify =()()+ ()F-7 if y =

A:

Q: Show that o () –1 is an implicit solution to 2 -2y on the interval (-00, 00). Inload our

A:

Q: Both Newton and Leibniz were satisfied that their calculus provided answers that agreed with what…

A:

Q: Show that |Aut(Z2 × Z2)| = 6

A:

Q: 1. Find z for x = 4.7 %3D 2. Find x if z = 3.2

A: Given  Sample is normally distributed with mean 5 and standard deviation 3.8

Q: 2. Evaluate f'(5) for y = v2x² – 1 hor Ju OIT

A:

Q: Express (2.ry+ 2x - 1) – i (x2 – y? – 2y) as polynomial in the binomial argument z = r+ iy. O -iz? +…

A: Solution

Q: If x is a n-700 as a. always b. real number Sometimes never such that 1x11, then x" -> -0

A: We want to find correct answer.

Q: 2.2 Use algebraic manipulation to prove that (x +y) · (x + y) = x.

A: As 2 Questions are given, I will solve only the first, We need to Prove that: x+y(x+y¯)=x Solving…

Q: Prove that y = e-3* (Acos 5x - Bsin 5x) + Cx; A, B and C are arbitrary constants will equalto y"(17x…

A: Given,            y =e-3xAcos 5x -Bsin 5x + Cx

Q: +prove by indirect method that i X+y >5 then or y>3. x>2

A: We need to prove that if x+y&gt;5 then x&gt;2 or y&gt;3

Q: 2. If f(2) = e*, describe the images under f(2) of horizontal and vertical lines, i.e. what are the…

A:

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: -2 0 b) Given -2 6. and X- show that x'Ax = 27, suggest that 5x + 6x + 7x - 4X,X, + 4X,X, -27

A:

Q: 27 1 2-r2 4. Evaluate: r dz dr de Jo

A: Solution

Q: 16) * Find y' if y In (x2-8), when x 4

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!