C 288 8. The algebraic identity (a2+b2)(c2 +d2) = (ac + bd)2 + (ad - bc)2 (ad+ bc(ac - bd)2 12. 11 appears in the Liber Quadratorum. Establish this identity and use it to express the integer 481 = 13.37 as the sum of two squares in two different ways. 13. Given rational numbers a and b, find two other rational numbers x and y such that a2b2 =x2 + y2. [Hint: Choose any two integers c and d for which c2+ d2 is a square; now write (a2 + b2)(c d2) as a sum of two 9. (a) squares.] (b) Illustrate part (a) by expressing 61 = 52 + 62 as the sum of squares of two rational numbers. t 10. Solve the following problem, which is one of the tournament problems that John of Palermo posed to Fibonacci. Each of three men owned a share in a pile of money, their shares being Each man took some money at random until nothing was left. The first man afterward returned of what he had taken,the second amount thus returned was divided into three equal parts and given to each man, each one had what he was originally entitled to. How much money was there in the pile at the start, and how much did each man take? [Hint: Let t denote the original sum, u the amount each man received when the money left in the pile was divided equally, and x, y, and z the amount of the total. and 3 . 2 , and the third. When the Tо fo (а) took. Then

Q: 6+w=4

A: The give equation is 6 + w = 4To find the value of w.

Q: a) How many students are taking Art?

A: the number of students taking Art if given by 6+10=16

Q: What is the Probability that a student is not taking either class?

A: From the given Venn diagram, it is observed that the number of students who are taking art only is…

Q: 3 3 x-5 1 322

A:

Q: C3x2 + – 4 kx - 5x- 6.

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Q: 4. 3*+4 72x-1

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Q: 24 = 3 + y

A: We have to solve the given expression for y. The expression is 24=3+y.

Q: do g please

A: From part e:For model 1; 95% CI and PI are: (168.5648, 175.9918) and (163.7609, 180.7957)For model…

Q: Let Mbe as in Equation (3.14) and let X = [1, 0, ½]¹. Show that the entries of Y=MX sum to 1.

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Q: Simplify. - 1 (3a "") (За За

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Q: limx→- f(x) limo+ f(x) limx→ = = =

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Q: 2. 9=x-2y 3x + 5 = 2y

A: The given equations are system of linear equations in variables x and y. We solve these by…

Q: 4 1/2 + 3 2/3=

A: Given,

Q: X 60° Y 503 5

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Q: limx→2 f(x) = lim, ¹x→−1+ f(x) =

A: Given graph of the function fx is   1. Find :  limx→2 fx. 2. Find :limx→-1+ fx.

Q: A О в C

A: Given: To Find: To find the slope of the following line segments:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.