nd the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant prrelation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the umber of stories of six notable buildings in a city. (a) x= 501 feet (c) x = 802 feet (b) x = 651 feet (d) x= 728 feet 496 483 eight, x tories, y 772 628 518 508 51 48 46 41 37 35

Q: Find m Z EFG. A BC D HX-6 E 3X+3

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Q: As indicated in class, the main motivation for using Google Trends data is that the average person…

A: Happiness Variable, as measured by the Google search intensity index for “Parks and…

Q: 1. (D² – D – 2) y = 30

A: Using auxiliary equation than pi  y=c.f + p.I   General solution

Q: Values a and b satisfy (a + 1)2 + (b − 23)4 = 0. Compute the value of ab.

A: We have been given the equation (a + 1)2 + (b − 23)4 = 0

Q: Find a x b

A: Given that a= 2i + j and b= i - j + k Our aim is to calculate a × b = ?

Q: Find w such that 2u + v- 3w = 0. %3D u = (0, 5, 7, 2), v = (-3, 4, -8, 1) W =

A: vector

Q: Solve for 19 a) =20 = a" (I+ JEi ) b) z²+ zi +1 = b) zt Zi t1 =0

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Q: V3 which of the following is equal to J, 1 dx ? 1+16x? 4 A. 3 O Option 1 Option 2 C. D. 12 Option 3…

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Q: 7 Determine the intgral

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Q: Find u × v, v × u, and v × v. u = 2, −9, −1 v = 9, −2, −6

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Q: Find u · v. u = 8, 2 v = −7, 3 u · v =

A: A dot product is also called Scalar product , is a way of multiplying two vector quantities to…

Q: 5. Prove that arg(z1zz) = argzi – argzz %3D

A: Introduction: For a complex number z=x+iy, where x is the real part and y is the imaginary part,…

Q: Let x be the r.v Such that ECx)=D2 ECx)=2a %3D [2+Qx}?) =2a3 %3D Findthe Value of a

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Q: Let à = 2i +4j - k. Find a.

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Q: The average monthly income of public school teachers is Php25,000 with standard deviation of Php800.…

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Q: Evaluate z dr 2(/z+1) + C o b. 2 - 1) C. + C - Vz+I Vz -1

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Q: V ₂ 2 P n P₁ U₁ P₂ Give the In for 2 side

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Q: S dx. 1 Evaluate and simplify its final answer. J 2x2-2x+1

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Q: M 15 J L

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Q: K M N х+3 7, 4x – 9 R 12

A: Topic-Geometry

Q: R =  C − S t ; S

A: R=C-St

Q: Expand completely. (3z 1) ar + ba + cr+ da² + ex + ƒ %3D d = and f=

A: Given 3x-15=ax5+bx4+cx3+dx2+ex+f To do  Find the value of a, b, c ,d ,e and f in the expansion

Q: Sketch the region R and evaluate the iterated integral f(x, у) dA. (1- 6x + 8y) dy dx y 2.0 3- 1.5…

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Q: A bag contains three red balls, two yellow balls, and two green balls. Suppose that we pick three…

A: let the number of red balls be denoted by R and number of yellow balls be denoted by Y. PR=0,Y=0=0…

Q: Find the most general antiderivative. Sex.6x+ 4) dx O 6x2 +6+ C (2x3 O 6x+12x+4x+ C 14+3x2+4x+ C…

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Q: e² 1+2e +e S Select one: O A. dx 1+6² 2 1+6² +C +C O B. OC. +C OD. +C -2 Ite -1 1+e

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Q: Determine values of x and y so that v · w = 0 and v · u =

A: There are vector representation given as, v=x1y , w=x-20  and u=0-9y. To find the value of  x  and y…

Q: 2y+8 6. 15y2 Зу+12 3m+9 7. 5m+10 4m+12 4m-8

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Q: SW TV. Find VW. 39 26 W V V 14 VW = %3D

A: The figure is given by To evaluate : VW

Q: Find the value of (-j)!nj.

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Q: Evaluate T. 8xyz dz dx dy 14 17 18 15 13

A: We have to perform 3 integrals in the given equation. So that we get a integer from that.

Q: cheyon ne mcoonald Find m Z EBC. 3X C

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Q: Let ā = (−4, −5, −3) and 6 = (-5, −4, 4) Find a × 6. V >

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.