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MathThe problem provides inconsistent information (there are not given C and D), hence, supposing that C is the coefficient of (x+1) and D is the constant term yields: `2x*x^2 + 2x*(4x) + 2x*1  3*x^2...

MathYou need to open the brackets moving from inside to outside such that: `2x+3yz{x+3y[y+2z(x2y4z)]} = 2x+3yz[x+3y(y+2zx+2y+4z)]` `2x+3yz[x+3y(y+2zx+2y+4z)] =...

MathWe will use the formula, h(x) = [kCx * (Nk)C(nx)]/NCn. But, let me clarify if its k = 3, instead of x = 3.

MathYou need to remember how to use the roots to form a quadratic equation such that: `x^2  sx + p = 0` Since s expresses the sum of roots and p expresses the product of roots, hence you may form the...

MathTh equation is equivalent to `a^2+ba+(cx^2)=0` Use the quadratic formula, Solutions : `a=(b+sqrt(b^24(cx^2)))/2` if `b^24c+4x^2gt=0` . and no solution if `b^24c+4x^2lt0`

MathYou need to remember that two planes are parallel if the normal vectors to these planes are parallel. The problem provides the information that the plane `P_1` passes through the point (4,1,3),...

MathCan you please check this for accuracy? When rolling a pair of dice, determine the probability of...You may get the following results when rolling the pair of dice such that: you may get the number 2 in 1 combination:(1,1) you may get the number 3 in 2 combinations: (1,2) or (2,1) 4  3...

MathYou need to remember that the tangent line to the graph of function is vertical and parallel to y axis if the slope of this tangent line is not defined. You need to use implicit differentiation to...

MathYou need to find t in terms of x and then you should substitute the expression in terms of x for t in equation `y = ln(1  t)` such that: `x = t^3 =gt x^(1/3) = (t^3)^(1/3) =gt root(3) x = t` `y =...

MathYou need to find derivative of the function g(x) such that: `g'(x) = (csc x + cot x)'` You need to remember that cosecant function is the reverse of sine function and cotangent function is a...

MathCan someone explain to me how regression is used to make predicitions when applying statistics to...It is not so much that regression is used to make predictions. You use regression to find the "bestfit" model  the model that fits the data best. Regression assures that the model created is...

MathRegression is used to predict an unmeasurable (dependent) variable or variables from a measurable (independent) variable or variables. The regression equation is any function of the independent...

MathYou need to use limit definition of derivatives such that: `lim_(hgt0) ((x+h)^2 + 5^(x+h)  x^2  5^x)/h` You need to form two groups of terms such that: `lim_(hgt0) ((x+h)^2  x^2)/h +...

MathThe function y=3x^3 2x +1 The extreme points of y lie at the solution of y' = 0. If the solution of y' = 0 is y = c, the maximum points lie where y'' for c is negative and the minimum lies where...

Math`y= x^3 x^2 14x + 24 ` Let x= 2 ==> 84 28 +24 = 0 Then (x2) is a factor of y. Now we will divide y by (x2). `x^2+x 12`...

MathThe equation x^2 + 5x +2=0 has to be solved. The solutions of the quadratic equation ax^2 + bx + c = 0 are x1 = `(b + sqrt(b^2  4ac))/(2a)` and x2 = `(b  sqrt(b^2  4ac))/(2a)` For x^2 + 5x...

MathThe equation x^2 + 5x +2=0 has to be solved. The solutions of the quadratic equation ax^2 + bx + c = 0 are x1 = `(b + sqrt(b^2  4ac))/(2a)` and x2 = `(b  sqrt(b^2  4ac))/(2a)` For x^2 + 5x...

MathPart I: (2/5) / (4) Step 1: Change 4 to an improper fraction. (2/5) / (4/1) Step 2: "Flip" the denominator's fraction; rewrite as a multiplication. (2/5) * (1/4) Step...

MathAfter travelling south for 7 1/2 h, how far is the ship from the port in terms of the Pythagorean...Step 1: Find the distance covered heading due west. d = rt d = 20 (10 ) d = 200 km Step 2: Find the distance traveling south after making a 90...

MathFind `int sqrt(1+4x^2)dx` : (1) Let `x=(tanu)/2` . Then `dx=1/2 sec^2udu` and `u=tan^(1)(2x)` Now substituting for x we get: `int sqrt(1+4x^2)dx=int sqrt(1+tan^2u)1/2sec^2u du=1/2int sec^3udu`...

MathYou need to remember the formula that helps you to evaluate the average molecular speed of `O_2` such that: `v = sqrt(3TR/M)` R expresses Boltzmann's constant = `8.314 J*K^(1)*mol^(1)` T...

Mathwhat is the equation of the line that has a slope of 1/4 and a y intercept of 3A. Y= 1/4X  3B....Slopeintercept form of linear equation is y=mx+b where m is slope and b is yintercept. So in our case `y=1/4x+(3)=>y=1/4x3` Thus the answer is C.

Mathsorry?

Matha) Multiply the cost of each item, admission or raffle tickets, by the number of items purchased. Admission=2 adults * cost per adult + 3 children * cost per child 2(8) + 3(5) = 16 +...

MathYou need to substitute `oo` for x in equation under limit to check if the limit is indeterminate such that: `lim_(xgtoo) (sqrt(x^2+2))/(sqrt(2x^2+1)) = (sqrt(oo))/(sqrt(oo))` `lim_(xgtoo)...

MathYou should use l'Hospital's theorem only if you find that the limit is indeterminate such that `0/0` or `oo/oo` , hence, you need to substitute `pi/2` for x in equation under limit such that:...

MathYou need to use l'Hospital's theorem if the limit proves to be indeterminate, hence you should check if it is the case such that: `lim_(xgt0) x/(tan^(1)4x) = 0/(tan^(1) 0) = 0/0` Since the limit...

MathYou need to use arcfunctions to solve the equation such that: `sin (x/3) = sqrt3/2 =gt x/3 = (1)^n*arcsin (sqrt3/2) + n*pi` `x/3 = (1)^n*pi/3 + n*pi` `x = (1)^n*3pi/3 + 3n*pi` `x = (1)^n*pi +...

MathHere are the first few entries of lacsap fractions; you would lay them out in a triangular array like pascal's triangle: `1/1` `1/2 ` `2/1` `1/3` `2/2` `3/1` `1/4` `2/3` `3/2` `4/1` If...

MathThis expression cannot be expressed in the form nPr. Recall the definition of nPr: nPr = n * (n  1) * ... * (n  r + 1) The given expression, (27*26*25*24) / (4*3*2*1) is not in this form. It can...

MathThe use of the word "may" makes the statement ambiguous. Based on this statement, there is no certainty about whether or not vitamin E will help fight cancer and heart disease.

MathEvery term in the first binomial must be multiplied by every term in the trinomial. Therefore, when multiplying 3x by every term in the second set of parentheses, you get: 3x^3  12x^2 + 6x and...

MathGiven the curve `y= x^2` and the line : xy + 2 = 0 ==> y= x+ 2 We need to find the intersection between both. ==> The, we will set the equations to equal each other. ==>`x^2 = x+ 2` `==gt...

MathDo you mean a SUM of three? If you are rolling a PAIR of dice (meaning two cubes,) then the probability of rolling a SUM of three, meaning adding the two numbers shown on top, is 2/36, or 1/18....

MathSolve `2/(x+3)<1` : `2<x+3` `x+3<2` or `x+3>2` Thus `x<5` or `x> 1` Thus the solutions are any x in (oo,5) and (1,oo) Solutions are x<5 or x>1

MathThe equation 9x^4+5x^24=0 has to be solved. Let y = x^2, this gives the equation 9y^2 + 5y  4 = 0 => 9y^2 + 9y  4y  4 = 0 => 9y(y + 1)  4(y + 1) = 0 => (9y  4)(y + 1) = 0 => y =...

MathThe specific numbers did not appear in the problem. The general method is: Given `(dp)/(dt)=kp` where `k` is a proportionality constant and `p` is the population at time `t` . We know that any...

MathThe equation for torque is given by `tau=rFsintheta` where `tau` is the torque, r is the length of the arm of the lever (in this case a wrench), F is the force applied and `theta` is the angle...

MathYou need to remember that indefinite integral of acceleration function represents the velocity function such that: `v(t) = int 3 sqrt (t+1) dt` You should come up with the substitution `t+1 = y =gt...

Mathnotes: from the property of vectors we have (l veca x m vecb) = lm(veca x vecb), as l veca x m vecb =  la .  lb . sin(la,mb). n without loss of generality ,we may assume that a,b are...

Math4/52

MathJustification: Cheng is 25 points behind Ben. Aisha is 22 points behind Ben. Together, they are 47 points behind Ben. Together they can win at most 10 (8+2) points and ben will win at least 1...

MathThe function f(x)=`ln(x^25)` . The second derivative f"(4) has to be determined. f(x) = `ln(x^2  5)` f'(x) = `(2x)/(x^2  5)` f''(x) = `(2*(x^2  5)  2x*2x)/(x^2  5)^2` => `(2x^2  10 ...

MathThe slope of the line tangent to the curve y^3+x^2 y^23x^2=9 at (1.5,2) has to be determined. The required slope is the value of y' at the point (1.5, 2) Use implicit differentiation to determine...

MathYou need to substitute 0 for h in equation under limit such that: `lim_(hgt0) (cot(5pi/6 + h)  cot (5pi/6))/h = (cot(5pi/6)  cot (5pi/6))/0 = 0/0` Since the limit is indeterminate, you may use...

MathHistogram Calculate a fixed bin width that would give a histogram with five uniform intervals for...Order the data: 5 5 6 6 6 7 7 7 7 8 9 9 9 9 10 10 10 10 10 11 11 12 12 13 14 The range is 145 = 9 We want 5 roughly equal groupings of equal bin width, so we simply divide the range...

MathTo graph `0<x<=5` you start by drawing the number line, then mark 0 and 5 on it. Make two small circles around those numbers. The circle around 5 should be bubled in to mark that x can take...

MathTo find the value of y at point x=13, we need to substitue x for its value in the equation. In other words, replace x with 13 in your problem. `y=5x=>y=5*13=65`

MathYou may simplify the function to its lowest terms, hence you should write the factored forms of numerator and denominator such that: f(x) = 4x(x3)/(x+1)(x3) = 4x/(x+1) You need to remember that...

MathPlease give a quick way of determining the product of 2 numbers if their sum is 14 and the sum of...If the sum of two numbers is known and the sum of their squares is known, their product can be determined in the following way. Let the two numbers be X and Y. (X + Y)^2 = X^2 + Y^2 + 2*X*Y =>...