The class outing ticket includes a snack-pack with three items, a cooldrink, chocolate and then chips or popcorn. The tree-diagram below indicates the possible choices of the snack pack. Ms Basson pre-packed the snack pack. TREE DIAGRAM: POSSIBLE CHOICE OF SNACK PACK Type of cooldrink Fanta (F) Sprite (S) Chocolate choice Aero (A) Tex (T) Aero (A) Tex (T) Chips or popcorn Chips (C) Popcorn (P) Chips (C) Popcorn (P) Chips (C) Popcorn (P) Chips (C) Popcorn (P) Possible Outcome for the snack pack FAC A FTC FTP B C STC STP Study the tree diagram and answer the questions that follow:

Q: Fill in The Unit Circle Positive: Negative: Positive: Negative: O O Positive: Negative: Positive:…

A: The unit circle is,

Q: 1 cos³x -dx =

A: The given integral is 1/Cos3x.

Q: D Question 24 Suppose that P= f(t) is the population (in millions) of the country & years after the…

A: We can find the answer as below.

Q: Type the left side of the equation of the ellipse. Which graph shown below is the graph of the…

A: Topic:- geometry

Q: How would you express a line with a zero slope? x = 0y - b y = 0x + b x = 0y + b y = 2x - 2b

A: Solving the problem by finding the zero slope equation.

Q: Identify the equation without applying a rotation of axes. 2 10x² -8xy + y² +9x+3y-6=0

A: Given, 10x2-8xy+y2+9x+3y-6=0

Q: (i) Consider the function f: R\{-2,3} → R defined by 2x³4x²5x - 3 x²-x-6 f(x)= - (a) Prove, using…

A:

Q: Graph f(x) = 2-√√5-4x Use the transformation of graphs techniques. Show all transformations. Label…

A:

Q: a) Determine the continuity of f(z) at z=2i where z² +4 f(z)={z-2i z - 2i, if z # 2i, if z = 2i.

A:

Q: 6. If a = 2, b = 2√√3,7 = 30°, solve for c and 3.

A: We know that cosine rule is c=a2+b2-2abcosγGiven data a=2, b=23 and γ=30c=22+(23)2-2*2*23*cos(30)…

Q: Find the equation of the parabola described below. Find the two points that define the latus rectum,…

A:

Q: The table shows various values of a linear function f(x). X-40250 -4 0 2 5 9 10 f(x) -11 1 7 16 28…

A:

Q: Verify the Divergence Theorem for the vector field and region: F = (3x, 5z, 3y) and the region x² +…

A:

Q: Express the given quantity in terms of −sin x or cos x. sin(3ℼ/2 - x)

A: The given trigonometric function is f(x)=sin3π2-x

Q: Find an equation for the ellipse whose vertices are at (-8-2) and (0-2), and focus is at (-2-2)…

A:

Q: Given f(x) = x² + 2x-5 and values of the linear function g(x) in the table, what is the range of (f+…

A:

Q: "풍 2 secx dx tan³x + 4 tanx

A:

Q: bounded by x² + 2y = 4 and - Sketch the area x+y+2=0 and determine: d) area using using horizontal…

A:

Q: Find the solution to ty""+612 y" +29ty-29y=0; y(1)=2, y'(1)=-3, y"(1)=19

A: The given equation is; t3y''' +6t2y'' +29ty' -29y=0, y(1)=2, y'(1)=-3, y''(1)=19.

Q: Which of the following is equivalent to 12 n=1 60 13 60 13 O-20 20 5 8 ?

A:

Q: A student was asked to determine the y-intercept for the logarithmic function f(x) = log₂(x + 3) +…

A:

Q: 4. S (y³+4)dy y(y+1)

A:

Q: The infinite series Σ a. series liner 8 n¯4 is a

A: We know that the p-series is the following. Thus, for             p=4.

Q: 2. f sin √tdt

A: To evaluate the given integral.

Q: sigma 4-0 (1-x)/sqaurerootx dx

A:

Q: a=, b= a) a-2b b) a + b c) à b d) The angle between a and b =) Find all vectors which are twice as…

A: We need to solve vector problem..

Q: A construction worker is pouring concrete stairs. The first step requires 1.8 cubic feet of…

A: Concept: Arithmetic sequence: The series where the common difference between any two next words…

Q: 5. S (2x²-3x+10)dx (x²+4)²

A: I have stated the used formulas in the solution

Q: 4. S du (u²+a²)²

A:

Q: Water is leaking out of an inverted conical tank at a rate of 11700 cubic centimeters per min at the…

A: Let's find rate of water is being pumped into the tank.

Q: Consider the smooth parametric curve defined by the equations t (t²-3) { = = 3 (t² - 3)' = where t E…

A:

Q: +31 Find the particular solution of the differential equation dy/dx = (4x^2-7x)/(3y^2+2) at x = 1,…

A:

Q: Given f(x)=√x + 2 and g(x)= x³, find ()(x) and write the domain of (x) in in interval notation.

A:

Q: Which of the following statements proves the series-128+96-72+54- O 2 is geometric?

A:

Q: Question 6 Find the limit, if it exists. lim (e²r + x) = 1-0+ 01 O e² 0 3 02

A: Given    limx->0+{e^(2x)+x}/(1/x)

Q: Solve the area bounded by the curve y = 4x-x and the lines x=-2 and y = 4. 12) Sketch of the curves:…

A: The given problem is solved below in detail.

Q: 3. S (5y-4)dy y³+4y²

A: We know, ∫dx/x= ln|x|

Q: [x=t+1 B- Find an equation plane pass through point (1,0,0). If the line L₁ y=-2t Z -3t…

A: Given: 1,0,0 x=t+! y=-2t z=-3t

Q: ) cos(cos-¹(35)) ) sec(tan-¹(5)) csc(sin-¹(n)) ) cos ¹(cos(29°)) (4π) 5 =) sin ¹[sin ]]

A:

Q: 2. Sketch the solution region of 2x − y − 1 > 0 (x − 5)² + (y + 1)² ≤ 25.

A:

Q: 6. (y -x + xy cot x) dx + x dy = 0 Answer: xy sin x = C + sin x - x cos. x.

A: We have to solve this question with exact formulation.

Q: Let = [1, -1, 1], [-2, -1, 3] and = [-1, 2, 2]. Find (u ×7)•w: O-14 07 O 10 Does not exist

A:

Q: Which of the following graphs represents x = -3?

A: Question: Which of the following graph represent x= -3 ?

Q: Determine if the series  ∞ (−1)n − 1e8/n n = 1  converges by the Alternating Series Test. If the…

A: We have to test to determine if the series converges or diverges.

Q: 1. y'= exp (2x - y). ANS. 2e" = e²2x + c.

A:

Q: 1. S xdx x²+6x+13

A:

Q: This exercise uses the population growth model. It is observed that a certain bacteria culture has a…

A:

Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

A: The objective is to determine the average rate of change for the function.

Q: √1-(In x)2

A: ∫1-lnx2xlnxdx Let 1-lnx2=y

Q: Calculate Sc 2xyds, where C is the arc of x²+²=4 from the point (2,0) to the point (1,√3)

A: We know that ∫C f(x,y) ds=∫ab f( x(t), y(t) ) dxdt2+dydt2 dt