Sequences & Series Questions and Answers

Andre and Rachel are planning their wedding reception. The venue they selected charges a $1200 rental fee plus a $75 per person catering fee. If they have $15,000 to spend on their reception, what is the maximum number of people that can attend the reception without going over their budget?

A garden has the shape of an isosceles triangle. The base of the triangle is 42 ft long, with an altitude of h ft. What is the area of the garden for h = 38 ft? The area of the garden is ft². Answer:

Which method of solving a system of equations (graphing, substitution, elimination) is best for the system below. Explain why your choice is better than the other options. You do not need to solve the system. 2x - 3y = 4 2x - 5y = -6

Write the function rule for the function shown below reflected in the given axis. f(x) = -7x; x-axis Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)? g(x) =

Determine whether each relation is a function. ((-5, 1), (0, -3), (-2, 1), (10, 11), (7, 1)} {(4,9), (5, 3), (-2,0), (5,4), (8, 1)) {(0, 1), (1, 0), (2, 1), (3, 1) (4, 2))

Solve the formula for the specified variable. h = da for d

According to the Airports Council International, the busiest airport in the world is Atlanta's Hartsfield International Airport, and the second busiest is Chicago's O'Hare Airport. Together they handled 150.5 million passengers in the first six months of 1999. If Hartsfield handled 5.5 million more passengers than O'Hare, how many were handled by each airport? Let a = Atlanta's Hartsfield; c= Chicago's O'Hare. Which system is a correct representation of the problem? a) a + c = 150.5 a = c +5.5 b) a + c = 150.5 c = a +5.5 Select one: a. a b. b

Describe the transformations of the parent function f(x). Choose all that apply. f(x) = -3x + 1 Select one or more: a. translate one unit up b. reflection over the x-axis c. translated one unit to the right d. vertical compression by 1/3

Which was not a good reason for Jefferson to buy the Louisiana Territory? To increase the size of the United States To protect U.S. shipping interests To anger England and Spain To gain new supplies and resources

Write an equation of variation that passes through (12, 8). Select one: a. y= 3/2x b. y= 3/2x +8 C. y= 2/3x +8 d. y= 2/3x

Of the options listed below, which gives the greater ending balance? Choice 1: Put $450 in an account that pays 8% interest compounded annually for 5 years. Choice 2: Put $450 in your room and add $3 to it each month for 5 years. Choice 1 Choice 2 They are the same.

A. Use double integral and polar coordinates to calculate the size of a tower bounded by the plane z = 0 and the paraboloid z = 1-x² - y²

Which could best serve as the theme of a story about holiday gift giving? gift giving The value of a gift is not in its price, but rather in its sentiment. Giving homemade gifts is better than giving store bought gifts. Miriam painted a picture of the ocean to gift to her brother for Hanukkah.

Determine which group is the population and which is the sample. Female diabetics between the ages of 19 and 25 in study All female diabetics in a study Female diabetics

Is the function y =(x-4)² a one-to-one function? Justify your answer.

There is a 75% chance that you will go shopping given that your friend can go. If there is a 62% chance that your friend can go, what is the chance that you go shopping and that your friend can go? Select one: a. 47% b. 46% c. 84% d. 72%

Is the function y = (x −4)² a one-to-one function? Justify your answer.

Let u = (2, 2, -3), v = (0, 3, -3), and w = (2, 4, 7). Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) − u× v = (?, ?, ?) (c) u x (v + w) = (d) w. (w × v) (?, ?, ?) (e) w x w = (?, ?, ?) (f) (6v2u) x (6v2u)= (?, ?, ?)

Determine by inspection whether the vectors are linearly independent. Justify your answer. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set of vectors is linearly dependent because times the first vector is equal to the second vector (Type an integer or a simplified fraction) B. The set of vectors is linearly dependent because neither vector is the zero vector. C. The set of vectors is linearly independent because neither vector is a multiple of the other vector.

Isabella had $500 in the bank. After making a few withdraws of $15 and one withdraw of $50, she now has less than $100 in the bank. Write and solve an inequality to determine how many $15 withdraws Isabella made.

Explain if these statements are true/false. (f) Suppose A is an n x n matrix and 2 is an eigenvalue for A. Then 8 must be an eigenvalue for A³. (g) If the determinant of a 2 × 2 matrix A is negative then there is an eigenbasis for A.

Determine the intervals on which the function is increasing, decreasing, and constant. List the interval(s) on which the function is increasing. (Type your answer in interval notation. Use a comma to separate answers as needed.) List the interval(s) on which the function is decreasing. (Type your answer in interval notation. Use a comma to separate answers as needed.) List the interval(s) on which the function is constant. (Type your answer in interval notation. Use a comma to separate answers as needed.)

Show that the substitution z = 1/y² into the differential equation dy/dx+y = xy³ transforms the differential equation dz/dx - 2z = -2x Hence, find the solution of the differential equation satisfying the condition y = √2 when x = 0. Give your answer in the form y = f(x).

Select the outlier in the data set. 42 32 36 38 41 44 37 39 26 60 decrease 24 81 30 If the outlier were removed from the data set, would the mean increase or decrease? 4)increase

Assuming that moving away from the mailbox is the positive direction; if an object travels 20 metres in 5 seconds back towards the mailbox, its average velocity would be: a) 4 m/s b) 100 m/s c) -100 m/s d) -4 m/s

The graph of the given function represents a function that is: a) both even and odd b) neither even nor odd c) odd d) even

. Solve each of the following quadratic equations. Express your solutions in simplest a+bi form. Check. (a) x² + 4x+20=12x-5 (c) 2x²-25x+27= -15x-10 (e) x² +6x+15=8x-2 (d) 8x² +36x+24=12x+5 (f) 4x² +38x+50=10x-35

Odd functions are symmetric about the: a) x-axis Ob) origin c) y-axis d) line y = x

This problem uses some strange units, but if you know how to perform a unit conversion in general, then you can do this problem. We want to convert 5.6 teeps² / kad into units of urts²/lan Here are some conversion facts for these strange units. Which facts will we need to use? [Select only the one(s) we actually need for the conversion.] 5 lans = 9 staps 2 urts = 3 teeps 7 lans = 8 kads 4 teeps = 6 pabs

Complete each of the following with the most correct word or phrase. a. Every _____ function has at least one asymptote. b. The equation of the ______ rational function can be determined by using the end behaviours of the C. The ______ are determined by setting the denominator of the simplified rational function to zero. d. A common factor involving x that occurs in both the numerator and denominator fa rational function results in a (n) ______in the graph of a rational function.

Combine and simplify each of the following. Note that each pair of fractions already has a common denominator. (a) 3x+7/x+2 + 2x+3/x+2 (b) 5x+2/4x-12 3x+8/4x-12 (c) 6x² - 8x/x²-25- 4x² + 2x/x² -25

What is the difference between a tangent line to a function and a secant line to the function? a) a secant line touches the curve at only one point b) a tangent line represents the value of the curve at a point c) a secant line does not have to touch the curve at all d) a tangent line touches the curve at only one point

Which linear equation BEST represents the line of best fit for the scatterplot? A) y= 1/3 x-1 B)y=-1/3x+1 C) y = 3x + 1 D) y = 3x - 1

For the right triangle below, find the length of x. Round to the hundredths. (2 decimal places)

Question 4. Draw a small life-cycle graph for female cheetah's, labelling each arrow, to confirm that you have a clear biological interpretation of the elements of L. Question 5. (Challenging question.) Show that Ad is more sensitive to changes in s5 than to changes in s1. Where should cheetah conservationists focus their efforts?

Divide as indicated. x + 4/5 + 5x+20/4 Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

3. The following is half of an identity: sec² x csc x/sec² x + csc² x =? Graph the left side on the coordinate axes with the window: [-27, 2π] by [-2,2] Label a few ticks marks on the axes. Use the graph to make a conjecture as to what the left side of the identity should be. Prove your conjecture. (Hint: first write the denominator in terms of sine and cosine)

4. Find the sum of each arithmetic series described below_ (a) The sum of the first 100 even, natural numbers.

What type of function is graphed? What do you notice about the graphs? Can you write the equation of the second graph?

Evaluate the given exponential expression. (4^4)3

Independent Practice/Homework Find the values of the six trigonometric functions for angle L.

Simplify the algebraic expression. 5(4x + 4)-9 5(4x + 4)-9=

Evaluate the given exponential expression. 6-4.6

Evaluate the given exponential expression. - 2⁰

Graph the following inequality on a real number line. 11>x≥5 Choose the correct graph below.

Simplify the exponential expression. (-21a³b4 / 7a7b-9) 3

Make Sense and Persevere Cindy found a collection of baseball cards in her attic worth $8,000. The collection is estimated to increase in value by 1.5% per year. Write an exponential growth function and find the value of the collection after 7 years.

Grayson is deciding which meat to get at the grocery store. If he buys bacon is 82%. If he brings home the bacon, there is a 60% chance that his roommate will eat it. What is the probability that Grayson buys bacon and his roommate eats it?

Perform the indicated computation. Write the answer in scientific notation. (2×104) (3.1×10³)

Phillip invested his $6, 600 savings in an account earning 73/4 % annual interest that is compounded continuously. How long in years, will it take to earn $400 in interest? Round your answer to the nearest tenth.