Sequences & Series Questions and Answers

State whether the following statement is true or false. The function notation f(x) means Choose the correct answer below. A. The statement is false because f1(x) denotes the reciprocal of values of f, whereas B. The statement is false because f-1(x) denotes the inverse of function f, whereas is the reciprocal of values of f. C. The statement is true because the notation f(x) denotes reciprocal of values of f which is the same as the inverse of function f. D. The statement is true because the notation f(x) denotes the inverse of function f which is the same as f(x) the reciprocal of values of f.

Find the unknown length y in the pair of similar triangles.

Mountains A hiker at the top of a mountain sees a farm and an airport in the distance. a. What is the distance d from the hiker to the farm? b. What is the distance y from the farm to the airport?

Testing the diagonals to determine the shape: Match each operation with the correct conclusion we can draw when testing diagonals in a quadrilateral. Test the midpoints and if they are the same then it is Test the slopes of the diagonals and if slopes are negative reciprocals, then it is a... Test the distance of the diagonals, and if they are congruent, then it is a... If all three tests: slope, midpoints, and distance all work out to be true, then we have a .... Test the slopes of the sides, and if we have only one pair of opposite sides parallel then we have a ... If none of the tests hold to be true, then we have a

A Super Happy Fun Ball is dropped from a height of 17 feet and rebounds of the distance from which it fell. How many times will it bounce before its rebound is less than 1 foot? It will bounce times before its rebound is less than 1 foot. How far will the ball travel before it comes to rest on the ground? It will travel feet before it comes to rest on the ground.

If in y = kx), then the graph of the parent function is compressed vertically by the factor k. 0<k<1 > 1 <0

Find the following for f(r)=r³-3r² + 2r + 1: The coordinate(s) (r. y) of any inflection point (s). The intervals where the graph of f(r) is concave upward and concave downward.

Harry took out a loan from the bank. The variable D models Harry's remaining debt (in dollars) t months after he took out the loan. D=-200t +9000 How much does Harry pay back each month?

Which is a valid conclusion that can be drawn from these statements. If a triangle is equilateral then it has three congruent sides. If a triangle has three congruent sides then it has three congruent angles. Most triangles have three congruent angles. All triangles have three congruent angles. An equilateral triangle has three congruent angles. Congruent angles are only present in triangles.

If f(x) = x³ +9, show that f¹(x) = ³√x-9. Select the correct choice below and fill in the answer box(es) within your choice. A. The inverse is f¹(x)=√x-9 because (f ¹ of)(x) = [ and (f of ¹)(x) = B. The inverse is f1(x)=√x-9 because C. The inverse is not f¹(x)=√x-9.

The fuel A costs $4 per gallon, and fuel B costs $8 per gallon. Peter can spend at most $24 on fuel. Write the system of linear inequalities to represent this situation. 4x+8y<24, x<0 and y <0 4x+8y ≤ 24, x ≥ 0 and y ≥ 0 4x+8y<24, x>0 and y> 0

Identify the system of inequalities from the following. 3a+b>2 and 3y <9 3x+a> 2 and 3y <2m 3x+y> 2 and 3y < 2x

For the given functions f and g, find the requested composite function. f(x) = 5x + 11, g(x) = 3x - 1; Find (fog)(x). 15x + 16 15x +32 15x + 10 15x + 6

Use the graph of f and g to evaluate the functions. a. (f+g)(-4) b. (fog)(-3) c. (f/g)(11) d. (gof)(6)

Select the false statement. Two right angles are always supplementary. Vertical angles are always congruent. Vertical angles are sometimes complimentary. Angles that form a linear pair are sometimes supplementary.

Find the x and y intercepts of the inequality 3x + 2y ≥ 15. 7.5 and 5 5 and 7.5 -7.5 and 5

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. Slope 2; through (9,8)

Graph the following inequality. 6x +2y > 12 Use the graphing tool to graph the inequality.

A square has diagonals 20 cm long. What is the length of the side? O 10√2 O 10√3 O 20√2 O 20√3

According to the formal definition, a transformation (also known as a function) y(t) = T(x(t)) is linear if and only if T(ax₁ (t) + bx₂(t)) = aT (x₁(t))+ bT(x₂(t)) = ay₁ (t) + by₂(t) and is time-invariant if and only if for Vr 20 T(x(t-1)) = y(t-t) Using this definition, evaluate if the following functions are linear or not: 1. T(x) = e-tx(t) 2. T(x)= x(t) dx(t) dt dx(t) 3. T(x)= t- dt [6 marks

The sum of two non-negative numbers is greater than 5, and their difference is less than 4. Find the system of Inequalities. Ox+y>4, x-y<5, x ≥ 0 and y20 Ox+y<5,x-y>4, x ≥0 and y 20 Ox+y>5,x-y<4,x20 and y20

Patrick owns a farm house. There are 40 hens and cows. The number of legs of the animals is 90 legs. Find the number of animals of each type. 20 cows and 20 hens. O5 cows and 35 hens 15 cows and 25 hens

3. Each student attempts to represent the number 189.75 in different ways. Please indicate if the student is correct or not. If the student is not correct, explain why (6 points): a. Student 1: 189.75 could be thought about as 189 ones and .75 hundredths. b. Student 2: 189.75 could be thought about as 1.8975 hundreds. c. Student 3: 189.75 could be thought about as 18 tens, 9 ones, and 75 hundreds.

Graph the solution set of the compound inequality. Choose the correct graph below. O A. O C. -12 -10 OA. The solution set is 0 -6 OB. The solution set is Ø. 2 -4 (Type your answer in interval notation. Simplify your answer.) -2 6 0 8 10 4 OB. Write the solution set in interval notation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O D. -12 -10 -2 -8 10 10

A bank offers an investment account with an annual interest rate of 1.52% compounded quarterly. Laura invests $3500 into the account for 5 years. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Assuming no withdrawals are made, how much money is in Laura's account after 5 years? $0 How much interest is earned on Laura's investment after 5 years? (b) S ?

Ali takes out a loan for his college tuition from a bank that charges simple interest at an annual rate of 5.35%. His loan is for $9100 for 8 months. Assume 1 12 each month is of a year. Answer each part below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.

The admission fee at an amusement park is $3.50 for children and $9 for adults. On a certain day, 324 people entered the park, and the admission fees collected totaled $1904. How many adults were admitted?

(1 point) If tan = 9/11, and if cos 0 <0, then sec 0 = cos 0 = sin = tan 0/2 = sin 20 = sin 0/2 = Note: The given information is for tan 0 = 9/11 and not 0 = something. Keep the difference in mind.

The next model of a sports car will cost 4.2% less than the current model. The current model costs $45,000. How much will the price decrease in dollars? What will be the price of the next model? Decrease in price: Price of next model: s

(5 points) An aggressive investment increases by 26% per year, compounded weekly (there are 52 weeks in a year). You invest $100,000 to start. How long until you have $250,000? Please round your answer to the nearest thousandths place (3 places after the decimal point). You must show your work for credit.

You want to create a 98% confidence interval with an error of no more than 5%. You do not have a guess about the value of p-hat. How many people should be in your sample group? O There isn't enough information O 542 people O 543 people 541 people

How many rows of A contain a pivot position? Does the equation Ax=b have a solution for each b in R4? A = 1 -2 -2 0-2 3 -7 11 4 - 2 5 - 10 01 - 6 2 How many rows of A contain a pivot position? A has rows which contain a pivot position.

If the inequality contains "s" or ">" symbol, then graph the equation using a dotted Osolid O dashed line.

A company manufactures and sells shirts. The daily profit the company makes depends on how many shirts they sell. The profit, in dollars, when the company sells I shirts can be found using the function f(x) = 10x - 40. Find and interpret the given function values and determine an appropriate domain for the function. f(-5) = profit of of the problem. meaning if the company sells dollars. This interpretation f(3) = profit of of the problem. f (5.5) profit of of the problem. meaning if the company sells dollars. This interpretation meaning if the company sells dollars. This interpretation shirts, they would make a in the context shirts, they would make a in the context shirts, they would make a in the context Based on the observations above, it is clear that an appropriate domain for the function is

A book store sells a textbook for $150. If the textbook is on sale with 12% off, and there is a sales tax of 8.25% added to the price of the textbook, what is the final price of the textbook, including sales tax? Round your answer to the nearest cent. Do not include the dollar sign, $, in your answer. Provide your answer below:

Jessica deposits $50,000 into an account that pays 3% interest per year, compounded annually. Tom deposits $50,000 into an account that also pays 3% per year. But it is simple interest. Find the interest Jessica and Tom earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits. Year First Second Third Interest Jessica earns (Interest compounded annually) $0 $0 $0 Interest Tom earns (Simple interest) $0 $0 Who earns more interest? O Jessica earns more. O Tom earns more. O They earn the same amount. O Jessica earns more. O Tom earns more. O They earn the same amount. O Jessica earns more. O Tom earns more. O They earn the same amount.

During 1 week an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 20 ounces and a standard deviation of 5 ounces. (a) What percent of the parcels weighed between 10 ounces and 25 ounces? (Round your answer to one decimal place.) % (b) What percent of the parcels weighed more than 35 ounces? (Round your answer to two decimal places.) %

Which graph shows the most accurate line of best fit on the scatterplot? Time Watching TV vs. Grade A. Grade (%) B. 100 80 60 40 20 Grade (%) 8 12 16 20 Time Watching TV per Week (hours) 100 80 60 40 20 Time Watching TV vs. Grade 4 8 12 16 20 Time Watching TV per Week (hours) C. D. Grade (%) Grade (%) 100 80 60 40 20 100 80 60 40 20 Time Watching TV vs. Grade 4 8 12 16 20 Time Watching TV per Week (hours) Time Watching TV vs. Grade 4 8 12 16 20 Time Watching TV per Week (hours)

Janet owns a farm house which contains birds and cows. There are 25 animals. She counted the number of legs as 70. Find the number of cows. 15 20 10

The construction crew for a new house will dig a hole in the shape of a rectangular prism for the house's foundation. The hole will be 51 ft long, 42 ft wide, and 12 ft deep. To haul away all of the dirt from the hole, a dump truck will take trips to a nearby landfill. The crew knows the amount of dirt the truck can hold each trip in cubic yards. (a) Find the volume of dirt that will be hauled away in cubic yards. Use the table of conversion facts, as needed. yd³ (b) Each trip, the truck can haul away 11 yd³ of dirt. To save gas, the crew wants to take as few trips as necessary to haul all of the dirt away. Since all of the dirt needs to be hauled away, the crew might have to take a partial load for one trip. How many trips are needed to haul away all of the dirt? Count each trip it makes the same, even if the truck isn't full. trips (c) If it costs $1225 for each trip that the truck makes, how much will it cost to haul away all the dirt? $0 Conversion facts for length 1 foot (ft) 12 inches (in) 1 yard (yd) 3 feet (ft) = 1 yard (yd) = 36 inches (in)

A swimming pool has a volume of 32,100 gal. Use the table of conversion facts to find out how many cubic yards of water it would take to completely fill the swimming pool. Round your answer to two decimal places. yd³ X Conversion facts for volume and capacity 1 cubic yard (yd³) 1 cubic foot (ft³)~ 231 cubic inches (in³) ≈ 201.97 gallons (gal) WONEN 7.48 gallons (gal) 1 gallon (gal) Note that means "is approximately equal to". For this problem, treat as if it were =

Find the solution to the lines y = 6x + 5 and y = 4x + 7. (1,-11) (1,11) (-1,11)

Frank knit scarves for his friends. Altogether, the scarves had a total length of 436.8 in. If he knit 7 scarves, and each scarf was the same length, how long was each scarf? Write your answer in feet. Use the table of conversion facts as necessary, and do not round your answer. Conversion facts for length 12 inches (in) = 1 foot (ft) 3 feet (ft) = 1 yard (yd) 36 inches (in) = 1 yard (yd) 5280 feet (ft) = 1 mile (mi) 1 mile (mi) 1760 yards (yd)

Let f(x) = 3. 3x² + 8x - 16 2x² 7x + 3 - - 1) The domain in interval notation is 2) The y intercept is the point 3. 3) The x intercept(s) is/are the point(s) (3x 4) (x + 4) (2x - 1)(x − 3) 1 4) The vertical asymptote(s) is/are Give the left asymptote first and enter DNE if there is only one vertical asymptote. 5) The horizontal asymptote is and

Question 3 Points 3 The cost of 5 dresses and 2 belts is $48. The cost of 3 dresses and 2 belts is $32. Find the cost of a dress and a belt. Let x denote the cost of a dress and y denote the cost of a belt. Ox=$8, y = $4 Ox= $5, y = $4 Ox= $7, y = $10

Gabriel invested $17,000 in an account paying an interest rate of 3% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $26,600?

In this question, the power series method is to be applied to find the general solution of a differential equation. The power series solution is expressed as: y = a0 + al*x + a2*x^2 + a3*x^3 + ... In representing your general solution to the given differential equation, use a format like that demonstrated above. After verifying that the power series method applies, find the general solution (to 5 terms) using the power series method to the DE: d'y dy dra +1 Guess solution: y = a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4 + ... Find recurrence relations (in terms of a0 and al) by equating the coefficients of a", for n=0,1,2,.... a2 = a3 = + 5y = 0. a4 = Find the general solution to 5 terms (i.e. to x^4 term) in terms of a0 and al: y = ao( +...) + a₁( +...) (6 marks)

If f(x) = -f(-x), then the graph of the polynomial function is symmetric about the O origin Ox-axis O y=x

Describe the transformation to f(x) that results in g(x): g(x) = f(x) - 4 Of(x) has been translated down 4 f(x) has been translated up 4 O No answer text provided. No answer text provided.

What are the transformations of the function y = -2√x - 5 compared to the parent function? Oshifted right 5 units, shifted down 2 units, and reflected over the x-axis reflected over the x-axis, vertical stretch, and shifted left 5 units reflected over the x-axis, vertical stretch, and shifted right 5 units shifted right 5 units and down 2 units