Sequences & Series Questions and Answers

State the identity that validate sin x = 3 cos(x-π/3) and hence show that tan x = -(6 + 9√3)/23

In a recent poll of 350 likely voters, 42% of them preferred the incumbent candidate. At the 95% confidence level, which of the following would be closest to the margin of error of this statistic? (1) 2.6% (3) 4.2% (2) 3.7% (4) 5.3%

A pendulum swings a length of 40 inches on its first swing. Each successive swing is of the preceding swing. Find the length of the sixth swing and the total length swung during the first six swings. The length of the sixth swing is in. (Round to the nearest tenth as needed.)

Determine the behavior of the polynomial function f(x) = (x - 1)(x + 1)^4(x – 3)²(x + 3)^3 at each of its zeros shown each row. Crosses over the x-axis. Does not cross the x axis. Row 1 Crosses the x-axis. Does not cross the x-axis. 3 Row 2 Crosses the x-axis. Does not cross the x-axis. 3 Row 3 Crosses the x-axis. Does not cross the x-axis. -1

The probability that a store sells all of their ground hamburger for the week is 0.75. The probability that the store sells all of it's steak for the week is 0.68. The probably that the stores wells all of both of the meals for the meek is 0.62. Given this information, are events A and B dependent or independent? Show your work

Which of the following show a line that crosses the y-axis at -2? through (-3,5) and (2, 0) m = 3 and through (2, 4) m = -(2/3) and through (6, -6) through (-3, -1) and (4, 6) m = -2 and through (2,-4) through (3, -1) and (-6, -4)

(1) Find the solution of the quadratic equation x² - 5x = 0 by factoring. (a) 5 (b) - 5 (c) 0 , - 5 (d) 0,5 (2)Find the solution of the quadratic equation x² + x - 6 = 0 by factoring. (a) – 2,-3 (b) 2 , -3 (c) 2 ,3 (d) - 2 , 3 (3) Find the solution of the quadratic equation x²- 5x + 6 = 0 by factoring. (a) 2 (b) 0 , 2 (c) 3 (d) 2 , 3

Given f and g below, find (f/g)(2). Simplify your answer. f(x) =-6x^7 + 8x^2 + 16x^5 g(x) = 2x^5 Do not include "(f/g)(2) = " in your answer. Provide your answer below:

Complete the equation describing how x and y are related. X 0 1 2 3 4 5 Y 0 1 2 3 4 5

Beatrice has $4,200 in a savings account which earns 6% interest compounded monthly. She made no additional withdrawals or deposits. What was the amount in the account at the end of the fourth month? $4,248.54 $4,240.66 $4,284.64 $3,185.44

A town has a population of 7000 and grows at 4% every year. What will be the population after 13 years, to the nearest whole number?

Add the following polynomials. Simplify your answer. (x² + 2x + 2) +(-4+5x + 4x² + 4x^3) Provide your answer below:

You are going on a vacation that will cost $8,000. You plan to pay for it using an installment plan but only want to finance $2,600. What percent of the total cost should the down payment be?

Tom and Jeremy have an above ground circular pool with a circumference of 47.1 ft? What is the area of the pool? Use 3.14 for pi. A 23.6 ft^2 B 15 ft^2 C 176.6 ft^2 D 183.5 ft^2

A student earned a total of 500 points on the first 6 tests. What score does she need on the next 2 tests to average 85 points ? 90 points 95 points 85 points 100 points None of the choices are correct.

Students will be able to think flexibly to [apply] an effective strategy to solve a problem. This question has multiple parts. Michael is saving up money to buy his first car. He has a choice between the following savings account interest rates: 1. 5% interest compounded yearly 2.4.95% compounded monthly 3. 4.9% compounded continuously Find the amount in each account after one year if $5,000 is put into each account initially. Putting yourself in this situation, what account would you invest you

A tiny cube shaped space inside a computer chip has been measured to be 0.000000253m wide, 0.000000033m long and 0.00000293m high. What is its volume? Write your answer in scientific notation. The volume is m³

Which number below is written in scientific notation? 33.5 x 10³ 0.335 x 104 3.35 x 100.06 3.35 × 105

A sun in a distant galaxy has an estimated Mass of 1.493 x 1030 kg and the earth has a mass of 5.972 × 1024 kg, how many earths would it take to equal the mass of the sun? Write your answer in scientific notation. It would take earths to equal the mass of the sun.

Capitol City Bank approves a home-improvement loan application for $18,000 at an annual simple interest rate of 8.25% for 150 days. What is the maturity value of the loan? (Round your answer to the nearest cent.)

According to a country's census, there were 32.7 million citizens living in poverty in 2001. By 2009, the number had increased to 43.9 million. Find the percent increase in the number of citizens living in poverty from 2001 to 2009.

Write the first five terms of the arithmetic sequence whose first term is 9, and whose common difference is - 5.

Sierra is a college student who plans to spend a summer in Detroit. She has saved $3,500 for her trip and anticipates spending $400 each week on rent, food, and activities. If she models her amount of savings y in dollars, with a representing the number of weeks since the trip started, a) what would the y-intercept represent? How many week since she started the trip. The amount of her account balance at the beginning of her trip. The amount of her account balance at the end of her trip. How many weeks her trip is. The amount of her account balance. How many weeks before she would run out of money. b) what would the x-intercept represent? The amount of her account balance at the end of her trip. The amount of her account balance. How many weeks before she would run out of money. The amount of her account balance at the beginning of her trip. How many week since she started the trip. How many weeks her trip is.

Suppose that the piecewise function f is defined by f(x) =S√3x + 4. -4/3<x≤1 -2x²+5x-2 x>1 Determine which of the following statements are true. Select the correct answer below: f(x) is not continuous at t= 1 because it is not defined at a f(1) exists, but /(x) is not continuous at. 1 because limf(x) does not exist. 2-1 f(1) and lim/(a) both east, but f(x) is not continuous at x = 1 because limf(x)/(1). Of(x) is continuous at x = 1.

Find the 7th term of the geometric sequence: 8, 44, 242, .. Answer:__________

Doomfist travels at an average rate of speed of 95 miles per hour for 5 hours. How far does he travel? A 570 feet B 570 miles C 475 feet D 475 miles

The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v₀feet per second is r =1/32v₀² sin(2θ) where r is the horizontal distance (in feet) the projectile travels. An athlete throws a javelin at 75 feet per second. At what angle must the athlete throw the javelin so that the javelin travels 115 feet? (Assume θ< 45°. Round your answer to two decimal places.)

Find the sum of the first four terms of the sequence. 2, 2/5,2/25

The height of an object thrown from a height of 20 feet is given by h(t) = -16t² + 76t+20, where h is measured in feet and t is measured in seconds. After how many seconds will the object hit the ground?

The range of a projectile fired at an angle with the horizontal and with an initial velocity of v₀ feet per second is r =¹⁄ ₃₂v₀² sin(2θ) where r is the horizontal distance (in feet) the projectile travels. An athlete throws a javelin at 75 feet per second. At what angle must the athlete throw the javelin so that the javelin travels 115 feet? (Assume 0< 45°. Round your answer to two decimal places.)

The regression line for a data set giving sales S, in dollars, t years after 2005 is given by the following: S = 1700t + 3900 What are the sales indicated for the year 2021? A. Sales $5,616 B. Sales = $27,200 C. Sales = $31,100 D. Sales = $3,435,700

Zarya has $22,000 worth of property damage liability insurance. She caused an accident that damaged a $3,000 fire hydrant and did $17,600 worth of damage to another car. How much of the damage must Zarya pay? A $22,000 B $20,600 C $3,000 D None

A circle is drawn to represent a pizza with a 12-inch diameter. The circle is cut into eight congruent pieces. What is the length of the outer edge of any one piece of this circle? (a) 3π/4 (b) 3π/2 (c) 2π (d) π (e) 3π

Orisa and Zenyatta are buying an $900,000 home. They know that they will have to bring their checkbook to the closing. What might they expect to pay in total at the closing? The rule of thumb is that they can expect the closing costs to run from 2% to 7% of the purchase price. (A) $15k-$50k (B) $180k-$630k (C) $18k-$63k (D) $17k-$59k

The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -7 ≤ x ≤ -4?

Simplify the following expression as much as possible: 4log4(log55) (a) 0 (b)4 (c)4log₄2 (d)1

Find the partial sum S₁₅ for the arithmetic sequence with a = 8, d = 4. S₁₅ =

A staircase handrail is made from congruent parallelograms. In PQRS, PQ = 17.5, ST = 18, and mQRS = 110°. Find each measure. Explain. 10. RS 11. QT 12. mPQR 13. mSPQ

Use the distributive property to simplify the equation below. 5(2x + 3y - 2) = [?]x +[]y -[]

Suppose that f is a linear function such that f(-3) = 10 and f(4) = -5 what is the slope of f? A 15 B. 5 C.-15 D. 1 E. 7

Find a general term an for the sequence, whose first four terms are given. 2, 6, 10, 14 an =

A loan of R12000 was secured at 20% p.a. effective. It was agreed to repay the loan via regular equal monthly payments of R310 per month and a final payment (F < 310) to be made one month after the last payment of R310. Payment started one month after the loan was granted. The client missed the 12th, 13th, 14th and 15th payments. The equal amounts, rounded to the nearest cent, that must be added to all the remaining payments, from the sixteenth month onwards, for the loan to be repaid in the same time period, are equal to R

Find the value of the logarithmic expression. log₁⸝₈8

A trainee in a computer company takes 0.9 times as long to assemble each computer as he took to assemble the preceding computer. If it took him 35 minutes to assemble the first computer, find how long it takes him to assemble the fifth computer. Find the total time he takes to assemble the first five computers. It takes minutes to assemble the fifth computer

Reaper found a job listed in the classified ads that pays a yearly salary of $56K. What is the weekly salary based on this annual salary? A $1,076.92 B $2,912.00 C $961.54 D $2,153.85

In the graph below the input a is the number of units produced by a machine in a factory. The output y is the profit made by the sale of these units when they are produced. Determine the intercepts and interpret the meaning of each. A. Give the coordinates of the x-intercept: B. Interpret the meaning of the x-intercept: C. Give the coordinates of the y-intercept: D. Interpret the meaning of the y-intercept: E. Determine the slope of the line: written as a reduced fraction.] F. Interpret the meaning of the slope. For each 2-unit increase in units sold there is a(n) G. Write the equation of the line in y = mx + b form: H. Use your equation to determine what quantity of units will yield a profit of $700: y (profit [in dollars])

A mouse wheel is 16 cm in diameter and the base of the wheel is 2 cm off the ground. If the hamster can spin the wheel 4 times each second, what is the reflected cosine function that describes the movement of the wheel if it starts at its lowest point? State first the Amplitude, Period, Equation of axes.

The population of the region is decreasing according to the formula y=y₀ e^ -0.0279t. In this formula, t is time in years and yo is the initial population at time 0. If the size of the population in 2002 was 11,715, use the formula to predict the population of the region in the year 2019. In year 2019 the population of the region will be approximately

Use the factorization A = PDP‾¹ to compute Aᵏ, where k represents an arbitrary positive integer.

Write the expression as a sum or difference of logarithms. Assume that variables represent positive numbers. log₆2/9z