Sequences & Series Questions and Answers

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.

Simplify the algebraic expression. 2(2x + 2)-3

Find the inverse: f(x) = log3 (x+1)-2. Present the answer using function notation. Sorry, that's incorrect. Try again? 3x+2-1

Solve the equation: 2 loga - log 36 = 0. Select all applicable answers. Select all that apply: 6 01 -6 No Solution

Simplify the algebraic expression. 7(3y-5)+ 4(5y + 3)

Use the order of operations to simplify the following expression. 21+3+3 2/(12-3.2)2

If money is invested in an account earning 3.15% annual interest that is compounded continuously, how long will it take the amount to double? Round your answer to the nearest tenth.

Use least-squares regression to find the equation of the parabola y = P₁ x + B₂ x² that best fits the data points (1,2), (2,3), (3,4),(5,2)

Suppose V is finite-dimensional with dim V> 0, and suppose W is infinite-dimensional. Prove that L (V. W) is infinite-dimensional.

Solve 81^2x+1 = 3 using the one-to-one property of exponential functions.

If the ratio 2x² +17x+42 / x+5 is placed in the form q(x)+ r/x+5 , where q(x) is a polynomial, then which of the following is the correct value of r? (1) -3 (3) 18 (2) 177 (4) 7

Scott invested $3,000 in an account earning 41% annual interest that is compounded continuously. How long will it take the investment to grow $5, 500? Round your answer to the nearest hundredth. Select the correct answer below: 3.71 years 3.71 months 13.47 months 13.47 years

The tree diagram represents an experiment consisting of two trials. P(A and C) = [?]

Consider the system of equations x³ + y³ z³ = 1, x² + y² + z² = 1, x+y+z = 1. Determine all solutions in C3 using the Elimination and the Extensions Theorems. You are allowed to use computer algebra software besides the commands that solve a system of polynomial equations directly. Explain your work.

Hence find all the roots of the equation 48x5 60x³ + 15x + 2 = 0.

Explain what absolute value means. Then, describe how to evaluate an ex- pression within an absolute value symbol. To help, consider the following absolute value expressions: |-18) = ? |18|=? Be sure to write in full sentences. 1pt for correct explanation of absolute value. 1pt for correct explanation of how to evaluate an absolute value.

The Soule's live on a corner lot. Often, children cut across their lot to save walking distance. The diagram to the right represents the corner lot. The children's path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. The walking distance that is saved by cutting across the lot is

A ball is thrown downward from the top of a 190-foot building with an initial velocity of 24 feet per second. The height of the ball h after t seconds is given by the equation h = - 16t² - 24t+190. How long after the ball is thrown will it strike the ground?

Find the point at which the line f(x) = 4x + 1 intersects the line g(x) = 5x + 2 -

Rewrite as a radical and then simplify: (-32)3/5 Provide your answer below:

Given LABC AEFG, with medians CD and GH respectively, AC = 9, EG = 6, CD = x + 2, and GH = 2x - 4. Find GH.

Eiko is wearing a magic ring that increases the power of her healing spell by 30%. Without the ring, her healing spell restores H health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring? Choose 2 answers: A 0.7H 130 100 H (₁+¹) H H-0.30H 30+ H

Refer to the model Q (t) = Qoe^(-0.000121t) used for radiocarbon dating. At an archeological site, scientists uncovered human remains. A sample from a human bone taken from the site showed that 32% of the carbon-14 still remained. How old is the sample? Round to the nearest year. Do not round intermediate calculations. The sample from the human remains is approximately______years old.

Let g(x) = 2x² - x + 4. Find the value of the function when x = 1. (A) -5 (B) 7 (C) 5

What is the interest earned if you deposit $3,500 that earns 8% for 4 years? (A) $1,120 (B) $1220 (C) $1,201 (D) $1102

True or False: If you deposit $1,800 and earn 4% interest for 2 years, your interest is $174. (A) True (B) False

9x <= -2y-3 -6y > 8x + 8 Determine if (-5,4) is a solution to the system of inequalities above. Select the correct answer below: (A) Yes (B) No

Autumn invested $2,800 in an account paying an interest rate of 6.2% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 8 years?

What is the surface area of the cylinder with height 3 mi and radius 7 mi? Round your answer to the nearest thousandth.

A radio disc jockey has 7 songs on this upcoming hour's playlist: 2 are rock songs, 2 are reggae songs, and 3 are country songs. The disc jockey randomly chooses the first song to play, and then she randomly chooses the second song from the remaining ones. What is the probability that the first song is a country song and the second is a reggae song? Write your answer as a fraction in simplest form.

Determine if (-8, -3) is a solution to the following system of inequalities. 5y < -9x - 3 3х – 7y ≤ 8 Select the correct answer below : A. Yes B. No

Evaluate the expression below for p = -2 and q = 3: [(p^2)q]^3

Jackson wants to buy cookies for his friend. The circumference of each cookie is 31.4 cm. What is the area of each cookie? (A) 100.48 cm2 (B) 78.5 cm (C) 19.65 cm?

Kara's Custom Tees experienced fixed costs of $500 and variable costs of $2 a shirt. Write an equation that can be used to determine the total expenses encountered by Kara's Custom Tees. Let x be the number of shirts, and let C(x) be the total cost of producing x shirts. Then, calculate the cost of producing 8 shirts. An equation that can be used to determine the total cost of producing x shirts is C(x)=____.

Is (-9, -7) a solution to the following system of inequalities? 5y <= -4 + (x + 2)³ 2+ |x³ + 3| > 5y Select the correct answer below: (A) Yes (B) No

$7,500 is invested in an account earning 6.2% interest (APR), compounded daily. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set property. From the biologist walks downstream x = 110 feet and sights to point C (see figure). From this sighting, it is determined that Θ =54º. Ho wide is the river?

Choose the correct graph for the solution set of the system of linear inequalities: x-y≥ -3 x +y ≥ 3

Answer the questions given the differential equation, x– 3x + 2x = 0, x(0) =1, x(0) = -1. Compute x =e^Atx(0)

Solve the following system of equations. Enter your answer as an ordered pair (x, y). Provide your answer below: 5x - 8y= 37 -3x - 7y= 25

Find the volume of the region between the planes x + y + 4z=5 and 2x +2y+z=10 in the first octant. The volume is (Type an integer or a simplified fraction.)

You purchase an RV by making a down payment of $10,800. The terms of your finance agreement have an annual interest rate of 2.66%, compounded monthly, and require you to make 36 monthly payments of $1,496.75 each. What is the cash price (in dollars) of your RV? (Round your answer to the nearest dollar.)

The one-to-one function fis defined below. f(x)= 3x-8/7x+6 Find f¹(x), where f¹ is the inverse of f.-1

Solve the problem. A ship sailing parallel to shore sights a lighthouse at an angle of 14" from its direction of travel. After traveling 2 miles farther, the angle is 24. At that time, how far is the ship from the lighthouse?

The base of a right pyramid is a regular hexagon with sides of length 8 m. The altitude is 4 m. Find the total surface area of the pyramid. The area is (Simplify your answer. Type an exact answer, using radicals as needed.)

Evaluate [F.dr if F(x, y) = (4e¹)i + (4xe')] and the curve C is line segments going from (0,0) to (5,4) to (1,2).

Solve the following LPP by two phase method. Max Z = 5x1 - 4x2 + 3x3 s.t. 2x1 + x2 - 6x3 = 20 6x1 + 5x2 + 10x3 ≤ 76 8x13x26x3 ≤ 50 x1, x2, x3 ≥ 0.

Find the standard matrix for the following transformation T: T is a composition of a counterclockwise rotation of R² through 5π/6rad followed by a reflection of R2 in the line 2x + y = 0

The population of Tempe, Arizona was 64000 in 1970. in 1980 it was 107000. a) Use the data to determine k in the growth model. b) Use the data to predict the population of Temp in 1995 c) Use the data to predict when the population will reach 300000.

Every two weeks, a solar panel company selects fifty of their modules and measures their power output. The most recent test gave an average of 320 watts, with a 95% confidence interval of [315, 325]. If they don't update their manufacturing process or design, about how many times a year will a sample have an average power outside this range? A. 1 B. 3 C. 5 D. 10