Sequences & Series Questions and Answers

A sparkling-water distributor wants to make up 200 gal of sparkling water to sell for $5.00 per gallon. She wishes to mix three grades of water selling for $8.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as the $3.00, water. How many gallons of each should she use?

The distance traveled at a constant speed is directly proportional to the time of travel. If Olivia traveled 182 miles in 6.5 hours, how many miles will Olivia travel in 8.1 hours at the same constant speed? Select one: a. 44.8 miles b. 226.8 miles c. 167.4 miles

Consider the function f(x)=1/3(3-x) (9) - 3 (a) Determine the roots of the function. (b) Determine the y-intercept of the function (c) Determine any asymptotes in the function. (d) Graph the function above using transformations. You should have at least 3 points on your graph. (e) Describe the transformations that would need to take place with in order to achieve the same function as above.

Divide the following complex numbers and express the result in standard form, a + bi, where a and b are fractions in lowest terms. 3+7i / 7+ i

Choose the correct description for graphing the solution set of the inequality. X>-5 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. Shade to the left of -5 and put a bracket on -5. Shade to the right of -5 and put a bracket on -5. Shade to the left of -5 and put a parenthesis on -5. Shade to the right of -5 and put a parenthesis on -5.

In blank a, enter conditional equation, contradiction, or identity. In blank b, enter the numerical solution, all real numbers, or no solution. 4x-1=2(x-1)+1+2x a. The equation is a (n) b. Solution:

What interval notation describes the solution set of the inequality? x> 50 Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. (-∞, 50] (-∞, 50) (50,00) [50, ∞)

A ride sharing company charges an initial fee of $1.50 plus $0.18 per minute for a car ride. How many minutes can a person ride for $5? a. Let X represent the number of minutes of the car ride. The equation that represents this situation is b. A person can ride minutes for $5. (Round to the nearest tenth.)

When solving a linear equation, the final equation is 2 = 2. What can you conclude about the equation? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. The equation is a conditional equation whose solution set is {1}. The equation is a contradiction whose solution set is Ø. The equation is an identity whose solution set is R.

Which of the following functions are linear? a.y=2x² +5 b. 5x +2y=10 c. y ==+3X

You rent an apartment that costs $1100 per month during the first year, but the rent is set to go up 8.5% per year. Write a recursive formula to show what the rent is during the nth year of living in the apartment. a1 an

What is the least common denominator of fractions whose denominators are 6 and 9?

Find the amount that results from the given investment. $50 invested at 12% compounded continuously after a period of 2 years

One side of a linear equation simplifies to 4x-5. For the equation to be a contradiction, which of the expressions can be on the other side of the equation? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 3+ 4(x - 2) b 3x + 4(x - 2) c x + 3(x - 1) d 2x + 3(x - 1)

Select one or more answers and submit. For keyboard navigation. To solve the equation -5x = -10, add 5 to each side to get x = -5. To solve the equation -5x = -10, divide each side by -5 to get x = 2. To solve the equation -5 + x = -10, add 5 to each side to get x = -5. To solve the equation -5x = -10, divide each side by -5 to each side to get x = 2.

You invested $14,000 in two accounts paying 8% and 9% annual interest, respectively. If the total interest earned for the year was $1160, how much was invested at each rate?

Find the inverse of the function. Then graph the function and its inverse. f(x) = -4x+ 2

Let f(x) = 5 - 5x + 11x². Calculate the following values: f(a) = f(a+h) = f(a+h)-f(a)/ h =

Your college newspaper, The Collegiate Times, has fixed production costs of $7000 per edition, and variable printing and distribution costs of $40 per copy. The Collegiate Times sells for $50 per copy. i. Write down the associated cost, revenue, and profit functions. ii. What profit (or loss) results from the sale of 500 copies of The Collegiate Times? iii. How many copies should be sold to break even?

Use algebra to find the inverse of the function f(x) = x + 8.

Please find the coefficient of the given term in the binomial expansion. Please use combination. x4 term, (x - 2)^12

Find the solution of the exponential equation 100 (1.03)2 = 500,000

Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f(x) = |x|. y = |x-6 +3 The vertex is (Type an ordered pair.)

Select all equations that are equivalent to the equation. 18 9-3(6x+3) Multiple answers: Multiple answers are accepted for this que Select one or more answers and submit. For keyboard navigation...

The intersection of the surface z = 3x²y + 8x +9y5+1 with the plane y = 1 is a curve C. Find an equation of the line tangent to C at the point (1, 1, 21).

Fill in each blank with the appropriate word or expression required to solve -3x = 12. a. To solve the equation, we must divide each side of the equation by b. Performing this operation gives the equation X = c. When the solution is written in solution set notation, it is written as -4

Including a 5% sales tax, an inn charges $150.15 per night. Find the inn's nightly cost before tax is added.

Suppose you deposit $2,000 in a savings account that pays interest at an annual rate of 4%, If no money is added or withdrawn from the account, answer the following questions. How much will be in the account after 3 years? b. How much will be in the account after 17 years? c. How many years will it take for the account to contain $2,500? d. How many years will it take for the account to contain $3,000?

Let f(n) be the number of weak ordered 2-partitions (S1, S2) of [n] = {1,2,...,n} which satisfies that |S₁| ≥1 and |S₂| ≥ 2. (a) Show that exponential generating function of(n) = (ex-1)(ex-1-x). (b) Find a closed formula for f(n).

6) Determine if a number is a solution of an equation. Fill in the Blanks Type your answers in all of the blanks and submit X₂ X* 2- Consider the equation 3(2x - 1) - 6 = 1 + 7x. When checking if -4 is a solution of the equation, the left side of the equation results in the number Type your answer here Therefore, the value - 4 and the right side of the equation results in the number Write your response here... Type your answer here (is or is not) a solution of the equation.

After a 60% reduction, you purchase a new sofa on sale for $224. What was the original price of the sofa?

Given the base 7 number 10203, answer the following. You might draw a place value chart in this base if that is helpful. What is the place value of the 2? What is the value of the 2? What is the place value of the 1? What is the value of the 3?

Solve the system by substitution. 2x + y = 4 3x + 2y = 1 Select one: The solution has one value that is zero. Ob. The solution has a negative x value. Oc. The solution has a positive x value. Od. The solution has a positive y value.

Given that f(x)=x²-13 and g(x)=5x+15, find (g-1)(-4), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete A. (g-1)(-4)= (Simplify your answer.) B. (g-1)(-4) does not exist

Find the solution of the exponential equation 100(1.03)2 = 500, 000 in terms of logarithms, or correct to four decimal places. t=____

Solve for y and check the solution: 3(2y - 6) + 8y = 12y + 2

Solve the equation. Enter the solution set below. If the answer is a fraction, use the / mark to enter the fraction as in 2/3. Recall that solution set notation is written in the form {p}, where P is the solution of the equation. (For example, if 2 is a solution, the solution set is {2}. -5(x-3) +6=4-(x - 2)

Write the general form of the equation of the circle. Center: (-4, 1); solution point: (1, 3) Write the general form of the equation of the circle. Center: (0, 0); radius: 3

Match the type of graph on the left with the number of solutions on the right. parallel lines same line intersecting lines

Determine whether y varies directly with x. y = 2x + 2 Choose... 2y = -7x y = 5x Choose... Choose...

9x - 6y = 24 6x - 4y = 16 The graph is Select one: A. the same line B.parallel lines C.intersecting lines

A store sells small notebooks for $8 and large notebooks for $16. If a student buys 6 notebooks and spends $80, how many of each size did he buy? He bought small notebooks and large notebooks. (Type whole numbers.)

y = -x +3 y = 3/2x-2 What is the x-coordinate of the solution? Answer: Check

The following system has infinitely many solutions: 2x + y = 10 -2x - y = 6 Select one: True False

Which investment would be worth the most after 20 years? An initial investment of $3000 compounded annually at a rate of 12% after 20 years. An initial investment of $3000 compounded quarterly at a rate of 11.9% after 20 years. An initial investment of $3000 compounded continuously at a rate of 11.8% after 20 years.

A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy 5 bags and spend $17, how many of each size bag did you buy? Show your work.

A population increases by 6% each year. What would be the annual growth factor or multiplier? 6 1.06 94 0.94

What is the differences between a corporation and a sole proprietorship? What are the key differences between a public and a private corporation?

Find the area of the sector associated with a single slice of pizza if the entire pizza has a 14-inch diameter, and the pizza is cut into 8 pieces. Show all work and write your approximate answer (to the hundredths) on the line provided. Use the sector formula A = ²0

Solve the equation. Enter the solution set of the equation. A solution set is of the form 1/5x - 4/5= 4