Sequences & Series Questions and Answers

While camping in the forest, Carina decided to go on a hike. From her campsite she first hiked to a waterfall located 3.46 miles west and 2.10 miles north of her campsite. She then hiked to a mountain spring located 2.77 miles west and 4.31 miles south of the waterfall. Find the resultant vector of her two hikes in component form.

What pair of factors should be used to find the complex solutions for x? 16x² + 4 = 0 Select one: a. (2x+4)(2x+4) b. (4x + 2i)(4x + 2i) c. (2x-4i)(2x - 4i) d. (4x + 2i)(4x - 2i)

Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function below. Graph the function to help you find the maximum volume for the domain 0 <h < 10. Round to the nearest cubic foot. V(h) = h(h-10)(h - 8) Select one: a. 107 cubic feet b. 110 cubic feet c. 10 cubic feet d. 105 cubic feet

If u = (2,-4,6), v = (-2,4,6) and w=(-5,-3,5) then u *v x w =?

Evaluate x/y for x = 3 and y=-3. Select the crrect choice below and fill in any answer boxes in your choice. A. x/y B. The answer is undefined.

Write using exponential notation. 9.9.8.8.8.8 9.9.8.8.8.8=

Name the property illustrated by the true statement. -8(y +5)= -8.y+(-8).5 Choose the correct answer below. A. Associative property of addition B. Associative property of multiplication C. Commutative property of multiplication D. Distributive property

The amount of water that a spherical tank can hold varies directly s the cube of the radius. If a tank with radius 7.5 ft holds 1767 ft³ of water, how much water can a tank with radius 16 ft hold? Select one: a. more than 17,000 ft³ b. less than 17,000 ft³ c. need more information to solve

Evaluate the following expression for x = −3, y = 3, and z = − 1. 2x - 5y-6z 2x - 5y-6z =

Solve the absolute value equation or indicate that the equation has no solution. |2x-1|=3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) B. The solution set is the empty set.

Evaluate the expression. -5² -5²=

Four times a number, subtracted from eight, is twice the number. Find the number. The number is. (Simplify your answer.)

Evaluate x/y and also xy for x = -8 and y = -4. Select the correct choice below and fill in any answer boxes in your choice. A. x/y B. The answer is undefined.

Evaluate xy and also x/y for x = 0 and y = -9. xy=

Evaluate the following expression for x = 1, y =3, and z = 3. xy(3+z-x) The answer is _____

Evaluate the following expression for x = 1 and y = 3. (2x + 4y)/2x The answer is _____

Evaluate the expression with the given replacement values. 2xy² when x=3 and y=6 The value of the expression is

Solve the linear inequality. Enter the solution set of the inequality in interval notation. Type "infinity" to represent ∞, if needed. Type "negative infinity" or "-infinity" to represent -∞, if needed. Be sure to use appropriate symbols on the endpoints of the interval. Do not enter any spaces in your answer. (2y+1)/5 - (y-2)/3 ≤-1/15

Use the product rule to simplify the expression. Write the result using exponents. (-9b⁶c⁴) (8bc⁵)

Evaluate the following for x = 3 and y = 4. 5xy²-5 The answer is

Evaluate the expression for x = 4 and y = 3. (xy + 4)² (xy+4)² =

One safe investment pays 7% per year, and a more risky investment pays 8% per year. a. How much must be invested in each account if an investor of $96,000 would like a return of $6,980 per year? b. Why might the investor use two accounts rather than put all the money in the 8% investment? a. $ ____ is invested in the 7% account.

Last month the average daily balance on Kaitlin's credit card was $1,646.69. If there were 30 days in that month, and her annual interest rate was 18.43 %, what is the amount of interest that she will pay on her credit card that month? Round your answer to the nearest penny. Do not input the dollar sign. Do not use a comma.

Solve the inequality. Graph the solution set and write it in interval notation. 2x <-6 Choose the correct graph below.

The last term in geometric progression is -96. if there are 6 terms whose sum is -63, find the first term

Use the slope-intercept form to graph the equation - 9x +y = -2. Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line.

Find the slope of the line y=-3. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Simplify your answer. Type an integer or a fraction.) B. The slope is undefined.

For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation. x-y=4 Complete the table below.

Verify the identity algebraically. Use the table feature of a graphing utility to check your result each step.) 4 sin(x) 4 sin(x) 4 csc(x) 4 csc(x) = 4 csc(x) 4 sin(x) 4 csc(x) - 4 sin(x) 4 csc(x) - 4 sin(x) = 4 csc(x) - 4 sin(x) (CSC(x))

True or false Write if the following expressions are true (t) or false (f) 1. U(8)≈U(5) 2. U(10)≈Z4 3.Z=Q

nd unit vectors that satisfy the given conditions: 1. The unit vector in the same direction as (5,-1) is <5/sqrt26, -1/sqrt26> .help (vectors) 2. The unit vector oppositely directed to i-3j+ 2k is 3. The unit vector that has the same direction as the vector from the point A= (-5, 3) to the point B = (-7,5) is

Find all possible Hamilton circuits in the given graph List the circuits using A as the startinglending vertex Choose the correct answer below A ABC.E.F.D. A and its mirror image B A,B,C,D,E,F.A and its mirros image C. A.B.C.D.E.F.A and A, B, E, D, C, F, A and ther mirror images i D. A,B,C,E,F,D,A and A, B, F, E, D, C, A and their mirror images

List K consists of 9 positive integers. The median of the integers in K is 6, and the average (arithmetic mean) of the integers is 8. Which of the following could be the greatest integer in K? Indicate all such integers. 10 15 24 40 50

A point on the terminal side of angle 8 is given. Find the exact value of the indicated trigonometric function of θ. (-15, 36) Find sin θ. -5/13 12/13 5/13 -12/13

Suppose in individual makes an initial investment of $1,400 in an account that earns 8.4%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawls at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.) (a) How much is in the account after the last deposit is made? (b) How much was deposited? (c) What is the amount of each withdrawl? (d) What is the total amount withdrawn?

Taking logarithms and antilogarithms is necessary to solve many chemistry problems. For practice, complete the following table, where N is a number.

Suppose an individual makes an initial investment of $1,400 in an account that eams 4%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years so that the account balance will be reduced to 50), (a) How much is in the account after the last deposit is made? (D) How much was deposited? (c) What is the amount of each withdrawal? (d) What is the total amount withdrawn?

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. log 3 324 - log 3 4

Cost, revenue, and profit are in dollars and x is the number of units. If the marginal cost for a product is MC = 8x + 90 and the total cost of producing 30 units is $700b, find the cost of producing 25 units.

What is the least common multiple of 24 and 60?

Solve the equation 7+ x - 3 /2 = 2 /3x + 3 x=

A population numbers 11,000 organisms initially and grows by 6.3% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a b^t where

Graph the given function by making a table of coordinates. f(x) = (1/2)^x

If 3000 dollars is invested in a bank account at an interest rate of 5 per cent per year, compounded continuously. How many years will it take for your balance to reach 30000 dollars?

Suppose you have $13,000 to invest. Which of the two rates would yield the larger amount in 1 year: 10% compounded daily or 9.94% compounded continuously?

Graph f(x) = 2^X and g(x) = log 2x in the same rectangular coordinate system. Choose the correct graph below.

Use common logarithms or natural logarithms and a calculator to evaluate the expression. log 1517

What would the scatter plot show for data that produce a Pearson correlation of r = +0.95? points clustered close to a line that slopes up to the right points clustered close to a line that slopes down to the right points widely scattered around a line that slopes up to the right points widely scattered around a line that slopes down to the right

Determine visually whether the graph is symmetric about the x-axis, the y-axis, or neither. If the graph represents a function, determine whether the function is even, odd, or neither. Is the graph symmetric about the x-axis, the y-axis, or neither A. The graph is symmetric about the y-axis. B. The graph is symmetric about the x-axis. C. The graph is symmetric about neither the x-axis nor the y-axis.

Estimate the slope of the line given to the right. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is B. The slope is undefined.