Sequences & Series Questions and Answers

True or False? f'(a)=lim: h→0 f(a+h)-f(a) h f'(x)=lim f(x+h)-f(x) h h→0 gives the derivative at a single point x = a and gives the derivative function.

In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 60° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle. The measure of the first angle is. BLECH

5 fluid oz. of a 2% acid solution was mixed with 11 fluid oz. of a 66% acid solution. Find the concentration of the new mixture. Only provide the numerical solution. Do not include the % symbol.

A supermarket is selling two types of candies, orange slices and strawberry leaves. The orange slices cost $1.27 per pound and the strawberry leaves cost $1.77 per pound. How many pounds of each should be mixed to get a 8-pound mixture that sells for $11.16?

Solve for y. y= 4x - 2y = 10 (Simplify your answer.)

Adrian leaves his house and walks down the road at a rate of 3.8 miles per hour. 0.75 hours later, his wife Mary leaves the same house and begins walking down the same road at a rate of 4.2 miles per hour. How long will it take for Mary to catch up to Adrian? Only provide the numerical solution. Round to the nearest thousandth. No units are necessary. How far from the house will Mary catch up to Adrian?

Write the following number in standard notation. 1.034 x 106 1.034×106 =

Select one variable to represent one quantity and express the second quantity in terms of the first. a 14-foot piece of wood is cut into 2 pieces.

Solve the following formula for t. D=B+Brt

we assume that ƒ(k) (x): = (k − 1)! (1 − x) k plz solve the question below. = ƒ(k+1)(x) = (- − (k − 1)! ( (1 x) (k − 1)! (1 - x) k 1 (1-x)k − (k − 1)! ((1 — − (k − 1)! (5) (1 − x) (0) (7)! (8) T) ' (4)

Value Rent-A-Car rents a luxury car at a daily rate of $39.22 plus 20 cents per mile. A business person is allotted $100 for car rental each day. How many miles can the business person travel on the $100? The business person can travel miles.

ve the system of equations by the addition method (4x+y = 17 3x-y=4 ct the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution is (Simplify your answer. Type an ordered pair.) There are infinitely many solutions: {(x,y) 4x+y=17) or ((x,y) |3x-y=4) There is no solution; {} or Ø.

A = {9, 3, 11, 7} B = {3, 5, 7, 9, 11, 13} C = {3, 5, 9} D = {13,11} Select all of the following that is false. OB CA OD C B OD CA AnD = 0

Graph the following linear equation. -x+2y=7

a. Rewrite the given equation 3x + 4y - 12=0 slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. - 3 a. The slope-intercept form of the equation is y= (Simplify your answer. Use integers or fractions for any numbers in the equation.) and the y-intercept is b. The slope of the equation of the line is (Type integers or fractions.) -x+3.

Complete each ordered pair so that it is a solution of the given linear equatio x-3y=-9; (,5), (-9,) The first ordered pair is (5).

Let f [0,2] → R be a continuous function, with ƒ(0) ≤ f(1) ≤ f(2). Show that there exists xo [0, 2] such that f(xo) = ƒ(0) + ƒ(1) + ƒ(2) 3

Use the given constraints and optimal solution to state the value of each slack variable. subject to 5x + 2y ≤ 1,715 46x + 31y ≤ 690 x ≥ 0, y 20 (x, y) = (15, 0) optimal solution The slack variables have values = $1 and S₂ =

Maggie wants to build up the money her bank account. She would like to have $2,000 in interest in her bank account after 19 years. If the simple interest rate is 2.4%, how much money will she need to deposit to reach her goal? Provide the numerical solution rounded to the nearest cent. You do not need to the $ symbol.

Josh is buying jeans. He finds a pair that is 42% off. If the sale price is $55, determine the original price of the pair of jeans. Round to the nearest cent and do not include the $ symbol.

On the graph of f(x) = cos x and the interval [2x, 4x), for what value of a does f(x) achieve a maximum? Choose all answers that apply. Select all that apply. 02T 05#

Jackie received $5,000 as a prize. She invested her money into a certificate of deposit for 8 years. When she redeemed the certificate of deposit, she received $6,200. What simple interest rate did she receive on her certificate of deposit? Provide the numerical solution rounded to two decimal places for the percent. You do not need to include the % symbol.

Simplify. See Example 5. (Objective 3) (5x^)(-2x) C

To determine the average of a set of test scores, add all of the scores and divide by the number of scores. Phil score 92, 77, 71, 63, 96, and 69. Determine what score Phil would need to earn on his seventh test to have an average of 80. Only provide the numerical solution. No units are necessary.

Solve the system of equations by the substitution method. [y=2x+1 4y - 6x=10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution is (Simplify your answer. Type an ordered pair.) OB. There are infinitely many solutions; {(x,y) y = 2x + 1} or {(x,y)|4y - 6x=10}. OC. There is no solution; {} or Ø.

Find the quotient using long division. 4x² - 18x+1 x-5 4x²-18x+1 X-5 = (Simplify your answer.)

what is the pattern between: 05-15-43-44-47-03 10-15-22-23-41-07 01-12-13-26-40-07

Attendance at a recent concert was 11% higher than last year's concert. If the attendance last year was 23,572, determine the attendance at the concert this year. Only provide the numerical solution. Round to the nearest person. No units are necessary.

Find the quotient using long division. 5x² + 12x +4 x + 2 5x² + 12x +4 x + 2 =(Simplify your answer.)

Shawn borrows $12,000 from the bank to help pay for a new car. The loan is for 7 years with a simple interest rate of 7.7%. When Shawn settles the loan at the end of 7 years, how much money, in total, must he pay? Round to the nearest cent (if necessary) and do not include the $ symbol.

2. Reshma's monthly income is 22% more than Neelam's monthly income. If Neelam's monthly income is Rs. 3500. What is the Reshma's monthly income?

Apply Laplace transform method to evaluate: t sint e-³t dt

Choose the inequality which best describes the graph. to b OFS-4 OM-4 OAY 4 <64 -8 -7 -6 10

Round to 2 significant figures. 5,239 Step 1: Identify the place value we need to check for rounding. What is the place value for our last significant figure? B. the hundreds D. the ones A. the thousands C. the tens

Solve each equation for y. Match the given equation with the correct equation that is solved for y. 7x - 4y = 28 7x + 4y = 28 -7x - 4y = 28 -7x + 4y = 28 4x - 7y = 28 4x + 7y = 28 -4x - 7y = 28 -4x + 7y= 28 [Choose ] [Choose ] [Choose] [Choose] [Choose] [Choose ] [Choose ] [Choose ] >

Evaluate the expression if x = −2, y = 3, and z = -4. (If an answer is undefined, enter UNDEFINED 4z²y 4(x - Z)

Hi, please only respond if you can answer all parts so that I do not waste a question and have to post it again, as many only get one response. Thanks for the help! Consider the graph given on the right and answer the questions below. C The shaded set of numbers shown on the x-axis can be expressed in interval notation as (Type your answer in interval notation.) This set represents the function's ▼

Given that f(x) = 2x + 2 and h(x) = x³, find (h of)(1)- (hof)(1) =

The equation y = 25 can also be written as: a) x= Ob) x = c) y y = d) Y log, y 2 log₂y 5 log₂x 5 log5x 2

Matt borrows $15,000 from the bank to help pay for a new car. The loan is for 6 years with a simple interest rate of 9.9%. Determine the amount of simple interest that Matt will pay for the loan. Round to the nearest cent (if necessary) and do not include the $ symbol.

Simplify. See Example 7. (Objective 4) (x²x³)5

Identify the base and the exponent in the expression. -2y5 base exponent

Solve the equation for x. -2(3x-9) + 2 = − 6x+20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. x= (Type an integer or a fraction. Simplify your answer.) B. The solution is all real numbers. OC. There is no solution.

Simplify. Assume no division by zero. See Example 8. (Objective 4) 2x 3y² 4

Find the function f(x) that satisfies the following conditions: f(-2) = f(1) = 0, f(x) < 0 when x < -2 and f(x) > 0 when x>-2 a) f(x) = (x + 2)(x − 1)² b) f(x)=(x-2)(x + 1)² c) f(x) = (x + 2)²(x-1) d) f(x) = (x - 2)²(x + 1)

Simplify. See Example 5. (Objective 3) -2y(y^³)

Solve the system by graphing. x+y = 3 x - y = 1

Identify the base and the exponent in the expression. (-8x)4 base exponent

Simplify the Expression 6. 4 5x 4x² - 4x +1 20x²5

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julle decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete? Oy-7.75x+4; discrete Oy-7.75x+4; continuous y4x+7.75; discrete y-4x+7.75; continuous