Sequences & Series Questions and Answers

What is the smallest non-negative integér z such that [r]= [116^129 +60^40] in Z7? Justify your answer. Hint: Find out simple numbers that 116 and 60 are congruent to modulo 7, and try to write the powers 129 and 40 in terms of 6.

Given the function f(x) = 4x 1, evaluate and simplify the expressions below. See special instructions on how to enter your answers. Instructions: Simplify answers as much as possible. Expressions such as 4(x + 2) and (x + 5)² should be expanded. Also collect like terms, so 3x + x should be written as 4x.

Bryson invests $4100 in two different accounts. The first account paid 7 %, the second account paid 14% in interest. At the end of the first year he had earned $497 in interest. How much was in each account?

The graph above is a transformation of the function f(x) = |x|. Write an equation for the function graphed above

The crime rate of a certain city is increasing by exactly 2% each year. If there were 350 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2015. Round to the nearest whole number.

A population numbers 17,000 organisms initially and decreases by 8.6% 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 = abt, where

A function and its first and second derivatives are given. Use these to find each of the following. (If an answer does not exist, enter DNE.) Find any horizontal and vertical asymptotes. (Enter your answers as a comma-separated list of equations.) Find any critical points. (x, y) = Find any relative maxima and relative minima. relative maximum (x, y) = relative minimum (x, y) = Find any points of inflection. (x, y) = Sketch the graph of the function.

Nahele invests $6900 in two different accounts. The first account paid 4 %, the second account paid 7 % in interest. At the end of the first year he had earned $324 in interest. How much was in each account?

Express the concentration of alcohol in parts per million if 925 mL of fermentation broth contains 12.7 μL of alcohol. Round your final answer to the nearest tenth. (0.5)

The DePeppo children, Ann, Debbie, Damian, and Adam, created a contest to test their athletic abilities and physical strength. They threw objects into the air to see who was the best. These four equations depict the travel of the objects they threw. yl=-16z² +62x+10 y2=-16x² + 75x y3 = -16z² +38x+60 y4=-16x² + 20x + 10

The discontinuity of f(x) = x²-1/x-1 at x= 1 is removable. True False

For f(x)=x²+x+ 3, determine all values for y for which f(y) = 93

How many square feet of carpet are needed to cover the floor of a rectangular room 14 ft. by 12 ft.?

Jose hopes to earn $700 in interest in 4.1 years time from $56,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds quarterly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.

The count in a bacteria culture was 100 after 15 minutes and 1400 after 30 minutes. Assuming the count grows exponentially, What was the initial size of the culture? Find the doubling period. Find the population after 70 minutes. When will the population reach 15000. You may enter the exact value or round to 2 decimal places.

In IEEE Single precision, find the next largest machine number (successor(x)) for the binary number z above. Identify successor (x), then write its Hexadecimal representation. Justify all steps.

An oil tanker can be emptied by the main pump in 5 hours. An auxiliary pump can empty the tanker in 7 hours. If the main pump is started at 5 PM, when should the auxiliary pump be started so that the tanker is emptied by 9 PM?

For a 4-node quadrilateral element, with an Aspect Ratio 2.3 and an element size of 10.70mm, find the value of the shape function N1 at node 1.

Three numbers sum up to 112. The smaller number is 1/4 are the three numbers? The smallest number is the larger and the middle number is the medium number is and the largest number is the larger. What

You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 5% compounded annually, and the third account pays 3 % compounded annually. After one year, you earn $44000 in interest. If you invest four times the money into the account that pays 4 % compared to 3%, how much did you invest in each account?

Evaluate the function f(x)=x²-8x+5 at the given values of the independent variable and simplify. a. f(8) b. f(x + 9) c. f(-x) a. f(8) 5 b. f(x +9)= x² + 10x + 14 c. f(-x) =

Given sec 0= 19, use trigonometric identities to find the exact value of (a) cos 0, (b) tan 20, (c) csc (90°-0), and (d) sin 20.

Consider the equation and the following ordered pairs: (5, y) and (x, 1). y = -2x+7 Step 1 of 2: Compute the missing x and y values so that each ordered pair will satisfy the given equation.

Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 60-kilometer mark while riding at a velocity of 36 kilometers per hour. Complete parts (A) through (C) below. (A) Find the cyclist's average velocity during the first two hours of the race. kilometers per hour (B) Let f(x) represent the distance traveled (in kilometers) from the start of the race (x=0) to time x (in hours). Find the slope of the secant line through the points (0.f(0)) and (2.f(2)) on the graph of y = f(x). kilometers per hour (C) Find the equation of the tangent line to the graph of y=f(x) at the point (2,f(2)). (Type an equation)

A rectangular prism is 4 units by 2 1/2 units by 1 1/2 units. How many cubes with a side length of 1/2 unit will completely fill the prism?

Let T: R³ → R4 be a one-to-one linear transformation and let S : R4 → R³ be an onto linear transformation. Let A and B be the standard matrices of T and S, respectively. Describe the possible reduced echelon forms of A and B.

The following function is given. f(x)=x³5x² - 4x + 20 a. List all rational zeros that are possible according to the Rational Zero Theorem. 1,1,2,2,20,20,5, -5,10,- 10,4,-4 b. Use synthetic division to test several possible rational zeros in order to identify one actual zero. One rational zero of the given function is 2. c. Use the zero from part (b) to find all the zeros of the polynomial function. The zeros of the function f(x) = x3 - 5x2 - 4x + 20 are

Evaluate the Riemann sum for f(x) = 0.9 1.6 sin(2x) over the interval [0, 2] using four subintervals, taking the sample points to be midpoints.

Evaluate the Riemann sum for f(x) = 0.7 -1.5 sin(2x) over the interval [0, 2.5) using five subintervals, taking the sample points to be right endpoints.

Suppose you deposit $2000 in a savings account that pays at an annual rate of 4%. If no money is added or withdrawn from the account, how many years will it take for the account to contain $3000? A = P(1+r)^n Select one: a. 6 years b. 8 years c. 11 years d. 4 years

Confidence levels are 90%, 95% and 99%. Which confidence intervals match with the correct level? (5.6, 14.4) (7.2, 12.8) and (6.6, 13.4)

What group promulgates forms for mandatory use by license holders? A) The Texas Association of REALTORS® B) The legislature C) TREC D) The broker-lawyer committee

The TREC Addendum for Property Subject to Mandatory Membership in a Property Owners Association provides that the seller is to provide information to buyer regarding material changes to the subdivision information A) as soon as possible. B) promptly. C) immediately. D) timely.

Which of the following methods of purchasing does NOT require the use of a TREC-promulgated addendum to define the transaction's financial details? A) Third-party financing B) Assumption of existing lien C) Seller financing D) Cash

If there is no dollar amount inserted in paragraph 23 of the TREC One to Four Family Residential Contract but the time period shows as being 10 days, the contract A) is void after 10 days. B) is voidable on the 11th day. C) does not have a valid option period. D) is terminated on the 11th day.

If you randomly select a letter from the phrase "Sean wants to eat at Olive Garden," what is the probability that you select a consonant? (Your answer must be in the form of a reduced fraction.)

Which of the following statements is FALSE? A) The promise of the purchaser to buy and the promise of the seller to deliver title are adequate consideration to create a legally binding executory contract. B) Earnest money is necessary to bind the contract. C) Earnest money is not consideration. D) Earnest money is applied to the sales price at closing.

If the buyer and seller agree that the seller will leave the living room television with the home after closing, they should use the A) Non-Realty Items Addendum. B) Notice to Prospective Buyer. C) Seller's Disclosure of Property Condition. D) Loan Assumption Addendum.

Use a half- angle to find the exact value of sin 157.5° b) Peter and Li leave their hotel on rented cars at the same time and travel along straight highways that differ in direction by 80°. One car averages 60 miles per hour and the other averages 50 miles per hour. How far apart will the cars be after 30 minutes? Round to the nearest tenth of a mile.

The original maker of a VA loan remains liable when the loan is assumed unless the veteran receives A) a Release of Liability B) a Certificate of Reasonable Value C) a Certificate of Eligibility D) a Partial Entitlement

All of the following are true about VA loans EXCEPT A) some of a veteran's dependents may be able to use the veteran's benefits to purchase a home. B) the appraisal for a VA loan is called a certificate of reasonable value. C) once approved and closed, the VA will insure the lender against any default by the veteran. D) the veteran must supply a certificate of eligibility.

One of the primary duties of the Federal Housing Finance Agency is to A) regulate Fannie Mae and Freddie Mac. B) maintain the Consumer Price Index to less than 2% annual growth. C) provide low-cost housing. D) supervise the mortgage industry.

When would a banker generally discuss a participation loan? A) When the borrower has insufficient funds to complete the transaction B) When the banker's loan to a borrower is at its limit C) If there is a cosigner D) When the banker believes the risk is too great

ECOA includes protection for all of the following protected classes EXCEPT A) sexual orientation B) marital status. C) age. D) receipt of public assistance.

When evaluating a loan application, a loan officer will consider all of the following EXCEPT A) the ability of the borrower to repay the loan. B) the applicant's past credit record. C) the borrower's rental payments for the previous two years. D) the value of the property being offered as security.

The promissory note is a A) negotiable instrument that may be sold. B) nonnegotiable instrument that may be sold C) nonnegotiable instrument that cannot be sold. D) negotiable instrument that cannot be sold.

Financial leverage is described as A) using an income stream from rental property to acquire more real estate. B) using other people's money to acquire something of value. C) "margin" purchasing, which is only used to buy stocks and bonds. D) using tax deductions to lower a property owner's taxable income.

An investor purchased shares in a REMT at the suggestion of a securities broker. The REMT derives income from all of the following EXCEPT A) registered debentures B) profits from buying and selling mortgages. C) mortgage interest. D) loan fees.

Which of the following information is on a credit report? A) List of assets owned by the borrower B) The borrower's marital status C) Status of the borrower's current credit accounts D) The borrower's income

Fannie Mae was created for the sole purpose of A) providing a loan exchange mechanism for qualified lenders. B) offering loan programs that require a 20% down payment. C) providing a secondary market for qualified loans. D) making loans to qualified borrowers.