Basic Math Questions and Answers

3a n 2 7 3an 3a n 7 3an Simplify your answer Use positive exponents only Use integers or fractions for any numbers in the expression

Assume that ho radicands were formed by raising negative quantities to even powers 2x y5 48x 2x y5 48x Type an exact answer using radicals as needed

Add the numbers below Express the result in polar form 1 91 71 31 2 2 11 216 21 What is the sum Simplify your answers Round to one decimal place as needed Use angle measures greater than or equal to 0 and less than

Simplify the given expression Express the answer with positive exponents 3 x 4 1 2 3x 5 24 x 4 1 1 2 B 3 x 4 3x 5 24 x 3x 5 24 x 4 Simplify your answer Type your answer using exponential notation Use integers or fractions for any numbers in the expression

Choose the sequence of steps below that verifies the identity O A csc t 1 cott csct 1 B O C D csct 1 csct 1 csct 1 cott cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 cott csct 1 csct 1 cott csct 1 cott csct 1 csct 1 csct 1 csct 1 csc t 1 cott csct 1 csc 1 1 cott csct 1 csc t 1 cott csct 1 cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 cott csct 1 cott csc t 1 cott csct 1 cott csct 1

Simplify by taking roots of the numerator and denominator Assume that all expressions under the radicals represent positive numbers 81y5 5 81y 6

tan x sec x csc x cot x Choose the correct proof below A E tan x sec X CSC X sin x COS X COS X sin x cos X 1 sin x X sin x cos X 2 COS cot x X OC tan x sec xcsc x sin x COS X sin x cos X 1 sin X sin x cos x 2 COS x cot x 1 sin x OB tan x sec X CSC X sin x 1 cos X COS X 2 1 sin x sin x cos x 2 cos X sin x cos x cot x OD tan x sec xcsc x sin x COS X 1 sin X sin x cos x 2 COS X sin x cos X cot x 1 sin x

Full Solutions be sure to show all your work 6 Write the quadratic y 2 x 3 7 written in standard form

3 The total cost for a certain business is given by C x 3000 In 20 x 10 17 000 a b Find the total cost of producing 50 units 5 pts C

The following table shows the daily cost data and demand schedule for a typical firm producing board games in a monopolistically competitive market in the short run Fill in the values in the Marginal Cost Total Revenue and Marginal Revenue columns in the following table and then answer the questions that follow Total Cost Marginal Cost Dollars Average Total Cost Dollars Quantity Price Board games Dollars per game Dollars 1 10 00 2 3 4 5 6 7 8 9 00 8 00 6 00 4 00 3 00 2 00 1 00 17 Based on your calculations the firm will 20 27 32 35 48 56 64 Under monopolistic competition a typical firm will produce Fill in the Average Total Cost column in the previous table Total Revenue Dollars board games at a price of itu in this monopolistically competitive market is Marginal Revenue Dollars A per board game in the short run

6 A restaurant is building a new addition that has a rectangular seating area with a semi circular windowed alcove as shown below SHOW YOUR WORK 10 marks 14 ft 9 in 3 45 m 2 84 m 38 ft 4 in a Find the floor area of the shape in square feet b The ceiling height will be 12 feet Find the volume of the space in cubic feet c The design requires 11 air changes per hour Calculate the total CFM needed for the space d The designed air speed in the duct work is 275 ft min Calculate the cross sectional area of the duct work needed for this air speed e If a circular duct is used to supply this air specify the diameter of the duct to be used

7 Which statements BEST describe the key features of the Law of April 6 1830 Select TWO correct answers It outlawed immigration from the United States It encouraged an influx of new American empresarios It slowed the economic development of ranching in Texas It imposed taxes on trade between foreign nations and Texas It relocated the settlers in Nacogdoches to new land near San 1 O D

9 Why is the Battle of Goliad referred to as the other Alamo O Both were brutal losses for the Texian Army Both were valiant victories for the Texian Army Both were brutal losses for the Mexican Army Both took place in the same area

Find the measure of the bigger arc 5x 10 3x 4 30

If the measure of arc QP is 76 degrees and angle 3 is 92 degrees what is the measure of arc SR P 1 3 R S

ches om wearing using such products in this building Outlook 2 K Homepage 23F Technology Mathemati 2 cos attacks respirator 1 Amylab pearson com Use a double angle formula to find the exact value of the given expression 2 8 P Pearson MyLab and Mastering Question 2 of 10 In class Qui This quiz 25 This questic 2 2 cos 1 8 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Prove the given identity Choose the correct proof below cos 0 cot 0 csc 0 sin 0 OA cos 0 cot 0 csc 0 cos 0 OB O C cos 8 cot 0 csc 0 cos 0 cos 8 cot 8 csc 0 cos 0 OD cos 0 cot 8 csc 0 cos 0 cos 0 sin 8 cos 0 sin 8 cos e sin 0 cos 0 sin 0 1 sin 8 1 sin 0 sec 0 1 sin 0 1 sin 0 sin 8 cos 0 1 cos 0 1 sin 8 cos 0 1 sin 0 Question 3 of 10 cos 0 1 sin 0 sin 0 sin 8 sin 8 sin 0 sin 0 sin 0 sin 0 sin 20 sin 8 sin 8 sin 8 sin 8

Simplify the given expression The result will be one of sin x cos x tan x cotx sec x or csc x cos x sec x tan x cos x sec x tan x Question 5 of 10

10 Give the general solution to the Cauchy Euler equation 4x y 16xy 9y 0

4 10 Suppose that the third order homogeneous linear differential equation ay by cy dy 0 has solutions y ex y2 e2x and y3 ex Is S y Y2 Y3 a fundamental solution set for the differential equation Answer yes or no and justify your answer

5 20 Give the general solutions to the following equations a y 5y 6y 0

3 10 Is the differential equation 2 e y dx 2 y dy 0 exact Answer yes or no and justify your answer DO NOT SOLVE THE DIFFERENTIAL EQUATION

1 point 4 Calculate the cross product assuming that u xw 3 4 w 0 00 3u 2w x w

Assignment 10 Problem 1 1 point Find the area of the parallelogram with vertices A 1 1 4 B 0 3 9 C 1 0 7 and D 2 2 12 Area 0

1 point Find the area of the triangle with vertices 0 0 0 1 2 5 and 1 3 3

Modern Age Solutions Co Ltd wants to recruit a250 representatives to work in its call centre offices located in Nairobi The call centre works 24 hours shifts The minimum qualifications required for the job are a graduate degree fluency in inglish sensitivity to customer needs and willingness to work a Draft a suitable advertisement for the job vacancies 6mks b Suggest suitable sources of recruitment which the company should employ 8mks c Recommend the selection procedure the company should adopt 8mks d Should the company use tests for selecting employees If yes recommend suitable types of tests 8mks

Carson is baking a cake and has mixed 460 mini chocolate chips into the batter Carson pours the batter is poured into a rectangular pan that measures 13 inches by 6 inches After poured the batter measures exactly 1 8 inches in height What is the density of chocolate chips in the batter Round your answer to two decimal places as necessary Show your work here

Let A 1 1 1 01 1 1 a Find the QR factorization of the above upper Hessenberg matrix A Hint Follow Algorithm 6 on Lec 23 b Using initial vector 0 1 1 1 compute the dominating eigenvalue and eigenvector of by using power method with scaling for two iterations where the norm is

Sketch the deed description below a Determine the interior horizontal angle at each corner b Express each distance in feet c Find the area Deed to land in Hodgenville Kentucky Grantees are Thomas and Nancy Lincoln Beginning at a large white oak 13 poles above the Sinking Spring or Rock Spring running the N9 degrees W 310 poles to a stake in John Taylor s field thence S 89 degrees E 155 poll to a forked Blackjack thence S 9 degrees E 310 poles to two black jacks thence N 89 degrees W 155 poles to the beginning

Use the purple rectangle diamond symbols to shade the area representing the revenue lost from selling fewer units of output Then use the green ectangle triangle symbols to shade the area representing the revenue gained from selling each unit of output at a higher price PRICE Dollars 100 90 80 70 60 50 40 30 20 10 0 0 20 9 8 Demand 80 100 120 140 160 180 200 QUANTITY Units This monopolist s marginal revenue equals Revenue Lost Revenue Gained Hint Enter the negative sign if necessary

Use the following to answer question 15 Figure AD AS Aggregate price level LRAS Y YpY SRAS AD AD AD Real GDP A SRAS will shift to the right B SRAS will shift to the left C AD will shift to the right D AD will shift to the left 15 Figure AD AS Suppose that initially the economy is at long run equilibrium Ther government decides to cut taxes as a result

Maximizing Profit The total daily revenue in dollars that a publishing company realizes in publishing and selling its English language dictionaries is given by R x y 0 005 0 003 0 002xy 20x 15y where x denotes the number of deluxe copies and y denotes the number of standard copies published and sold day The total daily cost of publishing these dictionaries is given by C x y 6x3y 170 dollars Determine how many deluxe copies and how many standard copies the company should publish each day to maximize its prifts Round your answers to the nearest whole number of copies deluxe coples standard coples What is the maximum profis realizable Round your answer to the nearest cent

A country s population in millions in 2001 and 2010 are given below Use this information and the exponential model A P 1 r to find the growth rate r for the country over this period population in 2001 137 million population in 2010 133 million The country s growth rate over this period was 0 33 Round to the nearest hundredth as needed

K Given the two terms in the Fibonacci sequence shown below find the specified term F35 9 227 465 F36 14 930 352 find F34

Use the following to answer question 10 Figure Inflationary and Recessionary Gaps Panel a LRAS Price level P3 P P Y Yp Real GDP SRAS AD Price level P3 P P Panel b LRAS Yp Y Real GDP SRAS B indicates that the economy is experiencing an inflationary gap C indicates that the economy is experiencing a recessionary gap D would be associated with considerable unemployment AD 10 Figure Inflationary and Recessionary Gaps In Panel b the level of real GDP represented by X A is potential output for this economy

4 If the Fed decreases the quantity of money in circulation A interest rates decrease investment increases and the aggregate demand curve shifts to the right B C interest rates increase investment decreases and the aggregate demand curve shifts to the left D interest rates decrease investment decreases and the aggregate demand curve shifts to the left interest rates increase investment decreases and the aggregate demand curve shifts to the right

3 Aggregate demand will shift to the right if A the aggregate price level increases the government purchases increase there is an increase in taxes there is a decrease in money supply B C D

1 According to the aggregate demand curve when the aggregate price level the quantity of A rises aggregate output supplied falls B falls aggregate output demanded falls C rises aggregate output demanded falls D rises aggregate output demanded does not change

If you have 10 000 in a bank account that is paying an interest rate of 8 percent that is being compounded annually how many years will it take to double your investment if the interest rate stays the same What is the doubling time years Do not round until the final answer Then round to the nearest hundredth as needed This question 1 point s possible EXOR

Which of the lines on the given graph have a zero slope f e C b d Select all lines with a zero slope U f b a C d e None of the lines have a zero slope

For the following arithmetic sequence a find the specified term a and b find the sum of the terms from a to an 6 8 10 12 find a10 a a 0 b The sum of the terms from a to a10 inclusive is This question 1 inclusive

Calculate the missing values in the following table Round to four decimal places wherever applicable a b C Percent 1 3 7 Decimal 2 5 Fraction or mixed number in lowest terms 00 250

6 each can break apart a 9 X 6 array into two smaller arrays for facts you know One way is to think of 9 as 5 4 Draw a line to show this way Then find the product 9 6 x 4x6 9 6 5 4 So Mark spent for 9 fish Share and Show 1 Draw a line to show how you could break apart this 6 X 8 array into two smaller arrays for facts you know What numbers do you multiply 3 and and 3 and Math Board What numbers do you add 6x8 6X 6x8 5x8 6x8 x 2

Assume that of the 330 000 people who immigrated to Canada in 2010 14 35 were from China 9 4 were from the Philippines and the rest were from other countries a Calculate the number of people who immigrated to Canada from China Round to a whole number b If the combined number of immigrants from China and the Philippines constituted 0 185 of the population of Canada calculate the population of Canada in 2010

Calculate P A or B in the following scenarios a P A 0 608 P B 0 135 A and B are mutually exclusive P A or B Round to 3 significant digits b P A 0 229 P B 0 204 P A and B 0 042 P A or B Round to 3 significant digits

Bryan and his two sisters purchased an office for 600 000 Their individual investments in the office were in the ratio of 10 2 8 respectively After the purchase they decided to renovate the office and purchase furniture so each of them invested an additional 40 000 Calculate the new ratio of their investment after the additional investments Express the ratio reduced to lowest terms

Evaluate the following expression 3a 8b15c 2a 5b 6c 3 where a 3 b 3 and c 5

The value of a currency appreciated by 5 10 of its value last month and then depreciated by 5 10 this month By what percent did the currency appreciate or depreciate over the 2 month period Express the answer with a positive sign for appreciation or negative sign for depreciation rounded to two decimal places

Arrange the following measurements in order from largest to smallest and select the correct answer click to select 5 4 L 7 5 qt 12 pt 1 gal 12 pt 7 5 qt 5 4 L 1 gal 7 5 at 12 pt 5 4 L 1 gal 5 4 L 7 5 qt 12 pt 1 gal

Given that x O a Ob O C 4 x 4 x 8 12 8 X 4 y 8 which one of the following represents y