Basic Math Questions and Answers

2 Given the equation y 4 5 a Does this equation represent growth or decay b What is the growth or decay factor c What is the initial value d What is the range

A B C G USE YOUR KNOWLEDGE OF TRIANGLES TO DRAG THE MISSING INFORMATION TO EACH WHITE BOX B D 67 40 A 7x 3 6x 60 C H 6x 3x 5 I X M A X Ma 2x 1 F D 2x 11 7x 5 L J E 3x 75 K X M F X M J 11 20 8 15 33 50 59 51 DRAG

How long is the pen in inches in cm 10 11 12 13 14 1

5 The population of a colony of birds triples every 10 years At the present time there are about 250 birds in the colony how many birds will there be in 6 years fau dividirs

6 Determine the value of and State the angle property used 3T 7a 48 112 144 87 56 OR I 36 OR

Evaluate f x 5 23x 3 at f 2 Round to 3 decimal places f 2

Solve for x Leave the answer as a reduced fraction and enter the numerator 4 3x 6 4 6x 5 1 X

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Question conter example or dis approve Prove by Mathematical induction yan 1 is divisible by I5 for nyo

Lagrange s polynomial p x that interpolates f x at x 0 2 and x 0 5 is Select one 0 5 O a p x 20 2 0 5 5 O b p x 5 05 2 0 2 0 2 z 0 5 0 5 0 2 Oc p x 5 0 2 1 0 5 0 2 0 5 0 2 0 5 Z 0 2 0 2 0 5 2 5 0 2 0 5 0 2 d p x 2 0 5 O e p x 50 2 0 5 Of p x 57 2 0 2 0 5 2 0 5 2 0 2 1 0 5 0 2 Z 0 2 0 5 0 2

Income Statement Sales Cost of goods sold Gross Profit Operating Expenses Depreciation expense General and Admin expense Total Operating Expenses Operating Income Interest expense Earnings before tax Net Income Taxes 573 000 297 000 276 000 66 000 79 000 145 000 131 000 4 750 126 250 50 500 75 750

In the accompanying data table the entries are for five different years and consist of the weights metric tons of lemons imported from another country and car crash fatality rates per 100 000 population The data are based on dat from a scientific publication Lemon Imports Crash Fatality Rate 226 16 3 Choose the correct answer below 263 362 16 2 16 1 473 16 2 538 14 8 Given that the data are matched and considering the units of the data does it make sense to use the difference between each pair of values Why or why not OA Yes it does make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because they are measurements obtained from the same year B No it does not make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because lemon imports and car crash fatality rates use different units of measurement OC No it does not make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because the terms should be added O D Yes it does make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because car crashes are caused by lemon imports

21 2 We call a circle Ca Yeppeun circle for P and P if C contains P and P C is tangent to the z axis at a point P 0 and the z coordinate of the point of tangency lies between the z coordinates of P and P that is 12 For example the circle C in the following diagram is a Yeppeun circle for the given P and P Given any two such points P and P above the z axis does a Yeppeun circle always exist Explain

here are 12 eggs in a dozen If a farmer s chickens produce an average of 666 dozen eggs in a m gs are reported per month 36 dozen x 12 eggs dozen his answer has Submit Answer significant figures Retry Entire Group eggs 9 more group attempts remaining

The following crosstabulation summarizes the data for two categorical variables x and y The variable x can take on values low medium or high and the variable y can take on values yes or no x Low Low High X 100 Medium 90 80 70 60 50 40 30 20 10 High Total Yes No Total 25 Medium 20 30 y 20 5 a Compute the row percentages Round your answers to three decimal places Yes 5 30 50 65 40 105 25 Lour Medium High b Construct a stacked percent frequency bar chart with x on the horizontal axis 100 90 80 70 60 50 No Total No Yes 40 30 20 10 LOW Medium High No Yes 100 90 80 70 60 50 40 30 20 10 Low Medium High No Yes 100 90 80 70 60 50 40 30 20 10 Low Medium High No Yes

In Italy the price of gasoline averages around 1 64 per liter Using unit analysis calculate the cost of gasoline in Italy in dollars per gallon 1 64 1 L X 128 fl oz 1 Drag and drop your selection from the following list to complete the answer 1 gal 3 79 L gal 29 6 mL 1000 mL

a When 48 68 and 39 24 are divided the answer should have significant figure s Enter the answer using the correct number of significant figures 48 68 39 24 b When 39 24 is subtracted from 48 68 the answer should have Enter the answer using the correct number of decimal places 48 68 39 24 P A digit s after the decimal point

Consider the following 13 18 25 18 17 19 23 22 22 21 17 21 25 26 18 15 19 20 22 12 18 19 23 26 22 20 21 25 21 19 12 14 2 Class 25 14 21 23 a Develop a frequency distribution using classes of 12 14 15 17 18 20 21 23 and 24 26 Class Frequency 15 17 2 18 20 2 21 23 2 24 26 2 Total 10 Total 25 15 15 b Develop a relative frequency distribution and a percent frequency distribution using the classes in pa 12 14 2 15 17 2 Relative Percent Frequency Frequency 18 20 2 16 21 18 21 23 2 24 26 2 10

Consider the following frequency distribution Class Frequency 10 19 20 29 30 39 40 49 50 59 Class less than or equal to 19 less than or equal to 29 Construct a cumulative frequency distribution and a cumulative relative frequency distribu Cumulative Relative Frequency less than or equal to 39 less than or equal to 49 10 less than or equal to 59 14 16 9 Cumulative Frequency

c Prepare a histogram Frequency 10 8 11 12 13 14 15 16 Hours per week in Meetings 4 Comment on the shape of the distribution The distribution is Select Frequency 10 006 8 Hours per week in Meetings 7 62 Frequency 10 8 2 Hours per week in Meetings 23 24 6 Frequency 10 8 PNA 11 12 3 19 A 15 16 17 18 Hours per week in Meetings 12 12

27 1 B 6 0 1 2 3 4 5 6 7 8 9 0 1 2 3 A 6 648 00 9 6 8 9 52 11 289NAS NA M M 6 6 6 7 5 7 3 3 2 9 X B fx 0 00 644 8 2 8 8 5 8 9 7 669 667 MIN 8 7 9 7 2 D Data 10 2377S76 666889 5 3 9 9 1886755778 D 10 10 8 13 8 9 66997 11 7 E

5 53 Modified see template for modifications to the problem You would like to have 500 000 in 20 years To accumulate this amount you plan to deposit an equal sum in the bank each year that will earn 7 interest compounded annually Your first payment will be made at the end of the year a How much must you deposit annually to accumulate this amount b If you decide to make a large lump sum deposit today instead of the annual deposits how large should this lump sum be Assume you can eam 7 on the deposit A B 4 c At the end of 10 years you will receive 100 000 and deposit this in the bank toward your goal of 500 000 at the end of 20 years In addition to this deposit how much must you deposit in equal annual deposits to reach your goal at 7 PV 1 nper pmt FV PV T nper pmt FV C Step 1 PV i nper pmt FV Step 2 PV i nper pmt FV 7 20 12 196 46 500 000 00 129 209 50 7 20 0 00 500 000 00 Hint first in Step 1 determine how much 100K will be worth at the end of 20 years 100 000 00 7 10 196 715 14 500 000 Hint in Step 2 for the FV figure use 500 000 minus the amount from Step 1 Instructions Questions P6 53M P6 54M P6 24M

10 CHALLENGE PROBLEM Yen Luong owns a used pickup truck that she wants to sell A used vehicle guide shows that its average retail value is 17 600 She adds 1 700 for 4 wheel drive 475 for an entertainment system 800 for a special trim package and 225 for power locks She also adds 125 for a sliding rear window 325 for a towing package 250 for power windows and 3 125 for a diesel engine She deducts 675 for having a manual transmission She adds 450 for having less than the expected mileage What is the average retail price of Yen s vehicle

Dropbox Assignments Calculate the break even point for a new toy that costs 12 to make and market and that will be sold for 15 The total quantity that will be sold at that price is 200 000 Submit your answer to the dropbox titled Factors Involved in Price Planning

The system dy t dt 2ty t x t is O 1 Distortion less but can distort some of the input signals O 2 None of the answers O3 With distortion and introduces frequency amplitude and phase distortion O4 With distortion and introduces only phase and amplitude spectra O 5 Distortion less

The average power contained in the frequency band 0 100 for the signal with fo 26 Hz for n 0 for n 0 the Fourier Series coefficients Xn O1 49 6 Watts 2 9 3 3 47 6 Watts 04 None of the answers n is

The Fourier series determines O 1 The expression of a signal as sum of its period O 2 None of the answers 3 The spectral representation of a periodic signal 4 The frequency response of a periodic signal O 5 The phasor representation of the response to any signal

Factor the expression completely This type of expression arises in calculus when using the Product Rule x 1 1 7 2x x2 1 8 7

Factor the expression completely This type of expression arises in calculus when using the Product Rule 5 x 5 4 2x x 3 4 x 5 5 4 x 3

Write the expression in simplest form If it is in simplest form enter the original expression Assume that the denominator is not 0 See Example 3 01 4x 2

Use the following information for the Quick Studies below Algo The following information applies to the questions displayed below On December 31 Hawkin s records show the following accounts Cash Accounts Receivable Supplies Equipment Accounts Payable Common stock Retained earnings December 11 Dividends Services Revenue Wages Expense Rent Expense Utilities Expense QS 1 17 Algo Preparing a balance sheet LO P2 Use the above information to prepare a December balance sheet for Hawkin Hint Retained Earnings on December 31 equal Assets HAWKIN Balance Sheet December 31 Liabilities 8 100 1 000 2 400 14 900 7 500 11 000 5 500 1 900 17 500 8 000 3 000 2 200 Total Liabilities Equity

Use the following information for the Exercises below Algo The following information applies to the questions displayed below On December 1 Jasmin Ernst organized Ernst Consulting On December 3 the owner contributed 85 460 in assets i exchange for its common stock to launch the business On December 31 the company s records show the following it and amounts Cash Accounts receivable Office supplies Office equipment Land Accounts payable Common stock 6 650 Cash dividends Consulting revenue Rent expense 18 650 4 640 19 560 Salaries expense 46 000 Telephone expense 9 890 Miscellaneous expenses 85 460 Exercise 1 18 Algo Preparing an income statement LO P2 Using the above information prepare a December income statement for the business ERNST CONSULTING Income Statement 3 490 18 650 4 920 8 500 890 700

Change each of the following to decimal degrees 25 45 12 26 74 18

Convert each of the following to degrees and minutes 15 35 4 16 63 2 17 16 25 19 92 55 21 19 9 18 18 75 20 34 45 22 18 8

There are ten balls in an urn They are identical except for color Four are red five are blue and one is yellow You are to draw a ball from the urn note its color and set it aside Then you are to draw another ball from the urn and note its color a Make a tree diagram to show all possible outcomes of the experiment O b Let P x y be the probability of choosing an x colored ball on the first draw and a y colored ball on the second draw Compute the probability for each outcome of the experiment Enter your answers as fractions P R R P R B P R Y P B R P B B P B Y P Y R DOY D

Compute P 10 10

See the previous question for the formula for computing the angular size of an object as observed from some particular distance The red orange star Betelgeuse located on the shoulder of Orion has a diameter 1000 times the diameter of the Sun where the Sun s diameter D 1 4 million kilometers Betelgeuse is located d 640 light years away where 1 light year distance traveled in one year at light speed and light speed c 300 000 kilometers per second What is the angular diameter of Betelgeuse expressed in percents of an arcsecond Calculate your answer in arcseconds multiply by 100 to get a percentage and enter in the blank The angular diameter of Betelgeuse is how many of an arcsecond

To calculate the angular size of an object with diameter D as observed from a distance d we compute D d and then convert from radians the natural angular rheasure to the more common degrees arcminutes arcseconds system a D d angle a in radians The planet Mars has a diameter of 6800 km What is the angular size of Mars in arcseconds when it is observed at a typical distance of 270 million kilometers from Earth Using a calculator express your answer in arcseconds 3600 arcseconds per degree 206 000 arcseconds per radian and write the answer in the blank The angular diameter of Mars in arcseconds under the above circumstance is

Total weekly salaries expense for all employees is 9 000 This amount is paid at the end of the day on Friday of each five day workweek April 30 falls on Tuesday which means that the employees had worked two days since the last payday The next payday is May 3 Prepare the required adjusting entry if any Note Enter debits before credits Date April 30 General Journal Salaries expense Salaries payable Debit 9 000 Credit 9 000

The Prepaid Rent account had a 5 600 debit balance at December 31 before adjusting for the costs of expired prepaid rent An analysis of the rental agreement showed that 4 910 of prepaid rent had expired Note Enter debits before credits Transaction e General Journal Debit Credit

Given the system 2 2cos 2t is 01 y t 20cos 2t O 2 dy t 3y t 10x t the steady state response of the system to dt O 5 TT y t 4cos 2t tan 4 TU y t 10cos 0 5t 4 tan 03 O 4 The system does not have a steady state response tan 1 TU y t 20cos 2t 4 tan

aste A B 3 0 1 2 3 4 5 LB B FV Stocks BIUV Cell Styles X fx You are trying to plan for retirement in 10 years and currently you have 150 000 in a savings account and 250 00 C DE F G H P6 24 Modified see template for modifications to the problem CRECHERCHEHEHEHE PV i nper pmt FV Note there are multiple methods that can be used to solve this problem The template below is laid out for one of those methods A FV Savings Savings PV 1 You are trying to plan for retirement in 10 years and currently you have 150 000 in a savings account and 250 000 in stocks In addition you plan to deposit 8 000 iper year into your savings account at the end of each of the next 5 years and then 10 000 per year at the end of each year for the final five years until you retire a Assuming your savings account returns 8 compounded annually and your investment in stocks will return 12 compounded annually how much will you have at the end of 10 years b If you expect to live for 20 years after you retire and at retirement you deposit all of your savings including stocks in a bank account paying 11 how much can you withdrawal each year after you retire making 20 equal withdrawls beginning one year after you retire so that you end up with a zero balance at death nper pmt FV Hv FV 8K Annuity years 1 5 Step 1 A PV 1 nper pmt 5 150 000 00 8 10 323 838 75 Alignment 250 000 00 Number 12 10 776 462 05 Cells Editing

Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles The results are as follows Lease Length in Months Percent of Leases of Leases of Leases 35 30 25 20 15 10 5 0 35 30 25 20 15 10 13 24 12000550 25 36 5 0 37 48 a Use the midpoint of each class and call the midpoint of the last class 66 5 months for purposes of estimating the expected lease term in months Also estimate the standard deviation in months of the distribution Round your answers to two decimal places expected lease term standard deviation 49 60 More than 60 b Sketch a graph of the probability distribution for the duration of new auto leases 35 30 25 20 13 3 36 7 18 5 30 1 19 6 0 3 x months x months 30 5 42 5 54 5 66 5 Lease Length in Months 18 5 30 5 42 5 54 5 66 5 Lease Length in Months of Leases of Leases 10 5 0 35 30 linnakes 15 10 5 0 18 5 18 5 30 5 42 5 54 5 66 5 Lease Length in Months 30 5 42 5 54 5 66 5 Lease Length in Months

What are the requirements for a probability distribution Select all that apply associated probabilities for each value of x The summation of the probabilities is 1 Each probability takes on values between 0 and 1 inclusive Each probability takes on a value of 0 or 1 a description of all the values of the random variable x Each value of x has the same probability The summation of the probabilities is 1 The summation of the probabilities equal 1

List the criteria for a binomial experiment Select all that apply The probability of success on each trial is constant a fixed number of trials repeated under identical conditions The trials have exactly three outcomes The probability of success can change from trial to trial The trials are independent The trials are mutually exclusive The trials have exactly two outcomes The trials may have two or more outcomes What does the random variable of a binomial experiment measure The random variable measures the number of successes in n trials The random variable measures the number of trials until the nth success The random variable measures the number of failures in n trials The random variable measures the number of trials until the 1st success

The Orchard Cafe has found that about 6 of the diners who make reservations don t show up If 83 reservations have been made how many diners can be expected to show up Round your answer to two decimal places 78 02 Find the standard deviation of this distribution Round your answer to two decimal places

Determine whether each statement is true or false You have one submission for each statement a For every function f x if lim f x does not exist then lim f x does not exist x a x a True False b For every function f x if lim f x exists then lim f x exists x a x a True False x c For every function f x if lim f x exists then lim f x also exists x a x a True False d For every function f x if lim f x and lim f x both exist then lim f x also exists x a x a x a True False e For every function f x if lim f x does not exist then lim f x does not exist x a x a True False f For every function f x if lim f x does not exist then lim f x does not exist x at x a True False

x k kx 4 Determine the value of k that will make f x continuous everywhere Let f x if x 4 if x 4 k

Directions Create a poem with each letter to describe empathy E M

Let f x x 16 X 4 kx if x 4 12 if x 4 Determine the value of k that will make f x continuous everywhere