Basic Math Questions and Answers

Your utility company charges 11 cents per kilowatt hour of electricity Complete parts a and b below a What is the daily cost of keeping lit a 150 watt light bulb for 14 hours each day b How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 10 watts of power a The daily cost of keeping lit a 150 watt light bulb for 14 hours each day is Round to three decimal places as needed

1 For a soil with D60 0 43 mm D30 0 22mm and D 0 0 06 mm calculate the uniformity coefficient and the coefficient of gradation 2 The following are the results of a sieve and hydrometer analysis Size mm 0 425 0 033 0 018 0 01 0 0062 0 0035 0 0018 0 0001 Percent Finer 100 90 80 70 60 50 40 35 a Draw the grain size distribution curve b Determine the percentages of gravel sand silt and clay according to the AASHTO system

Consider the following sets A 0 B 0 C 0 0 D 0 0 0 0 E 0 F 0 0 Group A B C D E and F into as few groups as possible so that all the members of each group have the same cardinalit Enter your answer as a comma separated list of groups For example if A B C are in the same group E F are in the same group different from the group of A and D is in its o group enter your answer as ABC D EF without the quotation marks The order doesn t matter

On each line put a checkmark if and only if 2 is an element of the set OA y y is the square of a real number OB 2 2 OC 2 D 2 2 2 OE 2 2 OF TER r is an integer greater than 1

On each line put a checkmark if and only if the statement is true DA 0 0 OB 0 0 0 OC 0 0 0 OD 0 0 OE 0 0 OF 0 0 0 OG 0 0 0

1 You received baby red potatoes on the produce delivery The as purchased cost of the potatoes is 1 29 per pound If the yield percent on the potatoes is 81 percent what is the EP cost per pound for the potatoes

2 Use the table to write an equation that defines the volume V in quarts of the air in the diver s lungs at a given pressure P in atmospheres 3 Using the equation you wrote and P 1 write an equation that defines volume V at a given depth d for finding the value y at a depth We V r d Given equation is P 1 P 1 Here V Volume d depth T radiw 33 d 33 P 1 put in equation V Tr 33 P 1 then the equation of Volume is V 3 TTY P 1 4 Use technology to graph your equation Sketch the graph here Volume qt 14 12 10 80 5 4 2 O y 0 33 66 99 Depth ft 132 165 5 Identify any asymptotes How do they apply to the real world situation Here are some Common types of asymptotes and their real Word applications Horizontal asynodotes in finance a stocks Price may approach the market Stability 2 Vertical asymtote In chemistry reactant Concentrations do to reaction Kinetics x 198 a Certain value but neve reach it do may approach zuo but never reach it

A function fis defined for all x and its values are given by 3 x if x 0 3 x if x20 Compute each of the following f 33 f 0 f 78 f x

Using limits find the slope of the tangent to the curve f x x 3 at the point where x 7

What is the type of economy in which the government controls the supply of goods but not the demand called O Command economy O Demand economy O Market capitalism

Assume that Shannon s brews and sells 3 720 barrels of beer in 2014 What will be Shannon s relative unit market share compared to its largest competitor in the DFW area Assume the total market size in barrels sold is 194 472 Express your answer in percent to two decimal places Do not include the symbol For example if you compute a market share of 5 785 percent you should enter 5 79

Assume that Shannon s brews and sells 3 470 barrels of beer in FY 2014 What will be Shannon s absolute unit market share in barrels sold during that period Round your answer to two decimal places but do not include the percent sign Assume the total market size in barrels sold is 194 472 For example if your answer is 6 7577 round to 6 76 again do not include the percent sign

1 The air in a diver s lungs takes up a volume of 4 qt at a depth pressure is 3 atm As the diver changes depth the pressure changes and so the volume of this air changes Find the pressure at each depth and use the fact that volume and pressure are inversely related to complete the table Depth ft 0 33 66 99 132 165 Pressure atm 3 Volume qt

5 Identify any asymptotes How do they apply to the real world situation

6 Solve the radical equation 2x 36 2x 6

5 The half life of caffeine is 5 h If you drink an energy drink with 80 mg of caffeine 5 the formula y 80 0 5 tells the amount of caffeine left in your system in mg after t hours How much caffeine will be left in your system after 8 hours Round as needed

4 8 12 2 Simplify the expression 81m n

3 Write 7 3 2 in reduced radical form

The results of the shirt sales research are as follows Demand Function P 600Q 180 000 Supply Function P 400Q 90 000 a If the government imposes a tax of Rp 10 000 per piece calculate the equilibrium price and quantity after the tax b Calculate the tax borne by consumers c Calculate the tax borne by producers d Calculate the tax revenue received by the government from these shirts

1 For each of the following statements i plug in at least four values of r on both sides of the point at which the limit is taken to obtain evidence not a proof that the statement is true ii Explain why the evidence in a is not a proof of the statement iii Prove that the statement is true by definition a lim 0 b lim 1 7 1 c lim 2 2 x 2 d limo 00 e lim In z 0 6 lim

2 Alison wants to use an affine cipher to encrypt messages containing capital let ters lower case letters and five symbols for punctuation period comma colon question mark and space a Verify that e x 28r 35 is a valid affine cipher for this extended alphabet b Calculate the decryption function for Alison s cipher c How many such ciphers are possible

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Generate another 10 integer values from 0 to 50 and divide these by 5 these will be your y coordinates Use your values from the FIRST generation of UNORDERED integers as your x coordinates Create a scatter diagram and describe any linear correlation Compute x y s s for each set of coordinates above Graph x y on its scatter x y diagram Divide diagram into quarters and label the quarters as high or low x and y values Label each quarter with the sign of x x y y Create a spreadsheet that calculates Ex Ex Ey Ey for each scatter x y diagram Use these values to calculate x y s s r for each of the scatter diagrams and state the formulas for each variable calculated on the scatter diagram

REDO 11 92 315 mg 12 8 787 792 ag 13 0 0020918 Tm 14 895 992 CL 15 0 0003285 GL 16 0 487 L 17 2 235 g 18 0 00049 km 19 0 035 dL 20 0 00012633 Kg g mL fg pg hL daL km m hL ag

A 44 Using the Venn diagram above find the following n U 4 n A 1 n AUB A B A nB 61 An B 44 61 85 X 18 X X 61 B 85

K 15 The following image shows four polygons Select all of the figures that are scaled copies of polygon ABCDE B D N 6 8 an S IM VI

86 430

5 11 881430

an explicit solution of the given initial value problem 2 dy dx y xy Y 1 6 ANAMITA DAHRE BUMIDE TOMAS honey Mabuto TERMIN KULETAMENT TRISH WE BE munc Banaan Uncanta TATRA

1 7 The evaporation rate from the surface of a 3 650 acre lake is 100 acre ft day Estimate the depth change in the lake in feet during a 1 year period if the net inflow to the lake is 25 cfs Is the depth increasing or decreasing What is the change in centimeters 177

If n A 12 n B 23 and n AUB 31 what do you know about n An B n An B Simplify your answer

solve an equation based on the following description 46 less than 8 times a number is the same as less than 6 times the number

Perform the following subtractions and round the answer to the same number of decimal places as the number with the least number of decimal places a 445 857 7 94 437 92 h 595 837 605 535 337

Perform the division and express the answer in scientific notation Choose the correct answer 9 418 x 10 2 77 10 O 3 4 x 10 O 3 4 x 108 O 6 648 x 10 O 6 648 x 108

2 Book rint rences Nakashima Gallery had the following petty cash transactions in February of the current year Nakashima uses the perpetual system to account for merchandise inventory February 2 Wrote a 350 check to establish a petty cash fund February 5 Purchased paper for the copier for 14 35 that is immediately used February 9 Paid 40 50 shipping charges transportation in on merchandise purchased for resale terms FOB shipping point These costs are added to merchandise inventory February 12 Paid 8 75 postage to deliver a contract to a client February 14 Reimbursed Adina Sharon the manager 72 for mileage on her car February 20 Purchased office paper for 69 77 that is immediately used February 23 February 25 Check my work Paid a courier 24 to deliver merchandise sold to a customer terms FOB destination Paid 10 30 shipping charges transportation in on merchandise purchased for resale terms FOB shipping point These costs are added merchandise inventory Paid 59 for postage expenses The fund had 26 34 remaining in the petty cashbox Sorted the petty cash receipts by accounts affected and exchanged them for check to reimburse the fund for expenditures February 28 The petty cash fund amount is increased by 100 to a total of 450 Required 1 Prepare the journal entry to establish the petty cash fund 2 Prepare a petty cash payments report for February with these categories delivery expense mileage expense postage merchandise inventory for transportation in and office supplies expense 3 Prepare the journal entries for required 2 to both a reimburse and b increase the fund amount February 27 February 28

Sales revenue Salaries expense Interest revenue Advertising expense Gain on sale of investments Cost of goods sold Insurance expense Interest expense Income tax expense Depreciation expense View transaction let Required Prepare the necessary closing entries on December 31 2024 Note If no entry is required for a transaction event select No journal entry required in the first account field Journal entry worksheet Note Enter debits before credits Record the entry to close the revenue accounts Date December 31 2024 Sales revenue 424 000 57 500 4 600 8 750 5 900 233 200 9 350 2 800 Retained earnings Interest revenue 24 500 13 000 General Journal Rotainod parning Debit Credit 424 000 4 600 424 000 4800

write down the main four formulas we ll be using on the test Explicit Formula for Arithmetic Sequences Explicit Formula for Geometric Sequences Period Partial Sum Formula for Arithmetic Series Partial Sum Formula for Geometric Series For the following sequences decide if it is arithmetic geometric or neither If it s arithmetic o geometric find the explicit formula Use it to find a 1 3 8 13 18 23 2 1000 500 250 125 67 5

Round each of the following numbers to three significant digits and to two significant digits 84 0999 Rounded to three significant digits Rounded to two significant digits 95 555 Rounded to three significant digits Rounded to two significant digits

Evaluate the following expressions 4 1 3 3 a b 2 2 8 14 8 14 Round to two decimal places 0 Round to two decimal places

Evaluate the following expressions wallisin LEWA BUNT ASTAN a 2 68 x 44 b 33 4 3

Evaluate a 5 3 Round to 3 decimal places b 4 Round to 3 decimal places

Evaluate the following expression 4 x 2

Compute 2 3 3 3 3 De con cau PEADERDAERW B

Simplify a 3 b 6 0 4

Evaluate the following expression

Select the symbol or that describes the relationship between the numbers below 4 6 click to select 7 10

Express 5 25 In 5 as a power of 5

Ex 3 47 Suppose that you are loss averse and that your value function is v x x for gains and v x 3x for losses a Represent the value function graphically in the manner of Figure 3 11 b Represent your indifference curves graphically in the manner of Figure 3 13 b assuming that your initial endowment is 3 4 Bananas v x V 1 1 t v 1 igure 3 11 Value function 3 1 Bananas 3 2 1 1 2 3 a Without loss aversion 2 3 b With loss aversion Figure 3 13 Indifference curves and loss aversion Apples Apples

Suppose Denmark produces only bikes and scooters The resources that are used in the production of these two goods are not specialized that is the same set of resources is equally effective at producing both scooters and bikes 1 The shape of Denmark s production possibilities frontier PPF should reflect the fact that as Denmark produces more scooters and fewer bikes the opportunity cost of producing each additional scooter increase decrease remains constant 2 Points 2 Graph the Production Possibilities Frontier for Denmark Make sure to label the graph your axes and draw the curve as accurately as you can based on the given information 5 Points I Determine whether the following statements analyzing policies are positive or normative 1 Point each 3 In the past decade U S companies have outsourced millions of jobs overseas 4 Companies that outsource jobs are acting immorally 5 If the U S government were to institute higher tariffs on imports companies would stop outsourcing jobs

Think about the idea of the terrible twos The idea that children around ages 1 5 3 years go through a phase in which they are unusually stubborn or obstinate Consider your information on the basic Developmental Issue of Continuity and Discontinuity consider the developmental changes that typically occur for children during this time such as development of self concept learning self control and autonomy Answer the following questions What do you think Do children and adults develop through stages or phases or does development follow a more gradual course Explain O Do you think that your own development has progressed through distinct developmental stages Discontinuous or is it more like a ramp and more gradual Continuous Give an example to support your answer