Basic Math Questions and Answers

Purchases Budget Rest Inn provides four star accommodations for the vacation traveler It is located just off a major interstate freeway There are three other competing motels at the same exit Hotel management is preparing its budget for the busiest three month period of the year June through August To differentiate themselves from the competition Rest Inn provides a complimentary spa package for each guest stay that includes specialty shampoo conditioner soap lotion toothpaste lavender essential oil slippers earplugs and a sleep mask Rest Inn purchases the spa package from a local vendor that puts the Rest Inn private label on the products The hotel follows a policy of purchasing enough spa packages to ensure that 40 of next month s bookings are in the current month s ending inventory Rest Inn s sales budget for guest stays for the next quarter is as follows June 2 500 guest stays July 2 700 guest stays August 2 300 guest stays How many spa packages should Rest Inn budget for purchase in July sna packages

Whitney s Inc sells on terms of 5 discount for cash and carry or 2 10 n 30 and estimates its total sale second calendar quarter of next year as follows April 900 000 May 720 000 and June 1 080 000 An ar operations indicates the following customer collection patterns In month of sale Cash at time of sale On account during discount period Portion of Total Sales 25 15 10 On account after discount period In month following sale On account during discount period 20 On account after discount period 10 In second month following sale On account after discount period 15 Average portion uncollectible 5 100 Prepare an estimate of the cash to be collected from customers during June Estimated Collections from Customers in June April Sales On account no discount May Sales On account no discount On account with discount June sales On account no discount On account with discount Cash Total estimated June collections

Use a computer algebra system to analyze and graph the function f x 5x 2 V x x 3 dentify any relative extrema and points of inflection If an answer does not exist enter DNE relative minimum x y elative maximum x y point of inflection x y Find the equations of the asymptotes Enter your answers as a comma separated list of equations If an answer does not exist enter

In his recent State of the Union address President Biden proposed a tax credit of 10 000 for first time homebuyers People purchasing homes will have their income taxes reduced by 10 000 If this is enacted who will benefit from it It depends on the relative elasticities of supply and demand Buyers will gain more if demand is more elastic and supply is less elastic People selling homes will get all the benefits because they will increase what they ask for homes by 10 000 First time homebuyers will get all the benefits because it will reduce the net price of the home they buy by 10 000 It depends on the relative elasticities of supply and demand Buyers will gain more if demand is less elastic and supply is more elastic Whoever realizes the benefit in question 1 how much will the total benefits that the public realizes add up to per home sold Less than 10 000 10 000 10 000

The company you work for produces right circular thin steel canisters for other companies to store their liquid products A customer has ordered 10 000 steel canisters The canisters must hold a volume of 7 cubic feet and includes the top and bottom Your company charges 0 30 per square foot of surface area of the canister and is always minimizing the cost for their customers What is the minimum cost for this customer s order round the radius the height and the minimal surface area to 3 decimal places

In the vicinity of a bonfire the temperature 7 in C at a distance of x meters from the center of the fire is given by T x 500 000 x 400 At what range distances from the fire s center is the temperature less than 370 C Assume x is positive Round your values to one decimal place Enter your answer using interval nota m

Find the domain of the given function Enter your answer using interval notation 4 X g x 4 x

Solve the inequality Enter your answer using interval notation 4 1 1 5 S X X

Solve triangle ABC if A 70 c 26 a 25 Round your answers to the nearest tenth Note If there is only one triangle enter the answers in Triangle 1 and enter none for Triangle 2 Triangle 1 Acute Triangle Angle B Angle C b Triangle 2 Obtuse Triangle Angle B Angle C b 0 0

Using synthetic division what is the quotient for 3x 3 5x 2 2x 37 by x 3 If the remainder is non zero express the remainder term as a fraction using the divisor as the denominator Provide your answer below

Use graphical methods to find all the real solutions of the following equation 3 2 0 97x 5 24x 3 55x 20 0

y varies inversely as the square root of x and when x 16 y 9

Evaluate the integral by changing the order of integration in an appropriate way 10x ZeZy2 dy dx dz 00x2 10xzeZy2 dy dx dz Type an exact answer

The future value of 6 000 for four years at 8 compounded semi annually will grow to do not include cents or round your calculation 8 991 8 950 8 211 9 990

FICA tax base Never changes Changes yearly Changes once every two years Is never more than 60 000 None of these

Jim Murphy borrowed 30 000 on a 120 day 14 note Jim paid 5 000 toward the note on day 95 On day 105 he paid an additional 6 000 The payment was applied first to the interest owed with the remaining payment applied to the principal balance Jim s adjusted balance after the first payment is 25 000 28 891 67 1 108 33 26 108 33 None of these

If you are paid twice a month you are being paid Weekly Biweekly Semimonthly Monthly None of these

Find the values of the six trigonometric functions using calculator if 0 26 Round answer to the nearest thousandth

Convert r 8 sin t to Cartesian Coordinates and Draw the Graph

6 Use the fact that einx is an orthogonal basis for L T to deduce that cos nx 0 sin nx 1 is an orthogonal basis for L and cos nx and sin nx 1 are or thogonal basis for L 0 n 0 Hint For the latter part consider the even or odd extension of f L 0 to

5x 6 line a Li are paralle 8x 7 16x 8 Find x

A tip in a restaurant has been typically figured at 15 of the total bill Complete parts a through c a If the bill is 52 what would be the typical tip The typical tip would be Round to the nearest cent as needed

The U Gym provides weight resistance through adjustments of incline The minimum weight resistance is 8 of the weight of the person using the U Gym Find the minimum weight resistance possible for a 230 pound man The minimum weight resistance possible for a 230 pound man is pounds Type an integer or a decimal

A 280 suit is on sale for a 30 discount What is the sale price of the suit

The purchase price of a camcorder is 984 What is the total price if the sales tax rate is 7 5 www

An owner of a repair service company estimates that for every 30 hours a repairperson is on the job he can bill for only 78 of the hours For the remaining hours the repairperson is idle or driving to or from a job Determin the number of hours per 30 hour week the owner can bill for a repairperson The number of hours per 30 hour week the owner can bill for a repairperson is Type an integer or a decimal

On a test of 73 items Pedro got 90 correct There was partial credit on some items How many items did he get correct incorrect Pedro got items correct Type a whole number or decimal rounded to two decimal places as needed

Marc had 50 boxes of candy to sell He sold 10 of the boxes How many did he sell Marc sold boxes of candy

a11 a12 Let A 221 222 and B b11 b12 b21 b22 be matrices in the vector space M2 2 Determine if the function defines an inner product on M2 2 Select all that apply A B a1b11 a12b12 a21b21 a22b22 Osatisfies A B B A Odoes not satisfy A B B A Osatisfies A B W A B A W Odoes not satisfy A B W A B A W Osatisfies c A B CA B Odoes not satisfy c A B CA B Osatisfies A A 2 0 and A A 0 if and only if A 0 does not satisfy A A 0 and A A 0 if and only if A 0

Verify the Cauchy Schwarz Inequality for the vectors u 8 3 v 5 2 Calculate the following values u v Iv We draw the following conclusion Since Ju v Select u V we Select verify that the Cauchy Schwarz Inequality for the vectors hol

Find all values of x so that the triangle with vertices A 4 4 x B 5 4 6 and C 7 2 8 has area 3 2

Find the distance between u and v u 0 2 1 v 1 4 1 d u v

Find the vector v with the given length and the same direction as u 3 u 0 1 1 3 V

Find the length of the vector v 0 1

On December 31 of the current year Plunkett Company reported an ending inventory balance of 215 500 The following additional Information is also available Plunkett sold and shipped goods costing 38 100 to Savannah Enterprises on December 28 with shipping terms of FOB shipping point The goods were not included in the ending inventory amount of 215 500 Plunkett purchased goods costing 44 100 on December 29 The goods were shipped FOB destination and were received by Plunkett on January 2 of the following year The shipment was a rush order that was supposed to arrive by December 31 These goods were included in the ending Inventory balance of 215 500 Plunkett s ending inventory balance of 215 500 included 15 100 of goods being held on consignment from Carole Company Plunkett Company is the consignee Plunkett s ending inventory balance of 215 500 did not include goods costing 95 100 that were shipped to Plunkett on December 27 with shipping terms of FOB destination and were still in transit at year end Based on the above information the amount that Plunkett should report in ending inventory on December 31 is Multiple Choice 194 400

Mohr Company purchases a machine at the beginning of the year at a cost of 47 000 The machine is depreciated using the units of production method The company estimates it will use the machine for 5 years during which time it anticipates producing 50 000 units The machine is estimated to have a 7 000 salvage value The company produces 10 900 units in year 1 and 7 900 units in year 2 Depreciation expense in year 2 is Multiple Choice 7 000 8 000 18 800 6 320

Multiple Choice Permanent account is another name for revenue accounts Temporary accounts carry a zero balance at the beginning of each accounting period The Income Summary account is a temporary account Permanent accounts remain open as long as the asset liability or equity items recorded in the accounts continue in e The closing process applies only to temporary accounts

Solve each equation x in radians and u in degrees for all exact solutions where appropriate Round approximate values in radians to four decimal places and approximate values in degrees to the nearest tenth Write answers using the least possible nonnegative angle 0 measures cos 1

A company purchased a delivery van for 24 800 with a salvage value of 3 300 on October 1 Year 1 It has an estimated useful life of 5 years Using the straight line method how much depreciation expense should the company recognize on December 31 Year 1 Multiple Choice 1653 90 4 960 1 075 4 300

On July 1 of the current calendar year Plum Company paid 7 900 cash for management services to be performed over a two year period beginning July 1 The adjusting entry on December 31 of the current year for Plum would include Multiple Choice A debit to an expense and a credit to a prepaid expense for 5 925 A debit to a prepaid expense and a credit to Cash for 5 925 A debit to an expense and a credit to a prepaid expense for 1 975 A debit to a prepaid expense and a credit to an expense for 1 975 A credit to a liability and a debit to a prepaid expense for 1 975

Peavey Enterprises purchased a depreciable asset for 28 000 on April 1 Year 1 The asset will be depreciated using the straight line method over its four year useful life Assuming the asset s salvage value is 3 200 Peavey Enterprises should recognize depreciation expense in Year 2 in the amount of Multiple Choice 7 000 00 5 166 67 24 800 00

The primary objective of financial accounting is to Multiple Choice Serve the decision making needs of internal users Provide accounting information that serves external users Monitor consumer needs tastes and price concerns Provide information on both the costs and benefits of looking after products and serv Know what when and how much product to produce

Determine the different possibilities for the numbers of positive negative and nonreal complex zeros for the following function 3 2 f x 4x 3x 4x 7 What is the possible number of positive real zeros of this function

b Solve the equation sin 4x sin 2x the identity sin a sin 3 2 sin a Mala of the f 0 on the interval 0 27 Begin by applying a b cos az 2 COS 2 al the

An arch is in the shape of a parabola It has a span of 220 meters and a maximum height of 15 meters Determine the height of the arch 57 meters from the center Write your answer rounded to two decimal places

Let 3 1 7 3 9 3 1 706 2 2 2 7 5 0 2 4 0 3 A and B 5 9 3 3 4 0 2 6 6 3 7 0 0 1 1 00000 can be shown that A and B are row equivalent a Find a basis for Row A b Can you find a basis for Row 4 that is a subset of the rows of A Hint Think about how we find a basis for Col 4 e Find a basis for Col A4 d Find a basis for Nul 4 Recall that the nullspace of a matrix A is the solution set of AZ 0 e Find the rank of A and the nullity of A f Verify that the rank nullity theorem holds here

m 14 m2 18 m3 26 x i 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

Evaluate the expression under the given conditions sin 0 tan e 4 3 e in Quadrant III 3 10 sin in Quadrant IV 1

If f x is a linear function f 5 3 and f 2 4 find an equation for f x f x

Write the sum as a product Next cos 24 3t cos 12 3t Note coefficients inside of the trigonometric functions should be entered as simplified decimal