Basic Math Questions and Answers

A food refrigerator is to provide a 15 000 kJ h cooling effect while rejecting 22200 kJ h of heat Calculate the COP of this refrigerator Round the final answer to three decimal places Reservoir QH 15 000 kJ h R Reservoir The COP of the refrigerator is

Use the properties of logarithms to evaluate each of the following expressions a 3 Ine Ine b log 3 log 4

What is the perpetual annual worth in the following situation First cost 80 000 Annual cost 10 000 Salvage value 25 000 Life 6 years Interest rate 10 O 16 749 18 426 23 768 25 129

Assume n is a positive integer Consider the loop below 0 for i 1 to 4n x x 4 i next i There are performed in this loon is operations performed in each run of the loop and the loop runs times so the total number of op

If Rita receives 44 54 interest for a deposit earning 6 simple interest for 70 days what is the amount of her deposit Round your answer to the nearest cent

Write 1 2 as a decimal and as a fraction decimal 0 012 fraction

Round the number to the given place value 78 70633 Hundredths X Suggested tutorial Learn It Round decimals to a specified place value

skipped part Tutorial Exercise Write as a fraction 12 1 2

Write the following as a fraction Enter a reduced fraction 11 ojo

Astro Company sold 21 000 units of its only product and reported income of 84 800 for the current year During a planning session for next year s activities the production manager notes that variable costs can be reduced 48 by installing a machine that automates several operations To obtain these savings the company must increase its annual fixed costs by 152 000 Total units sold and the selling price per unit will not change ASTRO COMPANY Contribution Margin Income Statement For Year Ended December 31 Sales 52 per unit Variable costs 44 per unit Contribution margin Fixed costs Income ASTRO COMPANY Contribution Margin Income Statement For Year Ended December 31 1 092 000 2 Prepare a contribution margin income statement for next year that shows the expected results with the machine installed Assume sales are 1 092 000 Note Do not round intermediate calculations Round your answers to the nearest whole dollar Contribution margin 924 000 168 000 83 200 84 800 Check my

3 es Henna Company produces and sells two products Carvings and Mementos It manufactures these products in separate factories and markets them through different channels They have no shared costs This year the company sold 47 000 units of each product Income statements for each product follow Sales Variable costs Contribution margin Fixed costs Income Contribution margin 2 Assume that the company expects sales of each product to decline to 30 000 units next year with no change in unit selling price Prepare a contribution margin income statement for the next year as shown above with columns for each of the two products Note Round per unit answers to 2 decimal places Income losed Carvings 813 100 487 860 325 240 194 240 131 000 Units Mementos 813 100 81 310 731 790 600 790 131 000 HENNA COMPANY Contribution Margin Income Statement Carvings Per unit Total Mementos Per unit Total Total Check my wor

Utilize the finite difference algorithm to approximate the solution for the following linear boundary value problem y 4 y x for 2 0 2 y 0 0 y 2 1 2 using a step size of h 0 5 Please provide the approximate values w for i 0 1 2 3 4 that you computed

ok t int ences Sunn Company manufactures a single product that sells for 104 per unit and whose variable costs are 127 per unit The company s annual fixed costs are 622 000 The sales manager predicts that next year s annual sales of the company s product will be 39 200 units at a price of 192 per unit Variable costs are predicted to increase to 132 per unit but fixed costs will remain at 622 000 What amount of income can the company expect to earn under these predicted changes Prepare a contribution margin income statement for the next year SUNN COMPANY Contribution Margin Income Statement per unit Contribution margin Units Check m

5 Sunn Company manufactures a single product that sells for 110 per unit and whose variable costs are 88 per unit The company s annual fixed costs are 308 000 Management targets an annual income of 550 000 S eBook Hint Print eferences 1 Compute the unit sales to earn the target income Numerator 1 1 Denominator 2 Compute the dollar sales to earn the target income Numerator 1 1 Denominator Units to Achieve Target Units to achieve target Dollars to Achieve Target Dollars to achieve target Check m

A diesel powered tractor with a cost of 250 040 and an estimated residual value of 4 400 is expected to have a useful operating life of 89 000 hours During April the tractor was operated 100 hours Determine the depreciation for the month If required carry out any division to two decimal places 600 X Feedback Check My Work Units of activity method allocates the cost of the asset equally over the hours operated The depreciation rate stays constant

A building acquired at the beginning of the year at a cost of 95 200 has an estimated residual value of 4 800 and an estimated useful life of four years Determine t following a The double declining balance rate 47600 X b The double declining balance depreciation for the first year Feedback 0 25 X Check My Work The double declining rate is two times the straight line rate When the double declining balance method is used the estimated residual value is not considered

1 Sunn Company manufactures a single product that sells for 135 per unit and whose variable costs are 108 per unit The company s annual fixed costs are 440 100 oints eBook Hint Print References a Compute the company s contribution margin per unit Contribution margin b Compute the company s contribution margin ratio 1 Numerator c Compute the company s break even point in units 1 Numerator 1 Numerator Denominator Denominator d Compute the company s break even point in dollars of sales 1 1 Denominator Contribution Margin Ratio Contribution margin ratio Break Even Units Break even units Break Even Dollars Break even dollars Check my world

B es Henna Company produces and sells two products Carvings and Mementos It manufactures these products in separate factories and markets them through different channels They have no shared costs This year the company sold 47 000 units of each product Income statements for each product follow Sales Variable costs Contribution margin Fixed costs Income Required 1 Compute the break even point in dollar sales for each product Note Enter CM ratio as percentage rounded to 2 decimal places Contribution Margin Ratio Numerator Break Even Point in Dollars Numerator 1 Mementos 813 100 Carvings 813 100 487 860 325 240 81 310 731 790 600 790 194 240 131 000 131 000 1 1 PRODUCT CARVINGS Denominator Denominator Contribution margin ratio Break even point in dollars Chec

Straight line depreciation A building acquired at the beginning of the year at a cost of 66 600 has an estimated residual value of 2 600 and an estimated useful life of 10 years Determine the following a The depreciable cost b The straight line rate c The annual straight line depreciation

8 3 points eBook Hint Print References Harrison Company expects to sell 130 000 units of its product next year which would generate total sales of 10 140 000 Management predicts that income for next year will be 1 180 000 and that the contribution margin per unit will be 32 Complete the below table to calculate the next year s expected variable costs and fixed costs HARRISON COMPANY Forecasted Contribution Margin Income Statement Units per unit Contribution margin 130 000 32 Check my

A truck acquired at a cost of 365 000 has an estimated residual value of 20 350 has an estimated useful life of 61 000 miles and was driven 5 500 miles during t year Determine the following If required round your answer for the depreciation rate to two decimal places a The depreciable cost b The depreciation rate c The units of activity depreciation for the year per mile

2 k ces Astro Company sold 21 000 units of its only product and reported income of 84 800 for the current year During a planning session for next year s activities the production manager notes that variable costs can be reduced 48 by installing a machine that automates several operations To obtain these savings the company must increase its annual fixed costs by 152 000 Total units sold and the selling price per unit will not change ASTRO COMPANY Contribution Margin Income Statement For Year Ended December 31 Sales 52 per unit Variable costs 44 per unit Contribution margin Fixed costs Income 1 Compute the break even point in dollar sales for next year assuming the machine is installed Note Round your answers to 2 decimal places Contribution margin Contribution Margin Ratio Numerator 1 1 1 092 000 924 000 168 000 83 200 84 800 Denominator Break even point in dollar sales with new machine Per unit Contribution Margin Ratio Contribution margin ratio CH

Assigm8 Problem 21 1 point Give a vector parametric equation for the line through the point 4 1 1 that is parallel to the line 4 4t 4 4t 5t 5 L t

Line Tollowing information applies to the questions displayed below j Dengo Company makes a trail mix in two departments Roasting and Blending Direct materials are added at the beginning of each process and conversion costs are added evenly throughout each process The company uses the FIFO method of process costing October data for the Roasting department follow Beginning work in process inventory Units started and completed Units completed and transferred out Ending work in process inventory Beginning work in process inventory Costs added this period Direct materials Conversion Total costs to account for Units 3 100 Cost per equivalent unit of production Cost of beginning work in process Equivalent units of production 19 300 22 400 2 500 252 880 1 107 594 Direct Materials Conversion Percent Percent Complete Complete 30 100 Materials 100 121 150 1 360 474 1 481 624 2 Compute cost per equivalent unit of production for both direct materials and conversion 70 Conversion Check my work

5 The following graph shows the number of car accidents occurring in one city in each 2007 etc The number of of the years 2006 through 2011 Year 1 2006 Year 2 accidents dropped in 2008 after a new speed limit was imposed Number of accidents 120 110 100 90 80 70 60 1 2 3 4 Year How is the bar graph misleading 5 6

9 Tom and Fred are 5 mi apart watching a rocket being launched from Vandenburg Air Force Base Tom estimates the bearing of the rocket from his position to be S 75 W while Fred estimates that the bearing of the rocket from his position is N 65 W If Fred is due south of Tom how far is each of them from the rocket

Find the LCD of the following expressions Write LCD in factored form 5 a 13a 40 LCD and 3a a a 20

A television show conducted an experiment to study what happens when buttered toast is dropped on the floor When 46 buttered slices of toast were dropped 28 of them landed with the buttered side up and 18 landed with the buttered side down Use a 0 01 significance level to test the claim that toast will land with the buttered side down 50 of the time Use the P value method Use the normal distribution as an approximation to the binomial distribution After that supposing the intent of the experiment was to assess the claim that toast will land with the buttered side down more than 50 of the time write a conclusion that addresses the intent of the experiment Let p denote the population proportion of all buttered toast that will land with the buttered side down when dropped Identify the null and alternative hypotheses to test the claim that buttered toast will land with the buttered side down 50 of the time Ho P 0 50 H p 0 50 Type integers or decimals Do not round Identify the test statistic Z Round to two decimal places as needed

1 Jake cycled 7 5 km in 25 min and 22 5 km in 75 min Rhona cycled 8 75 km in 35 min and 16 25 km in 65 min a Plot the points time distance for Jake on the grid shown b Plot the points time distance for Rhona on the same grid c Use the graph to indicate who cycled faster d Calculate Jake s rate of cycling in kilometres per hour e Calculate Rhona s rate of cycling in kilometres per hour

Assigm8 Problem 19 1 point Determine whether the following lines in R2 represented by the vector equations below intersect are parallel or are identical choose one choose one choose one 1 r t 5 t 4 2t and s t 5 3t 4 t 2 r t 2 3t 4 2t and s t 2 6t 10 4t 3 r t 1 2t 2 4t and s t 1 4t 6 8t Note You only have two attempts at this problem

1 Calculate the slope of each line segment where possible BY F 2 0 2 GI H C D 6 x Find the slope of the line passing through each pair of points 2 4 5 and 0 0 3 2 6 and 7 1 4 3 2 and 6 5 5 3 7 5 1 and 1 5 1 2 6 1 5 and 3 5 7 2 7 and 2 4

13 A ladder is leaning against a wall The base of the ladder is 1 5 m from the base of the wall The top of the ladder touches the wall at a point 4 m above the ground What is the slope of the ladder a Use slopes to determine whether each set of points is collinear or non collinear b If the points are collinear find the slope A 2 1 B 1 2 C 4 2 14 15 M 1 3 N 2 5 P 3 4 16 W 3 1 X 9 8 Z 5 5

Assigm8 Problem 20 1 point Find the intersection of the lines r t 4 2t 20 6t 26 8t and R s 5 38 15 5s 4 s Write your answer as a point a b c where a b and care numbers Answer Note If there is no intersection write none

Ex 2 The coordinates of the vertices of triangle FUN are F 1 1 U 1 4 and N 2 1 How can you tell if FUN is a right triangle show your work This is a right triangle since two of the sides are pendiculars 1 8 5 2 4 2 8 6 4 2 50 4 3w 3 8 6 e 72 2 24 7 6 6000 8 2 4 6 8 X Slope I m 3 slope 3 2 slune 2 ml 3 1 not Vic Sin line tou

Assigm8 Problem 1 1 point Below is a diagram of the dotted cube with edges of length 4 Suppose vectors u vectors 1 u v 2w 2 t 3 t 2r 4 u v w r s t 4 0 0 v 0 4 0 and w 0 0 4 Find the following

1 point Determine whether the points lie on a straight line Answer Yes or No 1 A 0 0 0 B 9 3 3 and C 27 9 8 4 2 D 9 3 3 E 10 1 6 and F 14 7 18 3 G 1 0 1 H 3 9 10 and I 8 27 28 Note You only have two attempts at this problem

1 point Find a vector equation with parameter t for the line through the points 1 7 4 and 12 7 1 Answer r t

1 point Are AB and PQ parallel and if so do they point in the same direction A 3 5 B 6 4 P 3 1 Q 9 5 Select Select

1 point Let A 3 3 and B 3 1 be points in R2 and let C 4 3 4 and D 0 3 2 be points in R a Find the distance between A and B help numbers b Find the distance between C and D help numbers c Find the distance between the point x y z and C help numbers d Find the length of the vector CD help numbers e Find the length of the vector 2BA help numbers

Assigm8 Problem 2 1 point Let a 3 1 1 and b 5 2 5 Show that there are scalars s and t so that sa tb 29 11 23 You might want to sketch the vectors to get some intuition

Assigm8 Problem 6 1 point Find the vector in AB R AB help vectors given in the figure 6 5 4 3 2 1 6 5 4 B 2 1 2 9 2 A X

Find the point P such that v PQ has the components 5 5 9 25 16 Q 3 5 0 75 9 B

cise 13 5 3 Compute exp 5 66

12 How many FUs can be drained for a 10 horizontal branch with a grade of 0 25 a Unlimited b 2500 c None d 2499 13 The maximum number of WCs that may be wet vented is a 1 b 2 3 d Unlimited 14 The maximum size of fixture drain with the exception of floor drains that may connect to a wet vent is a 1 b 3 c 1 d 2 15 A separately vented fixture s hydraulic load must be taken into account when sizing the continuous vent in a wet vented group a True b False c Sometimes d A and c 16 The length of a wet vent is limited to a One pipe diameter of fall b 1 2m c There is no limit d 2 5m 17 A wet vent extending through more than one storey may accept a maximum of how many fixtures units per storey on any storey above the first a 4 b 3 51 2

6 The minimum size of every sanitary building sewer and every sanitary building drain is a 4 b 3 c 6 d 2 7 A air conditioner discharges condensate at a rate of 3 liters per second what is its FU rating a 95 1 FUS b 86 3 FUS 8 FUS d 31 FUS 8 A vertical sanitary drainage pipe can carry a maximum volume of waste equal to a 35 b 25 69 d 29 9 A horizontal sanitary drainage pipe can carry a maximum volume of waste equal to a 65 b 25 c 39 d 69 10 Drains are designed to never run at full capacity a T b F 11 A building has a soil stack receiving 102FUs of waste There is a public washroom with 4 Di Flush Water Closets on the third floor What is the minimum size of the soil stack 3 b 4 c 5 d 6

12 How many FUs can be drained for a 10 horizontal branch with a grade of a Unlimited b 2500 c None d 2499 13 The maximum number of WCs that may be wet vented is a 1 b 2 c 3 d Unlimited 14 The maximum size of fixture drain with the exception of floor drains that may connect to a wet vent is a 1 b 3 c 1 d 2 15 A separately vented fixture s hydraulic load must be taken into account when sizing the continuous vent in a wet vented group a True b False c Sometimes d A and c inov toW 16 The length of a wet vent is limited to a One pipe diameter of fall b 1 2m c There is no limit 7031 stanswor

1 An undersized drain would experience what symptoms a It would carry too little drainage so there would be a lack of scrubbing b It may become air locked and impede the flow of discharge c Leftover solids may lead to a blockage d Higher velocity of flow 2 Fixture Units are based on what three factors 3 The minimum size of any regular WC fixture drain is a 2 b 3 c 4 d 4 A 3 horizontal branch can carry a maximum of how many WCs a 1 b 2 c 3 d 4 5 A 3 soil stack can carry a maximum of how many WCs a 2 b 3 c 4 PE glead me

se 13 5 1 Diagonalize 06

13 5 2 Compute 1 5 06

P D P R E Key Concepts P R E where P is profit R is revenue and E is expenses The vertex of a profit function lies on the axis of symmetry The vertex of a profit function contains the maximum profit Maximum profit can be found on the graph where the difference between the revenue and expense functions is the greatest Guided Exercises FunFleece Incorporated manufactures fleece hats It is considering making a new type of weatherproof fleece hat The expense and revenue functions are E 300p 150 000 and R 300p2 29 000p 1 Determine the profit function P Date Substitute the expense function for E and the revenue function for R P 300p2 29 000p 300p 150 000 P Mod The profit function is P 2 Use the equation from Exercise 1 Determine the maximum profit to the nearest cent Determine the price that yields maximum profit Find the maximum of the profit equation Axis of symmetry b 2a Substitute the price p into the profit equation from Exercise 1 Axis of symmetry 2