Basic Math Questions and Answers

Question 6 A farm has a population of 100 alpacas in the year 2016 Farmers are concerned because the alpaca population is decreasing at the rate of 5 per year If the population continues to decrease at this rate how long will it take until the population is only 30 alpacas 15 p

Phyllis teaches marketing at a local college She wants to select one freshman and one sophomore to attend a conference If she teaches 11 freshman and 9 sophomores how many combinations of students could be selected Your answer is

Penny has 7 books she wants to read If she randomly chooses one to read at a time in how many different sequences could she read all the books Your answer is

In year 2020 Jim was traveling for work He packed 7 unique masks 3 unique shirts 2 unique pairs of pants and 3 unique pairs of shoes How many outfit combinations has he packed Your answer is

Problem 6 Find all solutions in exact form expressed in radians 1 sin t cos 2t 0 2 sin 2t sin t 0 3 2 sin 2t sin 2t 1 0 4 tan 3x tan x 1 0 5 3 tan 2t 2 3 6 sec 4x 2

Problem 5 Solve each equation on the interval 0 27 Give exact answers a 3 sin 3 cos 3 3 cos 3 b 2 sin 3 sin 3 10 c 2sec x tan x 3 d 2 cos 6 3 cos B 1 0

6 In Figure 5 is the graph of f x ln x 1 for 0 x 4 It crosses the x axis at x e You will use Newton s method for f x 0 to create numerical estimates for e Y 1 SI Figure 5 Graph of y ln x 1 a Using Newton s method for the equation ln x 1 0 with x 1 tabulate an to find the first n for which n and n 1 agree to 5 digits after the decimal point b For the n you found in part a to how many digit

s 7 L 5 1 8 2 Determine the nu

The smallest positive integer in the set 24x 60y 2000z x y ze is a

Determine 6 1 L 8 1 4 2 C 2 4 s 1 3 L 2s 10 10 1 4 L g 48 8 5 L 7 s 7 s 1 s 2

7 Determine if the shaded amount is more less or equal to half

2 20 16 24 0

1 and 4 Apply Newton s method to estimate the solution of x x 1 0 by taking finding the least n such that n and n 1 agree to three digits after the decimal point

Tuesday 1 Find the number that makes an equivalent fraction 2 2 S 4 12 3 Use or to compare the fractions 3 3771 100 5 Use or to compare the fractions 122 20 8 7 Determine if the shaded amount is more less or equal to half 2 Find the number that makes an equivalent fraction 3 7 1 10 3 3 4 Determine if the fraction shown is less more or equal to half 3 3 3 1 1 20 6 Determine if the fraction shown is less more or equal to half 23 24 6 14 8 Determine which letter best represents an equivalent fraction A B 6 00 3 5 C 5

Determine 6 1 L 8 1 4 2 2 C 344 4 3 L s 1 s 2s 10 10 1 4 L g 48 8

Use Definition to determine the Laplace transform of the given function 1 t 2 et

Determine the Laplace transform 1 L t et sin 2t 2 L e t cos 3t e6t 1

coblem 1 Suppose that cos 0 7 and tan 0 0 Determine the values of sin 20 cos 20 and tan 20 25

3 A line passes through point 8 9 and has a slope of 4 Write an equation in Ax By C form for this line Use integers for A B and C 7 0 0

Solve the following I V P by using the Laplace transform y y 2y 0 y 0 1 y 0 0

We can also use Laplace transforms to solve n th order differential equations As the simplest example solve the following first order differential equation using the Laplace transform y 0 1 2t y 3y e t

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002 Tal ASTTUD 2 American Swiss Ltd s common stock paid 10 00 in dividends last year The investors require a return of 8 What is the price of the share if a the dividends grow at a constant rate of 3 per year b the dividends grow at a constant rate of 0 per year Ef a super woll c the dividends grow at a constant rate of 3 per year d Explain the outcomes la 19q8E2 701 anillog al 00 M to sladda nom 03 9717 DE

1 MacroCorp s common stock paid 3 00 in dividends last year and is expected to grow indefinitely at an annual 5 percent rate a What is the value of the stock if you require a 10 percent return b What is the value of the stock if you require a 7 percent return c What is the value of the stock if you require a 5 percent return d What is the value of the stock if you require a 4 percent return e Explain the outcomes 2700 SL 63 and go 01 8

A pizza parlor offers mushrooms onions and sausage as toppings for the plain cheese base How many different types of pizzas can be made different types of pizzas can be made KILD

Draw a bag diagram to illustrate the following set and find its cardinal number 0 The cardinal number is

If the monthly supply of math action figures t months after initial delivery to market is given by the logistic growth function s t find the carrying capacity of the market Carrying capacity 3000 7 14e 1 17t

ats eBook Hint Print Terences Required 1 Compute the a cost of products transferred from weaving to sewing b cost of products transferred from sewing to finished goods and c cost of goods sold Hint Compute the total production costs in each department and then subtract the ending inventory to get the amount transferred out of each department 2 Prepare journal entries dated June 30 to record a goods transferred from weaving to sewing b goods transferred from sewing to finished goods c sale of finished goods and d cost of goods sold Complete this question by entering your answers in the tabs below Required 1 Required 2 Compute the a cost of products transferred from weaving to sewing b cost of products transferred from sewing to finished goods and c cost of goods sold a Transferred from Weaving to Sewing b Transferred from Sewing to Finished Goods c Cost of goods sold

Question 14 Y A bank features a savings account that has an annual percentage rate of r 3 with interest compounded quarterly Abigail deposits 2 500 in to the account kt The account balance can be modeled by the exponential formula A t a 1 7 where A is account value after t years a is the principal starting amount r is the annual percentage rate k is the number of times each year that the interest is compounded T A What values should be used for a r and k a k B How much money will Abigail have in the account in 10 years Amount S Round answer to the nearest penny C What is the annual percentage yield APY for the savings account The APY is the actual or effective annual percentage rate which includes all compounding in the year APY Round answer to 3 decimal places Question Help Video 4

Solve the equation arctan x 1 1 Use decimal notation Give your answer to at least two decimal places

14 4 points The number of trees destroyed each day by a forest fire are given in the table Day 1 2 3 4 5 6 Number of Trees Destroyed per Day 555 611 672 739 813 894 a Which model appears most suitable for the data linear quadratic or exponential Justify your answer b Determine a suitable equation to model this data c Approximately how many trees will be destroyed on day 12

13 3 points A couple makes bi weekly mortgage payments of 978 88 monthly condominium fees of 325 and monthly utility expenses averaging 275 The combined household net income is 120000 per year Calculate the percent of the total income spent on costs associated with owning a home Show all your steps

c NTIzOTcyOTAyMDgx a NTIzOTczMjI5NjI5 details nent Q12324 pdf 1 Month 2 January February March April May June 234 4 567 6 7 8 July August September October 12 November 13 December 69 10 11 B Property Mortgage Taxes 2850 245 245 245 245 245 245 245 245 245 245 245 245 2850 2850 2850 2850 2850 2850 Open with Google Docs 2850 2850 2850 2850 2850 Electricity 90 90 90 90 90 90 90 90 90 90 90 90 Natural Gas 128 0 128 c What is the amount of their annual property taxes 0 128 0 128 0 128 0 128 0 Telephone Water and Internet 0 315 0 0 0 315 0 0 0 315 0 0 14 Total Annual Cost per Expense a In which months did Pouria and Amalia have the greatest home expenses b How much did they spend on mortgage payments for the year 75 75 75 75 75 75 75 75 75 75 75 75 A Total Monthly Expense

2 3 points A telecommunications satellite is orbiting Earth Students at two Ontario schools that are 500 km apart notice that the flight path passes directly over their schools At an instant when the satellite is between the two schools the students note that the simultaneous angles of elevation are 58 and 77 How far is the satellite from each school at this instant rounded to the nearest tenth of a kilometre

3 points In triangle AABC ZC 64 a 9 30 m and b 4 22 m Solve for ZB to the nearest degree Show all your steps

9 3 points Solve Show all your work 90 2x 1 274 3x 2

Section 2 Knowledge Understanding Directions For each of the questions in this section show all work to get full marks 4 4 points Simplify Show your steps a 25ab 0 49a

A toy race car travels along a circular race track that has a radius 25 meters long The race car starts at the 3 o clock position the easternmost part of the track Imagine an angle with its vertex at the center of the circular track that subtends the path the toy race car travels Suppose th ace car stops after rotating through an angle measuring 2 25 radians along the circular race track a The race car is how many radius lengths east of the track s center radius lengths b The race car is how many meters east of the track s center Preview meters Preview c The race car is how many radius lengths north of the track s center radius lengths Preview d The race car is how many meters north of the track s center

cinnamon teaspoons sugar tablespoons 2 One batch of pink paint uses 2 cups of red paint and 7 cups of white paint Megan made a large amount of pink paint using 28 cups of red paint How many batches of pink paint did she make Use a double number line to solve How many cups of white paint did she use Use a double number line to solve 14 Ad to My the it is to gdy du 3 In lemonade the ratio of cups of lemon juice to cups of water is 2 to 3 How many cups of water will you need if you use 7 cups of lemon juice Use a double number line to solve

ces Victory Company uses weighted average process costing The company has two production processes Conversion cost is added evenly throughout each process Direct materials are added at the beginning of the first process Additional information for the first process follows Beginning work in process inventory Units started this period Units completed and transferred out Ending work in process inventory Beginning work in process inventory Direct materials Conversion Costs added this period Direct materials Conversion Total costs to account for Cost assignment Weighted average Completed and transferred out Units FUR 69 000 859 000 745 000 183 000 422 240 122 730 2 825 760 2 331 870 Direct Materials Percent Complete 100 100 Cockt FUD Conversion Percent Complete 80 544 970 3 Assign costs to the department s output specifically to the units transferred out and to the units in ending work in process inventory Note Round Cost per EUP to 2 decimal places 5 157 630 5 702 600 40 Check my wor

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 Equivalent units of production EUP FIFO method 3 100 19 300 22 400 2 500 252 880 1 107 594 Direct Materials Conversion Percent Complete 1008 1008 Percent Complete 308 121 150 1 360 474 1 481 624 Required 1 Compute equivalent units of production for both direct materials and conversion Direct Materiale 708 Check my

2 es The following data reports on the July production activities of the Molding department at Ash Company Beginning work in process Direct materials Conversion Costs added this period Direct materials Conversion Total costs to account for Beginning work in process inventory Units started this period Completed and transferred out Ending work in process inventory 40 350 5 250 Unit Reconciliation Units to account for Units 574 050 342 750 3 500 44 500 44 000 4 000 45 600 916 800 962 400 Direct Materials Percent Complete 100 100 Conversion Percent Complete 20 60 Prepare the Molding department s production cost report using the weighted average method Note Round Cost per EUP to 2 decimal places Ch

es Cost per equivalent unit of production FIFO method Equivalent units of production Cost per equivalent unit of production rounded to 2 decimals Required b Cost assignment FIFO Beginning work in process To complete beginning work in process Direct materials Conversion Started and completed Direct materials Conversion EUP EUP Direct Materials Cost per EUP Cost per EUP Conversion Total cost Total cost

K After one semester a group of 15 freshmen were asked how many new friends they had made at college and responded as follows 12 8 6 8 12 7 13 14 7 11 6 12 14 8 7 Find the mean median and mode for the data set Explain which measure best describes a typical value in this distribution Find the mean Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mean is Round to two decimal places as needed OB There is no mean for these data Find the median Select the correct choice below and if necessary fill in the answer box to complete your choice OA The median is CALL Round to two decimal places as needed OB There is no median for these data Find the mode s Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mode s is are Round to two decimal places as needed Use a comma to separate answers as needed OB There is no mode for these data Which measure best describes a typical value in this distribution OA For this distribution the mean median and mode are equal so any value can be used to describe this distribution OB The mode best describes a typical value in this distribution since each values occurs roughly the same number of times OC The mean best describes a typical value in this distribution since the distribution is roughly symmetrical and does not contain any extreme values OD The median best describes a typical value in this distribution since the distribution appears to be slightly asymmetrical and contains some extreme values

4 k 2 t nces Required a Cost per equivalent unit of production Weighted average method Total costs Equivalent units of production Cost per equivalent unit of production rounded to 2 decimals Required b Cost assignment Weighted average Completed and transferred out Direct materials Conversion Total costs completed and transferred out Ending work in process Direct materials Conversion Total cost of ending work in process EUP EUP Costs EUP Direct Materials Cost per EUP Cost per EUP Total cost Total cost Costs EUP Conversion

Assume that 21 year old men s heart rates at rest are normally distributed with a mean of 64 beats per minute and a standard deviation of 6 beats per minute If 500 men are examined how many would you expect to have a heart rate of less than 67 Click the icon to view the standard normal distribution table How many men out of 500 would you expect to have a heart rate of less than 67 Type a whole number

Solve each problem 1 Which expression s are equivalent to 2 6 A 2 6 B 2 6 C 2 6 D 2 6 3 Which expression s are equivalent to 8 3 4 94 A 8 3 4 94 B 8 3 4 94 C 8 3 4 94 D 8 3 4 94 5 Which expression s are equivalent to 3 3 5 2 A 3 3 5 2 B 3 3 5 2 C 3 3 5 2 D 3 3 5 2 7 Which expression s are equivalent to c 2 Which expression s are equivalent to 7 6 A 7 6 B 7 6 C 7 6 D 7 6 4 Which expression s are equivalent to 4 5 A 4 5 B 4 5 C 4 5 D 4 5 6 Which expression s are equivalent to 5 18 3 54 A 5 18 3 54 B 5 18 3 54 C 5 18 3 54 D 5 18 3 54 2 Answe 6 8 Which expression s are equivalent to 4 9 A 4 9 B 4 9 C 4 9 D 4 9

K Construct a frequency table for the data Responses Frequency excellent poor Total Construct a relative frequency table for the data Responses excellent good fair O A 0 8 0 6 0 4 0 2 0 good fair OC poor Total Type integers or decimals Construct a bar graph for the data Choose the correct graph below 0 8 0 6 0 4 0 2 0 Excellent E Good 10 Excellent Good Relative Frequency 1 00 Fair Fair Poor on a teacher rating website fair fair poor excellent poor good fair fair poor fair Construct a frequency table a relative frequency table and a bar graph for the data Poor GILER OB 0 8 0 6 0 4 0 2 OD 0 8 0 6 0 4 0 2 01 Excellent Good Excellent Good Fair Fair Poor Poor

4 45 Points Determine the rate of seepage in cubic feet min under the dam by drawing flow net to scale and also determine the total uplift force in psf acting at the bottom of the dam at Point C per unit length of dam The permeability of the silty sand is 0 66 ft min The drawing is to scale Use the scaled drawing next page for your flow net sketching and pressure calculations evaluations Upstream water level is at El 94 ft Downstream water level is at El 68 ft Dam is 85 ft long and bottom is at el 57 ft Ground surfaces on both upstream and downstream sides are at El 64 ft U

K Use the frequency table that contains the weight loss by 34 participants in the television show to construct the corresponding histogram Click the icon to view the frequency table Choose the correct graph below A Frequency www O C Frequency 2009 wwwinn 0 1 2 3 4 5 6 7 8 9 10 Pounds Lost 0 1 2 3 4 5 6 7 8 9 10 Pounds Lost Data table Q Q Weight Loss Pounds Frequency 0 1 3 2 2 3 3 2 4 1 5 7 C 6 1 OB London 0 1 2 3 4 5 6 7 8 9 10 Pounds Lost OD Frequency MANNAL 7 5 0 1 2 3 4 5 6 7 8 9 10 Pounds Lost 8 2 9 4 10 D 4 X Q Q Q