Basic Math Questions and Answers

A 2 drum lottery has 48 white balls in the first drum and 36 red balls in the second drum How many lottery numbers can be drawn if the winning number consists of 5 white balls and one red The order the numbers are drawn does not matter

Which ordered pair is the best estimate for the system of equations y 4x 19 4 y 0 2x 4 2

The difference of the square of a number and 9 is equal to 8 times that number Find the positive solution

Also suppose that R x has the following zeros 2 5 1 41 Answer the following a Find another zero of R s 0 b what is the maximum number of real zeros that R x can have 0 c What is the maximum number of nonreal zeros that R can have 0 Hide Transcribed Text pose that R x polynomial of degree 10 whose coetficients are real numbers Also suppose th R x the following zeros 2 5 i 4i

Flexible Budgeting At the beginning of the period the Fabricating Department budgeted direct labor of 96 200 and equipment depreciation of 29 000 for 7 400 hours of production The department actually completed 9 500 hours of production Determine the budget for the department assuming that it uses flexible budgeting

O Macmillan Learning Consider the table of GDP and population for several imaginary countries Country Wrigleyville Longhornland Dinkytown GDP in millions of U S dollars Population in millions GDP per capita in U S dollars 171 0 171 133 00 523 0 2719 1 700 Using this information please answer the questions If there is not enough information to answer a question please enter 11 A What is the GDP per capita of Longhornland in U S dollars Express your answer rounded to one decimal place B What is the GDP of Dinkytown in millions of U S dollars Express your answer rounded to one decimal place

Macmillan Learning Wage rate per hour 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 0 1 S D 8 9 10 11 12 13 14 15 2 3 4 5 6 7 Labor quantity in millions of workers After the effects of the recession are felt what is the size of the increase or decrease in unemployment

The table shows the cost of a fixed basket of goods that a typical urban consumer would buy in the economy of Kindleberg The base period for the consumer price index CPI is the year 2010 Please specify answers to two decimal places Year 2010 2021 2022 Cost of a basket of goods What is the CPI for 2010 CPI for 2010 100 What is the CPI for 2021 4 150 00 5 500 00 7 725 00

In the figure where a 118 degrees Round the answers to three decimal places a Find sin 8 i b Solve for 8 i 46 6 degrees 10 cm c Find the area of the triangle 8 3c

A crane is being set up on a slope of 5 5 If the base of the crane is 8 0 ft wide how many inches should the downhill side of the base be raised in order to level the crane The downhill side of the base should be raised Round to the nearest tenth as needed in in order to level the crane TE 8 ft 5 5 X

Determine the remaining sides and angles of the triangle ABC A 59 Round to the nearest degree as needed bam Do not round until the final answer Then round to the nearest hundredth as needed GID 476m B

If tan A 5 12 with A in QIII find sec 2A Draw a diagram of angle A and 2A

9 128 Carmel picks an integer from 1 to 12 as a value for c in the equation y x 4x c What is the probability that the equation will have complex roots

2 of th Period 4 es Ruler 3 6 m X How to Register for 0 9 m 5 A cylinder with a radius of 12 feet and a height of 1 2 feet Math Assistant LATERAL SURFACE AREA 4 CAR TOTAL SURFACE AREA TOT

The population of stray cats in a small city follows the formula 250 2r 3 where 20 represents the number of months since the first stray cat appeared Sketch the graph of p t Answer 2 Points 150 125 Population 100 C 8 P 6 Months Enable Zoom Pan 8 p t 10 Population 150 P 125 100 75 50 C Months Keybo Enable Zoom Par 10

Suppose F t has the derivative f t shown below and F 0 5 Find values for F 2 and F 7 1 3 2 1 1 2 F 2 F 7 4 4 2 X 5 6

n the function f x 240x 48 a graph g x with the shaded region bounded by the graph of g x the x axis and the vertical lines x 0 and x 1 Include the Microsoft Excel graph with the shaded region along with the input and output values used to create the graph in

The population of a city is modeled by the equation P t 286 3390 25t where t is measured in years If the city continues to grow at this rate a What would be the population after 1 year b Set the equation and solve for time to answer in approximately how many years will it take for the population to reach one million Round your answer to two decimal places

A small country consists of seven states there are 160 seats in the legislature that need to be apportioned among the seven states and the population of each state is shown in the table G A B C D E F Population 1283 2374 2725 2155 1592 2511 2017 State Does the Alabama paradox occur using Hamilton s method if the number of seats is increased from 160 to 161 COO Yes No

A university is comprised of five schools A B C D and E The enrollment in each school is given in the following table C School Enrollment A 1170 B 1270 2120 Complete the table below There are 300 new computers to be apportioned among the five schools according to their respective enrollments Use Hamilton s method to find each school s apportionment of computers School Enrollment Hamilton s apportionment A 1170 B 1270 D 2930 C 2120 0 E 2830 D 2930 E 2830

The Mathematics Department is holding an election for department chair Each member ranks the candidates from first to third The preference table below shows the results of the ballots with candidates Clark C Jones J and Smith S Number of Votes 7 10 4 First J Second S Third C CSJ If the plurality method is used to determine the winner and Clark drops out is the irrelevant alternatives criterion satisfied OO Yes No S J FCS8 J CS 5

Savings equals investment in equilibrium ignoring government or foreign sector In equilibrium aggregate demand total planned spending must equal output and income Investment and savings are primarily functions of the rate of interest Demand particularly intended investment drives supply Capitalist economies will normally fail to reach full employment due to insufficient aggregate demand Interest rates fall when money saved exceeds the demand for those funds for investment until savings equals investment 1 neo classical 2 post Keynesian 3 Both

A university has 30 scholarships to be apportioned among the engineering students based on the enrollment in each department There are three departments Mechanical Engineering M Electrical Engineering E and Civil Engineering C The number of students in each department is given in the following table Department M E C Enrollment 233 297 153 Find the standard quota for the Mechanical Engineering Department Round your answer to two decimals OA 8 77 OB 9 41 OC 9 83 D 10 23

Macmillan Learning Use the information in the table to calculate a consumer price index CPI and the inflation rate The base year is 1975 Round answers to two decimal places Market basket A dozen eggs Calculator Microwave oven What is the CPI for 1975 What is the CPI for 1976 What is the inflation rate for 1976 Quantity 22 14 3 1975 prices 0 70 12 50 150 00 1976 prices 1 10 15 00 180 00

Employees at the Me My Mop and I cleaning service are choosing a new company logo The choices are a mop M a broom and dustpan B and a vacuum cleaner V Ea employee ranks the three choices from first to third The preference table below shows the results of the ballots Number of Votes First Second Third 18 M V B Determine the winner using the plurality method OA vacuum OB broom and dustpan OC mop 16 VMB HVBM 14 BBVM 18 2MBY V 11 B M V

Identify any bridges in the graph or say there are none A B C D E F O A CD OB DH OC CF and DG OD None J

Using the following graph find an Euler circuit that begins and ends with vertex A A B E foo OA A B C D BA OB OC No Euler circuit exists OD A B C D E A B A B C D B E A

Determine two different Hamilton circuits in the following graph B C E K F H A D G Select all that apply A A E B A D G H I F C B A B C I F E H G D A C A B C F I E H G D A D A E B C F I H G D A E A B C F I H G D A

Determine a spanning tree for the graph to the right Which of the following is a spanning tree for the given graph SOA B C O C A A F B F G C G D H D H E 1 E I O B O D C D XIX F G H A A B B F B F C G C G D H D E E I E H I

K The diagram on the right is a floor plan Letting vertices represent the room and the outside and edges represent the connecting doors which graph correctly models the floor plan Select the correct answer below A 8 E D E D E

Erik Allen repairs photocopy machines According to his schedule he needs to visit 9 different offices today How many ways can Erik visit these offices and return to his headquarters OA 72 OB 8 O C 9 OD 362 880

Suppose the sales of a particular brand of appliance are modeled by the linear function S x 90x 5 000 where S x represents the number of sales in year x with x 0 corresponding to 2010 Find the number of sales expected in 2022 if this trend continues OA 6 080 OB 5 990 O C 12 160 OD 12 070

An electrician charges a fee of 50 plus 5 per hour Let y be the cost in dollars of using the electrician for x hours Find the slope intercept form of the equation OA y 5x 50 OB y 50x 5 OC y 50x 5 OD y 5x 50

Use nodal analysis to find Vx in the circuit shown below where Is 20 A Please report your answer so the magnitude is positive and all angles are in the range of negative 180 degrees to positive 180 degrees Is The value of Vx j4Q m V 592 j3Q hjk J V 3 45 A 27

A homeowner planning a kitchen remodeling can afford a 300 monthly payment How much can the homeowner borrow for 4 years at 6 compounded monthly and still stay within the bu Round your answer to the nearest cent X

y 5 2 36 x 4 2 1 What is the length of the transverse axis

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Suppose output and income is equal to 13800 the marginal propensity to consume is 0 65 and autonomous consumption is 425 Calculate total saving for this economy assuming no public or foreign sector Round your answer to the nearest whole number Your Answer

Suppose that Jane s income increases from 1750 per month to 2300 At the same time her consumption changes from 1050 per month to 1300 month What is Jane s marginal propensity to consume Round your answer to two decimal places Your Answer

The equation y x 9 6 models the data in the table shown 1 2 3 4 5 6 y 5 8 8 7 2 9 0 8 5 1 1 7 X y 9 8 7 6 5 4 3 2 1 0 1 y x 9 6 2 3 4 5 6 X Identify the number of positive and negative residuals the residual with the greatest absolute value and the residual with the least absolute value Is the model a good fit There are positive residuals and residual with the least absolute value is The residual with the greatest absolute value is and the The absolute values of the residuals are relatively and in general the data points about the line of fit negative residuals So the equation y x 9 6 All evenly dispersed a good fit

Suppose a company has fixed costs of 41 600 and variable cost per unit of 2 5 3 dollars per unit a Find the break even points Enter your answers as a comma separated list x 1300 1665 b Find the maximum revenue Round your answer to the nearest cent 115509375 c Form the profit function P x from the cost and revenue functions P x 401596 333 dollars where x is the total number of units produced Suppose further that the selling price of its produ Find maximum profit d What price will maximize the profit Round your answer to the nearest cent

An investor is presented with a choice of two investments an established clothing store and a new book store Each choice requires the same initial investment and each produces a continuous income stream of 4 compounded continuously The rate of flow of income from the clothing store is f t 18 000 and the rate of flow of income from the book store is expected to be g t 16 000e0 06t Compare the future values of these investments to determine which is the better choice over the next 8 years The future value of the clothing store is Round to the nearest dollar as needed

The rate of flow f t of a continuous income stream is a linear function increasing from 3 000 per year when t 0 to 6 000 per year when t 6 Find the total income produced in the first 6 years The total income produced in the first 6 years is Simplify your answer

ind an equation of the hyperbola having foci at 3 5 and 5 5 and vertices at 2 5 and 4 5 7

of a car purchased in 2018 can be modeled by the function below where a is the f years since the car was purchased p a 32400 0 71 Identify the in Graphin

9 points Question 11 A researcher randomly purchases several different kits of a popular building toys The number of pieces in each kit is listed in the following list 169 54 274 359 54 305 118 217 359 113 270 179 180 100 Find the following a The mean round to the nearest whole number as necessary b The median do not round c The range d Is the list unimodal bimodal multimodal or does it have no mode Find the modes if any exist e Find the five number summary in ascending order separating each number with a comma

Zambia has a trade deficit of 1500 billion private savings of 3000 billion and a government budget deficit of 4000 billion Use the national savings and investment identity and the numbers given to determine the value of private investment investment 3000 billion

Extend 3 x 3 x x to a basis for P Enter your answers as a comma separated list 3 x 3 x x x x 3 X

3 A ceramic coffee mug is cylindrical with a radius of 2 inches and a height of 3 75 inches The inside of the mug is painted blue while the exterior of the mug is painted beige and red Find the surface area of the mug that is painted blue