Basic Math Questions and Answers

Suppose that you toss a coin and roll a die The sample space is shown in the figure below FOT a What is the probability of obtaining heads and a five Enter the probability as a fraction 1 12

a What is the probability of obtaining heads and a five Enter the probability as a fraction b What is the probability of obtaining heads or a five Enter the probability as a fraction Need Help Read It

a One airline has six across seating in coach three seats on either side of the aisle If seats are assigned randomly what is the probability that a person will be stuck in a middle seat Enter the probability as a fraction b Another airline has five across seating There are three seats on one side of the aisle and two seats on the other side of the aisle If seats are assigned randomly what is the probability that a person will have a window or an aisle seat Enter the probability as a fraction 24

A mad scientist has captured you and is showing you around his foul smelling laboratory He motions to an opaque formalin filled jar This jar contains one organ either a kidney or a brain he cheerily informs you His voice seems an octave too high as he gives you a twisted leer You watch as the madman grabs a brain lying on his worktable and drops it into the jar as well He then shakes the jar and quickly withdraws a single organ It proves to be a brain He turns to you and says What is now the chance of removing another brain Fearing that the scientist might remove your brain in his next ghoulish experiment you want to give him the right answer What is your response t Enter the probability as a fraction Need Help Read It

er is a common game in which players are dealt five cards from a deck of cards It can be shown that there are 2 598 960 different possible poker hands The winning hands from highest to est are shown in the table below Find the requested probability Use a calculator Show your answer to nine decimal places P royal flush Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3 744 hands Flush 5 108 hands Straight 10 200 hands Three of a kind 54 912 hands Two pair 123 552 hands Que noir 44 vv for Fore 44 4

Give the probability in decimal form correct to two decimal places A calculator may be helpful One year in Ferndale California it rained on 144 days If one day of that year is randomly selected what is the probability of rain on that day Assume that this was not a leap year Need Help Read It

Q4 Define isomorphism of a graph Show that the following three graphs are isomorphic X 2

Estimate 752 x 352 by first rounding each number so tha it has only 1 nonzero digit

Solve this linear programming problem using graphical methods Restrict x 0 and y 0 Maximize f 6x 3y subject to the following f 7x 3y 105 2x 5y 59 x 7y 70 X

Problem 1 40 Points Given A ball is thrown vertically upward from the top of a building with an initial velocity of V4 The initial height of the ball is yA The values of VA and yA are found on YOUR KEY Set the origin of the coordinate axis on the ground and assume that the ball s motion is of the rectilinear type Use the values on your KEY to Find of the the ball fo tion 09 C

radius r 12 139 A car is traveling along the circular curve of 300 ft At the instant shown its angular rate of rotation is 0 0 4 rad s which is increasing at the rate of 0 0 2 rad s Determine the magnitudes of the car s velocity and acceleration at this instant 8 0 4 rad s 0 2 rad s2 r 300 ft

Company for the years 2010 through 2015 can be approximidated by f x 30x 720x F x 30x 720X 3368 where x 10 corresponds to the 2010 year year did a local maximum profit aques what Occy b what was the maximum profit 3 A local extremum occurs at where the F Because the derivative exists for eative is Only critical numbese s occur Zero find the derivative of F X F x 267 a critical number of the A local maximum profit occured in the year year b The maximum profit was million Simpliky your answer Round to the nearest as needed orie

If you were to use the method of undetermined coefficients to solve the differential equations below wh would be an appropriate form for the initial guess for the particular solution yp t Where needed use the letters A B C in alphabetical order for your constants exponents in decreasing order For example A to B t C t D Don t forget to solve for the homogeneous equation first A y 2y y 9t 3t et The inital guess for yp t B y 2y y 8e cos 3t The inital guess for y t

A large manufacturer plans to move an operation from Country A to Country B in 2 years resulting in layoffs in Country A Management anticipates a severance pay for the laid off workers of 320 000 per month for 6 months Find the shortage in 2 years if they deposit 60 000 per month in an account Assume a rate of 6 that is compounded monthly Click here to view page 1 of the interest table for rate 0 5 Click here to view page 2 of the interest table for rate 0 5 The shortage is Round to the nearest cent as needed

Does the frequency distribution appear to have a normal distribution Explain Choose the correct answer below Temperature F 45 49 50 54 55 59 60 64 65 69 70 74 75 79 SIIM Frequency 1 3 10 15 10 4 1 A Yes because the frequencies start low proceed to one or two high frequencies then decrease to a low frequency and the distribution is approx symmetric OB Yes because the frequencies start low proceed to one or two high frequencies then increase to a maximum and the distribution is not symmet OC No because the frequencies start low proceed to one or two high frequencies then decrease to a low frequency and the distribution is approxi symmetric OD No because the frequencies start low proceed to one or two high frequencies then decrease to a low frequency and the distribution is not sym

8 10 pts Determine whether the graph below is bipartite If it is then give a bipartition V V a b h ic d 9

You would like to have 75 000 available in 15 years There are two options Account A has a rate of 8 5 compounded once a year Account B has a rate of 8 compounded daily How much would you have to deposit in each account to reach your goal Click the icon to view some finance formulas You must invest in Account A Round up to the nearest dollar

Which of the following statements is are TRUE i On May 31 George Dewey the American naval commander steamed into Manila Bay and destroyed the Spanish fleet ii Spain lost 1581 men and the United States lost 1 iii By August the Spanish troops surrendered to Americans rather than the Filipinos who had been fighting for freedom since 1896 Statements I and II O Statements II and III Statements III only Statements I and III

Several communities wish to establish a commuter rail system between cities labeled on the map to the right a Use Kruskal s algorithm to determine the minimum cost spanning tree that would link the cities using the shortest distance b If it costs 6900 per mile of railroad track how much does the commuter rail system determined in part a cost a Choose the correct minimum cost spanning tree below A 24 B 24 B 29 31 44 59 E 61 F 24 73 F b The commuter rail system costs 80 OB O D 24 B B 31 E 31 E 61 44 59 24 B 29 31 73 63 E HA 59 61 55 73 F 63 24

Next question At the time of her grandson s birth a grandmother deposits 7000 in an account that pays 5 5 compounded monthly What will be the value of the account at the child s twenty first birthday assuming that no other deposits or withdrawals are made during this period Click the icon to view some finance formulas The value of the account will be Round to the nearest dollar as needed

The angle subtebded bby an arc of length units at the centre of circle having radius r units then D None of these A Wh 1160 B 1260 C 1360

10 9 70 00 00 stem of equations is given a Identify the type of solution for the system unique solution no solution or infinitely many solutions Explain your reasoning The system has a unique solution because the coefficient array is an identity matrix The system has no solution because the coefficient array is not an identity matrix and has a row of zeros with a nonzero entry in the augment The system has no solution because the coefficient array is not an identity matrix and doesn t have a row of zeros with a nonzero entry in the augment The system has infinitely many solutions because the coefficient array is not an identity matrix and has a row of zeros with a nonzero entry in the augment The system has infinitely many solutions because the coefficient array is not an identity matrix and doesn t have a row of zeros with a nonzero entry in the augment x y z b For each system that has a solution rind it If the system has infinitely many solutions find the general solution in terms of x y and z If there is no solution enter NO SOLUTIO C

O V No olution 3 Help set of the inequality 4x 5y 120 4 2 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Fill G F

Find the inverse of the matrix 9 1 14 2 1

Approximate the real solutions to the quadratic equation to two decimal places Enter your answers as a comma separated list 1 02x2 2 05x 1 095 0 X 11

Solve the system using matrices If there are infinitely many solutions find the general solution in terms of x y and z If there is no solution enter NO SOLUTION x y 3x 6y z 7 z 12 2x y 5z 17 x y z

trix below D 43 13 Perform the indicated operation DT I

Use a graphing utility to graph the function Find any turning points Enter your answers as a comma separated list If an answer does not exist enter DNE y x 12x2 27x X

a f g x b f g x c f g x d fof x the following

xx 3 If f x a f 3 b f 0 c f 1 if x 1 4x 3 if x 1 d f 3 find the following

Find the average rate of change of f x x 35x 24 over the interval 10 50

Write the equation of the line described Slope and y intercept 9

1 In the summer time your friend wants to have a snow cone stand at a local grocery store parking lot You want to make sure he actually makes money The grocery store charges 300 per month All products are calculated to be 25 cents per customer Your plans are to sell each cone for 1 25 a Write a mathematical expression representing the cost of operation for a month b Write a mathematical expression representing sales c Create an equation that will represent overall profit of the operation for a month d Simplify the equation into slope intercept form and standard form What is the slope and explain its meaning in the context of selling snow cones What is the intercept and what is its meaning e Describe the method of graphing the slope intercept form and also the standard form of the equation f What is the domain and range of the equation Is the relation a function why g How many snow cones do you need to sell to break even in the first month h How much is the profit if you sell 425 550 or 700 snow cones in the first month of business B i U Font Family AAA FE

The database summarizes financial information for 32 companies and their perceived risk of default Convert these data into an Excel table Use table based calculations to find the average debt and average equity for companies with a risk of default and also for those without a risk of default Does there appear to be a difference between companies with and without a risk of default Click the icon to view the financial information for the 32 companies Convert these data into an Excel table Use table based calculations to find the average debt for companies with a risk of default The average debt for companies with a risk of default is S Round to the nearest whole number as needed 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2 Manufacturing 3 Manufacturing 4 Manufacturing 5 Service 6 Manufacturing 7 Service 8 Manufacturing 9 Service 10 Service 11 Manufacturing 12 Manufacturing 13 Service 14 Manufacturing 15 Manufacturing 16 Manufacturing 17 Manufacturing 18 Manufacturing 19 Manufacturing 20 Service 21 Manufacturing 22 Manufacturing 23 Service 24 Manufacturing 25 Manufacturing 26 Service 27 Manufacturing 714 4019529 2216629 No 732 171407 1782738 No 792 8084984 11918008 No 623 3170474 755648 Yes 702 13199975 4095573 Yes 764 4116956 6847610 No 690 7121992 5938446 No 802 7969203 11550605 No 610 14389772 3686534 Yes 590 8003572 19978215 No 824 583316 31212038 No 762 2252811 4519299 No 601 1776398 305758 Yes 655 39129388 14997345 Yes 792 4634857 4612049 No 721 3927187 14233030 No 750 12692273 11439891 No 762 5159636 18835016 No 598 2515454 538035 Yes 742 7075389 4262423 No 821 3668641 14139966 No 657 3815570 5221776 Yes 798 3102714 3263735 No 695 9877320 5642938 No 819 10076016 9212560 No 671 23680348 6665172 Yo

An assumed assumption can only exist when executives have minimal views but sufficient data to verify the assumption True False

Assumed assumptions are often included in strengths weaknesses opportunities and threats SWOT analysis True False

Strategy is about analysis while tactics are about execution True False

Strategy is short term while tactics are generally long term True False

Strategy is usually focused at a management level whereas tactics are more operational and detailed True False

A rectangular paperboard measuring 32 in long and 20 in wide has a semicircle cut out of it as shown below Find the area of the paperboard that remains Do not round any intermediate steps Round your final answer to the nearest hundredth and be sure to include the correct unit If necessary refer to the list of geometry formulas 20 in 1 32 in I 3 08 in in S in

coss sin Evaluate cos sin giving your answer as an exact value no decimals

A triangle is placed in a semicircle with a radius of 9 ft as shown below Find the area of the shaded region Do not round any intermediate steps Round your final answer to the nearest hundredth and be sure to include the correct unit If necessary refer to th list of geometry formulas 19 ft 7 ft X ft ft3

A rectangular piece of paper with length 27 cm and width 14 cm has two semicircles cut out of it as shown below Find the area of the paper that remains Do not round any intermediate steps Round your final answer to the nearest hundredth and be sure to include the correct unit If necessary refer to the list of geometry formulas 27 cm 14 cm 19 08 cm X cm cm

Question 9 1 point XOH 0 2 345 3 linear 6 O quadratic 11 15 What type of relation does the table represent exponential Y Qother 95437H 9 5

cos 7 Evaluate the expression sin 1

5 5 0 5 5 edit graph on desmos Determine an equation in factored form for this parabola

Follow the instructions below a Rewrite the percentage in the sentence below as a decimal The model was 5 of the size that the original was b Rewrite the decimal in the sentence below as a percentage In a recent poll 0 234 of the people surveyed were in favor of the new law Decimal Percent

6 5 2 3 2 1 1 2 The graph above is a graph of what function O y cos x Oy sec x Oy sin x Oy csc x Oy cot x

V Answer each part If necessary round your answers to the nearest hundredth a Austin runs 6 miles in 45 minutes How many minutes does he take per mile minutes per mile b Diane bought 20 pounds of sugar for 8 How many dollars did she pay per pound of sugar dollars per pound X

TU 2 2 1 1 TX2 R The graph above is a graph of what function Oy cot x y sin x Oy tan x Oy csc x Oy cos x 37 2 27 Q