Basic Math Questions and Answers

Evaluate or simplify the following the expression 100 2 O A 20 OB 40 O c 50 O D 10

Dit qui You want to have a 40 000 college fund in 6 years How much will you have to deposit now in an account with an APR of 5 and annual compounding OA 29 848 62 B 28 949 30 C 31 930 99 O D 24 949 06

What is the general form of the compound interest formula for interest paid once a year OA A PX 1 APR Y B A PXAPR OC A P APRXY OD A PXAPRY

The expenses and income of an individual are given in table form Find the net monthly cash flow it could be positive or negative Assume salaries and wages a after taxes that 1 month 4 weeks and that 1 year 12 months Round your answer to the nearest dollar Income Salary 29 000 year Jewelry sales 200 month OA 310 127 Expenses House payments 1400 month Groceries 90 week Household expenses 300 month Car insurance 350 semiannually Donations 300 year Miscellaneous 600 month KOOD

Although the earth formed about 4 6 Ga and there is evidence of some solid geologic materials by 4 4 Ga for this evidence for stable continental crust and oceans doesn t appear until about 3 0 Ga 2 0 Ga O 1 0 Ga 4 0 Ga f

To approximate the area of a lake a surveyor walks around perimeter of the lake taking the measurements shown in illustration Using this technique what is the approximate of the lake 35 ft 40 ft 80 ft 20 ft 100

If f x f x f x 2x compute the first and second derivatives of f x 4x 9 Submit Answer E

If f x 9x3 9x3 f x f x f x 1 3x 3x 7x 5 compute the first second and third derivative of f x 1

Let A be an 3 x 3 invertible matrix such that 2 is an eigenvalue of A with the corresponding eigenvector v Then one of the following is true 1 O a is an eigenvalue of A with eigenvector differ from v O b 2 is an eigenvalue of A 1 with the same eigenvector v Oc None O d 2 is an eigenvalue of AT with the same eigenvector v Oe 4 is an eigenvalue of A2 with the same eigenvector v

Answer saved Marked out of 2 00 If A O a O b C adj A 3 1 1 0 13 0 1 2 3 1 1 O d None O e 0 23 1 Clear my choice

One of the following ODES is an exact DE O a x y dx y 2x dy 0 O b x y dx 2xy dy 0 O c None O d y 2 dx 2x 1 dy 0

Of 2 00 The eigenvalues of the matrix A O a 1 3 O b 1 3 O c 1 3 O d None O e 1 3 1 1 4 are

Not yet answered Marked out of 2 00 The following differntial equation y x y is a first order linear ODE O True O False

The eigenvalues of the matrix O a A 0 2 3 O b A 0 1 3 Oc A 0 1 2 O d A 0 2 2 O e None 0 2 2 1 1 2 0 1 0

Let A 1 0 0 0 0 1 1 0 40 000 04 00 Then rank A O a 4 O b 2 O c 1 O d 0 O e 3

Question What trigonometric substitution should be used to find the arc length of f x 2 ln 2x over 1 4 The arc length is 1 da Leave a out of your answer and give the answer in terms of 0 For example If the substituti given by is a cos answer cos 0 Provide your answer below

2 Find Ex Let A and eigne vector A A Find the eigne value A A 21

A box contains three cards On one card there is a rectangle R on another card there is an apple A and on the third card there is a sun S Two cards are to be selected at random with replacement Complete parts a through below C OD RR RA RS SR SA SS c Determine the probability that two rectangles are selected The probability is Simplify your answer 9 d Determine the probability that a card containing a rectangle and then a card containing a sun are selected The probability is Simplify your answer 9 e Determine the probability that exactly one card containing a rectangle is selected The probability is Simplify your answer

For problems 22 25 refer to the weighted voting system 8 6 3 2 and the Shapley Shubik definition of power The three players are P1 P2 and P3 22 Which player in the sequential coalition P1 P2 P3 is pivotal A P3 B P1 C P2 D All three players F none of these 22

1 If ozone concentration is recorded as 0 15 ppm at a place where the pressure is 2 atmospheres and 30 C express this concentration in micrograms per cubic meter

As you mold yourself into a leader you want to really assess your current state of development and determine where you want to proceed from there The first phase in the development planning process is to conduct a GAPS goals abilities perceptions and standards analysis which involves the following steps Identifying career goals Identifying strengths and development needs related to the career goals Determining how one s abilities skills and behaviors are perceived by others by asking others for feedback or through performance reviews or 360 feedback instruments Think back on performance reviews or ask now Determining the standards one s boss or organization has for one s career objectives What feedback have you received informal or formal If you ve never had direct reports omit This is a simple self analysis for reference as you develop and grow Challenge yourself to continuously evaluate yourself as your continue to development your leadership skills Directions Refer to figure 3 2 A Sample GAPS Analysis on page 94 of your text In a WORD document create a simple 4 quadrant table like this figure and answer the questions as laid out in Figure 3 2 thoroughly After answering thoroughly see Figure 3 3 on page 96 Under your completed table address the Development Objectives Describe your current position and next proposed position

Watch the following video on Maite s experience caring for her mother with Alzheimer s disease Picture yourself as Maite Imagine the challenges both emotionally and logistically of being in her position What do you think would be the hardest aspect of this for you How would you prioritize the demands of daily life

For each problem below a point is rotating with uniform circular motion on a circle of radius r 35 Find v if r 2 inches and w 5 radians per second 36 Find v if r 8 inches and w 4 radians per second 37 Find w if r 6 centimeters and v 3 centimeters per second

Determine if the set is the empty set x x is a day of the week whose name begins with the letter Y OYes it is the empty set O No it is not the empty set

Find the distance s covered by a point moving with linear velocity v for a time t if 7 v 20 feet per second and t 4 seconds 8 v 10 feet per second and t 4 seconds 9 v 45 miles per hour and t hour

Let U q r s t u v w x y z A q s u w y B q s y z C v w x y z List the elements in the set BUC O A q r s t u v w x y z OB q s u w y OC v w x y z OD q s v w x y z

Determine the exact value of sin 17 12 points

Convert to degrees 13 points 8T 3

Determine the exact value of cos 5 12 points

The subsets A B and C of the universe U satisfy the following conditions n A 40 n B 48 n C 42 n An B 8 n An C 10 n BNC 4 n AnBn C 2 n ANBNC 81 Find n U

Convert 675 to radians 13 points

Student s t table use the closest d f that is smaller In some situations this choice of d f may increase the P value by a small amount and therefore produce a slightly more conservative answer In an effort to determine if rats perform certain tasks more quickly if offered larger rewards the following experiment was performed On day 1 a group of three rats was given a reward of one food pellet each time they ran a maze A second group of three rats was given a reward of five food pellets each time they ran the maze On day 2 the groups were reversed so the first group now got five food pellets for running the maze and the second group got only one pellet for running the same maze The average times in seconds for each rat to run the maze 30 times are shown in the following table A B C D E F Time with one food pellet 3 8 4 4 3 0 3 1 3 5 Time with five food pellets 3 1 3 5 2 8 3 3 2 8 3 0 Rat USE SALT H Do these data indicate that rats receiving larger rewards tend to run the maze in less time Use a 5 level of significance Let d one five a What is the level of significance 0 05 State the null and alternate hypotheses Enter for as needed Ho x X X Will you use a left tailed right tailed or two tailed test Otwo tailed left tailed Oright tailed 3 9 b What sampling distribution will you use What assumptions are you making We ll use the standard normal We assume that d has an approximately uniform distribution We ll use the Student s t We assume that d has an approximately normal distribution We ll use the Student s t We assume that d has an approximately uniform distribution We ll use the standard normal We assume that d has an approximately normal distribution What is the t value of the sample test statistic Round your answer to two decimal places c Find or estimate the P value OP value 0 250 0 125 P value 0 250 0 050 P value 0 125 0 025 P value 0 050 0 005 P value 0 025 P value 0 005

Two coins are tossed Assume that each event is equally likely to occur a Use the counting principle to determine the number of sample points in the sample space b Construct a tree diagram and list the sample space c Determine the probability that no tails are tossed d Determine the probability that exactly one tail is tossed e Determine the probability that two tails are tossed f Determine the probability that at least one tail is tossed www What is the sample space Choose the correct answer below A HH HT TH TT B H T OC H T H T OD H T HH HT TH TT c The probability that no tails are tossed is Simplify your answer

A box contains three cards On one card there is a rectangle R on another card there is an apple A and on the third card there is a sun S Two cards are to be selected at random with replacement Complete parts a through e below SKA List the sample space Choose the correct answer below O A RR RA RS AR AA AS SR SA SS OB RA AS SR OC RA RS AR AS SR SA O D RR RA RS SR SA SS A s A S R A S S SP R A

From the list shown Steve will purchase one appetizer one beverage and one dessert at random to bring to a party Complete parts a through e a Determine the number of points in the sample space The number of points in the sample space is Appetizer Chips and dip D Vegetable tray V Cheese plate C Beverage Lemonade L Soda S Dessert Brownies B Cake K Ice cream 1

The Flotterons plan to purchase paint for the walls and for the trim in their living room They select one color for the walls and one color for the trim at random from following colors Walls Taupe Mahogany Chocolate Sable Trim Vanilla Eggshell Alabaster Oyster Complete parts a through e a Determine the number of points in the sample space points in the sample space There are

Consider the following 5 4 3 domain range 1 y 5 4 3 2 1 1 2 3 Use the Vertical Line Test to determine OYes the curve is a function of x O No the curve is not a function of x 4 1 2 WebAssign Plot 3 4 5 whether the curve is the graph of a function of x If the curve is a function state the domain and range Enter your answers using interval notation If the curve is not a function enter NO Manter i X

In the weighted voting system 14 7 7 6 A P has all the power P2 and P3 are dummies B P1 and P2 have equal power P3 is a dummy C all three players have equal power D P1 and P2 have equal power P3 is not a dummy E none of these

Problems 9 11 For an election with 4 candidates A B C and D we have the following preference schedule Number of voters 20 14 872 A C D CD B B B DA CDABB DACA C 9 When using Copeland s Method which candidate wins in the comparison between candidate A and candidate D 1st choice 2nd choice 3rd choice 4th choice A A B Neither it is a tie C Cannot be determined from the information given D D E none of these A 0 B 1 C 2 D 3 D When using Copeland s Method how many comparisons does candidate A win of these 9 10

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time For 51 randomly selected runs bus line A was observed to be off schedule an average time of 53 minutes with standard deviation 17 minutes For 60 randomly selected runs bus line B was observed to be off schedule an average of 60 minutes with standard deviation 15 minutes Do the data indicate a significant difference in average off schedule times Use a 5 level of significance Let bus line A be population 1 and bus line B be population 2 USE SALT a What are we testing in this problem a single proportion a single mean a difference of proportions a paired difference difference of means b What is the level of significance 0 05 State the null and alternate hypotheses in minutes Enter for as needed Ho M1 1 H M 1 c What sampling distribution will you use What assumptions are you making We ll use the standard normal Since the sample sizes are not sufficiently large we need to assume the data are two independent random samples from the relevant populations and that the population distributions are at least mound shaped We ll use the Student s t Since the sample sizes are sufficiently large we only need to assume the data are two independent random samples from the relevant populations We ll use the standard normal Since the sample sizes are sufficiently large we only need to assume the data are two independent random samples from the relevant populations We ll use the Student s t Since the sample sizes are not sufficiently large we need to assume the data are two independent random samples from the relevant populations and that the population distributions are at least mound shaped Use the sample test statistic to compute the corresponding distribution value Test the difference Round your answer

Consider independent random samples from two populations that are normal or approximately normal or the case in which both sample sizes are at least 30 Then if o and are unknown but we have reason to believe that o we can pool the standard deviations Using sample sizes n and n the sample test statistic x x has a Student s t distribution where 2 with degrees of freedom d f n n 2 and where the pooled standard deviation s is n 1 s 2 n 1 5 n n 2 Note With statistical software select the pooled variance or equal variance options LAUSE SALT a There are many situations in which we want to compare means from populations having standard deviations that are equal This method applies even if the standard deviations are known to be only approximately equal Consider a report regarding average incidence of fox rabies in two regions For region I n 16 x 4 6875 and s 3 0489 and for region II n 15 x 4 and s 2 1381 The two sample standard deviations are sufficiently close that we can assume Use the method of pooled standard deviation to consider the report testing if there is a difference in population mean average incidence of rabies at the 5 level of significance Round your answer to three decimal places State the null and alternate hypotheses Enter for as needed H i th kh ng H M 12 Use the sample test statistic to find the corresponding t value Test the difference Round your final answer to two decimal places

Determine whether the subset of Mn n is a subspace of Mn n with the standard operations of matrix addition and scalar multiplication The set of all n x n matrices whose entries sum to one O subspace O not a subspace

Is W a subspace of the vector space If not state why Select all that apply W is the set of all vectors in R2 whose components are rational numbers OW is a subspace of R OW is not a subspace of R2 because it is not closed under addition OW is not a subspace of R2 because it is not closed under scalar multiplication

In this problem assume that the distribution of differences is approximately normal Note For degrees of freedom d f not in the Student s t table use the closest d f that is smaller In some situations this choice of d f may increase the P value by a small amount and therefore produce a slightly more conservative answer In environmental studies sex ratios are of great importance Wolf society packs and ecology have been studied extensively at different locations in the U S and foreign countries Sex ratios for eight study sites in northern Europe are shown below Location of Wolf Pack Males Winter Males Summer Finland Finland Finland Lapland Lapland Russia Russia Russia USE SALT a What is the level of significance 0 05 88 39 79 55 64 50 41 55 69 Will you use a left tailed right tailed or two tailed test Oright tailed two tailed left tailed 42 61 48 55 50 It is hypothesized that in winter loner males not present in summer packs join the pack to increase survival rate Use a 5 level of significance to test the claim that the average percentage of males in a wolf pack is higher in winter Let d winter summer 50 45 State the null and alternate hypotheses Enter for as needed Ho H b What sampling distribution will you use What assumptions are you making We ll use the Student s t We assume that d has an approximately uniform distribution O We ll use the Student s t We assume that d has an approximately normal distribution We ll use the standard normal We assume that d has an approximately uniform distribution We ll use the standard normal We assume that d has an approximately normal distribution What is the t value of the sample test statistic Round your answer to two decimal places

List the advantages of using paired data to conduct a statistical test Select all that apply Using paired data should theoretically reduce measurement variability and decrease the accuracy of statistical conclusions Using paired data should theoretically reduce measurement variability and increase the accuracy of statistical conclusions Using paired data should theoretically increase measurement variability and decrease the accuracy of statistical conclusions Using paired data often enhances the effect of extraneous or uncontrollable factors being present in our data Using paired data should theoretically increase measurement variability and increase the accuracy of statistical conclusions Using paired data often reduces the effect of extraneous or uncontrollable factors being present in our data

In this problem assume that the distribution of differences is approximately normal Note For degrees of freedom d f not in the Student s t table use the closest d f that is smaller In some situations this choice of d f may increase the P value by a small amount and therefore produce a slightly more conservative answer Are America s top chief executive officers CEOS really worth all that money One way to answer this question is to look at row B the annual company percentage increase in revenue versus row A the CEO s annual percentage salary increase in that same company Suppose a random sample of companies yielded the following data B Percent increase 22 25 27 18 6 for company A Percent increase for CEO 4 21 37 25 23 22 14 4 19 15 30 LUSE SALT Do these data indicate that the population mean percentage increase in corporate revenue row B is different from the population mean percentage increase in CEO salary Use a 5 level of significance Let d B A a What is the level of significance X You may have forgotten to multiply or divide by 100 State the null and alternate hypotheses in percent Enter for as needed Ho Check which variable s should be in your answer

Give the intervals on which the function is increasing decreasing or constant Simplify your answers completely Enter your answers using interval notation If an answer does not exist enter Objective 1 increasing decreasing constant 000

Find an equation for the line whose graph is sketched y 3 1 0 2 1 3 5 X

Assume that name is a variable of type string that has been assigned a value Write an expression whose value is a string containing the second character of the value of name So if the value of name were Smith the expression s value would be m

In the following diagram suppose side m 7 13 cm and side p 16 19 cm Determine the length of side q m q Your Answer P Round to the nearest tenth if needed Be sure to include proper units If the length cannot be determined put NULL in the answer box