Basic Math Questions and Answers

Consider the following inequality x 6 a Write the inequality in interval notation for a real number x Simplify your answer completely b List the values from x 0 1 2 3 4 5 6 7 8 9 10 11 that satisfy the given inequality Enter your answers as a comi separated list If there is no answer enter NONE

5 113 In the network in Fig P5 113 find R for maximum powe transfer and the maximum power transferred to this load 32 ksz 1kQ Figure P5 113 www 2 kn 4 mA 4kQ RL

Suppose 16 horses start a race In how many different ways can the horses place first second and third ways

For the amplifier in Fig P4 15 find the gain R1 4 1 KQ R2 47 KQ Figure P4 15 10 hundredth ex 5 is entered as 5 00 R R Notes on entering solution Enter your solution as a constant Give your answers with positive or negative sign Enter your solution to the nearest

Consider the interval 5 8 Rewrite the interval using plus minus notation Determine whether the number zero is contained in the interval Yes zero is contained in the interval O No zero is not contained in the interval

Perform the operation 10x 7x 7 4x 5x 9

Answer saved Mark Converts the following code from while to for loop main 1 int x i sum 0 cin x while x 5 O C O a main sum x i 1 while i sum Marked out of 1 00 O b main 1 5 cin x O b main main cout i i 2 int x i sum 0 for i 1 x 5 i O d main cin x sum x int x i sum 0 cin x for i 1 i sum i 2 cout i cin x for i 1 x 5 i int x i sum 0 cin x for i 1 x 5 i sum x for i 1 i sum i 2 cout i int x i sum 0 cin x cin x for x 5 sum x for i 1 i sum i 2 cout i cin x int x i sum 0 cin x for x 5 gumt 11

What is the output of the following code number 25 int int i int isPrime 1 for i 2 i number i if number i 0 isPrime 0 break cout i is i cout isPrime is cout isPrime endl O a iis 5 isPrime is 1 O b iis 3 isPrime is 1 O c i is 5 isPrime is 0 O d i is 2 isPrime is 0

c Let f x 15x3 x 2 Find f 1

Find the following limits 1 2 lim X 3 lim X 0 2 x 7 4 x 3 x 1 cos x tan 2 x

Write the vector 1 2 2 as a linear combination of the vectors 1 0 0 2 0 1 0 2 3

1 Consider the matrix A 0 0 0 0 1 0 2 3 a Find the eigenvaluue of A 2pts b Find the corresponding eigenvectors

Supposed the law prescribed the renter to vacate an apartment within 30 days after being served with an eviction notice To protect renters th government passes a new law under which the renter must vacate the apartment in 90 days The following graph shows the market for rental properties where the demand curve represents demand for apartments under the old eviction Adjust the following graph to show the effect of the new eviction law on the market for rental properties PRICE Apartment Ren 140 120 14 24 14 1 0 3021 QUANTITY Darents QUANTITY A falls rises sed on the graph the rental price rises QUANTITY Apartments Supply Demand to THE 100 Demand Supply 60 50 and the number of available apartments increases Grade It Now increases decreases

3 Determine the domain D and the range R of each relation and tell whether relation is a function Explain D R f 5 4 3 2 3 4

Scenario 1 Falling and Falling The value of some cell phones changes exponentially after initial release Here are gr the depreciation of two phones 1 2 and 3 years after they were released Analyze each graph and explain your answer in the boxes below Phone A value dollars 1 000 800 600 400 200 Analyzing and 2 0 1000 1 600 2 2 360 3 216 4 time years A Which phone is more expensive to buy when it is first released 6 Phone A was more espensive than phone B when it was first released D Which one is falling in value more quickly Explain or show how you know Phone A because the last point to less than the last point for phone B G If the phones continue to depreciate by the same factor each year what will the value of each phone be 4 years after its initial release 8 Phone B value dollars 1 000 800 600 0 840 O 1 630 2 472 5 O B What does the point 2 360 of Phone A represent in this situation Describe the point in the form of function notation After 2 years the priced decreased E Describe the domain of each function What does the domain mean in this situation What are the restrictions of the domain that arise from the context H Complete the phrase As each year x increases the value of f x decreases Explain or show how you know 3 354 38 4 time years 6 8 C How does the value of each phone change with every passing year It decays with each year passing F Describe the range of each function What does the range mean in context of the situation What are the restrictions of the range that arise from the context 1 For each cell phone write an equation that relates the value of the phone in dollars to the years since release t Use v for the value of Phone A and w for the value of Phone B

The figure shows the chain drive of a bicycle How far will the bicycle move if the pedals are rotated through 180 Assume the radius of the bicycle wheel is 13 5 inches The bicycle will travel approximately Round to the nearest tenth in www 1 14 in A

A 80 horsepower outboard motor at full throttle will rotate its propeller at exactly 4700 revolutions speed of the propeller in radians per second 4700 rev per min Round to th radians per sec

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model at a relative rate of 18 per hou Suppose that a sample culture has an initial population of 273 bacteria Find the population predicted after five hours according to the model Do not round any intermediate computations and round your answer to the nearest tenth 1 bacteria X S

Do bonds reduce the overall risk of an investment portfolio Let x be a random variable representing annual percent return for Vanguard Total Stock Index all stocks Let y be a random variable representing annual return for Vanguard Balanced Index 60 stock and 40 bond For the past several years we have the following data x 12 0 35 20 30 24 23 12 12 22 y 10 2 30 12 21 17 15 2 a Compute Ex Ex LAUSE SALT Compute Ex Ex Compute y Ey y S Compute Ey Ey S b Use the results of part a to compute the sample mean variance and standard deviation for x Round your answers to four decimal places x s 3 12 Use the results of part a to compute the sample mean variance and standard deviation for y Round your answers to four decimal places y s c Compute a 75 Chebyshev interval around the mean for x values Enter your answer in the form lower limit t Include the word to Round your numerical values to two decimal places Compute a 75 Chebyshev interval around the mean for y values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places Use the intervals to compare the two funds O 75 of the returns for the balanced fund fall within a narrower range than those of the stock fund 75 of the returns for the stock fund fall within a narrower range than those of the balanced fund O 25 of the returns for the balanced fund fall within a narrower range than those of the stock fund 25 of the returns for the stock fund fall within a wider range than those of the balanced fund d Compute the coefficient of variation in percent for fund x Round your answer to the nearest whole number Compute the coefficient of variation in percent for fund y Round your answer to the nearest whole number upper limit Use the coefficients of variation to compare the two funds For each unit of return the stock fund has lower risk For each unit of return the balanced fund has lower risk For each unit of return the funds have equal risk If s represents risks and x represents expected return then s x can be thought of as a measure of risk per unit of expected

The standard 4 point grading scale assigns a 4 0 to an A 3 0 to a B 2 0 to a C 1 0 to a D and 0 0 to an F Suppose that you earned an C in your 5 credit Chemistry class a B in your 1 credit Chemistry lab a C in your 3 credit History class and a A in your 3 credit Writing class Compute your grade point average In other words find the weighted average of your grades using the number of credits as the weights Round your answer to two decimal places

How hot does it get in Death Valley The following data are taken from a study conducted by the National Park System of which Death Valley is a unit The ground temperatures F were taken from May to November in the vicinity of Furnace Creek Compu the mean median and mode for these ground temperatures 148 150 167 173 185 179 180 185 179 167 179 USE SALT What is the mean in F Round your answer to four decimal places F What is the median in F F What is the mode in F 164 150 146

O O O y annual number of burglaries y annual number of burglaries a Make scatter diagram of the data Then visualize the line you think best fits the data y annual number of burglaries y y annual number of burglaries 25 20 15 10 70 60 50 40 30 20 70 60 50 40 30 20 25 20 15 25 10 USE SALT 20 72 10 10 39 23 15 30 30 40 x student enrollment in thousands 15 15 25 50 15 60 20 x student enrollment in thousands 20 x student enrollment in thousands 25 25 70

A location in Ireland is a place of great archaeological importance This region has been occupied by people for more than 4 000 years Geomagnetic surveys detect subsurface anomalies in the earth s magnetic field These surveys have led to many significant archaeological discoveries After collecting data the next step is to begin a statistical study The following data measure magnetic susceptibility centimeter gram second x 10 6 on two of the main grids of the location The data for the x variable Grid E is given below 13 10 5 70 19 70 14 95 21 50 17 35 27 55 16 85 24 00 32 50 40 85 5 00 17 65 28 45 The data for the y variable Grid H is given below 11 95 15 15 21 20 17 40 27 40 10 25 14 80 48 80 25 50 25 85 57 70 34 45 38 70 41 10 31 15 a Compute Ex Ex Compute Ex Ex Compute y y Compute Ey Ey USE SALT

A local swim club offers competitive meets throughout the season Some races are open competitions with no qualifying times Other races are qualified competitions For example 15 to 16 year old girls are eligible to swim the 100 meter freestyle in a qualified competition if they posted a time of 1 minute 8 second time or less during the qualifying period Consider the group of 15 to 16 year old females who swim the 100 meter freestyle in the open competitions and the group of 15 to 16 year old females who swim the 100 meter freestyle in the qualified competitions Which group s distribution of race times would most likely have the largest standard deviation O The group competing in the open competitions is most likely to have a higher standard deviation than the group competing in the qualified competitions O The group competing in the qualified competitions is most likely to have a higher standard deviation than the group competing in the open competitions O Some swimmers will swim in both competitions So both groups will likely have the same standard deviation O There is not enough information to predict the relative sizes of their standard deviations

Verify that Ex 173 Ex2 5 165 Ey 271 Ey2 14 345 and Exy 8 026 for the second set of data pairs Computer for the second set of data pairs Round your answer to four decimal places

Verify that Ex 157 Ex 3 923 2y 247 Ey2 9 921 and Exy 6 181 Computer Round your answer to four decimal places

c Use a calculator to verify that x 62 x 1 034 y 632 y 89 154 and xy 9 364 Computer Round your answer to four decimal places r

Write the statistical form of the line having the given slope and y intercept Let x be the independent variable and y be the dependent variable slope is 9 4 y intercept is at 3 6

The polynomial P x has integral coefficients and P 2 P 3 P 4 5 If the sum of the coefficients of P x is greater than 5 what is the least possible value of this sum

Factor each expression 1 16w 2w 3 3 k 81 5 8r 36r 6r 27 completely 2 18a b 33a b 4 c 5c 36 6 64 27x

You the graph of xx n in function

dar y kseliyor U nc z play nda 3m yukseldigine g re d rd nc kez z plad ktan sonra havada ol du u en y ksek noktada iken toplam ka m yol alm olur A 108 B 144 C 159 D 160 E 161

The inverse of O a O d T O b None O c 1 O e 1 NL 2 3 1 6381 0 1 2 1 2 3 2 3 2

The rank of the following matrix O a 3 O b 1 O c 2 O d None O e 0 1 3 000 1 2 6 3 is

The rank of the following matrix 1 1 3 3 0 0 2 6 0 is

The adjoint of the matrix O a None 1 O b O C O d O e 0 1 1 1 0 1 1 0 1 2 3 1 0 1 97 1 1 J is

x C361 65 If 2 O a None O b 2 2 O c 3 3 O d 3 3 O e 2 2 7 13 then x

Graph the line with slope b 1 5 passing through 0 3 3 10 2 6 3 5 0 3 3 X 10 5 5 10 5 10 O 10 5 10 51 5 10 5 10 10 5 2 6 3 10 5 5 5 10 10 0 3 3 5 10 0 334 3 5 5 10 10 X X Q

The number of graduates of the Code Tank Programming Institute was 758 in 2014 with a marginal change of b 10 graduate per year How many graduates did the Institute have in 2015 graduates

Suppose in 2010 there were 5 894 cases of a certain type of poisoning reported in the United States In 2014 the number of cases decreased to 5 045 a Compute the marginal change in cases per year Round your answer to one decimal place cases per year b Use the solution from part a to estimate the number of cases of this certain type of poisoning in 2015 Round your answer to the nearest whole number cases

The heart rate of a runner was measured after completing one mile and then again after two and a half miles The results are shown in the following table Miles Run 1 0 2 5 Heart Rate beats per minute 132 146 Compute the marginal change in beats per minute per mile and round to two decimal places beats per minute per mile

Graph the line with slope b 1 5 passing through 0 5 3 10 10 2 8 3 5 5 10 5 0 5 3 10 y 10 10 5 0 56 3 5 10 10 X X 10 10 2 6 3 5 10 5 10 y 10 5 0 5 3 10 5 2 8 3 0 5 3 5 10 10 X

Compute the slope of the line passing through 3 4 and 3 2 Write the slope as a rational number

Compute the slope of the line passing through 4 4 and 2 4 Write the slope as a rational number b

decimal places where necessary a x 2 4x 3r 8 5x b 4 2x 5 32 4 x 2 1052 Uph 18

S when P 1500 r Set up an algebraic equation and then proceed to solve each of the following word problems a Brad has 12 more than Pietro Together they have 84 Determine the amount of money that each has 365 b A jar contains four times as many washers as bolts If there are 80 washers and bolts altogether how many washers are there c A babysitter paid a bill a total of 77 quarters and dimes If there were 7 less dimes than quarters how many quarters did she use to pay the bill and what was the total dollar value of these coins d Tickets to a local concert cost 9 00 for adults and 6 50 for students A total of 950 people paid 7675 00 to attend How many students and adults attended the concert e The admission fee at a small fair is 1 50 for children and 4 00 for adults On a certain day 2200 people enter the fair and 5050 is collected How many children and how many adults attended

Rearrange and isolate the indicated variables a M in S C M b P in S P 1 rt

Consider the scatterplot shown y 15 10 in 5 C F G KO LO 10 NO MO H R 15 20 Identify the points to the right of the line x 10 Enter your answers as a comma separated

Consider the scatterplot shown 15 10 5 A B 5 DO G H KO LO 10 MO R 15 P 20 Identify the points below the line y 10 Enter your answers as a comma separated list

to 405 A flight from Toronto to Singapore takes 19 hours 11 hours after the flight leaves 2 3 3 Toronto how long until it reaches Singapore Answer in lowest terms NO DECIMALS