Math - Others Questions

3 1 point Simplify 32 N M b 1 16 44 d 16

6 1 point a 625 625 625 is equal to b 15 C 25 d

nt 3x 3x WIL is equivalent to b 3x6 3x d 27x

Question 5 swer y t A 0 123 0 6 0 4 1 4 1 2 0 8 0 2 1 5 15 20 25 t sec A periodic signal has the waveform shown in the figure above where y t for the first cycle is defined as 10 y t e 4 y t e 4 The mean value of y t is closest to which of the following LEASE REMEMBER TO SHOW ALL WORK THAT LEADS TO YOUR ANSWER B 0 245 D 0 487 for 0 t 4 for 4 t 8 C 0 250 01 09 E None of the these

5 1 point Evaluate 42 2 3 2 Express your answer using only positive exponents C d 65 144 72 144 97 144

3 1 point Evaluate AU 4 M W H 2 w U MT d 27

point Express 3 5 1 as a power with a negative exponent b 3 C 7 d 74

d d E Consider F w a complex function of a real variable w F w 2 jw 3 j4w a Express F w in Cartesian form and its real and imaginary parts 5 points b Express F w in polar form and find its magnitude F w and angle ZF w 5 points DDR

8 Consider the following equation x 1 y 1 dt a Using the above equation show that the correlation between sin 2nt and cos 2 zero 10 points

A random variable is characterized by an exponential probability density distribution PDF shown below What is the probability that x will have a value less than or equal to 1 0 Note PDF 0 for x 0 15 points P D F 3 5 3 2 5 2 1 5 1 0 5 Exponential Distribution PDF 4exp 4x 0 5 1 1 5 2

2 Consider a periodic signal shown below 7 6 X2 1 1 1 2 1 5 3 2 a Find the fundamental period of this signal b Consider following two signals xi t and x2 t obtained from the above signal find their corresponding Fourier transforms x t 1 x 1 0 1 0 1 2 3 4 56 7

otherwise specified S 4 Find the delay between x t cos 10t 20 and x t sin 10t 10 5 points 5 Represent the following numbers in the complex plane and express them in Cartesian 10 points a 2ejn3 b b 4e 134 C c 2014 d d 2e j4x

The standard deviation of y t in the preceding problem is closest to which of the following Answer A 0 065 B 0 254 C 0 402 D 0 653 E None of the these

15 points The signal y t is generated by convolving a band limited signal x1 t with another bandlimited signal x2 t that is y t x1 t x2 t Where frequency responses of x1 t and x2 t are expressed as X1 w 0 for lw 1000m and X2 w 0 for w 2000 respectively Impulse train sampling is performed on y t to obtain 00 y t y nT 8 t nT 111 00 Specify the range of values for the sampling period T which ensures that y t is recoverable from y t

15 points A waveform r t 10 cos 1000xt 3 20 cos 2000xt 6 is to be uniformly sampled for digital transmission a What is the maximum allowable time interval between sample values that will ensure perfect signal reproduction b If we want to reproduce 1 hour of this waveform how many sample values need to be stored

2 In the following cases express the f t as a single sinusoid a f t cos wot 3 sin wot 5 points b f t 3 cos wat 4 sin wot 5 points

32x5 202 x 1 10

Partially Correct Your answer is incorrect Suppose that the dollar value 1 of a certain car that is f years old is given by the following exponential function 1 24 500 0 92 Find the initial value of the car 24500 Does the function represent growth or decay growth O decay By what percent does the value of the car change each year

Mercedes is using periodic functions to model waves in the ocean A crest is considered a maximum and a trough is considered a minimum Values for y represent the vertical position in feet above or below the line of equilibrium midline and values for x represent the distance in feet from a fixed point W Troughs 1 Mercedes tries this technique to model waves she observes at sunrise The crests average 3 8 ft the troughs average 3 8 ft and the frequency is Write a function that could represent this situation Explain 20 Crests equilibrium

Suppose that 2000 is loaned at a rate of 12 5 compounded semiannually Assuming that no payments are made find the amount owed after 10 years Do not round any intermediate computations and round your answer to the nearest cent

The one to one functions g and h are defined as follows g x 2x 3 h 8 5 7 4 4 8 3 0 Find the following g t 0 g g 1 0 h 8 3 X

Your answer is incorrect Equation c Your answer is incorrect Fill in the missing values to make the equations true a log 5 log 9 log 45 b log 5 log 8 log c log 81 27log 3 in co 8 X

3 A hot air balloon is on the ground 300 feet from Mercedes She watches the balloon as it fires its burner and begins to ascend straight up into the air Write a function that models the height h in feet of the balloon as a function of the angle of inclination from Mercedes

2 At sunset Mercedes observes a series of ocean waves modeled by y 4 2 sin x How do the period and amplitude compare to the function you wrote to represent the sunrise waves Explain

4 The graph of y tan x is stretched verticaly by a factor of 4 and compressed horizontally to have a period of What is the equation of the new graph

5 The price of a certain brand of phones is normally distributed with a mean of 430 and a standard deviation of 70 What percentage of these phones cost less than 525 Round as needed and explain your answer

3 A data set with a mean of 34 and a standard deviation of 2 5 is normally distributed Part A According to the Empirical Rule about what percentage of the data is between 34 and 39 Part B About what percentage of the data is less than 36 5

5 What are the amplitude and period of y 2 sin x 6 What is the average rate of change of the function y 3 sin 2x on the interval 0 12

4 Keenan scored 80 points on an exam with a mean score of 77 points and a standard deviation of 4 9 points Rachel scored 78 points on an exam with a mean of 75 points and a standard deviation of 3 7 points Part A Find Keenan s z score for his exam and Rachel s z score for hers Part B It is meaningless to compare Keenan s and Rachel s scores directly because they each took a different exam How could you use statistics to compare Keenan s

1 Find the five number summary for each data set Describe whether each data set is skewed left skewed right or symmetrical Data Set A Data Set B 24 31 30 32 23 25 34 32 25 21 22 29 35 33 32 21 22 23 24 25 24 22 25 25

7 What equation is represented by the graph O X

4 Using a two way radio Melissa can talk to anyone within an 8 mile radius of her location Oscar is 30 west of south from Melissa s location What is Oscar s exact location relative to Melissa s location at the greatest distance where they can talk using two way radios West 8 30 8 North South Wo East

7 The equation for f and the graph of g are given How do the period and the amplitude of the functions compare f x 2 cos x g x 21X MA 8 High fides at a beach occur at intervals of 12 hours 25 minutes Yesterday high tide was measured at 5 feet above sea level and low tide was measured at 1 foot above sea level A cosine function models the depth of the water in feet as a function of time in hours What is the amplitude of the cosine function Explain

1 What are the sine and cosine of 12

Solve for x log42 log4 x 3 log49 X 0 3 N solu

The circle graph shows how Ashley s family budgets a total of 75 000 for the year Category Food Clothing Insurance 2250 Utilities 6000 Entertainment 6750 Insurance Clothing 9000 Transportation 5250 Savings 4500 Find the percentage of the total budgeted for each category listed below Taxes 15 750 Percentage 0 0 Food 12 000 Housing 13 500

Solve for x 102x 10 10 24 0 Round to the nearest hundredth if necessary If there is more than one solution separate them with commas x 0 0 0

Write the expression as a single logarithm 4 log log logx 2log y log w

Graph the logarithmic function g x log1 3x Plot two points on the graph of the function and also draw the asymptote Then click on the graph a function butto X

study is done on the population of a certain fish species in a lake Suppose that the population size P 1 after years is given by the following exponent unction P 1 400 0 81 Find the initial population size 1 Does the function represent growth or decay O growth O decay By what percent does the population size change each year

Write the expression as a single logarithm 3 log y 4log z 3log w 00 0 3 X

A principal of 2800 is invested at 6 25 interest compounded annually How much will the investment be worth after 12 years Use the calculator provided and round your answer to the nearest dollar 0 X

Rewrite each equation as requested a Rewrite as an exponential equation lnx 5 b Rewrite as a logarithmic equation e 9 a b 0 Olog In 3 0 0

2 Use the equation below to analytically determine the RMS value of the waveform shown below with amplitude of 3 0 volt and a period of 0 5 sec Hint You can use the symmetry of the waveform to reduce the calculation required 15 points 1 2 x1ms x 13 dt x v 0 3 0 VAMA 0 25 0 25 3 0 Time sec

Assume you have a student loan that you will pay off in 10 years How much will you save in interest if you refinance at the new rate Use the accompanying table of monthly payments on a 1 000 loan Amount of Loan 22 000 Original Rate 12 Click the icon to view a table of monthly payments on a 1 000 loan The total savings in interest will be Round to the nearest cent as needed New Rate 5 H Monthly Payment on a 1 000 loan Annual Interest Rate 4 5 6 8 10 12 3 29 53 29 97 30 42 31 34 32 27 33 21 T Number of Years for the Loan 4 10 20 22 58 10 12 6 06 23 03 10 61 6 60 23 49 11 10 24 41 12 13 25 36 13 22 26 33 14 35 7 16 8 36 9 65 11 01 T E 30 4 77 5 37 6 00 7 34 8 78 10 29 X

Suppose a woman has decided to retire as soon as she has saved 1 000 000 Her plan is to put 900 each month into an ordinary annuity that pays an annual interest rate of 1 8 In how many years will she be able to retire She will be able to retire in approximately years Round to the nearest year as needed

Savings institutions often state a nominal rate which can be thought of as a simple annual interest rate and the effective interest rate which is the actual interest rate earned due to compounding Given the nominal rate it is easy to calculate the effective interest rate as follows Assume that 1 is invested in an account paying an interest rate of 6 compounded monthly n 12 Using the compound interest formula A P 1 r m 0 06 12 1 0617 So the effective interest rate is 1 0617 1 0 0617 or 6 17 Find the effective interest rate for the investments with a nominal yield of 10 compounded daily The effective annual yield is Round to two decimal places as needed with P 1 r 0 06 m 12 and n 12 A 1

In your group review the timeline Come to a consensus on the sequence of events in the history on Earth Compare your timeline to other groups and come to a class wide agreement on a common timeline In your group use your timeline and all of the resources from the unit to a Propose a set of criteria that could be used to find evidence of life or past life on other planets such as Mars b Propose a set of conditions that would need to be met in order for humans to create and set up a colony on Mars Individual Final Reflection ions Individually respond to the following prompts on a separate sheet of paper On your timeline have you placed the atmosphere card that indicates an increase in oxygen before or after the emergence of cyanobacteria Support your choice using your understanding of biology Be Fore need otsen more emergence of Ctan obacteria because Hanobacteris even though atmosphere 1 it cess carbon dioxide On your timeline have you placed the emergence of eukaryotic organisms before or after the s becasse emergence of prokaryotic organisms Support your choice using your understanding of biology tail Band It has no membran Fore rganism Look back at all of the organism event cards which do you consider as alive and which do you Sunnort your choices using your understanding of biology

Suppose Christian stops for coffee a given number of times a week Use the information in the following table to calculate how much Christian would save if he deposited the amount he woul spend on coffee into an ordinary annuity instead Assume there are four weeks in a month Number of Coffees Per Week 8 Price of One Cup 4 45 Christian would have in the annuity Round to the nearest cent as needed Interest Rate for Annuity 2 8 Number of Years 17

According to a certain central bank from 2000 to 2016 the average price of a new home in a certain region increased by 68 to 432 thousand What was the average price of a new home in 2000 The average price of a new home in 2000 was Do not round until the final answer Then round to the nearest thousand as needed www