Questions

Differentiate the function y y 4x 9 3 8x 3

Identify the level of measurement of the data and explain what is wrong with the given calculation In a set of data internet speeds are represented as 100 for slow 200 for medium and 300 for fast The average mean of the 798 internet speeds is 231 2 The data are at the level of measurement What is wrong with the given calculation OA The true average mean is 195 4 OB Such data should not be used for calculations such as an average mean OC One must use a different method to compute the average mean of such data OD There is nothing wrong with the given calculation

A student eamed grades of B C A B and D Those courses had these corresponding numbers of credit hours 5 3 3 3 and 1 The grading system assigns quality points to letter as follows A 4 B 3 C 2 D 1 F 0 Compute the grade point average GPA If the dean s list requires a GPA of 3 00 or greater did this student make the dean s list The student s GPA is Type an integer or decimal rounded to two decimal places as needed This student make the dean s list because their GPA is 3 00

c Given the following logical circuit with three inputs A B and C A44 DYDD L Use the boolean algebra notation and write down the boolean expression of the output of this circuit ii Simplify the logical expression in i Explain your answer 4 mar 15 mar

Which of the following is NOT a requirement of the Combinations Rule Cr n rl n r for items that are all different Choose the correct answer below OA That there be n different items available OB That order is taken into account consider rearrangements of the same items to be different sequences OC That order is not taken into account consider rearrangements of the same items to be the same OD That r of the n items are selected without replacement

K On their first date Kelly asks Mike to guess the date of her birth not including the year Complete parts a through c below a What is the probability that Mike will guess correctly Ignore leap years Type an integer or a simplified fraction b Would it be unlikely for him to guess correctly on his first try C OA It is impossible for Mike to guess correctly on his first try as the probability of a correct guess is 0 OB No it is not unlikely for Mike to guess correctly on his first try as the probability of a correct guess is very high OC Yes it is unlikely for Mike to guess correctly on his first try as the probability of a correct guess is very high O D No it is not unlikely for Mike to guess correctly on his first try as the probability of a correct guess is very low OE It is impossible for Mike to not guess correctly on his first try as the probability of a correct guess is 1 OF Yes it is unlikely for Mike to guess correctly on his first try as the probability of a correct guess is very low c If you were Kelly and Mike did guess correctly on his first try would you believe his claim that he made a lucky guess or would you be convinced that he already knew when you wes as the probability of a correct guess is Mike

A group of adult males has foot lengths with a mean of 26 53 cm and a standard deviation of 1 44 cm Use the range rule of thumb for identifying significant values to identify the values that are significantly low or significantly high Is the adult male foot length of 29 7 cm significantly low or significantly high Explain Significantly low values are cm or lower Type an integer or a decimal Do not round Significantly high values are 0 cm or higher Type an integer or a decimal Do not round Select the correct choice below and fill in the answer box es to complete your choice OA The adult male foot length of 29 7 cm is not significant because it is between Type integers or decimals Do not round cm and O B The adult male foot length of 29 7 cm is significantly high because it is greater than Type an integer or a decimal Do not round OC The adult male foot length of 29 7 cm is significantly low because it is less than cm Type an integer or a decimal Do not round cm cm

Brittany s new lunch box is only 5 centimeters in height so it fits in her backpack along with all her books The lunch box has 3 sections for different types of food The length and width of the lunch box are 22 centimeters and 14 centimeters What is the volume of Brittany s new lunch box

Evaluate Be sure to check by differentiating S 2t 9 1 dt Determine a change of variables from t to u Choose the correct answer below OA u t 9 OB u 2t4 9 O c u t OD u 2t 9 Write the integral in terms of u 4 S 214 9 1 dt JA 8 Type an exact answer Use parentheses to clearly denote the argument of each function Evaluate the integral du 18914 S 21 9 1 dt 4 4 Type an exact answer Use parentheses to clearly denote the argument of each function C

POSSIBLE POINTS Solve the equation for x Use the properties of exponents and logarithms as needed to rewrite the equation Round to 2 decimals when necessary logs 44 logs 72 PO Separate answers with a comma Extraneous Solution s Type answer or type none if there are no extraneous solutions

Solve the equation for x Use the properties of exponents and logarithms as needed to rewrite the equation Round to 2 decimals when necessary 16 256 1

U How many binary sequences of length 10 start with a 1 and end with a 200 45022896 1 100003 E 2

d The function is given by f x ln 4x 2 where 2 R and r i Find an expression for x in its simplest form ii State the range of f z iii Solve the equation z 1

1 Given the plot of the function f t in one period determine completely the Euler coefficients and write its Fourier series expansion 3 f 1 1 5 3 3 3

dP If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at 6 9 per year the balance P grows at the rate given by 0 069P dt a Find the function that satisfies the equation Write it in terms of Po and 0 069 b Suppose that 1000 is invested What is the balance after 1 year After 4 years c What is the rate of change of the balance after 1 year After 4 years a P t b The balance after 1 year is The balance after 4 years is Type integers or decimals rounded to two decimal places as needed c The rate of change of the balance after 1 year is Type integers or decimals rounded to two decimal places as needed GILLED The rate of change of the balance after 4 years is V

4xe5x dx Which of the following shows the correct uv 5x 5x OA 4 4x dx 5 OB 5 4x dx O C 4x S x o dx O D 4x5 54 dx 4x25x Evaluate S4x5x 5x dx Sva dx www du formulation Choose the correct answer below

A rabbit farm had 200 rabbits in 2015 The number of rabbits increases by 30 every year In what year would there be 13 308 rabbits You should be able to set up the exponential equation and then solve algebraically DO NOT JUST GUESS AND CHECK

Homework The equation of a line is y 5x 20 1 What is the value of y when x 450 Show all your work 2 Is the ordered pair 3 60 on the line y 5x 20 Show work

Solve the equation for x Write your answer both as an exact solution in log form and as an approximate solution rounded to 3 decimal places 3 12 R log a log b an b Approximate Solution POSSIBLE PO Exact Solution

Simplify arccos tan 3

a List the elements of the following sets i rr Z r 6 ii zx Z r 9 iii zr ENA z mod 2 1 I 10

Determine which functions are solutions of the linear differential equation Select all that apply y y y y 0 X ex e x xe X

Raggs Ltd a clothing firm determines that in order to sell x suits the price per suit must be p 180 0 75x It also determines that the total cost of producing x suits is given by C x 5000 0 5x a Find the total revenue R x b Find the total profit P x c How many suits must the company produce and sell in order to maximize profit d What is the maximum profit e What price per suit must be charged in order to maximize profit a R x b P x c suits d The maximum profit is e The price per unit must be BILB

D Given the following truth table for a four input logic circuit ABCD Out 0000 0 0001 0 0010 0 0011 0 0100 a 0101 0 0110 0 01110 1000 1001 10 10 10 11 1100 1101 1110 1 1 1 1 0 7771000 i Write the sum of products expression for this truth table ii Use the laws of Boolean algebra to reduce this expression to its simplest form iii Translate the truth table into its corresponding Karnauph map iv Minimise the sum of production expression in i using karnauph map 2 ma 2 ma 2 ma 2 ma

The domain of discourse consists of all positive intergers Z What are the truth values for each of the following i Vzy r y ii Vzy x y 0 iii 3zVy r y iv 3z3y ry 0

3 Complete the chart below Assume a one year investment period Return on Investment ROI Net Profit 4 30 25 4 10 4 000 Investment 60 100 10 ROI 100 20 40

10 Let p and q be two propositions Which one of the following logical expressions is equivalent to p g Select all the apply OpVq Opv q

a Re write the following statements without any negations on quantifiers i rP x ii yP x y iii 3rVyP x y

Find the area of the polygon shown on the grid below HINT Break the figure into shapes you can find the area of Use your formula sheet O 10 square units O 15 square units O 21 square units O 27 square units

Find the Wronskian for the set of functions e x e 2x

Given the coordinate matrix of x relative to a nonstandard basis B for R find the coordinate matrix of x relative to the standard basis B 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 2 x s x B 2 1 1 2 1 3 2

a Use the product rule to find the derivative of the given function b Find the derivative by expanding the product first h z 3 2 2 3z 5 a Use the product rule to find the derivative of the given function Select the correct answer below and fill in the answer box es to complete your cho OA The derivative is 3 2 2 3z 5 OB The derivative is 3 z2 OC The derivative is 3 2 3z 5 OD The derivative is 3 2 2 3z 5 O E The derivative is 2 3z 5 b Expand the product 3 2 2 3z 5 Using either approach d SEXIES Simplify your answer 3 2 2 32 5

Let p and q be the following propositions concerning a positive integer n where p means n is divisible by 3 and q means n is even Which one of the following logical expressions is a correct formalisation of the sentence below n isn t neither divisible by 3 nor it is an odd number Choose ONE option 0 p g 0 p q 0 q p 0 p q

Which of the following RECTANGLES has the same area as the triangle given below 13 cm 12 cm 21 cm O an 11cm by 13 cm rectangle O an 18 cm by 7 cm rectangle O a 12 cm by 8 cm rectangle 20 cm

Which one of the following correspond to statement Every comedian is funny where C x is the statement x is comedian and F x is the statement x is funny and the domain consists of all people Choose ONE option Ox C x F x OVx C x F x Ox C x F x Choose ONE option Ox C x F x OVx C x F x Ox C x F x Vx C x F x 3 4 5 6 7 8 9 10

Each year the high school guidance counselors conduct a survey to estimate the proportion of students at the high school who cheat on their homework Based on a random sample of 300 students from the high school a 99 confidence interval for the proportion of all students at the high school who cheat on their homework is 0 052 to 0 192 Name two changes the counselors could make to reduce the margin of error decrease the confidence level AND decrease the sample size increase the confidence level AND increase the sample size O decrease the confidence level AND increase the sample size

Each year the high school guidance counselors conduct a survey to estimate the proportion of students at the high school who cheat on their homework Based on a random sample of 300 students from the high school a 99 confidence interval for the proportion of all students at the high school who cheat on their homework is 0 052 to 0 192 Name two changes the counselors could make to reduce the margin of error decrease the confidence level AND decrease the sample size increase the confidence level AND increase the sample size O decrease the confidence level AND increase the sample size

Differentiate the function G x x4 6x G x

Monica wants to carpet the room shown in the diagram below How many square feet of carpet will she need EXPLAIN your answer and SHOW YOUR WORK HINT Break the figure into shapes you can find the area of Use your formula sheet 24 ft 20 ft 12 ft 12 ft

2 Which of the following functions are one to one Select all that apply Of2 Z Zwith f2 x x4 Of3 RR with f3 x e Ofi Z Zwith fi x x Ofa R Zwith f x

A company determines that its marginal revenue per day is given by R t where R t is the total accumulated revenue in dollars on the fth day The company s marginal cost per day is given by C t where Cit is the total accumulated cost in dollars on the th day R t 130e R 0 0 C t 130 0 3t C O 0 a Find the total profit P T from t 0 tot 10 the first 10 days P T R T C T R C at The total profit is Round to the nearest cent as needed b Find the average daily profit for the first 10 days The average daily profit is Round to the nearest cent as needed GREEN

3 Which one of the following degree sequences cannot represent a simple graph O 1 2 2 3 O2 4 3 3 O 2 2 2 2 O 3 3 3 3

Rico s dad is moving his company to a new office space He finds a potential new space but wants to know how many square meters of space he would have 10 mi How many square meters of office space would he have O 140 square meters O280 square meters O24 square meters 14 m O 70 square meters a

D Write the ratios sinc COS C tan C C 1 A X 25 24 MULTIPLE CHOICE 3 which trig function is best a sin 30 R 29 b cos c tan 2 Write the patios B 17 8 50 X 15 10 u MULTIPLE CHOICE 4 which trig function is best a sin Sin B cos B tan B b cos c tan

5 What is the number of edges in a complete graph K10 O 10 O45 O 90

Michelle is trying to find the area of this triangle but is confused about which number represents the base and which number represents the height 13 cm Select 18 cm Which value represents the base and which value represents the height The base of the triangle is Select Select 13 cm 5 cm 5 cm 18 cm and the height of the triangle is

Which one of the following correspond to statement Every comedian is funny where C x is the statement x is comedian and F x is the statement x is funny and the domain consists of all people Choose ONE option Ox C x F x Vx C x F x Or C x F x

6 In how many ways a committee of 5 members can be selected from 6 men and 5 women consisting of 3 men and 2 women 200 O 180 O 720 None of these options

Each year the high school guidance counselors conduct a survey to estimate the proportion of students at the high school who cheat on their homework Based on a random sample of 300 students from the high school a 99 confidence interval for the proportion of all students at the high school who cheat on their homework is 0 052 to 0 192 Describe how untruthful answers might lead to bias in this survey Does the margin of error account for this possible bias O The margin of error does NOT account for this bias Students may lie and say they don t cheat when they actually do O The margin of error DOES account for this bias Students may lie and say they don t cheat when they actually do O The margin of error does NOT account for this bias Students respond truthfully

Differentiate the function G x x 6x 3 x