Functions Questions and Answers

On a test that has a normal distribution a score of 32 falls two standard deviations above the mean and a score of 2 falls three standard deviations below the mean Determine the mean of this test Question 1 5 Points May 31 8 00 06 PM h

Identify the fractions labeled with the letters A and B on the scale below Give your answers as proper or improper fractions 0 A Letter A represents the fraction Letter B represents the fraction B

Find the area of the figure pictured belo 8 yd Area 3 yd 11 yd 72 2 ya Q

The following expression gives an approximate value of the total average credit card debt in a U S household in dollars t years after 1995 399t 5140 Use this expression to predict what the total average credit card debt was or will be in the year 2006 Answer In the year 2006 the total average credit card debt for a U S household will be or was dollars

Use the distributive property to simplify the expression 5 6x 4 2y Answer

Question 10 2 Evaluate 4m x for m 4 x 3

Question 16 Use the distributive property to simplify the expression 9 7x 3y

lestion 12 A small company is creating a new product to sell to buyers They have estimated that it will cost them 15 to produce each item and they will have start up costs of 216000 This leads to the following expression which gives the total cost in dollars to produce q of these new products 15q 216000 Use this expression to predict how much it will cost them to produce 18100 items Answer It will cost them dollar sign or any commas in your answer or it will be marked incorrect dollars to produce 18100 items Do NOT include a

Question 6 Complete the input output table 2n 9 n 1 2 J

Question 9 Evaluate m 3m 4 when m 3

Question 7 Evaluate the expression 9y 8 when y 8 Answer

Question 4 Manuel s age is 3 years less than twice Niko s age If we let y represent Niko s age write an algebraic expression for Manuel s age

Desmond is 3 inches taller than Niki If we let r represent Niki s height in inches write an algebraic expression for Desmond s height

Evaluate the expression 2 NOTE Your answer cannot be an algebraic expressio

Question 12 Subtract the following 10 11 10 11 10 11 10 11 Next Question

John s bank account was overdrawn The status of his account was 228 He did not realize the problem and wrote another check for 44 The bank charged him a 19 fee for being overdrawn What was the new status of John s account at this point

Write the vector v in the form v i V j given Iv and the direction angle 8 of v No work no credit Circle your final answer Ivl 7 0 2T

Given the graph above which statements best describe the graph As yooand as zx y00 There are four x intercepts at x 2 1 1 2 The graph includes two intervals of increasing and two intervals of decreasing The y intercept of the graph is a positive value W N As 0 yand as y x There is an x intercept at x 0 The graph includes three intervals of increasing and two intervals of decreasing The y intercept of the graph is a negative value As to y cand as xx There are four x intercepts at 2 1 1 2 The graph includes two intervals of increasing and no intervals of decreasing The y intercept of the graph is a negative value As r yxand as rx y x There is one x intercept at x 0 The graph includes two intervals of increasing and two intervals of decreasing The y intercept of the graph is a positive value

Is the PTA s raffle a mathematically fair game Why or why not The PTA is holding a raffle to raise money for the elementary school They are selling 500 raffle tickets for 5 00 each They will draw tickets randomly and will be awarding a grand prize of 750 a second prize of 100 and five prizes of 20 Complete the probability distribution table if all tickets are sold and answer the questions that follow Amount of Prize X Probability of Winning P X 750 100 20 0 OYes it is fair because every ticket has an equal chance of being a winner OYes it is fair because the expected value is more than the cost to play OYes it is fair because the expected value is the same as the cost to play O No it is not fair because the expected value is less than the cost to play O No it is not fair because most people win nothing

Solve the inequality 4 x 1 3x 1 Step 1 To solve a linear inequality we will isolate the variable on one side of the inequality 4 x 1 3x 1 4x 3x 1 4x 3x 1 Simplifying we get the following inequality D t

Solve the equation Give an exact answer Do not round 7x 4 1 x 1 21 2 x 14 X 7 X

o q is false and r is false find the A a Vr 50 alue e truth value of p a V rwhen p is true q is false and r is false Choose the correct ans 10 MEETIN

s tv u Fill in the missing values in the table Fill in the blanks below tv u s S U

s t v u Fill in the missing values in the table Fill in the blanks below U tv u st

p is raise p qr DISO False True www lect the truth value of p qr when p is false q is true and r is false Choose the correct answer be

se a truth table to determine whether the P q p s the statement p q p a tautology self contradiction or neither O Self contradiction O Tautology ONeither

2 V 1 or 9v 36 8 1 0 1 2 96 345 6 7 8 9 10 11

POSSIBLE POINTS 1 9 You are going to order a one topping pizza for dinner You can get either thick or thin crust cheese or extra cheese and you have a choice of 9 different toppings How many combinations of pizza can you get O 18 O 36 09 24

Let f be a smooth function and F a smooth vector field both defined on R Which of the following expressions are NOT meaningful Select one or more OVX Vx f V F OV V V OV V x VX F OV Vx V

Let x y z x y 2z Find V 00 Oyi 2rk O zi yj 2zk

5 Renee is saving for a trip to Australia She wants 10 000 in 5 years How much should Renee deposit at the end of each month into an account that pays 6 4 compounded monthly 6 Suppose you make a deposit at the end of each month into an account that pays 7 6 compounded monthly for 7 years The amount at the end of the 7 years is 10 000 How much do you invest Answers 1 a 7153 29 c 9639 51 2 a 929 46 3666 70 3 a 397 29 c 58 98 e 53 12 b 5218 54 d 10 625 56 b 2342 60 d 7215 02 b 530 08 d 189 86 164 47 4 a 103 22 b 624 63 c Monthly option because Matt has to deposit less money 5 141 86

8 0 y hea Iosy 0 sy to to t 4 y 2 Y h 1 Y3 Y

Write the equation given the following polynomial graph 25 2 O f x x 3 x 2 x 1 O f x 2 3 x 2 x 1 O f x 2 3 x 2 x 1 O f x x 3 x 2 x 1

An influenza epidemic spreads at a rate proportional to the product of the number of people infected and the number not yet infected Assume that initially 140 people are infected in a community of 35 000 people and 700 are infected 10 days later a Write an equation for the number of people infected y after t days b When will half the community be infected a Complete the equation below 35 000 Do not round until the final answer Then round to two decimal places as needed

4 Prove that is continuous on 0 Hint Remember the difference of squares formula 5 Let I 2 U 2 and consider the following real valued functions defined on

Students at Lake Mean PE class ran a 5K with a mean run time of 31 minutes and a standard deviation of 4 minutes Approximately finished between 23 and 27 minutes

Students at Arrowhead High School took an English test with a mean of 120 and a standard deviation of 25 Approximately 95 of the IQ scores are between and

A particular solution and a fundamental solution set are given for the nonhomogeneous equation below and its corresponding homogeneous equation a Find a general solution to th nonhomogeneous equation b Find the solution that satisfies the specified initial conditions y 4 4y 5 sinx y 0 1 y 0 0 y 0 0 y 0 1 Yp sin x ex cos x ex sinx ex cos x ex sin x a Find a general solution to the nonhomogeneous equation y x Do not use d D e E i or I as arbitrary constants since these letters already have defined meanings

Which of the following is a definition of the one to one function Select ALL that applies If codomain of the function f equal to the rang of f Of a f b whenever ab for all a b in the domain of f The function is injective and surjective at the same time Of a f b implies that a b for all a b in the domain of f

Let A and B be nonempty sets Function f maps A to B Click on the image of a on the graph below a A f b f a B

The hydraulic cylinder CF which partially controls the position of rod DE has been locked in the position shown Member BD is 15 mm thick and is connected at C to the vertical rod by a 9 mm diameter bolt Knowing that P 2 kN and 75 determine a the average shearing stress in the bo b the bearing stress at C in member BD 100 mm 200 mm 45 mm Fig P1 26 175 mm C 20 8 E

Determine the largest interval a b for which Theorem 1 guarantees the existence of a unique solution on a b to the initial value problem below xy 9y e y x5 7 y 6 1 y 6 0 y 6 2 Type your answer in interval notation

Determine whether the given functions are linearly dependent or linearly independent on the specified interval Justify your decision x 1 2 on 0 00 CEEEH Select the correct choice below and if necessary fill in the answer box to complete your choice OA The functions are linearly dependent because c x c x 1 c3 2 0 has the solution Type integers or simplified fractions OB The functions are linearly independent because c x c x 1 c3 2 0 has no solutions for constants C C and c3 that are not all zero C and c 1 and c3

Sketch the exponential function f x and its inverse function f x Include at least two points the asymptote s and the line of symmetry 1 messy 14 f x y 1 2 X 1 2 4 log 2 x 4 3 X 3 X Y 22 log x 3 6 31 4 1 2 0 X Y 13 12 4 10 S 6 7

A student is researching the use of public transportation in her state She found the pie chart and took notes about it How People Travel to Work bus 12 carpool 13 drive alone 60 Based on the pie chart which note is accurate A More people take a taxi to work than bicycle bicycle 6 taxi 4 walk 3 motorcycle 2 B Walking and biking to work are more popular than driving Other forms of transportation are better than driving alone About the same percentage of people carpool as take a bus to work

ne the following a the function s domain b the function s range c the x intercepts if any d the y intercept if any e the function value indicated below 1 a What is the function s domain Type your answer in interval notation b What is the function s range OA The x intercept s is are Type your answer in interval notation c Enter the x intercept s Select the correct choice below and fill in any answer boxes within your choice 2 A The y intercept is OB There is no y intercept e Find the value of the function Previous question Type an integer Use a comma to separate answers as needed B There is no x intercept d Enter the y intercept e Select the correct choice below and fill in any answer boxes within your choice Type an integer

Si u 3 5 v 4 7 entonces la magnitud de 3 2 es O a O b 1130 290 012 2 O d 2 138

12 Use the graph of g x to answer each question 10 pts 6 5 14 3 Domain O 2 b Evaluate g 3 Increasing Decreasing Constant 1 5 4 2 0 1 2 2 O 3 4 5 a Find the domain and range of g x Write the answers in interval notation 6 d What are the x and y intercepts of the graph 8 Range c On which interval s is the graph increasing decreasing or constant 9 10 11 12 73

he entire graph of f x is given on the right From among the graphs sketched below dentify the graph of f 2x 2 O a

4 points A cylinder filled with water has a single hole at the bottom The rate at which the water level decreases is directly proportional to the square root of the depth of the water in the cylinder At time t 0 th depth is 20 cm and the rate of leakage is 4cm min Write and solve a differential equation that expresses this situation Find the time at which the cylinder becomes empty Round to the nearest tenth of a minute Work