Algebra Questions

when x 2 and y 3 2x 12y

3 Calculate the requested measures in parts a through f for bonds A and B assume that each bond pays interest semiannually Coupon Yield to maturity Maturity years Par Price Bond A Bond B 9 8 8 8 2 5 1000 00 1000 00 1000 00 1004 055 a What is the price value of a basis point for bonds A and B b Compute the Macaulay durations for the two bonds c Compute the modified duration for the two bonds d Compute the approximate duration for bonds A and B using the shortcut formula by changing yields by 20 basis points and compare your answers with those calculated in part c e Compute the convexity measure for both bonds A and B f Compute the approximate convexity measure for bonds A and B using the shortcut formula by changing yields by 20 basis points and compare your answers to the convexity measure calculated in part e

The polynomial function f has exactly one positive zero Approximate the zero correct to two decimal places 3 f x 2x 16x 5x 8x 3 The positive zero of f is approximately Round to two decimal places as needed

Find bounds on the real zeros of the polynomial function f x x 3x 4 The lower bound is and the upper bound is IC

One solution of the equation x 12x 21x 2 0 is 2 Find the sum of the remaining solution Dil

3 Find k such that f x x kx kx 8 has the factor x 4 Simplify

Click here to watch the video 4 3 List the real zeros of f x x x 2x 4x 8 4 3 2 The real zeros of f x x x 2x 4x 8 are Use a comma to separate answers as needed

Use the rational zeros theorem to list the potential rational zeros of the polynomial function Do not attempt to find the zeros 7 5 4 f x 2x x 2x 20 Find the potential rational zeros Choose the correct answer below OA 1 1 2 2 4 4 5 5 20 20 1 1 2 2 OB 1 1 2 2 4 4 5 5 10 10 20 20 OD 1 1 2 2 4 4 5 5 20 20 O C 1 1 2 2 4 4 5 5 10 10 20 20 1 1 2 2 1 1 20 20 1 1 2 2 1 IN NG 1 5 5 2 2 2 2 3 5 NIG 2 21 I 1 1 1 20 20 1 20 20

Determine which statement matches each inequality x 10 x 10 x 10 Literal Inequalities Review 10 a Carrie can own up to 10 fish b Carrie must work at least 10 hours c Carrie gets a discount until she is 10 years old d Carrie is working to earn more than 10

List the potential rational zeros of the polynomial function Do not attempt to find the zeros 4 3 2 f x 2x 7x x x 1 Choose the answer below that lists the potential rational zeros O A 1 1 11 1 1 2 2 7 7 1 1 11 OB 1 1 2 2 7 7 22 77 1 1 2 2 20 1 1 2 2 O C 1 1

5 Given f x 9x5 6x 7x 5 how many sign changes are there in the coefficients of f x Choose the correct answer below O 2

Solve the system of equations by graphing 2x 8y 50 x y 13 3 2 2 3 1 2 2 1

2 9 Solve x 6 x 4 Step by Step Solution Step 1 Determine the domain of the variable in the rational equation

3 Sketch the graph of this line Label at least two points on each line 3 y x 1 A

The diagram shows a simplified distance time graph model of Jordan s and Clark s performances in a 200 m race Jordan allowed Clark an advantage of a certain distance a b c 200 Distance m Clark Jordan 10 Time s 20 30 What was the advantage in terms of distance given to Clark Find Jordan s speed in the race When and where did Jordan overtake Clark d Who won the race How much faster in seconds was the winner

69

2 37 The angle between the lines 2x 3y Z and 6x y 4z is theta Then value of os theta n 4 is

If f x 10 18x and g x 11 1 2 3 for what values of x is g x f x

6 3 8 6 6 18 11 Type integers or decimals

Problem 5 1 2 points Give an orthonormal basis of R using the Gram Schmidt algorithm starting from the linearly independent family v1 V2 V3 where v 2 1 2 v2 0 3 3 and V3 0 0 1

Given use the reduced row echelon form above to solve the system f necessary parametrize your answer using the free variables of the system 1 8 0 0 1 1 1 2 ON 0 0 0 x 2z x y 2z 1 0 2 2 0 1 4 5 00 0 0 0 2

Find the indicated root or state that the expression is not a real number 4 81

on 3 of 13 Macmillan Learning Convert an angle of degree measure 20 to radian measure Give an exact answer Use symbolic notation and fractions where needed 20

4 1 Score 2 53 2 16 answered Question 12 Quectic Assuming the function f is one to one and f 6 8 find f 8 f 8

Score 2 53 2 16 answered O Question 15 Y Find f for the function f f x 6x 3 AD f x What is the domain of f x Answer in interval notation Hint Look at the range of f x

Score 0 53 0 16 answered Question 5 Given f x 7 4x and g x 2 I find the following a fog x b Domain of fog x in interval notation c gof x d Domain of gof z in interval notation A 2 e

4 1 Score 2 53 2 16 answered Question 16 For the following exercise find f x for the function f x I x 5 f x Question Help R

Score 2 53 2 16 answered Question 14 Find the inverse of the given function f x 4x5 2 Question Help Video Post to forum

Question 4 e Given f x swered 2 a fog x b the domain of fog x in interval notation c gof x d the domain of gof x and g x x 2 find the following 2

Score 2 53 2 16 answered Question 9 For the following exercises use the graph of f shown below 103 78 43 Solve f x 5 40 0 5 J 6 16 6 7 2 8

4 1 Score 2 53 2 16 answered Question 8 For the following exercises use the graph of f shown below 10 9 8 7 6 54 3 2 1 Find f 2 10 9 8 7 6 3 2 5 4 2 23 3 4 SA 8 5 6 10 7 2 3 6 7 8 9 10

Question 3 For the following exercise use each pair of functions to find f g x and g f x Simplify your answers 1 x 2 f g x 6 g x 2 x g f x Question Help VIDEO Written Example Post to forum

1 Write the recursive formula for the following sequence 3 2 7 12 17 4 Write the explicit equation for the following sequence U 3 U Un 1 2 n22 7 Write the explicit equation for the following sequence 3 2 7 12 17 2 Write the explicit equation that represents the sequence for any whole number n 4 12 36 108 5 Write the explicit equation defined by the following sequence U 800 Un Un 1 0 26 n21 8 Write the recursive routine for the following sequence 4 12 36 108 3 Write a recursive formula represented by the equation y 4x 10 6 Write a recursive formula represented by the equation y 2 5x 9 Write a recursive formula represented by the equation y 3 1 2

A large chess tournament starts with 1024 players After each round half of the players are eliminated Part A Write an equation that represents the number of players P that remain after r rounds and explain how you determined your answer Part B How many players will there be remaining after 6 rounds

A grocery store was introducing a new product by setting up a display for people to try the product Between 2 00 pm and 3 00 pm 11 people tried the product Out of those 11 people 1 said they did not like it 5 said they were undec and 5 said that they liked it The store manager said that this survey was biased but the store owner thought that the survey is not biased What is true about the survey O A B D It is not biased because 5 times as many people like the product compared to those who do not It is not biased because the people who tried the product chose to participate in the survey It is biased because only 11 people tried the product It is biased because almost half of the people said that they were undecided about the product

Researchers are conducting a study to test the effectiveness of a new medication Subjects are randomly divided into two groups the first group is given the medication and the second group is given a placebo Researchers observe the subjects for two months after which subjects are asked to answer a questionnaire about their response to the drug and any potential side effects that they may have had This is an example of A an experiment B C D a sample survey an observational study a random phenomenon

A peer reviewed medical journal publishes a report on the results of a clinical trial for a new drug It reports that the clinical trial had 1 042 participants who were given either the drug or a placebo Based on the data the journal reports tha there was no statistical significance in the difference between the effects of the drug and of the placebo Select the true statement regarding this report A No conclusions were made regarding the results of the clinical trial The results of the trial are still valid even though there was no statistical significance The clinical trials methodology was flawed which is why there was no statistical significance No statistical significance indicates that the results of the clinical trial were not medically important 00 B C D

A student was finding solutions to the equation 4 x 5 0 and wrote down these steps Step 1 x 5 4 2 Step 2 x 5 4 Step 3 x 5 16 Step 4 x 11 Which statement is an accurate interpretation of the student s work A B C D The student found the correct solution to the original equation x 11 x 11 is a solution to the equation in Step 2 but not to the original equation The student made an error in Step 3 The student made an error in Step 1

A population characteristic is normally distributed Approximately what percentage of the population lies within two standard deviations of the mean A 48 B 68

Solve Simplify your answer log x 1 T L N K K

Which of these represents the value of log 200 rounded to the nearest hundredt A B C D 2 30 3 29 20 00 40 00

Which answer is a value for x if 2 log 37 A 8 OOC B C O 9 32 64

Maggie claims that the function g x Which statement provides a correct analysis of Maggie s claim A B C D 4 is the inverse of the function of f x 3x 4 Maggie s claim is correct because if you add 4 to g x and then multiply it by 3 you get f x Maggie s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when f x is substituted into every occurrence of x in g x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 8 therefore g x is not the inverse of f x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

Simplify A B C y x y x y ri 2

Which function is the inverse of f x x 3 g x x 3 A B Oc O D g x x 2 g x x 3 g x x 2

Which graph represents the function f x 2 3 A B 0 2 0 3 0 4

What is the value of 16 O O O A B C D 2 4 8 32

Which expression OOC A B C D is equal to 9x 15 6x 15 9x 9 15 9 15m

Given 2 64 Which of the following expressions is the value of x O A log 64 log64 2 64 O O C B

Solve for x logg 4 x A B O C 2 3 3 2 C 32 096