Algebra Questions

a Which expression below is equivalent to 30 2x 5 50 2x 5 b 3x 3x 2 5 7x 1 0 2x 7 x 1 d 20x 2x 3 5 10 Combine like terms in the expression below x3 2x 4x 2x

8 Find the difference of 3x 10 and 4x 4

Find the difference of 3x 10 and 4x 4

6 Find the sum of 3x 4x and 2x 2x Which of the following expressions is equivalent to 3

3 Which expression below is equivalent to x 4x a 2x 7x 14 b x 7x 14 c 21x d 23x 10 x 3x 47 4 Combine like torms in the expression below 2 x 2x 4 4x 3x 2

4 Combine like terms in the expression below x 2x 4 4x 3x 2

2 Combine like torms to simplify the expression below x 2x 6 2 3x 4 3 Which expression below is equivalent to 4 10 a 2 7x 14 b 8 7 14 6 21

Change the exponential statement to an equivalent statement involving a logarithm ex 17

2 Combine like terms to simplify the expression below x 2x 6 2x 3x 4

Use the given function f to answer parts a through f below f x In x 6 1 f Graph f Choose the correct graph below O A Q G B 10 10 K7 10

Use the given function f to answer parts a through f below X 4 f x 3 2 b Choose the correct graph of f below O A 10 B 10 57 C 10 D

Graph the following function Based on the graph state the domain and the range and find any intercepts f x X In if 0 x 8 if x 8 x Q E

Use the given function f to answer parts a through f below f x In x 6 b Graph f Choose the correct graph below O A 10 B www Q K X 10

Change the logarithmic statement to an equivalent statement involving an exp In 11 x

Find the exact value of the logarithm without using a calculator In Ve

Find the exact value of the logarithm without using a calcu log 12144

Change the exponential statement to an equivalent statement involving a logarit ex 19

Solve the equation log 4256 2x 2 Change the given logarithmic equation to exponential otic Do implif 1

Use a calculator to evaluate the expression 10 In 1 9 In 20

9 7 99x 119x 76x 96 11x 12 A 9r 1 6 2 11x 12 3 11x 12 B 91 x 8 C 9x x 8 D 9x x 7 2 11x 12 9 21 154p 104p 172p 2 14p A 11p 9p 12 B 11p 7p 10 C 11p 6p 8 D 11p 9p 11 2 1 7p 5 2 14p 1 2 14p 1 2 14p 88 12 153 48 45 12v 9 A 12v 8 3 B v 12v 4 10 C 12v 7 D y 12v 5 10 224x 49 90 14x 14x 7 8 14x 7 1 2x 1 4 A 4 14 B 4x 15 4 3 4v 3 2 3 4v 3 1 4v 3 C x 4x 11 D x 4x 13 14x 7 10 14x 7

The table gives the values of a function obtained from an experiment Use them to estimate 3 4 5 6 7 8 9 f x 3 5 2 1 0 6 0 3 0 9 1 4 1 8 fro f x dx using three equal subintervals with right endpoints X a Estimate R3 If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than greater than one cannot say S F X f x dx using three equal subintervals with left endpoints b Estimate L3 If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than Ogreater than one cannot say 1 x f x dx using three equal subintervals with right endpoints left endpoints and midpoints c Estimate M3 x f x dx using three equal subintervals with midpoints If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than greater than

11 2 3 2 5

12 4 3 1 2V

Suppose a sample of O rings was obtained and the wall thickness in inches of each was recorded Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed Click here to view the table of critical values for normal probability plots Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table ALLER Using the correlation coefficient of the normal probability plot is it reasonable to conclude that the population is normally distributed Select the correct choice below and fill in the answer boxes within your choice Round to three decimal places as needed Save OC No The correlation between the expected z scores and the observed data critical value Therefore it is reasonableto conclude that the data come from 0 190 0 192 0 192 0 197 0 206 0 221 0 232 0 235 0 254 0 266 0 283 0 291 0 302 0 311 0 307 0 318 OA Yes The correlation between the expected z scores and the observed data Therefore it is reasonableto conclude that the data come from a normal population OB No The correlation between the expected z scores and the observed data critical value Therefore it is not reasonableto conclude that the data come from a normal population does not exceedthe D Yes The correlation between the expected z scores and the observed data Therefore it is not reasonableto conclude that the data como exceedsthe critical value a normal population does not exceedthe exceedsthe critical value

10 3 2 0 Find the exact value of tan Given sin0 A 41 41 B 41 C 41 41 D 41 41 21 and 0 they lost a bet it was their friendship anniversary they had nothing better to do they wanted to do something fun

i want to calculate theta 3 and theta 4 please 0 712 Cos 3 Cos 04

Exercise 27 5 Let f A B be an injective function and let S be an arbitrar subset of A a Prove that fls SB is injective b Prove that f is a bijection

For each of the following you must show all work in setting up and solving a quadratic equation and clearly state the answer to the given question Please note that trial and error or successive guessing is not awarded marks 1 The area of a rectangular field is 3400m The field is enclosed by 236m of fencing What are the dimensions of the field 5 marks

Find a singular value decomposition A PDQT where A 0 88 Enter the matrices P D and QT below Any empty entries are assumed to be 0 P 1 QT 1 1

Suppose 1 2 lies on the terminal side of angle x when is drawn in standard position Find the following sin 2x cos 2x In which quadrant does the terminal side of angle 2x lie Answer 1 2 3 or 4 2

Solve the equation over the interval 0 2x then support your solutions graphically 2 cos 2x 2 cos x 0 Select the correct choice below and if necessary fill in the answer box to complete your choice O A 2 4x The solution set is 0 33 Use a comma to separate answers as needed Type exact answers using a as needed OB The solution is the empty set

Numbered disks are placed in a box and one disk is selected at random If there are 6 red disks numbered 1 through 6 and 2 yellow disks numbered 7 through 8 find the probability of selecting a red disk given that an odd numbered disk is selected 34 1 1 30 00

Write short answers Consider the inverse tangent function defined by y tan x or y arctan x Complete parts a d a What is its domain 0 00 Type your answer in interval notation Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression b What is its range T 2 2 Type your answer in interval notation Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression c Is this function increasing or decreasing CLE increasing decreasing d Is there any real number x for which arctan x is not defined If so what is it or what are they Yes No Use a comma to separate answers as needed

Solve for exact solutions over the interval 0 2 cos2x 3 2 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Use a comma to separate answers as neede OB The solution set is

For what value of k will both O A 2 B 0 O C 1 2 O D 1 n 1 n 1 2k and n k n converge

The table shows the number of employed and unemployed workers in the U S In thousands in 2000 Male 67 761 2433 Female 58 655 2285 Total 126416 4718 Employed Unemployed Total 70194 60940 131134 Assume that one person will be randomly selected from the group described in the table Find the probability of selecting a person who is employed given that the person is male 67761 70194 2433 67761 2433 70194

O You are dealt one card from a standard 52 card deck Find the probability of being dealt a picture card 3 13 1 S 3 52 3 26

You are dealt one card from a 52 card deck Find the probability that you are not dealt a 4 09 10 12 13 1 10

You randomly select one card from a 52 card deck Find the probability of selecting a black ten or a black queen 1 26 12 1 13 13

A die is rolled The set of equally likely outcomes is 1 2 3 4 5 6 Find the probability of getting a 6 1 Listen 0 6 6

A single six sided die is rolled twice The 36 equally likely outcomes are shown below Find the probability of getting two numbers whose sum is 5 Second Roll First Roll OOOHH 1 1 12 3 1 6 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 2 1 36 4 1 9

Suppose that you earned a bachelor s degree and now you re teaching middle school The school district offers teachers the opportunity to take a year off to earn a master s degree To achieve this goal you deposit 1500 at the end of every three months in an account that pays 6 5 compounded quarterly Value of Annuity A P 1 T 11 n ext 1 a How much will you have saved at the end of 6 years b Find the interest a 31 617 b 4383 a 135 910 b 99 910 a 43 602 b 7602 a 41 429 b 5429

Which of the following are possible rational roots for the given polynomial f x x 8x x 146x 15 146 3 2 15 2 1 3 3 73 8 U 4 5 8 000 5 15 0 1 POSSIBLE POINTS 73 146 4

Find the orders of all the nonzero elements of GF 3 x 2x 2

Find the mean for the data items in the given frequency distribution Round to the nearest tenth if necessary Score x 1 2 3 4 5 6 7 8 9 10 5 5 7 4 6 2 06 7 Frequency f 5 2 1 6 7 10 9 12 11 11

K Question 5 6 2 11 Use the unit circle shown here to solve the trigonometric equation Solve over 0 360 2 2 sin 8 HW Score 0 0 of 15 points O Points 0 of 1 4 1 0 180 The solution set is Do not include the degree symbol in your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed 150 210 120 LAS 270

Find all of the real solutions to the following equation Write your answers in order from least to greatest 5x x 4x X X X

Use the given display to find the median Round to the nearest tenth if necessary Frequency Listen 20 10 5 4 N 21 7 201 10 20 30 40 50 Score

Solve the equation for all exact solutions where appropriate Round approximate answers in degrees to the nearest tenth Write answers using the least possible nonnegati csc 0 1 0 Choose the correct answer below O A 270 360 n 315 360 n where n is any integer O B 270 360 n where n is any integer OC 270 180 n where n is any integer OD 270 180 n 315 180 n where n is any integer

Use the given display to find the mean Round to the nearest tenth if necessary A 10 11 12 13 14 15 Score Frequency 13 5 4 12 5 12 6 12 4