Logarithms Questions and Answers

The discrete time system y n ex n 2 is O 1 None of the answers O 2 None linear and causal O 3 None linear and none causal O 4 Linear and none causal O 5 Linear and time invariant

In the following problem check that it is appropriate to use the normal approximation to the binomial Then use the normal distribution to estimate the requested probabilities It is known that 77 of all new products introduced in grocery stores fail are taken off the market within 2 years If a grocer store chain introduces 61 new products find the following probabilities Round your answers to four decimal places LUSE SALT a within 2 years 47 or more fail b within 2 years 58 or fewer fail c within 2 years 15 or more succeed d within 2 years fewer than 10 succeed

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood Assume that x has a distributi that is approximately normal with mean 7 600 and estimated standard deviation 1 700 A test result of x 3 500 is an indication of leukopenia This indicates bone marrow depression that may be the result of a viral infection LUSE SALT a What is the probability that on a single test x is less than 3 500 Round your answer to four decimal places b Suppose a doctor uses the average x for two tests taken about a week apart What can we say about the probability distribution of x The probability distribution of x is approximately normal with The probability distribution of x is not normal The probability distribution of x is approximately normal with 7600 and The probability distribution of x is approximately normal with 7600 and What is the probability of x 3 500 Round your answer to four decimal places 7600 and 850 1700 1202 0815 c Repeat part b for n 3 tests taken a week apart Round your answer to four decimal places

Expand fully log 6 O log x 7 O 6 7 log a 5 7 x6y 5 24 4 log y log z 7 5 log y 7 4 7 log z

Solve for x Leave the answer as a reduced fraction log 9 log 5x 6 2 X

Choose the correct exponential form for the following logarithms a log 5125 3 O 35 125 O 5 125 O 125 35

4 State the equation of the line y 8x after it undergoes reflection in the x axis followed by a translation up 6 units 2C

The population of a small mining town was 13 700 in 2000 Each year the population decreases by an average of 5 a Explain why the situation described is an example of exponential decay b Write an exponential function that models this situation Explain each part of the equation c Use your equation to estimate when the population will drop below 5000

Insert the missing parentheses into each of the following formulae NOTE Click here for info on typing symbols and formulae in activities Question 19

STRUCTURE Consider the function f x x 3 2 and the function g x shown in the graph a Determine which function has the greater maximum value Explain your reasoning b Compare the domains of the two functions c Compare the average rates of change of the two functions over the interval 6 13 BRH2D8642 18 16 14 12 10 0 52 6 glx 2 4 6 8 10 12 14 16 18

Clay Harden borrowed 29 000 from a bank at an interest rate of 11 compounded monthly The loan will be repaid in 36 equal monthly installments over three years Immediately after his 22th payment Clay desires to pay the remainder of the loan in a single payment Compute the total amount he must pay The total amount Clay must pay immediately after his 22th payment will be Round to the nearest dollar

The braking distance for a certain type of vehicle at various speeds is shown in the following table Speed miles per hour Braking distance feet 30 75 4 60 302 2 a Use the information in the table to compute the marginal change in feet per mile per hour Round your answer to decimal place feet per mile per hour b As this vehicle s speed increases by 10 miles per hour what happens to the braking distance Round your answer to nearest whole number The braking distance increases by feet for every 10 miles per hour increase in speed

3 Harry walked 2 km each day for 3 days His wife Marta walked 3 km each day for 5 days 8 How much further did Marta walk Answer in lowest terms Show all work NO DECIMALS

X M 5a 86 98 182 P lb 140 R la 54 L 8 X 102 0a 98 10b L M 88 5b 2a 84 R

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Date 5 4 51 737 50 If you deposit 700 into an account paying 12 interest compounded continuously how many years will if take for the original investment to triple Round your answer to the nearest tenth of a year 5 9 If you deposit 450 into an account paying 17 interest compounded quarterly how 112 7 1 11 9

Select the greater fraction from the following 27 6 Question 8 of 8 30 7

Read the following sentence which contains grammatical errors The puppies one was brown and one was grey yelped happily when Bonnie came into the room Which revision best corrects the sentence Select one O The puppies one was brown and one was grey yelped happily when Bonnie came into the room The puppies one was brown and one was grey yelped happily when Bonnie came into the room O The puppies one was brown and one was grey yelped happily when Bonnie came into the room The puppies one was brown and one was grey yelped happily when Bonnie came into the room

Read the following sentence which contains grammatical errors Alexander finally answered after taking a few seconds to think that he did not want to go to the game Which revision best corrects the sentence Select one O Alexander finally answered after taking a few seconds to think that he did not want to go to the game Alexander finally answered after taking a few seconds to think that he did not want to go to the game Alexander finally answered after taking a few seconds to think that he did not want to go to the game Alexander finally answered after taking a few seconds to think that he did not want to go to the game

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or continuous the number of stars a movie receives from critics where 1 star represents poor and 5 stars represents an epic Choose the smallest set of numbers to represent the possible values O integers irrational numbers natural numbers Orational numbers real numbers whole numbers Are the values continuous or discrete continuous Odiscrete

A certain radioactive substance decays by 3 7 each year Find the half life of the substance to 2 decimal places

lot the number 0 00046 on the log scale below 105 104 103 102 101 100 101 10 10 104 105

The number line below shows a value on a log scale 5 3 2 1 0 What is the value of the point X log x

A house was valued at 105 000 in the year 1991 The value appreciated to 170 000 by the year 2005 A What was the annual growth rate between 1991 and 2005 Round the growth rate to 4 decimal places T B What is the correct answer to part A written in percentage form 96 T C Assume that the house value continues to grow by the same percentage What will the value equal in the year 2008 value S Round to the nearest thousand dollars

c Solve the following logarithmic equation 2log log 6x 1 Show your work

1 Determine whether each of the following sentences is an atomic statement a compound statement or not a statement at all i I am in the mood for sushi ii This sentence is false iii If I go swimming today then I will not go running 2 Assume that the given compound statement is true Determine the truth value of each propositional variable i p q ii p q p 3 Let A a b c and B c d Compute each of the following i A B ii P A B

7 Solve the following equations State exact answers a 5 pts log x log x 2 3 b 5 pts 4x 23x 5

6 Given y 9 sin 8x 7 6 determine a 4 pts the amplitude b 4 pts the period 4 pts the phase shift and direction

1 6 pts Find all solutions to 2 cos x 2 0 on the interval 0 x 2 Don t forget to show your work Give exact solutions

Graph the equation y 5 4 3 2 1 2 1 4 3 1 2 3 4 1 3 5 I 2 1 2 3 A LO

14 Building an Emergency Fund You are working two part time jobs Working at the local library pays 15 per hour and working as a personal trainer pays 20 per hour Last week you made 750 and worked 45 total hours 1 Write a system of equations to represent the scenario Remember to define your variables 2 Solve the system to find out how many hours you worked at each job Solve 3 You want to build an emergency fund of 10 000 You have 0 in savings currently If you make the same 750 each week and apply the 50 30 20 rule how much do you save each week 4 How many weeks until you have reached your goal of saving 10 000

Cash flows from used for operating activities indirect method The net income reported on the income statement for the current year was 106 800 Depreciation recorded on store equipment for the year amounted to 41 700 Balances of the current asset and current liability accounts at the beginning and end of the year are as follows Cash Accounts receivable net 19 700 54 000 52 000 6 000 18 500 6 400 a Prepare the Cash flows from used for operating activities section of the statement of cash flows using the indirect method Use the minus sign to indicate cash outflows cash payments decreases in cash or any negative adjustments Statement of Cash Flows partial Inventories Prepaid expenses Accounts payable merchandise creditors Wages payable End of Year Beginning of Year 24 100 65 000 47 200 3 250 23 400 4 700 Line Item Description Cash flows from used for operating activities Net income Adjustments to reconcile net income to net cash flows from used for operating activities Depreciation Changes in current operating assets and liabilities Increase in accounts receivable Decrease in inventories Decrease in prepaid expenses Increase in accounts payable Decrease in wages payable Amount 106 800 41 700 1 100 X 4 800 2 750 X Amount

Answer the question about the following quote from a news source The unemployment rate has risen more than a percentage point to 8 6 in February from 7 1 last November What is the relative change in the unemployment rate expressed as a percenta The unemployment rate has risen Type an integer or decimal rounded to the nearest tenth as needed

K Verify the identity secx secx sin x cos x Choose the sequence of steps below that verifies the identity O A OB O C O D 1 secx 1 sin x cos x cos x cos 2x secx secx sin x secx secx sin x secx 1 sin x secx secx sin x secx sin x 1 secx secx sin x 1 sin x cos x 1 cOS X 1 COS X cos x COS X cos x cos x

Solve the equation logg x 2 logg x 8 3 O 11 1 1 11 12

Solve the exponential equation Express the solution set in terms of natural logarithms 2 6 3 In 2 O I 6 In 3 O I2 In 6 In In 3 In 3 In 2 6 O In 3 In 2 In 6

Change the exponential statement to an equivalent statement involving a logarithm 1 9 a 01 9 log2a 01 9 log 2 02 loga1 9

XX Simplify your answer Type an integer or decimal rounded to four decimal places as needed

Solve the given equation log 5x 1 log x 2 1 X Type an integer or a decimal Round to two decimal places as needed Use a comma to separate answers as need

Use logarithms to solve the equation symbolically Inx Inx 3 X Round to the nearest thousandth

If x varies directly as y and x 8 when y 4 find x when y 6 X

6 The short run aggregate supply curve would shift to the left for all the following reasons EXCEPT A a decrease in productivity B an increase in nominal wages C an increase in interest rates D an increase in the price of commodities used for production

9 A positive demand shock will result from a sudden increase in nominal wages A B C D an increase in the potential GDP a move by the Federal Reserve to lower the interest rate consumers and firms becoming more pessimistic about the future

7 In the long run nominal wages are A sticky downward but flexible in an upward direction B sticky upward but flexible in a downward direction sticky in both an upward and downward direction flexible because contracts and informal agreements are renegotiated in the log C D run

K Solve for x 10 5 9 X Round to five decimal places as needed

Show that the Bell state y 1 2 100 111 is an entangled s

Show that the Bell state y 1 2 100 111 is an entangled s

Assume two satellites A B are in the same orbital plane Compute the in plane satellite positions XA YA for A and XB YB for satellite B given rA is 26 705 km and rp is 27 512 km and the true anomaly fA B 22 8 and fB 95 30 respectively Compute the coordinate YB O 30687 251 km 7645 897 km 27394 378 km

A certain radioactive isotope has a half life of 3 62 minutes If we initially have 384 grams of this substance how many half lives will remain Your answer should be a whole number pass help numbers Part 2 What length of time is needed for this decay process to occur Round your answer to the nearest tenth help numbers minutes until 6 grams

nts 0 of 1 In 2022 the country will have a population of million Round to the nearest integer as needed Sa The population and the growth rate as of 2013 for a country are shown below Assume that the growth rate remains the same from year to year Determine the size of the population in 2022 Population in 2013 155 million growth rate 0 698