Basic Math Questions and Answers

The standard deviation of y t in the preceding problem is closest to which of the following Answer A 0 065 B 0 254 C 0 402 D 0 653 E None of the these

15 points The signal y t is generated by convolving a band limited signal x1 t with another bandlimited signal x2 t that is y t x1 t x2 t Where frequency responses of x1 t and x2 t are expressed as X1 w 0 for lw 1000m and X2 w 0 for w 2000 respectively Impulse train sampling is performed on y t to obtain 00 y t y nT 8 t nT 111 00 Specify the range of values for the sampling period T which ensures that y t is recoverable from y t

Suppose that 2000 is loaned at a rate of 12 5 compounded semiannually Assuming that no payments are made find the amount owed after 10 years Do not round any intermediate computations and round your answer to the nearest cent

Your answer is incorrect Equation c Your answer is incorrect Fill in the missing values to make the equations true a log 5 log 9 log 45 b log 5 log 8 log c log 81 27log 3 in co 8 X

2 At sunset Mercedes observes a series of ocean waves modeled by y 4 2 sin x How do the period and amplitude compare to the function you wrote to represent the sunrise waves Explain

4 Keenan scored 80 points on an exam with a mean score of 77 points and a standard deviation of 4 9 points Rachel scored 78 points on an exam with a mean of 75 points and a standard deviation of 3 7 points Part A Find Keenan s z score for his exam and Rachel s z score for hers Part B It is meaningless to compare Keenan s and Rachel s scores directly because they each took a different exam How could you use statistics to compare Keenan s

1 Find the five number summary for each data set Describe whether each data set is skewed left skewed right or symmetrical Data Set A Data Set B 24 31 30 32 23 25 34 32 25 21 22 29 35 33 32 21 22 23 24 25 24 22 25 25

The circle graph shows how Ashley s family budgets a total of 75 000 for the year Category Food Clothing Insurance 2250 Utilities 6000 Entertainment 6750 Insurance Clothing 9000 Transportation 5250 Savings 4500 Find the percentage of the total budgeted for each category listed below Taxes 15 750 Percentage 0 0 Food 12 000 Housing 13 500

Write the expression as a single logarithm 3 log y 4log z 3log w 00 0 3 X

2 Use the equation below to analytically determine the RMS value of the waveform shown below with amplitude of 3 0 volt and a period of 0 5 sec Hint You can use the symmetry of the waveform to reduce the calculation required 15 points 1 2 x1ms x 13 dt x v 0 3 0 VAMA 0 25 0 25 3 0 Time sec

Assume you have a student loan that you will pay off in 10 years How much will you save in interest if you refinance at the new rate Use the accompanying table of monthly payments on a 1 000 loan Amount of Loan 22 000 Original Rate 12 Click the icon to view a table of monthly payments on a 1 000 loan The total savings in interest will be Round to the nearest cent as needed New Rate 5 H Monthly Payment on a 1 000 loan Annual Interest Rate 4 5 6 8 10 12 3 29 53 29 97 30 42 31 34 32 27 33 21 T Number of Years for the Loan 4 10 20 22 58 10 12 6 06 23 03 10 61 6 60 23 49 11 10 24 41 12 13 25 36 13 22 26 33 14 35 7 16 8 36 9 65 11 01 T E 30 4 77 5 37 6 00 7 34 8 78 10 29 X

Suppose a woman has decided to retire as soon as she has saved 1 000 000 Her plan is to put 900 each month into an ordinary annuity that pays an annual interest rate of 1 8 In how many years will she be able to retire She will be able to retire in approximately years Round to the nearest year as needed

Savings institutions often state a nominal rate which can be thought of as a simple annual interest rate and the effective interest rate which is the actual interest rate earned due to compounding Given the nominal rate it is easy to calculate the effective interest rate as follows Assume that 1 is invested in an account paying an interest rate of 6 compounded monthly n 12 Using the compound interest formula A P 1 r m 0 06 12 1 0617 So the effective interest rate is 1 0617 1 0 0617 or 6 17 Find the effective interest rate for the investments with a nominal yield of 10 compounded daily The effective annual yield is Round to two decimal places as needed with P 1 r 0 06 m 12 and n 12 A 1

In your group review the timeline Come to a consensus on the sequence of events in the history on Earth Compare your timeline to other groups and come to a class wide agreement on a common timeline In your group use your timeline and all of the resources from the unit to a Propose a set of criteria that could be used to find evidence of life or past life on other planets such as Mars b Propose a set of conditions that would need to be met in order for humans to create and set up a colony on Mars Individual Final Reflection ions Individually respond to the following prompts on a separate sheet of paper On your timeline have you placed the atmosphere card that indicates an increase in oxygen before or after the emergence of cyanobacteria Support your choice using your understanding of biology Be Fore need otsen more emergence of Ctan obacteria because Hanobacteris even though atmosphere 1 it cess carbon dioxide On your timeline have you placed the emergence of eukaryotic organisms before or after the s becasse emergence of prokaryotic organisms Support your choice using your understanding of biology tail Band It has no membran Fore rganism Look back at all of the organism event cards which do you consider as alive and which do you Sunnort your choices using your understanding of biology

According to a certain central bank from 2000 to 2016 the average price of a new home in a certain region increased by 68 to 432 thousand What was the average price of a new home in 2000 The average price of a new home in 2000 was Do not round until the final answer Then round to the nearest thousand as needed www

Use the formula for computing future value using compound interest to determine the value of an account at the end of 6 years if a principal amount of 12 000 is deposited in an account at a annual interest rate of 7 and the interest is compounded monthly The amount after 6 years will be Round to the nearest cent as needed

Main plant Marigold Tagetes Other plants also included in lab Vinca Catharanthus roseus Begonia Level of soil per pot Pot 1 5 cm e Pot 2 7 5 cm Pot 3 12 cm Pot 4 15 cm IV Level amount of soil in the different pots DV Amount of leaves on each branch of the plant within each pot Research Question How does the mass of soil affect the amount of leaves on each branch of a marigold plant Constant variables Watered evenly same amount of sunlight same location time span Directions Using the information above please write a few paragraphs answering the questions below in the format of an IB Biology IA Lab report Background The background sets the research question into context need and importance are clear Appropriate and relevant background biology of the entity being investigated is correctly described and explained Background research includes scientific name of organism if relevant Genus species Background research on the manipulated variable supports and explains manipulation of the variable Background research on the responding variable indicates it is a good variable to measure response to manipulation Research into research methods is well described and selected methods are justified

A student borrows 5000 at 15 for 6 months to pay tuition Find the total amount due using simple interest The total amount due after 6 months is

The number 27 is what percent of 180 The number 27 is of 180 Type an integer or a decimal

Perform the elementary row operation 2R R3 R3 on the given matrix Write numbers as integers or simplified fractions 142 2 4 3 321 Resulting matrix 4 1 G

Perform the elementary row operation 4R R R on the given matrix 3 1 4 12 Resulting matrix X

Write a system of linear equations represented by the augmented matrix Give your answer in standard form using the variables x and y The equations in the system should be in the same order as the rows in the given augmented matrix 6 7 4 6 2 System of Equations 0 0

or the diagram below the table gives the total number of blocks y in figure number x What pattern can you use to omplete the table Represent the relationship using words an equation and a graph Figure 1 Figure 2 present the relationship in words Choose the correct answer below A The total number of blocks y is three times the figure number x B The total number of blocks y is two raised to the figure number x c The total number of blocks y is the cube of the figure number x D The total number of blocks y is three raised to the figure number x apresent the relationship using an equation Figure 3 CELES Figure Number Total Blocks Ordere Pair x 1 1 2 8 3 27 M E 1 2 3 4 5 Y 1 8 27 B 16

IN 5 4 3 2 1 N 1 S 77 1 2 3 4 a Find the slope of the above graph SA vali fration syntay

3x124 4x

Given a line passing through 7 18 and 17 7 which of the following is the correct slope of the line 17 7 7 18 Om Om Om Om Om O m 17 7 7 18 m Om 1 7 18 17 7 7 18 17 7 7 18 17 7 17 7 7 18 17 7 7 18 7 18 17 7 Question Help Video M Message instru

Match each slope with the type of line it will produce Slope Type of Line 1 DNE a Horizontal b uphill left to rt c downhill left to rt d Vertical

5 Use the graph on the right At what rate does the airplane descend into the airport Answer to the nearest tenth a Altitude ft 2400 1200 Number of days Descent Altitude 60 1500 80 160 200 0 Time s Band Rental Rates

semicircle is cut out of a rectangular paperboard measuring 20 in long and 16 in wide as shown below What is the perimeter of the paperboard that emains after the semicircle is removed o not round any intermediate computations Round your final answer to the nearest hundredth and be sure to include the correct unit If necessary refer to he list of geometry formulas 16 in 20 in 0 in in in

A company makes storage containers with sheet steel walls The containers are shaped like rectangular prisms as shown below If the company has a total of 912 m of sheet steel available how many storage containers can be made Heef 8 m 2 m 6 m containers X

Great Migration refers to a Ob Oc Od the movement of thousands of African Americans north in search of employme the movement of troops across France the movement of troops across the Atlantic as the United States entered the war the movement of thousands of refugees fleeing the destruction of war

1 If a letter is picked at random from the Venn diagram shown what is the chance that it will be an element of W A X f c b h t u k n B P y i set A ii set B only iii neither set A or set B iv AUB v AnB Give all your answers as a fraction a decimal Co

Cash account balance During the month Bavarian Auto Co received 441 950 in cash and paid out 373 000 in cash a Does this information indicate that Bavarian Auto Co had net income of 68 950 during the month No Net income is the net change in all assets and liabilities from operating revenue and expense transactions b If the balance of the cash account is 99 900 at the end of the month what was the cash balance at the beginning of the mont

Journal entry for fees earned Journalize the entry on October 19 for cash received for services rendered 14 000 If an amount box does not require an entry leave it blank Oct 19 Cash Foor Farme

The mixing department has 51 000 equivalent units of direct materials and 28 000 equivalent units of conversion costs The direct materials cost 40 000 and the conversion costs are 15 000 Assumir no beginning inventory the total cost per equivalent unit is Round any intermediary calculations and your final answer to the nearest cent OA 1 08 OB 1 32 OC 0 78 OD 0 54

This question 1 point s possible A pizza company produces frozen pizzas in three departments assembly freezing and packaging In assembly crust ingredients are added at the beginning of the process After the crust is made the sauce cheese and toppings are added at the end of the process Conversion costs are added evenly Data for the assembly department includes Beginning WIP Inventory Units started Units completed transferred to freezing Ending WIP 65 through assembly Crust ingredients added Cheese added Sauce and toppings added Direct labor Manufacturing Overhead Question 4 of 10 OA 1 14 OB 1 29 OF 0 89 OD 1 25 0 units 28 000 units 22 500 units 5 500 units 34 880 22 000 7 000 24 000 5 830 Submit q

Candle Company has two sequential processing departments Assembly and Shaping The Shaping Department reports the following information Conversion costs are applied evenly through process Beginning WIP Inventory Transferred in costs in beginning WIP Inventory Direct materials costs in beginning WIP Inventory Conversion costs in beginning WIP Inventory Units transferred in Transferred in costs Units completed Costs added materials Costs added conversion Ending WIP Inventory OA WIP Shaping Dr WIP Assembly Cr 744 000 OB WIP Assembly Dr WIP Shaping Cr 744 000 OC WIP Shaping Dr WIP Assembly Cr 646 000 OD WIP Assembly Dr WIP Shaping Cr 646 000 9 000 units 98 000 25 600 23 750 47 000 units 646 000 43 000 155 040 230 710 13 000 units CECA

Angela s bank gave her a 5 year add on interest loan for 6 930 to pay for new equipment for her antiques restoration business The annual interest rate is 6 31 How much interest will she What are her monthly payments She will pay in interest on the loan Round to the nearest cent Her monthly payments are Round to the nearest cent LITE

Use the compound interest formula A P 1 r and the given information to solve for r A 2100 P 1500 t 7 r Round to the nearest hundredth

Often through government supported programs students may obtain bargain interest rates such as 6 or 8 to attend college Frequently payments are not due and interest does not accumulate until the student stops attending college A student has borrowed 57 000 at an annual interest rate of 7 2 Calculate the amount of interest due 4 months after the student must begin payments The interest due is Round to the nearest cent as needed PIXE

Kirby is buying a new gas barbecue grill that has been reduced for an end of summer sale by 20 to 416 What was the original price of the grill The original price of the grill was C

In 36 38 use the graph to solve 36 The fastest speed a table tennis ball has been hit is about 13 07 times as fast as the speed for the fastest swimming What is the speed for the table tennis ball 37 Look for Relationships How fast would 1 5 times the fastest rowing speed be Before you solve tell the number of decimal places in your answer 38 Which activity has a recorded speed about 7 times as fast as the fastest rowing speed Miles per Hour 110 100 90 80 70 60 50 40 30 20 10 0 5 35 Fastest Sporting Speeds 27 79 13 99 95 69 Fastest Fastest Swimming Running Rowing Luge 106 Fastest Fastest Fastest Thrown Baseball Human Activity

Listen The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars Use the information in the figure to answer the question Dollars 3 500 9000 2500 2000 1500 1000 500 No 400 Yes 600 R x 3x C x 1500 Break even Point 750 2250 X 200 800 Binoculars Produced and Sold Is there a profit when 752 binoculars are produced

Listen Given the cost function C x and the revenue function R x find the number of units x that must be sold to break even C x 5000x 18 000 R x 7000x 9 units 11 units 10 units 3 units

5 Fill in the boxes below to complete your answer Use the Show Work feature to provide related calculations and additional reasoning to support your answer

Let a a and b be integers Prove that if a b 1 and a b 1 then aa b 1

If any 3 in a vector space V is a linear combination of vectors a An prove that dim V n

2 2 In Applied Life Data Analysis Wiley 1982 Wayne Nelson presents the breakdown time of an insulating fluid between electrodes at 34 kV The times in minutes are as fol lows 0 19 0 78 0 96 1 31 2 78 3 16 4 15 4 67 4 85 6 50 7 35 8 01 8 27 12 06 31 75 32 52 33 91 36 71 and 72 89 Calculate the sample average and sample standard deviation Construct a dot diagram of the data recogniz The data 50 77 3 sample s 2 6 P tures is a study to

Use the value of the ratio to fill in the following two multiplicative comparison statement a The number of pancakes made is 1 5 b The amount of cups of flour needed is times the amount of cups of flour need of the number of pancakes made If Alyssa has to make 70 pancakes how many cups of flour will she have to use

2 14 The shear strengths of 100 spot welds in a titanium alloy follow Construct a stem and leaf diagram for the weld strength data and comment on any important features that you notice 5408 5431 5475 5442 5376 5388 5459 5422 5416 5435 5420 5429 5401 5446 5487 5416 5382 5357 5388 5457 5407 5469 5416 5377 5454 5375 5409 5459 5445 5429 5463 5408 5481 5453 5422 5354 5421 5406 5444 5466 5399 5391 5477 5447 5329 5473 5423 5441 5412 5384 5445 5436 5454 5453 5428 5418 5465 5427 5421 5396 5381 5425 5388 5388 5378 5481 5387 5440 5482 5406 5401 5411 5399 5431 5440 5413 5406 5342 5452 5420 5458 5485 5431 5416 5431 5390 5399 5435 5387 5462 5383 5401 5407 5385 5440 5422 5448 5366 5430 5418