Math - Others Questions

Determine if the following equation is linear If the equation is linear convert it to standard form ax by c 9x 4 y x 5 Answer Keybo Selecting an option will enable input for any required text boxes If the selected option does not have any associated text boxes then no further input is requir Standard Form I O Linear O Not Linear

Consider the following equation Step 1 of 2 Find the x and y intercepts if possible Answer 6y 2x 12 Selecting a button will replace the entered answer value s with the button value If the button is not selected the entered answer is used x intercept y intercept absent Dabsent

Union and intersection of finite sets Sets A and I are defined as follows A 1 4 5 I 2 1 0 3 4 8 Answer each part below Write your answer in roster form or as a Find the intersection of A and I AnI 0 b Find the union of A and I AUI 0 www X 010 8 0 0 0 5

Ratios 3 ft 1 yd 32 5 laps 1 As part of an annual fundraiser to help raise money for diabetes research Heather joined a bikeathon The track she biked on was 1408 yd long Heather biked 32 5 laps Her sponsors agreed to donate an amount of money for each mile she biked How many miles did she bike First fill in the blanks on the left side of the equation using three of the ratios shown Then write your answer on the right side of the equation X 1 yd 3 ft 5280 1408 yd 1 lap 1 lap 1408 yd 5280 1 5280 ft 1 mi 1 mi 5280 ft 1408 1 21 45760 22 miles ft clo X yd 23 in 24 mi Espan 25 D BE

n Jane took out a loan for 4800 and was charged simple interest at an annual rate of 11 5 The total interest she paid on the loan was 138 months How long was the loan for in months Do not round any intermediate computations If necessary refer to the list of financial formulas X 6

13 14 15 16 Melissa invested 3000 in a fund for 2 years and was paid simple interest The total interest that she received on the investment was 120 As a percentage what was the annual interest rate of her investment If necessary refer to the list of financial formulas X 3

Brian deposits 6000 into an account that pays simple interest at an annual rate of 5 He does not make any more deposits He makes no withdrawals until the end of 3 years when he withdraws all the money Answer the following questions If necessary refer to the list of financial formulas a How much total interest will Brian earn 0 b What will the total amount in the account be including interest 0 X S E 0 D SICHER 13

Your answer is incorrect Amanda took out a 24 000 loan for 1 month and was charged simple interest The total interest she paid on the loan was 118 As a percentage what was the annual interest rate of Amanda s loan Do not round any intermediate computations If necessary refer to the list of financial formulas 0 X

3666mpanying bar graph shows the resident population and the land area of a particular country for selected years from 1800 through 2000 Use the information to find the population density of a certain country for the year 1900 to the nearest tenth expressed in people per square kilometer Click here to view the bar graph The population density in 1900 was approximately Round to the nearest tenth as needed Bar Graph and Data Resident p 100 50 Year 1800 1900 1800 1900 1940 Year Population 5 308 483 71 408 587 1 in 1 yd2 1980 6 5 cm 0 09 m 0 8 m 2000 Land Area square miles 864 746 2 895 118 1 0

Prove FG 140 2 Given FROG FG 15 25 3 1 4 5 6 7 8 2x 6 F Statement FROG FG 152 25 FR RO OG FG 33 3x 8 3x 25 2 11 R FG 15x25 82 4 2x 6 8x 4 2x 6 15x 25 Substitution 12x 8 15x 25 O Reason Given G Combine like terms Division Property of Equality Given T Substitution Segment Addition Postulate Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality X 47

1 Find the distance between A and B 6 S AB T M A 2 d 644 th 321 3 2 C1 1 506 3 16 N B 4 5 6 7 8 x Round your answer to the nearest hundredth

A physician orders 7 teaspoons daily of a certain drug in four equally divided doses Refer to the appropriate entries in the table of English and Metric Equivalents for Capacity to convert given units to the unit indicated Complete parts a through d Click to check the table of English and Metric Equivalents for Capacity SIXE a How many milliliters of the drug should be administered daily Round to two decimal places as needed b How many cc of the drug should be administered daily Round to two decimal places as needed c How many fluid ounces of the drug should be administered daily Round to two decimal places as needed d How many fluid ounces of the drug should the patient receive in each divided dose Round to two decimal places as needed English and Metric Equivalents for Ca English and Metric Equivalents for Cap 1 teaspoon tsp 5 milliliters mL 15 milliliters mL 1 tablespoon tbsp 1 fluid ounce fl oz 1 cup c 1 pint pt 1 quart qt 30 milliliters ml 0 24 liter L 0 47 liter L 0 95 liter L 3 8 liters L 1 gallon gal Hint 1 cc 1 cm 1 mL

K2 8611 meters and Annapurna I 26 545 feet Click the icon to view a table of English and Metric Equivalents The taller mountain Round to the nearest meter as needed is taller by approximately meters English and Metric Equivalents English and Metric Equivalents

Convert the given unit of weight to the unit indicated 17 2 kg to g

olve the following exponential equation using the common base method 8 4 x 6

6 Solve the traveling salesman problem for this graph by determining a Hamilton circuit with minimum total distance 10pts 3 F Start point 8 5 5 E B 2 3 Answer

5 Find an Euler circuits and or Euler paths for the following graph If your answer is yes please write the circuit and or path 10pts e b Euler circuit Yes No Euler path Yes No

Find gof a g f a for each a E Student Id Student Id Student Score 1001 1002 1013 1015 1016 1021 1023 1030 75 45 90 70 65 80 53 86 y 10 8 7 6 5 4 I 1 ceiling function Answer 3 2 1 Grade Table A B C D F g Student Score y Student Score g Student Score Average of Student Score x6

4 a Are G and H graphs isomorphic Please explain with reasons 10 pts C Answer D G G graph S H graph b Is H graph planer Please explain with reasons 5 pts Answer c Find the chromatic number of H graph 5 pts Answer

Upper and lower bounds Find the upper and lower bounds of these numbers given that they have been rounded to the degree of accuracy shown 65 17 7 9200 40000 7 21 Level of accuracy Nearest whole number 1 d p Nearest 100 1 s f 2 d p Lower bound Upper bound 00000

a and b have been rounded to 2 d p a 4 04 b 7 15 Work out the smallest possible answer for a b a b 2 3 d p 2 Work out the biggest possible answer for b a 2

What is the balance after 3 years on a CD with an initial investment of 2 200 00 and a 2 95 interest rate A 6 490 00 B 2 329 80 C 2 400 50 D 2 205 90

Beginning Balance 1200 19 Jul ACH Outgoing Transfer 720 20 Jul Incoming App Transfer 2000 23 Jul ACH Incoming Transfer 25 112 24 Jul E bill Pay Utilities A 3833 00 B 4057 00 C 1193 00 D 2393 00 What is the ending balance on this account after these transfers are completed

6 Find Maclaurin series for F x te dt and use it to evaluate F 1 to an accuracy of 3 decimal places Note 6 720 7 5040

Let f x y and h x differ an tiable functions are given such that f f x y dy h x and h x dx 12 According to the below graph if A 2 A 2A 3A represents the area of the given regions what is the result of the integral f x y dx dy hod LAHT 2A 1A 21 4 25 2 3 C 18 DJ E 20

After coming in Kepler 22b you have noticed some negative impact on your health due to the gravity difference In order to keep yourself healthy you decided to exercise everyday and drink a special blue drink from this place that will help keep you healthy You are required to take 1000ml of this drink every 3 hours for 6 days If you take the drink now about half of the drink will be in your body after 3 hours A Make a table of values showing the amount of blue drink remaining in the body after 3 hour period of time B Write the amount of blue drink remaining after each 3 hour period as a sequence wire a recursion ormulator the sequence C Graph the sequence D Describe what happens to the drink in your body over time

9 15 Usco antiderivatives a x 1 x dx 2023x b Je dx c sinr cos x dx TUGS USHIG22 TUGS USHIG22

It takes 15 minutes for a cup of coffee at 130 F to cool to 100 F in a 70 F room The function T that describes the amount the coffee cools after t minutes can be modeled by T t Ts To T e kt where T t represents the Temperature of the coffee in degrees Fahrenheit t represents the number of minutes after the coffee is poured and set to rest T represents the surrounding temperature in degrees Fahrenheit To represents the initial temperature of the coffee as it is poured and set to rest and k represents a constant A What is the total amount of time needed for a 130 F cup of coffee poured and set to rest to reach 80 F in a 70 F room B Over time to what temperature does the coffee cool Explain your reasoning 7 S

There are three factors that can affect the shape of the Treasury yield curve r t IPt and MRPt and five factors that can affect the shape of the corporate yield curve r t IPt MRPt DRPt and LP The yield curve reflects the aggregation of the impacts from these factors Suppose the real risk free rate and inflation rate are expected to remain at their current levels throughout the foreseeable future Consider all factors that affect the yield curve Then identify which of the following shapes that the US Treasury yield curve can take Check all that apply Downward sloping yield curve Inverted yield curve Upward sloping yield curve Identify whether each of the following statements is true or false Statements If inflation is expected to decrease in the future and the real rate is expected to remain steady then the Treasury yield curve is downward sloping Assume MRP 0 All else equal the yield on new bonds issued by a leveraged firm will be less than the yield on the new bonds issued by an unleveraged firm The yield curve for an AA rated corporate bond is expected to be above the US Treasury bond yield curve Yield curves of highly liquid assets will be lower than yield curves of relatively illiquid assets True False

The pure expectations theory or the expectations hypothesis asserts that long term interest rates can be used to estimate future short term interest rates Based on the pure expectations theory is the following statement true or false The pure expectations theory assumes that a one year bond purchased today will have the same return as a one year bond purchased five years from now False O True The yield on a one year Treasury security is 5 3800 and the two year Treasury security has a 6 4560 yield Assuming that the pure expectations theory is correct what is the market s estimate of the one year Treasury rate one year from now Note Do not round your intermediate calculations 7 543 9 5796 6 4116 8 599 Recall that on a one year Treasury security the yield is 5 3800 and 6 4560 on a two year Treasury security Suppose the one year security does not have a maturity risk premium but the two year security does and it is 0 45 What is the market s estimate of the one year Treasury rate one year from now Note Do not round your intermediate calculations 7 5647

6 Graph of y f x is shown Find a precise estimate for the values of f 2 f 3 and f 4 Answer f 2 0 3 f 3 2 f 4 3 6

11 Karen deposits 60 000 into an account that pays simple interest at a rate of 3 per year David deposits 60 000 into an account that also pays 3 interest per year But it is compounded annually Find the interest Karen and David earn during each of the first three years Then decide who earns more Interest for each year Assume there are no withdrawals and no additional deposits Year First 13 Second Third Interest Karen earns Simple interest 0 0 s Interest David earns Interest compounded annually S 1 Who earns more interest O Karen earns more O David earns more O They earn the same amount O Karen earns more David earns more O They earn the same amount O Karen earns more David earns more O They earn the same amount

9 Implied interest rate and period 6 09 8 26 Consider the case of the following annuities and the need to compute either their expec 9 45 of return or duration 7 00 Raul needed money for some unexpected expenses so he borrowed 4 234 01 from a f of 1 250 at the end of each year The agreement is offering an implied interest rate of agreed to repay the loan in four equal installments Raul s friend Nicholas wants to go to business school While his father will share some of the expenses Nicholas still needs to put in the rest on his own But Nicholas has no money saved for it yet According to his calculations it will cost him 30 044 to complete the business program including tuition cost of living and other expenses He has decided to deposit 4 200 at the end of every year in a mutual fund from which he expects to earn a fixed 7 rate of return It will take approximately for Nicholas to save enough money to go to business school

15 4 16 17 18 19 20 a Find the interest that will be owed after 183 days 21 22 23 b Assuming the print shop doesn t make any payments find the amount owed after 183 days 0 24 25 A print shop borrows 3700 from a credit union for 183 days The credit union charges simple interest at an annual rate of 8 25 for this loan Assume each 1 day is of a year Answer each part below 365 Do not round any intermediate computations and round your final answers to the nearest cent If necessary refer to the list of financial formules 26

15 16 17 18 19 20 21 a Assuming no withdrawals are made how much money is in Raina s account after 2 years b How much interest is earned on Raina s Investment after 2 years 0 22 23 24 25 Raina received a 1500 bonus She decided to invest it in a 2 year certificate of deposit CD with an annual interest rate of 1 15 compounded monthly Answer the questions below Do not round any Intermediate computations and round your final answers to the nearest cent If necessary refer to the list of financial formulas 26 27

11 Question 11 of 35 1 point Question Attempt 1 of 1 2 Unit Here are some facts about units of volume fluid ounce cup pint quart gallon Fill in the blanks P3 72 fl oz x 0c Symbol 11 oz K 4 gt Fact 1c 800x 1pt 2c 1gt 2pt 1 gal 4 gt 75 46

Final Exam Question 13 of 36 1 point Question Attempt 1 of 1 2 3 4 5 6 7 a Find the volume of water that the tank holids in cubic inches Use the table of conversion facts as needed b The particular species Deshaun plans to raise requires at least 1850 in of water per fish If there is any amount less than this no matter how much less the pet store will not accept Deshaun s fish What is the largest whole number of fish that he can keep in the aquarium 10 c The pet store will pay 3 49 for sach fish If he fully populates his aquarium and sells all the fish how much money will he collect 1 Deshaun has a new aquarium The tank is in the shape of a rectangular prism 7 ft long 3 ft wide and 4 fi deep He plans to raise fish and sell them to a local pet store The pet store will inspect the aquarium to make sure that the fish are being kept in a healthful environment One of the main concerns is that each fish has enough water Deshaun looks up the amount of water needed for the species of fish he plans to raise He finds the answer but it is given in cubic inches 11 Conversion facts for length 12 inches in 1 foot 1 I yard d I yard 36 inches in 12 13 A Submit Ass

1 2 grams 4 5 7 8 10 11 12 13 The half life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass Starting with 130 grams of a radioactive isotope how much will be left after 6 half lives Use the calculator provided and round your answer to the nearest gram

K 11 12 13 14 15 16 17 18 19 20 21 22 Rachel invested 800 in a fund for 2 years and was paid simple interest The total interest that she received on the investment was 80 As a percentage was the annual interest rate of her investment If necessary refer to the list of financial formulas

1 2 The next model of a sports car will cost 13 9 less than the current model The current model costs 46 000 How much will the price decrease in dollars What will be the price of the next model Decrease in price Price of next model X 0

1 2 a Write 0 027 as a percentage b Write 5 34 as a decimal a 0 027 3 b 5 34 4 X 5 6

Question 2 of 38 1 point 3 7 There are 13 apples in a basket 5 of these apples are green The rest of them are red a What is the ratio of all apples in the basket to red apples 0 b What is the ratio of red apples to green apples 0 8 0 0 X 9

1 2 3 4 Round 1 4 to the nearest whole number X 5 5

C Give the following using the sets given in A and B above i Bn AUC ii C AI

The label on a bottle of medicine reads Each 5 mL teaspoonful contains glucose 1 87 g levulose 1 87 g and phosphoric acid 21 2 mg a Find the amount of phosphoric acid in the recommended dosage of two teaspoons b If the bottle contains 3 ounces find the quantity of phosphoric acid in the bottle 1 oz s 30 mL 1 tsp s 5 mL a There are mg of phosphoric acid in two teaspoons Simplify your answer Type an integer or a decimal

A triangle is made such that the hypotenuse is 25 cm and one of the shorter sides is 5 cm longer than the other Find the dimensions of the triangle

4 A Given the set A 1 2 3 4 and relations R defined on set A as follows R 1 1 1 2 2 1 2 2 3 3 4 4 i Represent the relation R in a directed graph ii By explaining from the directed graph Is the relation R reflexive Symmetric Asymmetric Transitive Equivalence B Solve the following recurrence relations using an appropriate method for each i Un Un 1 n with Uo 3 ii Un 7Un 1 1 with U 1 iii Un 3Un 1 4Un 2 with Uo 2 and U 3 20 Marks

D i Use the direct proof technique to prove x odd and y odd x y eve ii Use the proof by contradiction technique to prove x rational and y irrational x y irrational

6 A Give the graphical representation of the following deterministic finite state automata with its transition function K 90 91 92 E 0 1 90 A 9 Transition function Present State 70 71 72 Next State for Input 0 90 92 72 Start symbol S P S AB Aa Bb B b Next State for Input I B Give the languages and their natures descriptions generated by the following grammars i N S A B a b ii N S A B a b Start symbol S P SAB AaAla BbBlb 9 9

5 A SJHS student swam 56m with the current and 48m against the current in the same length of time What is the swimmer s speed in still water if the current is 4km h 313x 15 10 T