Math - Others Questions

1 Draw the graph of a polynomial function that has all of the following characteristics f 2 40 f 3 0 and f 4 0 The y intercept is 0 f x 0 when x 3 and 0 x 4 f x 0 when 3 x 0 and x 4 The range is the set of real numbers

Write the equation of a sine or cosine function to describe the graph 2x 2x 4x 2x K 8x 3 10x 3

An object moves in simple harmonic motion with period 5 seconds and amplitude 6 cm At time t 0 seconds its displacement d from rest is 0 cm and initially it moves in a negative direction Give the equation modeling the displacement d as a function of time t TT 3 16 co

Vrite the equation of a sine or cosine function to describe the graph 2x 3 2x 3 2x 8x 3 10x 0

buoy floating in the sea is bobbing in simple harmonic motion with period 4 seconds and amplitude 11 in Its displacement from sea level at time t 0 seconds is 11 in and initially it moves upward Note that upward is the positive direction Give the equation modeling the displacement d as a function of time 1 d 0 R 2 16 Osin cos

A person sitting on a Ferris wheel rises and falls as the wheel turns Suppose that the person s height above ground described by the following function h t 21 2 19 7 cos 1 1t In this equation h t is the height above ground in meters and I is the time in minutes Find the following If necessary round to the nearest hundredth Frequency of h revolutions per minute Minimum height above the ground meters Time for one complete revolution minutes X

Scientists are studying the temperature on a distant planet They find that the surface temperature at one location is 20 Celsius They also find that the temperature decreases by 3 Celsius for each kilometer you go up from the surface Let 7 represent the temperature in Celsius and let H be the height above the surface in kilometers Write an equation relating T to H and then graph you equation using the axes below Equation 0 0 X 0 0 8 5 2547 154 10 X 3

Eric is driving on the highway He begins the trip with 12 gallons of gas in his car The car uses up one gallon of gas every 20 miles Let G represent the number of gallons of gas he has left in his tank and let D represent the total distance in miles he has traveled Write an equation relating G to D and then graph your equation using the axes below Equation 14 12 G 10 14 0 0 X S

Eric is driving on the highway He begins the trip with 12 gallons of gas in his car The car uses up one gallon of gas every 20 miles Let G represent the number of gallons of gas he has left in his tank and let D represent the total distance in miles he has traveled Write an equation relating G to D and then graph your equation using the axes below Equation 0 0 X 00 12 G X

Write the equation of a sine or cosine function to describe the graph tnt 0 5 J 0 0 X 19 sin

is driving to Chicago Suppose that the distance to his destination in miles is a linear function of his total driving time in minutes Chau has 68 miles to estination after 24 minutes of driving and he has 58 4 miles to his destination after 36 minutes of driving How many miles will he have to his destination 50 minutes of driving Remaining distance in miles Driving time in minutes miles

Exercise 2 4 5 Find A when 4 a 3A 1 b 24 T 1 2 2 d 1 247 c 1 3A e f 3 10 21 22 1 1 8 AT 21 2 2 3 4

ppose that the credit remaining on a phone card in dollars is a linear function of the total calling time in minutes When graphed the function gives a lin th a slope of 0 16 See the figure below ere is 34 96 in credit remaining on the card after 31 minutes of calls How much credit was there after 24 minutes of calls Remaining credit in dollars 3496 Calling time

The average monthly temperature changes from month to month Suppose that for a given city we can model the average temperature in a month with th following function f t 59 25 sin 70 6 In this equation f t is the average temperature in a month in degrees Fahrenheit and t is the month of the year January 1 February 2 Find the following If necessary round to the nearest hundredth Maximum average temperature in a month Fahrenheit Period off months Frequency of fcycles per month X S

ppose that a household s monthly water bill in dollars is a linear function of the amount of water the household uses in hundreds of cubic feet HCF When aphed the function gives a line with a slope of 1 55 See the figure below the monthly cost for 16 HCF is 46 17 what is the monthly cost for 13 HCF Monthly cost 46 17 in dollars 16 Water usage in HCF s X

2 4 4b Given A 1 2 1 1 3 0 1 0 5 b Find a matrix B such that AB 1 1 2 0 1 1

Find the necessary sample size Weights of women in one age group are normally distributed with a standard deviation o a 17 lb A researcher wishes to estimate the mean weight of all women in this age group Fin how large a sample must be drawn in order to be 90 percent confident that the sample mean will not differ from the population mean by more than 2 0 lb O 208 O 278 O 194 O 196

Based on Exhibit 7 7 what would be the monthly mortgage payments for each of the following situations Round your answers to 2 decimal places a A 162 500 15 year loan at 7 5 percent b A 217 500 30 year loan at 7 5 percent c A 195 000 20 year loan at 7 5 percent 1 571 70 Term Rate 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 30 Years 4 22 4 49 4 77 5 07 5 37 5 68 6 00 6 32 6 65 25 Years 4 74 5 01 5 28 5 56 5 85 6 14 6 44 6 75 7 07 20 Years 5 55 5 80 6 06 6 33 6 60 6 88 7 16 7 46 7 75 15 Years 6 91 7 15 7 40 7 65 7 91 8 17 8 44 8 71 8 99

ose that the weight in pounds of an airplane is a linear function of the total amount of fuel in gallons in its tank When graphed the function gives a slope of 6 4 See the figure below 50 gallons of fuel in its tank the airplane has a weight of 2220 pounds What is the weight of the plane with 20 gallons of fuel in its tank Airplane weight in pounds 2220 50 Amount of fuel in gallons pounds X

The Sugar Sweet Company is going to transport its sugar to market It will cost 4200 to rent trucks and it will cost an additional 150 for each ton of sugar transported Let C represent the total cost in dollars and let S represent the amount of sugar in tons transported Write an equation relating C to S and then graph your equation using the axes below Equation 0 0 4000 500 3000 4500 4000 3500 3000 2500 2000 1500

fight pairs of species 16 species in all from Alabama Mississippi Tennessee Kentucky South Carolina and North Carolina and brought them all back to the lab In some species pairs the color patterns were very similar and in some they were very different For each species pair he put five males of both species and five females of both species in the same fish tank and observed their behavior for five hours He did this eight times once for each species pair for a total of 1 280 fish During the five hour observation period he recorded 1 how many times females mated with males of their own species or of a different species and 2 how many times males were aggressive towards males of their own species or of a different species He used these data to calculate an index of bias for each behavior to show whether individuals had stronger reactions towards members of their own species He used the following equation where A and B represent two different species and AxA represents how individuals in species A acted towards other members of species A index of bias AxA BxB AxB BxA AXA AxB BxA BxB Another way to write the same equation is index of bias events within species events across species total of events If the index of bias value is positive greater than zero this means that the behavior happened more often with members of the same species If the index of bias value is negative less than zero this means that the behavior happened more often with members from a different species Michael also measured color differences between each pair using digital pictures The larger the color difference score the more different the color pattern is between the two species Scientific Question In what ways do color pattern differences between different darter species influence female mating decisions and male aggression What is the hypothesis State Dr Martin s alternative hypothesis from the above text I

Module Knowledge Check Write an equation of the form y a sinbx or y a cosbx to describe the graph below 0 51 NLC 9x 2 8 sin cos 0 0 Question

Ben and Carla Covington plan to buy a condominium They will obtain a 223 000 30 year mortgage at 6 5 percent Their annual property taxes are expected to be 1 950 Property insurance is 510 a year and the condo association fee is 235 a month Based on these items determine the total monthly housing payment for the Covingtons Use Exhibit 7 7 Round your intermediate calculations and final answer to 2 decimal places Total monthly housing payment

Bippy Corporation has 400 in debt and 600 worth of equity First calculuate the capital structure weights by filling in cells E20 E22 and E24 E25 Next calculate the Weighted Average Cost of Capital in cells E27 E29 and E31 Tax rate 25 Cost of debt 6 Cost of equity 10

Suppose A and B are angles in standard position with sin A and sin B Find the exact value of cos A B if A is in Q2 and B is in Q3

What is the rate of change 1 B X y 2 3 4 5 4 6 8 10

What is the rate of change 1 A Your answer 10 7 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 X

6 Use bracket s with the expression 5 3x4 6 2 so that it simplifies to 8 Show your work to prove your solution works

2 An instructor has given a short quiz consisting of two parts For a randomly selected student let X the number of points earned on the first part and Y the number of points earned on the second part Suppose that the joint pmf of X and Y is given in the accompany ing table p x y 550 10 0 02 04 01 5 06 15 15 y 10 02 20 14 15 10 10 01 a If the score recorded in the grade book is the total number of points earned on the two parts what is the expected recorded score E X Y b If the maximum of the two scores is recorded what is the expected recorded score

5 Simplify the expression 5 2 8 12 4

4 Simplify as much as possible Leave the final answer in exact form

Exercise 1 6 Find a b and c so that the system x ay cz 0 bx cy 3z 1 ax 2y bz 5 has the solution x 3 y 1 z 2

Distribution Date 10 19 2023 Due Date 10 23 2023 1 The hydraulic conductivity of a sand at a void ratio of 0 5 is 0 022 cm s Estimate its hydraulic conductivity of a void ratio of 0 7 equation 7 31 2 Given the following information of a layered soil 3 layers what is the ratio of equivalent permeability KH eq kv eq H 1 5 m H 2 5 m H3 3 0 m k 10 5 cm s k 3 0 x 10 3 cm s k3 3 5 x 10 5 cm s NOTE Show all the calculation steps

3 4 5 6 7 8 9 1 9 Anthony s parents have decided to reduce heat costs by installing new storm windows and adding insulation Anthony s parents offered him 10 for every storm window he installs and they owe him 25 for spreading the insulation He wants to earn more than 200 Write and solve an inequality to find out how many windows he must install Click on show your work to type or write your work Show Your Work

3 7 5 7 8 Type a response 9 Elisha wants to buy book marks to give to her teachers she has a total of 60 to spend Each book mark costs 6 00 and she wants to also buy her mom a cookbook that costs 23 00 Write and solve an inequality to find the greatest number of book marks she can buy Click on show your work to type or write your work The greatest number of bookmarks she can buy is enter number only

Preparing Entries for A note payable was executed by Sterling Inc and sent to Miami Finance Company Sterling Inc used 240 000 of its accounts receivable as collateral for the loan The contract provided that Miami would advance 85 of the gross amount of the receivables Sterling Inc continues to collect payments for the receivables and the cash from customers is then remitted to the finance company The cash remitted is first applied to the finance charges with the remainder applied to principal During the first month customers owing 164 000 paid cash less sales returns and allowances of 6 400 originally recorded as a refund liability The finance charge at the end of the first month was 1 400 During the second month the remaining receivables were collected in full except for 1 600 written off as uncollectible Final settlement was effected with the finance company including payment of an additional finance charge of 600 Required a Record the entry for Sterling to record the secured borrowing b Record the first month entries for Sterling to record 1 the collections and 2 the payment to Miami c Record the entries for Sterling to record 1 the collections for the second month and 2 the final payment to Miami a Cash C b Cash Note Payable To record the secured borrowing Refund Liability Account Name Accounts Receivable To record collection on receivables for first month Interest Expense Note Payable Cash To record payment to Miami for the first month Cash C V v V Allowance for Doubtful Accounts Accounts Receivable To record collection on receivables for second month Kerung Liability V Interest Expense Note Payable Dr 204 000 157 600 400 0 1 400 156 200 0 600 155 400 Cr 0 204 000 0 0 164 000 0 0 157 600 0x 0x 156 000 x Accounts Receivable To record collection on receivables for first month Interest Expense Note Payable Cash To record payment to Miami for the first month Cash Allowance for Doubtful Accounts Accounts Receivable To record collection on receivables for second month P Cash To record payment final payment to Miami 6 400 0 1 400 156 200 600 155 400 0 600 155 400 0 0 164 000 0 0 157 600 0x 0x 156 000 x 0 0x 156 000 X

You may use a calculator or spread sheet application to work on this quiz 5 pts 1 The prevalence of Hutchinson Guilford Progeria is 1 per 22 million individuals in Japan The disease is caused by a Mendelian dominant mutation The disease mimics premature aging and affected persons rarely live past 13 years old With an average mutation rate in this population estimated at 1 x 10 5 what is the predicted selection against this allele Explain your calculated result 1 sentence

In order to get characteristic X rays using Mo as a target metal what is the minimum voltage to be used O 10 kV O 15 kV O 20 kV O 25 kV O Any voltage

5 Determine the nature of roots a 2x 8x 14 6 c 8n 7n 16 b 4a 4a 6 0 d 8b 6b 3 5b

1 Determine the value of the function a f x x 11 at f 4 b g x 3x 2x 1 at g 5 2 Determine the value of x for each function a k x 5x 4 when k x 19 c h x 2 x 4 at h 3 b p x 7 3x when p x 9

Emma hits the ball is given by y 0 01x 0 5x 0 2 where y is the vertical height in yards above the ground and x is the horizontal distance from the tee in yards Round all answers to one decimal place a How far does Emma hit the golf ball

5 Emma hits a golf ball off a tee The height of the ball is given by y 0 01x 0 5x 0 2 where y is the vertical height in yards above the ground and x is the horizontal distance from the tee in yards Round all answers to one decimal place a How far does Emma hit the golf ball

8 An object is through off a building h t 16t 48t 160 where h is the height in meters and t is the time meas seconds a What was the height of the building where the object was launched from b How long will it take the object to strike the ground c What time s is the object at a height of 192m d What is the height of the hall after 3 5 seconds

Evaluate the following expressions given the functions below g x 4x 5 b f 8 f x x 3x a g 6 d Find x if h x 9 Solve the following quadratics by factoring a 15a 3a 3 7a 6n 18n 18 6 h x 2x 1 c h 7 e Find x if g x 13 b n 10n 22 2 d 3r 16r 7 5

4 Solve the following quadratics using the quadratic formula Round to the nearest hundredths a 2m 7m 13 10 b 8x 4x 16 x c 2a 36a 0 Bird 3 d 8n 7n 15 7

The domain and range of some relations are given Each relation consists of five points Is the relation given a function Justify your answer a Domain 1 2 3 4 5 Range 4 b Domain 3 1 1 3 5 Range 0 9 c Domain 2 3 6 Range 4 6 7 11 15 d Domain 2 Range 9 10 11 12 13

son science and The new education system was initiall soon Soviet model of education In particular it was geared to the drive technology As a result a privileged technological intelligentsia for industrial development with the greatest emphasise emerged widening the separation between intellectual and manual work equal opportunities for all also appeared Educational expansion was Other social inequalities despite the CCP s formal commitment to greater in urban than rural areas in addition admissions to schools beyond the primary level tended to favour the children of Party cadre government employees and technicians primary education throughout China the lack of surplus finance meant this had Although the government aimed to provide free and universal p 1950s most village children had some primary education and the numbers in by no means been achieved by 1955 Nonetheless by the mid secondary education had almost tripled ACTIVITY Carry out some additional research on the educational reforms of the period 1949 55 Then write a couple of paragraphs to explain why full educational equality was not achieved by these reforms Health and living standards During the 1950s there were important advances in health care which Defore 1949 had been almost completely absent from rural areas The CCP quickly established clinics in most counties and health workers were sent to deal with the most common diseases Young people were ained to help people in rural areas identify and report contagious seases and to give instruction in the importance of hygiene d sanitation

3 Given f x 2x 3 x 5 x 2 answer the following questions a List the zeros of the function b What is the degree of f x c As x o f x d As x o f x IDDLESEX

UREMENT AND MATTER Counting significant digits when measurements are multiplied Multiply or divide the following measurements Be sure each answer you enter contains the correct number of significant digits 7 8084 cm x 3 2 cm 9021 m 0 69 s 608 22 m 0 77 s cm 0 0 X 5

2 Here are graphs of x 4 and x y 12 Complete the graphs by shading regions and adjusting line types as needed to show all the allowable numbers of widgets and zurls that the factory can produce in one day 11 1 12 4 12 10 8 6 4 2 3 Does each ordered pair represent an allowable combination of widgets and zur produced in one day 4 5 10 12 3 9