Basic Math Questions and Answers

Which of the following graphs shows the solution set for the inequality below 3 x 1 9 O A 7 B H D 6 OC H 7 6 1 0 1 2 3 4 10 1 2 3 5 1 0 1 2 3 4 5 6 5

To identify the most efficient model for a windmill Gandalf Engineering Company designs the windmill shown The design consists of four right triangles arranged equally around point O such that point O is the midpoint of BF and DH

A disinfectant spray bottle says it eliminates 90 of bacteria with each application You apply the disinfectant once to a countertop in the shipping department and then apply the disinfectant again to the same countertop If the bottle is correct what percentage of the bacteria originally on the tabletop have been eliminated

A man is looking down from his roof to a puddle on the ground We are not sure why The angle of depression is 40 degree and the distance from the ground t his eyes is 25 feet How far is the puddle from the house 40 25 feet Round to one decimal place

A baseball is hit from an initial height of 3 feet and reaches a maximum height of 403 feet Which function could be used to model this situatior where h t is the height in feet after t seconds OA h t 16 t 403 3 OB h t 16 t 5 3 OC h t 16 t 3 403 OD h t 16 t 5 403

Select all the correct answers Rachel and Jeffry decided to start saving for college Rachel has 1 500 to start her savings account and Jeffery has 1 200 Rachel s bank offered her an interest rate of 7 5 compounded annually Jeffery decided to keep his money in a safe in his bedroom and he adds 200 to his safe each year Suppose that A represents the accumulated money in each one s savings fund and t represents the number of years Choose the equations that form the system that best models this situation A 200t 1 200 A 1 200 1 2 O A 7 5t 1 500 A 1 500 1 075 O A 1 200 1 075 t

Lisa is opening both a checking and savings account at her local bank She deposits 50 000 into her checking account and 2 000 into he savings account She will be withdrawing funds from her checking account over the course of each year to pay bills at an average rate of 2 500 Her savings account earns interest continuously at a rate of 5 If B represents the balance of the account and t represents the time in years since the account was opened then which of the following systems of equations can be used to determine how long it will be before the balance in each account is equal OA OB OC OD B 50 000 2 500 B 2 000 100 B 50 000 2 500 B 2 000 0 05 B 50 000 2 500 B 2 000 0 05 B 50 000 2 000 B 2 500 05

Enter the correct answer in the box The local animal shelter throws a dog themed party Humans h and dogs d are both invited The event space imposes two restrictions on the party there can only be 120 dogs and humans combined and to keep things manageable there must be 1 human to every 3 dogs This situation can be represented by a system of two linear equations One of these equations is given Write the second equation in the box h

14 The following information is given about a trapezoid A trapezoid is isosceles if its non parallel sides are congruent Trapezoid ABCD is not isosceles Based on the information which statement is a valid conclusion about Trapezoid ABCD The non parallel sides are not congruent The parallel bases are congruent One base and one non parallel side are perpendicular The non parallel sides are perpendicular

1 point Find the quotient and remainder using long division for 2x 14x 7x 33 2x 5 The quotient is The remainder is

A typical high income household in 1980 earned 125 556 A similar household in 2009 earned 180 001 What was the relative increase in income for these households from 1980 to 2009 Round to the nearest one percent

When an object is dropped from a height of h feet the time it will take to hit the ground can be approximated by the formula t 2h where t is the time in seconds for the object to fall h feet If V 18 you want an object to fall for 8 seconds from what height should the object be dropped your answer input will be number only

Grace is an hourly employee and the line that models her total pay in dollar as it relates to the number of hours she has worked has a slope of 45 and a intercept of 35 Which statement is true

He was He was an exceptional athlete actor singer cultural scholar author and political activist revered for his talents and his accomplishments yet his radical political beliefs he expressed admiration for the Soviet Union America s ideological enemy eventually cost him his popularity and his reputation Question What best expresses the main idea of the passage O Success is ultimately measured by accomplishments not popularity O The more talented a person is the more likely that person is to be criticized Paul Robeson s performances were liked by some people and disliked by others O Paul Robeson was a talented man whose reputation was hurt by his political beliefs

9 A bird leaves a point on the ground and flies in a straight line to a point on a mountainside th is 3 miles east and 2 miles north of the point on the ground as well as 1 mile higher What is the distance from the point on the mountainside to the point on the ground O 6 miles O 14 miles O6 miles O 14 miles

A certain affects virus 0 1 of the population A test used to detect the virus in a person is positive 89 of the time if the person has the virus true positive and 14 of the time if the person does not have the virus false postive Fill out the remainder of the following table and use it to answer the two questions below Positive Test Negative Test Total Infected Not Infected Total 100 99 900 100 000 a Find the probability that a person has the virus given that they have tested positive Round your answer to the nearest tenth of a percent and do not include a percent sign P Infected Positive Test b Find the probability that a person does not have the virus given that they test negative Round your answer to the nearest tenth of a percent and do not include a percent sign P Not Infected Negative Test

OA V B C ladder 13 feet According to the diagram a 13 foot ladder leans against a 12 foot wall The distance from the base of the ladder to the base of the wall is 5 12 Based on this information which trigonometric ratio has the value 5 OD tan C cos C tan A 90 sin A wall 12 feet B

A space agency compiles data on space shuttle launches and publishes them on its website The following table displays a frequency distribution for the number of crew members on each shuttle mission over a 30 year period Let X denote the crew size on a randomly selected shuttle from this time period Complete parts a through e below Crew size Frequency 3 4 5 7 6 31 7 24 a What are the possible values of the random variable X Use a comma to separate answers as needed 8 74 9 1 D ww

8 There are one hundred forty two students in a high school band These students represent two ninth of the total students in the high school How many students attend the school A 587 B 613 C 639 D 665 820c 380r 4 360 The above equation models the amount of calories in a snack of c cups of cashews and r cups of raisins The amount of calories per cup of cashews is 820 and the amount of calories per cup of raisins is 380 According to the equation how many cups of raisins are used if 3 cups of cashews are used to make the snack A 3 B 4 C 5 D 6

An ice block is in the shape of a rectangular prism Danny cuts the block so that each side is its original length How do the volumes of the ice blocks compare OA The new volume is the original volume B The new volume is the original volume OC The new volume is D The new volume is the original volume the original volume

It s never a good feeling to find out that you spent MORE money than what you had available then getting a fee added on top of that overspending In this activity you will practice calculating the overdraft fees associated with major banks checking accounts compare the fees from the different banks and reflect on some of these key ideas to help you feel prepared when you are selecting your own checking account Part 1 Calculate the Fees Read Joshua s scenario in the box below Then use the links provided to help you calculate his overdraft fees The Scenario When the day begins Joshua has 116 in his checking account and he has overdraft protection Before school he buys his cousin a round trip bus fare for 4 using his debit card He then uses the card to get gas in his car for 43 Once the banks open a check he gave the school for his senior yearbook clears and 75 comes out of his account Joshua s Netflix account subscription is automatically debited today too so another 10 leaves the account After school he heads out with friends and uses his debit card to buy a 3 coffee He sends a person to person payment of 15 to his friend Bryant for his share of dinner Finally he finishes out the day with some shopping to buy new soccer gear for 35 using his debit card at the store A Open the link in a new tab the current overdraft fees in NerdWallet s Overdraft Fees by Bank B Using the information provided by NerdWallet determine how much Joshua would pay in overdraft fees at the following banks Alliant Credit Union Ally Bank Citibank Fifth Third Bank SunTrust Wells Fargo Part II Compare the Fees 1 How much did Joshua spend on actual purchases throughout the course of the day BALANCE

2 Earning Money Marcus works at an ice cream shop He earns 10 50 each hour Use Marcus s timesheet for the week to answer the questions Date April 11 April 12 April 13 April 14 April 15 Time In 8 45 9 00 7 30 8 00 8 30 Time Out 12 00 12 00 12 00 1 15 11 15 a How many hours did Marcus work for the week Show the number of hours he worked each day in your work 4 points b How much money did Marcus earn for the week Show your work 4 noints

6 A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position The team then measured the distance the wheel had rolled and found it to be 30 cm To the nearest tenth what is the area of the wheel O 71 6 cm 286 6 cm 23 6 cm

QUESTION 7 Read the scenario and determine if it will change the supply or the demand of the market listed Will equilibrium price increase or decrease Will equilibrium quantity increase or decrea Market Chunky Monkey Ice Cream Scenario Social Media Influencer superstar Van Camp advertises Kemp s Vanilla Frozen Yogurt to her 100 million Instagram followers Supply or demand Equilibrium price Equilibrium quantity

A law office orders business stationery The cost is 17 05 per box a Write a function that represents the cost C x in for x boxes of stationery b There is a 6 sales tax on the cost of merchandise and 9 58 for shipping Write a function that represents the total cost T a for a dollars spent i merchandise and shipping c Find TC x d Find TC 5 and interpret its meaning in the context of this problem

5 meters A water sprinkler has a range of 5 meters as shown The jet of water from the sprinkler sweeps out at an angle of 85 as the nozzle turns What is the area watered by the sprinkler Use the value 3 14 and round your answer to one decimal place O A 15 6 square meters OB 17 8 square meters 18 5 square meters 19 2 square meters OC 85 OD

You give up a full time salary of 45 000 a year to go to school for 2 years The total cost of going to school is 30 000 If you want to be able to recover your investment in 5 years or less what is the minimum salary you would need to earn upon earning your degree a 51 000 b 60 000 c 69 000 75 000

11 The equation c 2 5t represents the cost c for t tickets to the school play Does a value of 3 5 for t make sense in this situation Explain your reasoning Show your work What does t represent

Does the geometric sequence converge or diverge Explain 320 40 5 0 625 The sequence diverges because r 8 which is less than one The sequence diverges because r 8 which is greater than one The sequence converges because r 0 125 which is less than one The sequence converges because r 0 125 which is less than one

For the following graph determine if the graph represents a polynomial function If it is a polynomial function then determine the number of turning points and the least degree possible This is not a polynomial There are no turning points as the curve represents an odd function Yes this graph represents a polynomial There are two turning points and the least degree possible is three Yes this graph represents a polynomial There are two turning points and the least degree possible is two This is not a polynomial There are no turning points as the curve is always increasing

38 4 Place the steps required to simplify the given sum into one simplified rational expression in the correct orc Drag the tiles to the correct boxes Not all tiles will be used Tiles 8 8 3 3x x 1 3 8 1 3 3x x 1 8 3x x 1 4 4 x 1 8 x 1 32 x 1 112 8 32 3 1 32 x 1 3 x 1 32 x 1 Sequence PORO K

A right cone has a base with diameter 10 units The volume of the cone is 100 cubic units What is the length of a segment drawn from the apex to the edge of the circular base aka the slant height

10 Select the correct answer A construction company is analyzing which of its older projects need renovation Building B was built two years before building C Building D was built two years before building B The product of building B s age and building D s age is at least 195 If x represents the age of building C which inequality represents this situation A OB OC O D 12 8x 16 195 12 61 8 2 195 12 4x 4 195 12 4 195 Reset Next D

The Math Team sells crunchy and fruity trail mixes to raise money The ratio of fruit to nuts in each mix and the price they charge for an 8 oz or cup bag of each mix are given in the table below Hint The ratio of fruit to nuts in the 2 1 crunchy trail mbx is 1 3 So of each bag is fruit and of each bag is nuts Crunchy trail mix Fruity trail mix Ratio of fruit to nuts Price of an 8 oz or cup bag 1 3 5 3 2 50 3 50 They have 30 cups of fruit and 50 cups of nuts to use in their trail mixes So they need to know how many bags of each type of mix they should they make They let c represent the number of bags of crunchy trail mix and frepresent the

Select the correct answer The table shows the maximum daily temperatures in degrees Fahrenheit recorded in a Texas town in May 84 86 84 88 83 85 90 84 88 84 85 83 85 84 90 84 85 85 83 85 Which data display s can be used to find the median of the maximum daily temperatures 1 box plot II dot plot III histogram OA I and II OB OC OD I II and III II and III I only

The line graph shows the average number of awakenings during the night for men and women of different ages Use the graph to estimate the difference between the average number of awakenings during the night between 25 year old men and 25 year old women SCIE The difference between the average number of awakenings during the night between 25 year old men and 25 year old women is Round your answer to the nearest tenth as needed Number of Awakenings During the Night 6 00 66 N men women VIVA 30 40 50 60 70 80 Ago 5 through 75 Q

3 The function s f t gives the position of a body moving on a coordinate line with s in meters and t in seconds Find the body s displacement and average velocity for the given time interval s 3t 3t 10 0 t 2 A 38 m 19 m sec B 18 m 9 m sec C 12 m 15 m sec D 18 m 18 m sec

At the candy store Julie found a special scale that would measure the number of pounds p of candy and then calculate the cost c when you typed in the name of the candy For her favorite candy chocolate gummy bears she wrote this table P C 0 25 1 69 0 45 3 04 0 75 5 06 1 25 8 44 Choose all of the following statements that are true Select one or more a none of these b The total cost of the candy depends on the weight and the cost per pound of the candy c c 6 75p Od The cost of the candy is 0 15 times the number of pounds e The cost of the candy is 6 75 times the number of pounds

Jim Goodman an employee at Walgreens earned 38 400 an increase of 16 5 over the previous year What were Jim s earnings the previous year Round to the nearest cent Earnings

A system of inequalities is graphed below The variable x represents the number of cans someone is buying and y represents the number of bottles Conditions on the maximum amount of total weight and volume lead to two of the inequalities 180 160 140 120 100 80 60 40 20 5 10 1400 bottlon 15 Which descriptions correspond to solutions of this system 7 cans and 140 bottles 9 cans and 70 bottles 12 cans and 40 bottles

Find the derivative 10 sin x 1 cot x y ncvps instructure y 10 csc x cotx sec x y 10 csc x cotx csc x y 10 cos x csc y 10 csc x cotx sec x x

Eliza went to the store and bought 3 lbs of apples at 1 99 per lb two loaves of bread at 89 per loaf a boz of cereal at 3 99 per box and a gallon of milk at 3 19 per gallon If Eliza paid with 20 how much change did she receive O 5 70 O 14 93 O 5 07 20

TIME REMAINING 01 38 18 A supervisor finds the mean number of miles that the employees in a department live from work He finds x 29 and s 3 6 Which mileage is within a z score of 1 5 O 21 miles O 24 miles 36 miles O41 miles

Complete the sentence below The polynomial 2x5 3x4 12x 2 is of degree The polynomial 2x5 3x4 12x 2 is of degree Type an integers or decimals The leading coefficient is The leading coefficient is

height m 5 42 4 45 4 53 4 29 3 96 5 42 5 64 3 74 4 45 4 11 weight kg 1273 1257 1152 1059 1070 1260 1310 1046 1139 1084

A sociologist wants to investigate the question Is there a relationship between texting during class and grade point average GPA among high school seniors in a large district Which study design is most appropriate Before the semester starts randomly select 40 seniors from each high school who do not text during class Assign 20 to the texting treatment group text three or more times during every class meeting and 20 to the control group no texting during class At the end of the semester obtain each student s GPA from the appropriate admissions and records office Compare the GPA of students who routinely text during class to the GPA of students who do not text during class Obtain the cell phone numbers of all seniors in the district Send a text survey to each student asking about the student s texting habits during class Obtain each student s GPA from the appropriate admissions and records office Compare the GPA of students who routinely text during class to the GPA of students who do not text during class Obtain a list of seniors in the high school district Randomly select 300 seniors and survey them about their texting habits during class Obtain each student s GPA from the appropriate admissions and records office Compare the GPA of students who routinely text during class to the GPA of students who do not text during class

80 Watt 400 Watt Total B C According to the table above 100 Watt bulbs made what fraction of the working lightbulbs D 1 230 3 614 2 384 3 614 271 398 Working 1 230 2 384 3 614 2 384 2 655 Defective 127 271 398 Total 1 357 2 655 4 012

In Kawhi Leonard s previous 6 playoff games he scored the following amount of points 26 28 31 33 34 36 In his most recent playoff game he struggled and scored only 6 points Decide which statements are true or false about the influence of the outlier 6 The new outlier of 6 will increase the mean The new outlier of 6 will increase the median The new outlier of 6 will increase the standard deviation 3 4 5 6 Data Set 2 2 The frequency distributions of two data sets are shown in the dot plots below Choose the correct answer om the choices on the next page Data Set 1 3 2000 Select the one correct statement that describes these data sets The mean and median are greater for Data Set 1 The mean and median are greater for Data Set 2 The mean and standard deviation are greater for Data Set 1 The mean and standard deviation are greater for Data Set 2 True 4 False 000 8 9 10 11 12 Justify your reasoning for the choice you made above

2 The senior class is having a fundraiser to help pay for the senior trip Selling a box of chocolates yields a profit of 2 45 while selling a box of cookies yields a profit of 2 70 The demand for cookies is at least twice that of chocolates but the amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolates produced Assuming that the senior class can sell every box that they order how many boxes of each should they order to maximize profit if they cannot order more than 1950 boxes combined Show work

Solve the system by substitution 4y 3x x No solution 5 7y 15