Math Questions

You are building a patio of the back of your house The diagram shows the plan for the patio Each unit in the coordinate plane represents 1 5 feet Find the area of the patio to the nearest square foot TY 10 8 6 A B OC D 2 about 57 ft 2 about 39 ft 2 about 38 ft 2 about 26 ft 2 4 house 6 8

The area of a rectangular living room is 450 square feet The length of the room is 15 feet less than three times the width Find the equation in terms of w that could be used to find the dimensions of the living room in feet Your answer should be in the form of a polynomial equals a constant Provide your answer below

The person s income increased from 27 000 to 40 000 over the last year What is the percent change Select the correct answer below O 48 15 decrease O 32 50 increase O 48 15 increase 67 50 increase

Using this table as needed calculate the required information for the mortgage Round dollars to the nearest cent Number of 1 000s Financed Amount Interest Financed Rate 165 300 5 25 Term of Loan years 15 Table Factor in 69 Monthly Payment in Total Interest in

6 Which statements describe the altitudes of triangles Select all that apply An acute triangle has altitudes inside the sides of the triangle A right triangle only has two altitudes The point of concurrency for a triangle s altitudes is called the orthocenter An obtuse triangle has altitudes along the legs of the triangle

In the figure shown below E and G lie on AC D and F lie on AB DE and FG are parallel to BC and the given lengths are in feet What is the length of AC in feet A D O O O O 8 O F 7 B C D 16 A 13 26 29 42 LL 6 B 48 E G

ANDLI A water tank can be filled using pipe A pipe B or both pipes It takes pipe A twice as long as pipe B to fill the tank when working alone When both pipes are working it takes only 8 hours This expression represents the situation Which expression also represents this situation 123

What is the equation of the line of best fit for the following data Round the slope and y intercept of the line to three decimal places OA 1 383x 1 526 OB y 1 526x 1 383 OC 1 526x 1 383 OD 1 383x 1 526 X 4 7 5 7 10 12 12 14 13 18 CO

A farmers group conducted an experiment to determine which fertilizer is better for plant growth One fertilizer contains a urea supplement while the other does not contain the urea supplement For the experiment they randomly selected 20 plants of the same species growing in their area The farmers tested the urea enhanced fertilizer on 10 plants and the non urea fertilizer on the other 10 plants After three months they reported their findings as shown Plant Growth Report Number of Plants with Above Average Growth A A 3 B N Month 2 with urea supplement without urea supplement What can be concluded from the farmers data Month 1 O C O D Month 3 Both types of fertilizer are equally effective The fertilizer with the urea supplement is more effective than the fertilizer without it There is not enough information to draw any conclusions from the data The fertilizer without the urea supplement is more effective than the fertilizer with it

Select the correct answer from each drop down menu Jane bought a new rectangular placemat with an area of 126 square inches The length of the placemat is four times the quantity of nine less than half its width Complete the equation that models the area of the placemat in terms of the width of the placemat w w w The width of the placemat is inches W

The water line on a dental unit fits through a rubber tube that is lined with insulation to maintain the temperature of the water If the water line has an outside diameter of 0 1875 inches in how thick is the layer of insulation Hint Remember that the insulation is on both sides RUBBER TUBE INSULATION WATER LINE 0 1875 IN INSIDE DIAMETER 1 4 IN I OUTSIDE DIAMETER 3 4 IN

Shelly Van Doren hired a contractor to refinish her kitchen The contractor said the job would take 45 hours To date the contractor has worked the following hours Monday Tuesday Wednesday 5 Thursday Friday 34 91 Number of hours 71 10 How much longer should the job take to be completed

A directed line segment begins at F 10 4 ends at H 8 4 and is divided in the ratio 6 to 2 by G What are the coordinates of G 3 3 5 O None of the other answers are correct O 1 6 5 O 3 5 2 O 2 5 2

22 Sporting Goods For 1998 through 2005 the sales S in billions of dollars of sporting goods can be modeled by S 0 007 0 1t2 1 4x 70 analis Towin where t is the number of years since 1998 In which year were sales about 78 billion

eason that best supports Statement 3 in the give proof A Subtraction Property of Equality B Multiplication Property of Equality C Addition Property of Equality D Substitution Given m A 5 mzB and m B 20 Prove mzA 100 Statement 1 mzA 5 m B 2 m B 20 2 mzA 5 20 Reason 1 Given 2 Given 3

The time t in minutes you need to type a certain paper varies inversely with the rate r in words per minute that you can type When typing 40 words per minute you can finish in 50 minutes Find the constant of proportionality and write an equation relating t and r t

Let A a 2 x 2 be a square matrix such that Tr A 5 If f x det A xl and f A A aA 31 where I is identify matrix of order 2 then The value of Tr 3A 1 2 a 1 3A 1 31 is O 0 05 07 O10

Special Cases and Applications Progress The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer Esmerelda rents a car from a company that rents cars by the hour She has to pay an initial fee of 50 and then they charge her 8 per hour She has 150 available to spend on car rental What is the greatest number of hours for which she can rent the car The car cannot be rented for part of an hour O 12 hours O 18 hours O 13 hours 12 5 hours Question ID 120659

829 Exercises 10 16 write the first four of each sequence whose general term is given 1 a 3n 2 2 a 4n 1 3 An 3n 4 An 5 An 6 An 7 An 8 An 9 an 10 An 11 1 3 3 n 1 3 1 n 3 1 n n 4 2n n n 4 3n n n 5 1 1

Which pairs of triangles appear to be congruent Check all that apply 1 3 2 4 A Triangles 3 and 4 B Triangles 2 and 3 C Triangles 2 and 4 D Triangles 1 and 3 E Triangles 1 and 2 F Triangles 1 and 4

Determine if the triangles can be Write your answer on the line provided If not congruent write not congruent 1 2 3 5 4 A Complete the proofs using the most appropriate method Some may require CPCTC 7 Given LBAC ZEDC BC EC Prove AABC ADEC 8 Given IKIM ZIKM LMK 6 D M B

At a bowling alley the cost of shoe rental is 2 25 and the cost per game is 4 25 If f n represents the total cost of shoe rental and n games what is the recursive equation for f n Of n 2 25 4 25n n 0 Of n 2 25 4 25 n n 0 Of n 4 25 f n 1 f 0 2 25 Of n 2 25 4 25 f n 1 f 0 2 25

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

Question 13 of 15 Which of the following systems of linear inequalities is represented by the solution graphed below OA x22 and y x OB x 2 and y2 x C v 2 and s

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

114 Listed below are prices in dollars for one night at different hotels in a certain region Find the range variance and standard deviation for the given sample data Include appropriate units in the results How useful are the measures of variation for someone searching for a room 145 The range of the sample data is 198 dollars Round to one decimal place as needed The standard deviation of the sample data is Round to one decimal place as needed 99 Part 2 of 4 278 207 Points 0 29 of 1 80 146 274

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

An unusual number cube with 6 sides has the numbers 2 2 4 4 6 and 6 on its faces It is rolled once Match the outcome to its probability 1 P2 or 4 2 P multiple of 2 3 P multiple of 3 4 Plodd prime numbers 0 1 3

In Texas the distance from Austin to Brownwood is 141 miles It is 171 miles from Brownwood to Corsicana and 157 miles from Corsicana to A Determine the angle between the routes from Brownwood Show your work

13 A camper wants to protect her bag of food from bears She decides to tightly stretch a rope between two trees and hang her bag from a point exactly halfway along the length of the rope The first tree is 10 feet east and 6 feet north of her firepit The second tree is 5 feet west and 8 feet north of her firepit The rope is attached at a height of 8 feet to the first tree and a height of 9 feet to the second tree Let the firepit represent the origin movement east of the firepit represent movement in the direction of positive x movement west of the firepit represent movement in the direction of negative x movement north of the firepit represent movement in the direction of positive y and movement above the firepit represent movement in the direction of positive z 1 Write the coordinates of the points on the trees where the rope is attached 2 Find the distance between the points in part a Use sqrt to indicate a square root For example 3 would be written sqrt 3 3 Find the coordinates of the point where the food bag is hung 4 If the food bag is 1 2 feet long when hung and bears can reach a height of 7 5 feet when ar s food safe from haars2 Explain why not

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

Determine whether CA CB is defined If it is defined express the result as a single matrix if it is not say not defined 44 B 2 A 06 4 11 5 1 C 52 52 21 58 2 21 0 Select the correct choice below and if necessary fill in the answer box to complete your choice A The expression CA CB is defined CA CB B The expression CA CB is not defined

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

The map of a campground is shown below Campsite C first aid station F and supply station S lie along a straight path The path from the supply station to the tower T is perpendicular to the path from the supply station to the campsite The length of path FS is 400 feet The angle formed by path TF and path FS is 72 The angle formed by path TC and path CS is 55 Campground Map C 55 A Campsite F 72 Tower 400 ft First aid Supply station

5 A ladder is leaning against the side of an empty display pool at the local aquarium The top of the ladder is touching the 25 foot mark on the pool wall at a 59 angle a What is the angle of elevation from the foot of the ladder to the top of the ladder b Estimate the length of the ladder Round your answer to the nearest whole number if necessary

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