Basic Math Questions and Answers

Kristen and Martha have a company making widgets When working alone Kristen can make a widget in 6 minutes When working alone Martha can make a widget in 2 minutes How long would it take them working together to create a widget Round to 1 decimal place

Which graph shows this set of transformations applied to the parent cosine function A reflection across the x axis A shift of 2 units up A vertical compression by a factor of 0 5 7 6 5 3 2 1 1 2 K

A salesperson is given a choice of two salary plans Plan 1 is a weekly salary of 800 plus 5 commission of sales Plan 2 is a straight commission of 7 of sales How much in sales must she make in a week for both plans to result in the same salary How much in sales must she make in a week

The volume of coffee that must be dispensed is 354 mL 0 002 mL of coffee per cup The company randomly tested several cups of coffee from four different machines The average volume per cup from each machine is recorded in the table below Machine 1 2 3 4 Average Volume ml per Cup 353 995 354 001 353 998 354 005 Do all of the machines tested meet the specified tolerance Which machine s is acceptable if any Justify your answer using words and numbers Answer

Select the correct answer Polygon XYZW is dilated by a scale factor of 2 with point 7 as the center of dilation resulting in the image XYZW If point Tlies on YZ what can be said about Y Z OA Y z passes through point 7 but has a different slope than YZ OB Y z passes through point T and has the same slope as YZ OC Z does not pass through point T but has the same slope as YZ OD Y z does not pass through point 7 and has a different slope than YZ

Communication is an important skill in quantitative literacy Two statements are given below Give at least two reasons why Statement 2 is better than Statement 1 Statement 1 The population doubled in about 40 years Statement 2 The world population doubled from 1960 to 2000 from about 3 billion people to 6 billion a period of 40 years

The population of India was about 1 380 000 000 people in 2020 Which number best approximates the population as a single digit times a power of 10 A 1 10 OB 3 108 OC 1 10 9 OD 3 10

Three students attempt to define what it means for AB and CD to be perpendicular Fo O B D Can you match the teacher s comments to the definitions Definition of perpendicular lines Daniela s definition AB is perpendicular to CD if the measure of LAOC equals the measure of ZAOD Ori s definition AB is perpendicular to CD if AB and CD intersect perfectly sideways Kaori s definition AB is perpendicular to CD if one line can be mapped to the other by a rotation about point O of 90 Teacher s comments 27 Well done I hadn t previously considered defining perpendicular lines in terms of a rigid transformation like rotation but by golly it works Please rework your definition to use more precise mathematical language Well done Because the measure of ZCOD is 180 by the definition of a straight angle the measures of angles LAOC and LAOD must both be 90

1 Edgar is getting better at math On his first quiz he scored 57 points then he scores 61 and 65 on his next two quizzes If his scores continued to increase at the same rate what will be his score on his 9th quiz Show all work I a Write an explicit formula for the sequence Explain where you found the numbers you are putting in the formula b Identify the value of n and explain where you found it Use the explicit formula to solve the problem Write your final answer as a sentence

e Name Write your name here FOR EACH PROBLEM Write an equation in slope intercept form for the line that passes through the given point and is parallel perpendicular to the graph of the given equation Begin at the Start box and work your way through the maze until you reach the Finish box Passes through 4 3 Parallel to y x 5 Iy 2x 5 Passes through 1 4 Cerpendicular to y 2x 9 Iy 3x 7I Passes through 9 4 Parallel to y x 4 y 3 x 7 Passes through 14 2 erpendicular to y 2x 9 y x 5 Passes through 4 1 erpendicular to y x 11 y x 5 y x 2 x 11 y 3x 11 y 3x 2 y 3x 2 y x 9 y x 7 y x 9 Passes through 6 2 Perpendicular to y 3x 4 y 3x 2 Passes through 6 9 Perpendicular to y 3x 2 y 3x 7 Passes through 2 8 Parallel to y 3x 11 Ly x 2 Passes through 2 3 Perpendicular to y x 7 y x 9 Passes through 7 9 Parallel to y 2x 4 y 3x 4 y x 4 y 2x 4 y 2x q y 2x 15 25 y x 1 y x 5 not be used y x 15 Passes through 3 7 Parallel to y 2x 7 Iy 2x 4 Passes through 4 6 Perpendicular to y x 2 y 2x 2 Passes through 6 3 Parallel to y 2x 5 Iy 2x 9 Passes through 1 6 Perpendicular to y x 4 y x 1 T finish Amazing Mathemat

A factory began dumping toxic waste materials into a countryside lake Before the dumping began the estimated population of striped bass in the lake was 40 000 Since the dumping of toxic waste materials began the population has decreased by one half every month Determine the equation that represents this situation and use it to decide which of the following graphs represents the population of striped bass f x x months after the factory began dumping toxic waste materials into the lake f x 50 000 40 000 30 000 20 000 10 000 0 f x 50 000 40 000 30 000 20 000 10 000 0 1 2 1 W 3 2 3 Y 4 4 5 5 x f x 50 000 40 000 30 000 20 000 10 000 0 f x 50 000 40 000 30 000 20 000 10 000 0 1 1 2 3 X 2 Z 3 4 4 5 5 Xx

O Shown here are the three essential steps in a proof of the Pythagorean Theorem Why is the color blue kept the sa steps A B C DY because the blue areas remain constant in size because the blue areas are bnverted to squares because blue is used on the edges of the squares because the blue regions never equal the other regions in size Eliminate

O You are an accountant for a manufacturer of radios The demand function for the tablets is p 40 4x where x is the number of tablets produced in millions It costs the company 15 to make a tablet i Write an equation for the manufacturer s profit as a function of the number of tablets produced ii The company currently produces 1 million tablets and makes a profit of 21 000 000 but you would like to scale up production a bit What greater number of tablets could the company produce to yield the same profit 9 marks

Mr Cutler makes clay bricks and clay tiles to sell at maker fairs It takes him 10 minutes to make a brick and 20 minutes to make a tile Each bri uses 3 pounds of clay and each tile uses 2 pounds of clay He has 160 minutes available for making the bricks and tiles and has 20 pounds of clay on hand If he makes a profit of 2 on each brick and 3 on each tile how many bricks and tiles should he make to maximize his profit A OB OC OD Mr Cutler should make 7 bricks and 0 tiles to maximize his profit Mr Cutler should make 0 bricks and 8 tiles to maximize his profit Mr Cutler should make 7 bricks and 2 tiles to maximize his profit Mr Cutler should make 2 bricks and 7 tiles to maximize his profit

A rectangle is placed around a semicircle as shown below The width of the rectangle is 8 cm Find the area of the shaded region Use the value 3 14 for and do not round your answer Be sure to include the correct unit in your answer 00 8 cm cm cm cm S

The top of a ladder is resting on a tree branch If the ladder is 17 feet long and the base of the ladder is 8 feet from the tree how high is the tree branch Answer

Use a system of equations to solve the following problem How many ounces of a 33 alcohol solution and a 43 alcohol solution must be combined to obtain 35 ounces of a 41 solution Answer How to enter your answer opens in new window ounces of 33 alcohol solution

potent source of bias if any Using random digit dialing 1599 people were called and asked what obstacles such as childcare kept them from exercising Source Yankelovich Partners Inc for Shape Up America Not asking enough people Maybe they don t have children No source of bias Using the word obstacles

Select the correct point on the coordinate plane Which point can be used to form a right triangle to derive the distance formula to find the length of the line segment 4 4 N 20 2 4 2 X

Anna wants to rent movies from either Service A or Service B Service A charges 37 92 as a subscription fee with a charge of 2 18 per movie Service B charges 33 25 as a subscription fee plus 3 55 per movie Service B is running a special offer where the first movie is free Given that Anna always rents at least 1 movie in a given subscription period how many movies would she have to rent for the average cost per movie to be equal at Service A or Service B OA 6 OB O O C 1 OD 7

Seaside Fish Market sells halibut for 16 49 per pound and red snapper for 11 69 per pound What is the total cost of 1 55 pounds of halibut and 2 77 pounds of red snapper Round to the nearest cent O 63 80 total O 55 78 total O 63 08 total O 57 94 total

The figure below shows line r points P and T on line r and point Q not on line r Also shown is ray PQ Consider the partial construction of a line parallel to line r through point Q shown below The final step of the construction is to draw a line through points Q and S Once the construction is complete which reason contributes to proving the validity the construction When two lines are cut by a transversal and the vertical angles are congruent the lines are parallel When two lines are cut by a transversal and the corresponding angles are congruent the lines are parallel Definition of an angle bisector Definition of a segment bisector

The following list shows the grams of fiber per serving for each flavor of oatmeal at a grocery store 3 6 3 4 2 4 4 3 5 2 1 4 1 2 Create a histogram that correctly displays the data 7 6 atmeal Flavors 5 986 4 3 Fiber Content in Oatmeal 2

The rotation maps all 60 about O the center of the regular hexagon State the image of B for the following rotation B F R 2 OD O m E F A E D C

Camila invested 9 100 in an account paying an interest rate of 4 6 compounded continuously Assuming no deposits or withdrawals are made how much money to the nearest dollar would be in the account after 14 years

CR and DS are perpendiculars dropped from AB to PQ and AB is perpendicular to CR and DS If CR DS which statement must true O R OA M RCD mzSDB 2 OB m RCD m ACD C m RCD m2ACD 2 OD m RCD m2ACD 3 com ACOX D S B

Select the correct answer from each drop down menu A cash card has a starting value of 25 If the card is not used within the first year of its purchase the value on the card begins to decreas 2 50 per month The relationship between the number of months after the first year and the amount remaining on the card is The independent variable is the The dependent variable is the

At a supermarket oranges cost 1 30 per pound and pears cost 1 90 per pound Misha spent less than 10 00 on 2 pounds of oranges and x pounds of pears Which inequality represents this situation O 1 30 1 90 x x 10 00 O2 1 30 1 90x 10 00 2 1 90 1 30x 10 00 2 1 30 1 90 x 10 00

Skye says that the two triangles below are congruent Margaret says that the two triangles are similar 5 cm 12 cm 5 cm 13 cm Are Skye and Margaret both correct Explain why

Savannah and her children went into a grocery store and she bought 22 worth of peaches and mangos Each peach costs 1 75 and each mango costs 1 50 She bough 6 more mangos than peaches Write a system of equations that could be used to determine the number of peaches and the number of mangos that Savannah bought Define the variables that you use to write the system Let P Let 111 the number of peaches the number of mangos System of Equations

A sphere fits inside a cube with the sphere s diameter equal to the width of the cube 20 centimeters What is the approximate volume of the cube not filled by the sphere O O O A 4189 cm B 3811 cm C 8000 cm D 5644 cm Volume of cube Voume of sphere p

Jacob is working two summer jobs making 12 per hour washing cars and making 8 per hour landscaping In a given week he can work no more than 13 total hours and must earn a minimum of 120 Also he must work no more than 10 hours washing cars and at least 3 hours landscaping If a represents the number of hours washing cars and y represents the number of hours landscaping write and solve a system of inequalities graphically and determine one possible solution

Jim began a 209 mile bicycle trip to build up stamina for a triathlon competition Unfortunately his bicycle chain broke so he finished the trip walking The whole trip took 9 hours If Jim walks at a rate of 3 miles per hour and rides at 31 miles per hour find the amount of time he spent on the bicycle What amount of time did Jim spend on the bicycle

achna has nickels dimes and quarters in her piggy bank She has 4 65 altogether She has three more quarter an dimes and twice as many nickels as quarters How many quarters does Rachna have 8 11 O22 O 41

Chris and Amy leave from work and drive in different directions Their paths are at a 90 degree angle from one another as shown in the following illustration OA 401 60 t 2 300 OB 40 60 t 2 Chris is traveling at 40 mph Amy leaves two hours later and is traveling at 60 mph Assuming that t represents the time that Chris has been driving which of the following equations can be used to calculate the values of t for which the distance between Chris and Amy is 300 miles OC 60t 40 t 2 OD 40 60 t 2 300 300 Chris 300 Amy

C1 6000 5000 4000 3000 2000 1000 0 payment in dollars S Benita Avi T 5 7 10 5 15 2 X 20 day Which rule do you think will pay more on Day 20 Use math to support your answer Use the sketch tool on the graph if that helps to illustrate your thinking Avi s Rule Benita s Rule

Write a rule to describe the transformation X M M R OA rotation 90 clockwise about the origin B rotation 90 counterclockwise about the origin C reflection across y x Reset Selection D rotation 180 about the origin

Select the correct answer An electronics store advertises that one lucky customer will be given a television at the store s 10th anniversary celebration On the day of the celebration 150 customers of which 82 are less than 30 years old and 68 are 30 years old or more complete a form to enter for the chance to win the television The manager of the store wants to select the winner by drawing a form out of a box but the box can only hold 100 forms Which method ensures both that the manager can use the box for the selection and that each customer has a fair chance of winning O A Divide the forms into two lots based on age Then randomly select one of the lots and place it in the box Randomly select the winning customer s form out of the box OB Randomly divide the 150 forms into five equal sized groups Then randomly select 4 of the groups and place them in the box Randomly select the winning customer s form out of the box OC Sort the forms alphabetically by last name Then place the first 100 forms into the box Randomly select the winning customer s form out of the box OD Randomly divide the 150 forms into three equal sized lots Then randomly select two of the lots and place them in the box Randomly select the winning customer s form out of the box

After the drama club sold 100 tickets to a show it had 300 in profit After the next show it had sold a total of 200 tickets and had a total of 700 profit Which equation models the total profit y based on the number of tickets sold x A y 300 4 x 100 OB y 300 2 5 x 100 OC y 300 4 x 100 D y 300 2 5 x 100

Julie ran a race 2 minutes faster than Teri did If Julie ran the race in 28 minutes which equation can be used to find the number of minutes m it took Teri to run the race OA m 2 28 OB m 2 28 OC 2m 28 D m m 28

Guided Practice The areas of two similar rectangles are 540 ft and 135 ft2 Find the similarity ratio of smaller rectangle to the larger rectangle A 1 2 B 1 3 C 1 4 D 2 5

Question 2 of 10 A community sports league is raising money by making custom shirts to sell at league games They plan to sell the shirts for 15 Each shirt costs 8 to make They spent 55 for advertising Use n to represent the number of shirts they sell Multiply this by the money they make for each shirt then subtract the advertising cost Which expression represents the money that the league raises A 55 158 n 8 55 OB 15n 8 O C 15 8n 55 O D 15 8 n 55

Karen Pete Rose and David are comparing their solutions to a homework problem below 3 675 Select the student who correctly subtracted the rational expressions Karen 8 7 F 2 1 5 Rose H 8 7 s 8 2 s 5 7 1 2 5 71 8 1 3r 10 7 14 1 4 10 7r 14 Pete 8 5 7 1 2 2 5 13 40 7 14 5 35 10 12 61 54 r 3r 10 David 18 7 2 x 5 2 3 10

Solve 7p 5q 19p 12 for p Select one O a 5q 12 12 O b 12 5q O c 12 5q 12 O d 5q 12 Solve 17p 2q 5p 6 for q Select one O a 12p 6 O b 12p 6 O c 22p 6 O d 6p 3 Solve 13a 3 b 5 for b Select one O a 13a 3 5 O b 5 13a 3 O c 5 13 3a O d 5 13a 3

Given 3 m A 90 and m B m A Prove m B 30 Statement 1 3 m A 90 2 mA 30 3 m B m A 1 m B 30 Reason 1 Given 2 3 4 Transitivo Prar

Kylie went into a grocery store and bought 3 apples and 4 bananas costing a total of 6 50 Lily went into the same grocery store and bought 10 apples and 5 bananas costing a total of 17 50 Write a system of equations that could be used to determine the price of each apple and the price of each banana Define the variables that you use to write the system Let Let the number of apples the number of bananas System of Ed the price of each apple the price of each banana the number of items the price of all items

The sail of a boat is in the shape of a right triangle as shown below O a Which expression shows the length in meters of the base of the sail 6 points Ob Oc 50 d 7m 7 cosec 50 7 sec 50 cos ec50 7 cot 50

Solve for Q 5x 3xy for x Select one O a 5 3y Q O b Q 5 3y OC Q 5 3y O d 5 3y Q Solve T mv 2 2 for m Select one O a v T O b v 2T O c 2T v O d 2T v Solve 7x 11y 17 for y Select one Qa 7x 17 b 17 7x 11 O c 7x 17 11 O d 17 7x

A radioactive substance has a decay rate of 0 079 per minute How many grams of a 200 gram sample will remain radioactive after 1 hour Round the answer to the nearest tenth of a gram and do not include the unit in your answer Provide your answer below

Aidan went over a jump on his skateboard His height above the ground changed according to the equation y 16x 27x where x time in seconds and y height in feet If this equation is graphed is the point 1 7 0 a good approximation of an x intercept O No because Aidan spent about 0 6 seconds in the air 4 of 8 QUESTIONS No because Aidan reached a maximum height of about 0 6 feet Yes because Aidan reached a maximum height of about 1 7 feet Yes because Aidan spent about 1 7 seconds in the air