Math Questions

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

Data was collected for 158 randomly selected 10 minute intervals For each ten minute interval the number of people entering the atrium of a large mall were recorded The data is summarized in the table below Number of Guests 80 99 100 119 120 139 140 159 160 179 Frequency Class width 54 12 43 40 9 What is the class width for this Frequency Distribution Table

If 25 American car owners are chosen at random what is the probabili that 23 or fewer people in the sample drive a car with an automatic transmission Assume independence between car owners 0 188 0 375

Cadmium a heavy metal is toxic to animals Mushrooms however are able to absorb and accumulate cadmium at high concentrations Some governments have a safety limit for cadmium in dry vegetables at 1 3 parts per mill ypothesis test is to be performed to decide whether the mean cadmium level in a certain mushroom i s not equal to the government s recommended limit Complete parts a through c below Determine the null hypothesis toi ppm Type an integer or a decimal Do not round

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

Calculate the perimeter of the rectangle shown below Enter the value for the perimeter in the first blank and enter the units in the second Enter units as ft or square ft or cubic ft Round your final answer to tenths if rounding is necessary Them 7 4 ft CahaA 5 8 ft

6 CDs can be manufactured for 0 19 each The development cost is 210 000 The first 500 discs are samples and will not be sold a Write function for the average cost of a disc that is not a sample b What is the average cost if 5000 discs are produced Show work c How many discs must be produced to bring the average cost under 10 Show work

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

An ellipse is formed when a plane slices through a cone Which of the following describes the relationship between the plane and the cone The plane is parallel to the base of the cone The plane is perpendicular to the base of the cone The plane is parallel to the slant edge of the cone and intersects the base of the cone The plane is at a slight angle with respect to the base of the cone but does not intersect it

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

Suppose K K and K3 are three independent and unbiased estimators of Their variances are in the ratio of 6 8 2 Z and Z3 are three other estimators of such that Which among Z Z and Z3 are unbiased estimators of OA Z Z and Z3 are all biased OB Z and Z3 are unbiased but Z is biased OC Z and Z3 are unbiased but Z is biased OD Z Z and Z3 are all unbiased Which among Z Z and Z3 would be the best estimator for OA Sufficient information is not provided to determine which estimator would be the best OB Z should be chosen since it is both unbiased and has the least variance OC Z should be chosen since it is both unbiased and consistent bo obogen since they are unbiased and have the least variances Z Z Z3 3K K K3 5 K 3K K3 5 K K 3K3 5

On a dogleg golf hole one golfer hits the ball 270 yards and then another 170 yards to reach the green The angle between the two hits is equal to 100 degrees How far would the golfer have to originally hit the ball for it to go directly to the same position on the green 150 463 yards 710

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

A study was conducted to determine the mean birth weight of a certain breed of kittens Consider the birth weights of kittens to be normally distributed A sample of 45 kittens was randomly selected from all kittens of this breed at a large veterinary hospital The birth weight of each kitten in the sample was recorded The sample mean was 3 56 ounces and the sample standard deviation was 0 2 ounces What is the margin of error for a 90 confidence interval on the mean birth weight of all kittens of this breed 0 20 0 049 0 1645 0 392

Ezra is training for a track race He starts by sprinting 100 yards He graduall increases his distance adding 5 yards a day for 21 days The explicit formula that models this situation is an 100 n 1 5 How far does he sprint on day 21 OA 200 yards OB 100 yards OC 225 yards D 205 yards

Tim works for a cell phone company and is testing their new biometric security feature He conducted a test in which 4 000 attempts were made to unlock the phone Of the attempts to unlock the phone 25 were made by someone other than the phone s owner The results of the test are shown in the table Owner Not the Owner Total OA 6 2 OB 8 8 OC Unlocked 2 418 232 2 650 9 6 Did Not Unlock 582 768 1 350 What is the probability that someone who is able to unlock the phone using the biometric security feature is not the owner Total 3 000 1 000 4 000

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

Suppose the circle graph shows the percent of people in a certain region with the various types of blood If one person in the egion is selected at random use the graph to determine the probability that the person has AB blood The probability is Simplify your answer Question Help AB AB B 2 B A 8 A 3 0 6 O

The value of a particular rookie baseball card was 2 00 when it was first printed Five years later when the player was at his peak the card wa valued at 25 00 Ten years after printing the card was valued at 8 00 Model the above scenario showing the value of the card y with respect to years since it was printed x Write the equation in standard form y ax bx c where a b and care real numbers rounded to the nearest tenth o 0 10 y Vo d X S 2 X 0 x 0 T a A B E 9 P P sin cos tan sin cos csc sec cot log log In tan 1 LANE U O

instructul Skyward bhoney cake pictur Harry surveyed soccer athletes on what drink they preferred during their athletic competition The results are in the following Two Way Frequency Table Gender Gender O 0 36 0 48 Girl Boy Total When converting the above frequency table to a two way relative frequency table what is the value of E O 0 75 Preferred Drinks Powerade 3 9 12 Girl Boy Total Gatorade 5 8 13 Preferred Drinks Powerade B Gatorade A D G tur E Total 8 17 25 H Total U LL

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

Katherine wants to determine the height x of a nearby tree She stands 53 feet from the base of the tree The measure of the angle of elevation from Katherine to the top of the tree is 41 Select all of the following that can be used to find the height of the tree Ox 53 sin 41 53 sin 49 Ox 53 cos 41 X 53 cos 49 Ox 53 tan 41 X X 53 tan 49

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