Math Questions

he number of theater screens in a country in 2012 was 39 444 By 2017 the number had grown to 40 789 Let y be the number of theater screens in the sam country in year x where x 0 represents the year 2012 a Write a linear equation that models the number of theater screens in the country in year x b Use this equation to predict the number of theater screens in 2019 a The linear equation that models the number of theater screens in the country in year x is given by y Type your answer in slope intercept form Use integers or decimals for any numbers in the equation

Sean used cross multiplication to correctly solve a rational equation He found one valid solution and one extraneous solution If 1 is the extraneous solution which equation could he have solved OA The equation is OB OC The equation is O D 10 2 1 cross multiplying The equation is multiplying ts t cross multiplying The equation is cross multiplying 15 3r S because 1 makes a denominator equal zero and is a solution of the equation derived from because 1 is a solution of both the original equation and the equation derived from cross is because 1 makes a numerator equal zero and is a solution of the equation derived from 10 10 because 1 makes a denominator equal zero and is not a solution of the equation derived from

Select the correct answer from each drop down menu Of the 16 cards drawn from a standard deck of 52 cards experimental probability of drawing a spade is a spade from a standard deck of cards is 5 of the cards are spades Based on the cards that were drawn the and the difference of the experimental and theoretical probabilities of drawing

Caleb was given a gift card for a coffee shop Each morning Caleb uses the card to buy one cup of coffee The original amount of money on the gift card was 45 and after buying 8 cups of coffee the card had a 25 remaining balance Write an equation for A in terms of x representing the amount money remaining on the card after buying x cups of coffee

Find a function of the form y Asin Bx or y Acos Bx whose graph matches the function shown below Leave your answer in exact form 5 A 3 2 M 19 18 17 16 15 14 13 12 11 10 986 54 3 2 1 2 3 5 1 2 3 4 5 6 7 8 C a

submitting this assignment Let s put your knowledge of linear programming to the test Recall in the video that Mr Green needed help figuring out how many plants to buy in order to maximize profit during the Bastille Day Sale Here is the information that Mr Green provided us Type of Plant Giant Potted Hanging Basket 105 100 95 90 85 70 65 Square Footage 7 4 Mr Green has 168 square feet of space available 210 gallons of soil and a budget of 252 Mr Green sells each giant potted plant for 28 and sells each hanging plant for 8 Goal Write a system of inequalities and determine which combination of plants will maximize profit for Mr Green 60 Gallons of Soil 14 2 Cost 14 5 4 Graph the system of inequalities 25 points 5 points for each inequality Algebra 2A 66505 05 Evaluate Graded Assignment

03 06 MC The hyperbolic orbit of a comet is represented on a coordinate plane with center at 0 4 One branch has a vertex at 0 10 and its respective focus at 0 14 Which equation represents the comet s orbit O O O y 4 x 36 y 4 x 100 36 64 52 1 64 1 x y 4 100 36 1 y 4 1 36

A race director is preparing for an upcoming marathon and estimates that the mean time to finish is 315 minutes Assume that the times are normally distributed with a standard deviation of 60 minutes Use this table or the ALEKS calculator to find the percentage of times that are shorter than 453 minutes For your intermediate computations use four or more decimal places Give your final answer to two decimal places for example 98 23

Tiffany sells two kinds of homemade tomato sauce A quart of her Tuscan sauce requires 6 tomatoes and 1 cup of oil A quart of her marinara sauce requires 5 tomatoes and 1 cups of oil She makes 4 profit on each quart of her Tuscan sauce and 5 profit on each quart of her marinara sauce She has 45 tomatoes and 10 cups of oil on hand Tiffany wants to maximize her profits from selling the sauce Let x represent the number of quarts of Tuscan sauce and y represent the number of quarts of marinara sauce Tiffany makes What are the constraints for the problem 6x y24 5x 2y25 O 02 54 56 x 45 y 10 6x 5y 45

The graph shows the approximate U S box office revenues in billions of dollars from 2000 to 2012 where z 0 represents the year 2000 U S Box Office Revenue Y 10 8 Revenue billions of dollars 02 4 6 8 10 12 x Year 0 2000 a Estimate the slope and y intercept of the graph Slope 1 intercept b Interpret your answers in part a in the context of the problem The approximate U S box office revenue Increased by about 0 22 billion each year from 2000 to 2012 and was 4 billion in 2000 The approximate U S box office revenue increased by about 0 22 billion each year from 2000 to 2012 and was 8 billion in 2000 The approximate U S box office revenue Increased by about 0 4 billion each year from 2000 to 2012 and was 8 billion in 2000 The approximate U S box office revenue Increased by about 4 billion each year from 2000 to 2012 and was 8 billion in year 2000 c How can you use your answers in part a to predict the U S box office revenue in 2018 O Write a linear model in slope intercept form then substitute 18 for y and solve for z Write a linear model in slope intercept form then substitute 18 for 2 and solve for y O Multiply the slope by 18 to predict the revenue There is no way to make a prediction because the rate of change is not constant

The graph shows the distance Henry drives on a trip What is Henry s speed Distance miles 160 Driving Time and Distance A 60 miles per hour B 30 miles per hour C 70 miles per hour D 40 miles per hour Time hours

Select the correct answer from each drop dow John and Hank work as gift wrappers at a toy store In 4 minutes John can wrap 2 small boxes In 5 minutes Hank can wrap 3 small boxes small boxes and Hank can wrap small boxes So Hank can wrap in 20 minutes John can wrap 20 minutes than John can Reset Next more small boxes in

The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d 30 sin 30 above the ground after t seconds How long will it take for the Ferris wheel to make one revolution 60 seconds 30 seconds 20 seconds 15 seconds t 15 where d represents the distance in feet of the person

4 Renato collected 100 pennies and recorded the data on each penny Here are his results of pennies 60 50 40 30 20 10 0 1960 1980 2000 Date on penny Which interval contains the median date a 1970 1980 b 1980 1990 c 1990 2000 d 2000 2010 O 2010 2020 2020

An amusement park is holding a contest for people who are in line before 7 00 a m The 42nd person in line wins free admission and so do the six people before and after that person Which graph could be used to determine the winners Difference in Position HORISO ference in Position 9 99 4488885 ITTTTT 45 21 18 15 12 18 24 30 36 42 48 54 60 66 72 78 84 Position in Line Difference in Position ference in Position 12 9 H 6 12 18 24 30 36 42 48 54 60 66 72 78 84 Position in Line

Fill in the blanks so that the resulting statement is true The equation 9x 4y 36 can be written in standard form by The equation 9x 4y 36 can be written in standard form by both sides by both sides by

A city is built on the banks of a river and some Islands in the river The map below shows the bridges connecting the various land masses Draw a graph that models the connecting relationships in the map below The vertices represent the land masses and the edges represent bridges connecting them Island Cis little more than a sandbar and is uninhabited A B C D E 171 Is it possible to find a path through the city that uses each bridge once If so enter the sequence of land masses vertices adrited fo

Select the correct answer from each drop down menu Mike and Breanna like to run after swim practice each day Usually they run the same distance x miles Today however they ran different distances Mike ran at 7 miles per hour and ran 2 more miles than usual Breanna ran at 6 miles per hour and ran 1 more mile than usual Complete the table to show each person s distance and rate which could be used to create rational equation relating their distance rate and time Mike Distance Rate

The endpoints of the line segment AB are 2 4 and 2 9 If the line segment AB is reflected across y axis then find the endpoints of the reflected line segment OA 2 4 and B 2 9 OA 2 4 and B 2 9 OA 2 4 and B 2 9 OA 4 2 and B 9 2

The access code for a garage door consists of three digits Each digit can be any number from 1 through 6 and each digit can be repeated Complete parts a through c a Find the number of possible access codes b What is the probability of randomly selecting the correct access code on the first try c What is the probability of not selecting the correct access code on the first try a Find the number of possible access codes The number of different codes available is b What is the probability of randomly selecting the correct access code on the first try The probability of randomly selecting the correct access code is Round to three decimal places as needed c What is the probability of not selecting the correct access code on the first try

SEQUENCES b Describe the domain and the range of the sequence SEQUENCES Post Te

Select the correct answer from the drop down menu A number cube is biased to land on the number 3 about 50 of the time It is rolled 42 times and the outcomes are recorded The least likely result for the number cube to land on the number 3 is times 25 18 et Next

O cm cm cm cm cm s The function V r models the volume of a basketball that is deflating due to a puncture If V r is measured in cm and r is measured in cm what are the units of V r 1 point rm s

LT 8 Three telephone wires connect two towers and the station How much wire is needed to connect Tower B to the station Tower A Station 130m 440 Tower B Round to the nearest tenth Just enter the number

12 The sales of lawn mowers t years after a particular model is introduced is given by the function y 5500 In 9t 4 where y is the number of mowers sold How many mowers will be sold 4 5 after a model is introduced Round the answer to the nearest whole number 9065 mowers 20 875 mowers 20 361 mowers

Single Over 0 But not over The tax is 7 825 7 825 31 850 31 850 77 100 77 100 160 850 160 850 349 700 349 700 And Over 10 of the amount over 0 3 Found the amount over S 788 15 of the amount over 7 825 4 Multiplied line 3 by 4 386 25 of the amount over 31 850 5 Added Lines 2 and 4 15 699 28 of the amount over 77 100 Aaron had a taxable income of 165 000 He figured his tax from the single taxpayer table above 39 149 33 of the amount over 160 850 1 Find his earned income level 101 469 35 of the amount over 349 700 2 Entered the base amount 11 en 6 Computed his monthly withholding would be

D Question 9 Which conclusion logically follows the true statements If negotiations fail the baseball strike will not end If the baseball strike does not end the World Series will not be played O If negotiations fail the World Series will be played O If negotiations fail the World Series will not be played O If negotiations do not fail the baseball strike will not end O If the baseball strike ends the World Series will be played Question 10

Final marks in Maria s Data Management course are based on 70 for term work 15 for the exam and 15 for the final course project What term mark did Maria receive if her final mark was 87 and she received 84 on the exam and 95 on her final project a 87 b 83 c 85 d 86

In a certain country people own a total of about 350 million fish cats and dogs as pets The number of fish owned is 14 million more than the total number of cats and dogs owned and 14 million more cats are owned than dogs How many of each type of pet do people in this country own A CHITETT The number of fish owned by people in this country is million the number of cats owned by people is million the number f dogs owned by people is million Type whole numbers

Carlos begins his workout by stretching Then he spends an equal amount of time on each workout machine The equation y 8x 10 represents the total time in minutes of Carlos workout if he uses x workout machines Explain what the slope and y intercept of the equation represent in this situation A Carlos spends 10 minutes on one machine and 8 minutes on another OB Carlos uses 8 workout machines for 10 minutes each OC Carlos spends 8 minutes stretching and 10 minutes on each workout machine OD Carlos spends 10 minutes stretching and 8 minutes on each workout machine

Select the correct answer A ferry takes several trips between points A and B It moves at a constant speed of 0 35 miles minute and takes the same route on each trip The total duration of a round trip from point A to point B and back is 80 minutes ignoring the time spent stopped at point B If d is the ferry s distance from point A in miles and t is the time in minutes which equation models the ferry s distance from point A for the duration of the trip O A O B OC d 10 35t 40 40 d 10 35t 80 80 d 10 35t 281 28

2 Complete the table below to show that m42 or theorem specifically for your reasons column Statements m22 m23 E H m21 m 4 mZEHF 90 mZGHF 90 Given mZEHF mZGHF mZEHF mZ1 m22 m GHF m23 m24 m21 m22 m23 m24 m23 Make sure to state the postulate Reasons Substitution Property of Equality

Christina owns a caf The graph shows the number of cups of tea that were sold at her caf each hour past noon Cups of Tea 250 225 175 150 125 100 75 50 25 1 12 2 3 4 5 6 7 Hours Since Noon T She can expect to sell approximately 00 8 9 Based on the model approximately how many cups of tea can Christina expect to sell during the eighth hour cups of tea

2 Cameron is forming a password containing 3 characters He has decided that the first character will be a capital letter and the last character will be a digit All other characters will be lower case letters How many unique passwords could Cameron form A 39 B 780 C 4056000 D 6760

11 A right triangle has a percent grade of 30 The slope of the triangle in lowest terms would be A 30 100 B 3 10 C 1 3 D Not enough information is given 12 Fill in the blanks The higher the percent grade is the of elevation is Therefore the higher lower the angle more less steep a ramp is

11 15 12 13 17 Use the diagram of the picnic table to answer the questions m 1 m2 Find the measure of all of the numbered angles m 3 m25 m 27 m 2 m 26 In the diagram AB EC m 1 58 m 2 47 and m2 3 26 Find the measure of each angle m 8 m22 m 4 14 16 18 m25 m23 m 4 m 29 26 1 56 2 3 A 1 A 4 E 6 5 7 26 5 82 8 9 D B

Consider a circle whose equation is x y 2x 8 0 Which statements are true Select three options The radius of the circle is 3 units The center of the circle lies on the x axis The center of the circle lies on the y axis The standard form of the equation is x 1 y 3 The radius of this circle is the same as the radius of the circle whose equation is x y 9 wwww 01 13 23

If f x exe 8 and g x f x lim x 0 g x 2x then Your answer needs to be in exact form Your written work should use calculus methods to find the limit and inlcude a justification for why you are able to use those methods

A class in Borrego Springs CA the desert placed a kiddie pool out in the big rainstorm When then came to school on Monday it had 5 inches of water On Tuesday it had 4 75 inches and on Wednesday it was 4 5 inches It continued this pattern until the pool was dry Choose the equation that models this pattern Select one O a H d 5 d O b H d 5 d O c H d 5 d O d H d d 5

Given this function f x 35 arcsin 11 an equation for the line tangent to the graph of y f x at the point where x Y is

30 2 points The pressure gauge which is reading in gauge pressure on a cylinder with a volume of 2310 cu in reads 1475 psig If the gas were transferred to new cylinder with a volume of 3465 cu in what would the pressure gauge on the new cylinder read Assume the temperature remains constant Boyles Law P V P V u 993 11 psig 978 43 psig 983 33 psig

Malik drew a scale drawing of a kitchen In real life a countertop in the kitchen is 3 feet wide It is 6 inches wide in the drawing What scale factor does the drawing use Simplify your answer and write it as a fraction

the diagram AC BB Show that AB CD using the segment addition postulate addition property and substitution property Fill in the table below A B Statements Given Segment addition Segment addition Addition property Substitution property 23 N 4 E H Statements m21 m24 mZEHF 90 mZGHF 90 mZEHF mZGHF mZEHF mZ1 m22 m GHF m 3 m24 m21 m22 m23 m24 2 Complete the table below to show that mZ2 m23 Make sure to state the postulate or theorem specifically for your reasons column Given D Reasons Reasons Substitution Property of Equality

Penn stacks all of his snowballs in a square pyramid The number of snowballs P n in n layers of the square pyramid is given b P n P n 1 n Which could not be the number of snowballs Penn has OA 5 OB 14 O C 30 OD 25

You are hiking and are trying to determine how far away the nearest cabin is which happens to be due north from your current position Your friendr walks 220 yards due west from your position and takes a bearing on the cabin of N 21 2 E How far are you from the cabin O Friend 21 2 A 608 yards B 589 yards C 638 yards D 567 yards 220 yd X You

Select the correct answer Here s another situation where we use radical equations and inequalities with various formulas from engineering science and physics One such formula is the formula for kinetic energy which is the energy that the movement of an object generates Kinetic energy can be calculated with the formula KE mass of object velocity of object where mass is in kilograms and velocity is in meters second Suppose the hardest a high school pitcher can throw a baseball is 35 meters second roughly 78 miles hour If the mass of the baseball is 0 145 kilograms which inequality symbolizes the velocity of the baseball O O 2 K 0 145 35 2 0 145KB 35 0 145 KE35 2 2K 35

Daniel is printing out coples of a presentation It takes 3 minutes to print a color copy and 1 minute to print a black and white copy He needs to print at least 6 copies and must have the copies completed in no more than 12 minutes If the solution region represents the number of color copies and black and white copies that Daniel can print determine which graph represents the solution set to the system of inequalities representing this situation

Which equation best models the set of data shown in this table y 0 11 2 19 OA OB y 2x 17 y 11 x 0 3 OC y OD 4 27 y 2x 17 11 x 0 3 4 3 4 3 6 35 8 37 10 40 12 44 14 45 16 48

Fill in the blanks to complete the coordinates for each point indicated in the first quadrant of the unit circle below 90 Z A 60 3 BLJ 45 C R 30 6 DJ 0 0 E Q Point Coordinates A B C D E D Type an exact answer for each coordinate using radicals as needed Use integers or fractions for any numb the expressions

The TSP tours starting at vertex A and returning to vertex A for the weighted graph below Find the cheapest route suggested by the NEAREST NEIGHBOR ALGORITHM 240 210 310 a 999 Ob 1020 Oc 915 d 960 200 230 D