# Basic Math Questions and Answers

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Basic Math
How many marbles each with a volume of 36 cubic centimeters are needed to fill in a cylindrical vase with a radius of 6 centimeters and a height of 28 centimeters O 6 marbles 09 marbles O 14 marbles O 28 marbles
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Here is a right cylinder What is the one shape of cross section we could create by slicing the cylinder perpendicular to its base Choose 1 answer Rectangle Ellipse Shape with two edges one straight and one curved
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points Identify the recursive formula for the sequence 900 850 800 750 f n f 1 900 f n f n f n f n f n 1 50 if n 1 f 1 900 f n f n 1 50 if n 1 f 1 900 f n f n 1 50 if n 1 S f f 1 850 f n f n 1 50 if n 1
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Situation A 15 gram sample of a substance that s a by product of fireworks has a k value of 0 1401 N Noe kt No initial mass at time t 0 N mass at time t k a positive constant that depends on the substance itself and on the units used to measure time t time in days Find the substance s half life in days Round your answer to the nearest tenth Enter the correct answer DONE
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5 A band is trying to decide how to price tickets for its next concert Their market research suggests that if they price the tickets at 20 per ticket then they will sell 1000 tickets For each 2 increase in ticket price the number of tickets they will sell decreases by 5 Write a formula for N p the number of tickets they will sell if they price the tickets at p dollars per ticket
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In camellia plants flower color is controlled by a single gene with codominant alleles A camellia plants with red flowers RR is crossed with a camellia plant with white flowers WW What are the expected phenotypes of the offspring of this cross OA O B OC O D All will have red flowers Half will have red flowers and half will have white flowers All will have pink flowers All will have both red and white flowers
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Directions Use the given scenarios and the information you have learned about Fiscal and Monetary policy to complete the questions that follow Over the past 3 years prices in Belarus have risen by 4 as overall economic growth has increased by 5 while unemployment rates are 1 3 Aram is finding that all goods even necessities cost more at the stores He is worried he may have to cut back on certain purchases The Results As the money supply increases decreases When that happens Aram will see prices rise fall businesses will get more less as the economy expands contracts money and eventually unemployment increases decreases
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The equation of a circle in general form is x y 18x 36y 369 What is the equation of the circle in standard form O x 9 y 18 36 x 9 y 18 81 x 18 y 36 36 x 18 y 36 81
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Two dice are rolled one after the other Construct a sample space and determine the probability that the sum of the dots on the dice total 6 The probability that the sum of the dots on the dice total 6 is Type an integer or a simplified fraction
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Which of the following statements are equivalent to There exists a prime number greater than 2 that is even Choose each correct answer Select all that apply All prime numbers greater than 2 are odd Some prime numbers greater than 2 are even Some prime numbers greater than 2 are odd All prime numbers greater than 2 are even
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In response to rising concerns about identity theft the number of models of paper shredders a company manufactures increased approximately steadily from 3 models in 1994 to 35 models in 2008 Finc average rate of change of the number of shredder models manufactured per year between 1994 and 2008 The average rate of change of the number of paper shredders manufactured per year between 1994 and 2008 was Type an integer or decimal rounded to two decimal places as needed
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Drag each coordinate pair to the correct location on the table Each coordinate pair can be used more than once but not all coordinate pairs will be used A system of inequalities is graphed below 2 5 6 4 5 1 3 3 6 4 Inequality 1 1 2 Y 4 6 4 4 6 2 2 Determine if each point satisfies one of the inequalities or the system graphed Then place each solution point in the correct category If the point is a solution for more than one category place the point in each category that is satisfied h 1 1 2 6 Inequality 2 6 X 3 4 System
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14 The polygon below was a square with 20 sides before a triangle was removed What is the new perimeter of the polygon in meters F 66 G 70 304 H 76 J 78 K 80 20 12 14 garning Targets
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Suppose that there were a positive correlation between the variables u and v If vis 24 when u is 10 which of these is most likely to be the value of v when u is 20 OA 24 OB 6 O C 12 O D 48
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Guided Practice 20 100 ft Angles of Elevation and Depression Find the value of x Round the length to the nearest tenth Click or tap Math Notes to see the definitions of sine cosine and tangent A 94 0 ft B 36 4 ft C 34 2 ft Text to Spe D 0 342 ft
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15 When Brad threw the winning touchdown pass was 15 yards behind the 50 yard line and 17 yards from the sideline as shown in the figure below How far was Brad from the center of the end zone when he threw the pass Round your answer to the nearest yard 54 A 66 B 71 C 76 D 79 E 84 50 15 120 17 10
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One of the lamp posts at a bank has a motion detector on it and the equation x 15 y 12 25 What is the greatest distance in feet a person could be from the lamp and be detected O 5 ft 10 ft 50 ft O125 ft describes the boundary within which motion can be sensed 2 3 4 5 6 7 8 9 Ne
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John ran the 100 m dash with a time of 9 99 sec If this pace could be maintained for an entire 26 mi marathon what would his time be Notice that 1 m3 281 ft and 1 mi 5280 ft His time would be hr min sec Round the final answer to the nearest integer Round all intermediate answers to the nearest integer as needed
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T t models the temperature in degrees Celsius in Windhoek Namibia when it s t hours after midnight on a given day t 6 9 13 T t 19 25 31 When did the temperature increase faster Choose 1 answer B Between 6 am and 9 am Between 9 am and 1 pm The temperature increased at the same rate over both intervals
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At Imelda s fruit stand you bought 5 apples and 4 oranges for 10 and your friend bought 5 apples and 5 oranges for 11 Using this information is it possible to determine the cost of one apple and one orange from the fruit stand If so what do they cost If not why not Choose 1 answer A B Yes they should charge 1 00 for an apple and 1 25 for an orange Yes they should charge 1 20 for an apple and 1 00 for an orange No the system has many solutions No the system has no solution