Math Questions

In a lottery the top cash prize was 655 million going to three lucky winners Players pick four different numbers from 1 to 52 and one number from 1 to 43 A player wins a minimum award of 400 by correctly matching two numbers drawn from the white balls 1 through 52 and matching the number on the gold ball 1 through 43 What is the probability of winning the minimum award

1 The bicyclists were 300 miles apart at 3 p m and were headed toward each other If they met at 9 p m and one was traveling 20 miles per hour faster than the other what was the speed of each bicyclist

6 The surface area of a small toy ball is 18 square inches If the radius of the ball is tripled what will be the surface area of the new larger ball in square inches F 18 in H 54 in G 36 in 2 J 162 in 2

24 Mason is building a 3 D model of a house for a project His model consists of a triangular prism on top of a rectangular prism as shown in the diagram 5 in 8 in 14 in 9 in Which measurement best represents the total volume of Mason s model house in cubic inches F 1 218 in 3 H 1 638 in 3 G 1 323 in 3 5 040 in 3

Given the image below where the circle is tangent to two sides of the rectangle and has a radius of 3 cm The width of the rectangle is 8 cm What is the probability of choosing a point in the unshaded area Round your answer to the nearest hundredth

Consider the figure where line segment MN is parallel to line segment PQ M P 1 4 2 3 5 N Q Which statement must be true Since m 1 m 2 m 3 180 m 1 m 4 and m 3 180 m 1 m 4 and m 3 m25 we can prove tha m 4 m 2 m 5 180 Since m 1 m 2 m 3 180 m 1 m 5 and m 3 m 4 we can prove that m 5 m 2 m 4 180 Since m 1 m 2 m 3 360 m 1 m 4 and m 3 m 5 we can prove that m 4 m 2 m 5 360 Since m 1 m 2 m 3 360 m 1 m 5 and m 3 m 4 we can prove that m 5 m 2 m 4 360

Select the correct answer from each drop down menu Javier purchased a digital camera for 384 The value of the camera depreciates by 25 every year This situation represents exponential decay The rate of growth or decay r is equal to year It will take years for the value of the 0 75 0 25 1 25 So the value of the camera each year is a to reach 162 Reset Next times the value in the previous

There are 28 dogs and 12 cats at Oasis Pet Resort There are 19 dogs and 6 cats at Happiness Pet Hotel Choosing which two animals describes a pair of dependent events SOA OB C OD one of the dogs at Oasis Pet Resort and then a second dog from Happiness Pet Hotel one of the cats at Happiness Pet Hotel and then a second cat from Happiness Pet Hotel one of the dogs at Oasis Pet Resort and then one of the cats at Happiness Pet Hotel one of the dogs at Oasis Pet Resort and then one of the cats at Oasis Pet Resort

The function P m 2m represents the number of points in a basketball game P as a function of the number of shots made m Given that the number of shots made is 40 find the number of points label required

4 A company manufactures cylindrical containers that each have a volume of 6 cubic feet For a new container design the company plans to keep the same height for the container and double the radius Which statement best describes how this change will affect the volume of the container F The volume will be multiplied by a H The volume will be multiplied by a factor of 0 5 factor of 2 G The volume will be multiplied by a factor of 4 J The volume will be multiplied by a factor of 0 25

A particle is moving along an axis Its displacement s units at time t seconds is determined by s t t 4t 5 At t 3 seconds is the particle moving toward or away from the axis origin At t 3 seconds is the particle speeding up slowing down or neither Explain

Refer to the following scenario and diagram below to solve the following problems A ski team with 14 members has eight 8 members who ski downhill five 5 members who ski cross country and seven 7 members who are jumpers Some skiers participate in more than one event according to the overlapping regions in the Venn diagram Find the probability of each event if a skier is selected at random Downhill 3 3 2 2 1 Cross country 2 0 Jumpers 12 does not ski cross country

Select the correct answer from each drop down menu Elwood invested 5 000 in a money market account and has been tracking its progress He found that after 3 years the account held 7 100 and after 8 years the account held 10 350 Use this information to complete the statements Over the first 3 years the value of the account increased at the value of the account increased at an average rate of approximately over the last 5 years Over the entire 8 years annually

Tessa has recently inherited 5600 which she wants to deposit into a CD account She has determined that her two best bets are an account that compounds monthly at an annual rate of 4 7 Account 1 and an account that compounds semi annually at an annual rate of 5 1 Account 2 Step 1 of 2 Which account would pay Tessa more interest Answer Keypad Keyboard Shortcuts

The number of bats in a colony is growing exponentially After 3 years there were 280 bats After 5 years there were 1120 bats If the colony continues to grow at the same rate how many bats are expected to be in the colony after 11 years Do not include units in your answer

Question 20 Find the inverse of f x I f x Question Help Video 2x 5x 2 4

A rectangular auditorium seats 2408 people The number of seats in each row exceeds the number of rows by 13 Find the number of seats in each row Answer How to enter your answer opens in new window seats EEEF Keyboard

Let M be the region in the first quadrant bounded above by the graph of y 3x and below by the graph of y 2 Which of the following gives the volume of the solid generated when region M is revolved about the vertical line 3 3 3 dy A v L 1 6 dy 2 4 1

5 To find the height of a pole a surveyor uses a theodolite The theodolite is 4 ft tall The surveyor stands 140 feet away from the base of the pole Then she measures the angle of elevation to th top of the pole to be 44 What is the height of the pole Round the answer to the nearest foot O O X 139 ft 147 ft 135 ft 140 ft 44 4 ft

Use the frequency histogram to complete the following parts a Identify the class with the greatest and the class with the least relative frequency b Estimate the greatest and least relative frequencies c Describe any patterns with the data a The class with the greatest relative frequency is 35 to 36 centimeters Type integers or decimals Do not round Use ascending order The class with the least relative frequency is 39 to 40 centimeters Type integers or decimals Do not round Use ascending order b The greatest relative frequency is about Relative frequency 0 25 0 24 0 15 0 1 0 05 Female Fibula Lengths 30 5 31 5 32 5 33 5 34 5 35 5 36 5 37 5 38 5 Length in centimeters

Aldo has two coupons for pants Coupon A 55 rebate on 87 pants Coupon B 60 off of 87 pants Choose the coupon that gives the lower price Then fill in the blank with the correct value Coupon A gives the lower price The price with coupon A is less than the price with coupon O Coupon B gives the lower price The price with coupon B is less than the price with coupon A

The table below describes phone calls made on the planet K 2L last year The columns show calls dialed by men versus women and the rows show the distribution of call lengths Note that this is not real data There were 312 480 000 phone calls made by women that lasted 30 minutes or more How many calls made by men lasted 0 to 5 minutes

A Triangle DEF is shown If a circle is inscribed in the triangle which angle bisectors will pass through the center of the circle B D only the bisector of angle D E the bisectors of angles D E and F only the bisectors of angles D and E D only the bisectors of angles D and F

An investor puts 2 500 into a life insurance policy that pays 8 5 simple ann interest If no additional investment is made into the policy how much accumulated interest should the investor expect at the end of 10 years

The graph of a polynomial is shown below Which of the following identifies the ordered pair coordinates of the extreme value 10 10 10 A 2 2 B 1 2 C 2 2 D 2 2 10

Express your answer as a polynomial in standard form f x 2x 7x 3 g x 3x 13 Find gof x

Summer is buying a condominium that sells for 140 000 The bank is requiring a minimum down payment of 15 To obtain a 15 year mortgage at 3 5 Summer must pay 2 points at the time of closing What is the cost of the 2 points on the mortgage Cost of points

2 Match the steps for constructing a congruent line segment to their pictures 1 Step 2 Draw a second line segment that is longer than the first Y 2 Step 3 Without changing the compass setting put the compass point on the new endpoint on a new line Make a small arc that intersects the line 3 Step 1 Put the point of the compass on one endpoint of the segment to be copied Change the compass setting so that the pencil end is just touching the other endpoint make a small arc to see this 4 Step 4 That intersection is the final endpoint of the copied segment a b A A A A B B B

Performance Task Interior Designer You are an interior designer and plan to have part of a floor tiled with a pattern that requires 36 square tiles The tiles come in whole number side lengths from 2 to 6 inches You need to decide which size would be most appropriate so you utilize some of your mathematics know how For this Performance Task use these definitions to make sense of the problem and to calculate your final answers Area formula The area of a square is given by following formula Area width height But since the width and height are by definition the same the formula is usually written as Area s where s is the length of one side Interior designer Interior designers create and improve interior spaces in homes and buildings making them safe functional and visually pleasing They must understand the geometry of spaces 1 Write a function for the area where x is the side length of the tile 2 points Area Hint Multiply the area of each tile by the total number of tiles

The table shows the favorite cookie of 50 children in a survey Favorite Cookle Chocolate chip Oatmeal Peanut butter Sugar Other If this data were to be made into a circle graph how many degrees would be needed for the chocolate chip cookie section A 25 B 50 C 72 D 90 Number of Children 25 5 10 5 5 E 180

h each transformation or sequence of transformations to an equivalent transformation or sequence of transformal a 90 counterclockwise rotation about the origin a 180 rotation about the origin a 90 clockwise rotation about the origin a 90 counterclockwise rotation about the origin and then a 180 rotation about the origin a reflection across the x axis and then a reflection across the y axis a 90 clockwise rotation about the origin and then a rotation 180 about the origin

Assume that the sales of a computer retail store are approximated by a linear function Sales were 790 000 in 1981 and 2 020 000 in 1986 Let x 0 represent 1981 Find the equation in y mx b form giving yearly sales Estimate sales in 1989 Oy 246 000x 790 000 y 2 758 000 in 1989 Oy 307 500x 790 000 y 3 250 000 in 1989 Oy 307 500x 790 000 y 2 942 500 in 1989 Oy 205 000x 790 000 y 2 635 000 in 1989

Use the graph to write an equation of the line Interpret the slope Tree height feet The height increases feet each year The height Increases 1 foot every 1 5 years Tree Growth 2 Age years 4 X The height increases 1 5 feet each y The height Increases 3 feet every 24 05

The table below shows the results of a consumer survey of annual incomes in 100 households Income 0 14 999 15 000 24 999 25 000 34 999 35 000 44 999 45 000 or more What is the probability that a household has an annual income less than 25 000 OA 0 28 B 0 55 OC 0 21 Number of households 7 21 27 30 15 D 0 72

A garden is shaped like a regular hexagon Each side of the hexagon measures 10 meters and the heigh of one of the isosceles triangles in the hexagon is about 9 meters Using these dimensions what is the area of the hexagon The area of the hexagon is m

Let D be the domain and let f be the possible function Determine if the relation is an example of a function D xl x is a person s social security number f x the person s name Yes One output results in one input Yes One input results in one output No At least one input results in two outputs No At least one output results in two inputs

Classify the following statistic as descriptive or inferential 14 out of the 25 students taking Mr Howard s College Algebra class passed the course Descriptive

Nikki walked on a straight road for 4 kilometers at a direction that is 30 to the north from the eastward direction Here are a few vectors where a d 4 km

All changes saved 14 Macy s starting balance in her checking account was 654 98 She wrote one check in the amount of 321 45 and made a deposit that she forgot to write into her check register At the end of the month Macy s ending balance was 452 78 Find the amount of the deposit 114 38 116 74

Which cube root equation shows a y axis reflection a vertical stretch a left horizontal translation and an upward vertical translation Oy 3 2 1 2 Oy x 1 2 Oy 4 5 1 Oy x 2 3

A retailer needs to purchase 10 printers The first printer costs 57 and each additional printer costs 3 less than the price of the previous printer up to 15 printers What is the total cost of 10 printers 552 90

A metallurgist has one alloy containing 21 aluminum and another containing 63 aluminum How many pounds of each alloy must he use to make 48 pounds of a third alloy containing 53 aluminum Round to two decimal places if necessary

Mario started at home walked from the post office to the grocery store and then back home Assuming his walk is represented by the image provided calculate the total distance he traveled Each unit on the graph represents one mile 6 5 4 Home 2 2 O 13 41 miles O 16 miles O 15 41 miles O 18 miles 4 3 3 2 1 0 1 2 1 ND 2 3 4 1 2 3 Post Office 3 2 4 5 6 7 8 9 10 11 Grocery Store 6 2 12

Celect the correct answer arah sells fruit trays at a salad shop Last week she sold 450 frult trays for 8 per tray In previous weeks she found that for ever 0 85 Increase in the price she sold 15 fewer fruit trays Which equation can be used to find Sarah s weekly sales income in dollars y after x price Increases of 0 85 O A y 12 75x2 262 5x 3 600 OB y 12 75x2 482 5x 3 600 O C y 12 75x2 272 5x 3 600 12 75x2 502 5 3 600 D y

Suppose you plot points 1 8 5 5 0 0 and 6 3 and you are told that the resulting figure QRST is a parallelogram Which of the following statements about the parallelogram is not true T 5 5 75 1 8 105 Q 0 0 Side SR is congruent to side QT The diagonals bisect each other Side ST is congruent to side SR The measure of ZQ is 105 75 R 6 3

6 You and a friend are playing horseshoes on a very uneven lawn You both throw a horseshoe toward a stake in the ground Think of the point where the stake enters the ground as the origin Your horseshoe lands 2 3 feet east of the origin 1 5 feet north of the origin and 0 5 feet below the origin Your friend s horseshoe lands 1 7 feet west of the origin 2 5 feet north of the origin and 0 5 feet above the origin What is the distance between the horseshoes 17 feet 3 2 feet 33 feet 6 feet 1

The value y in dollars of a painting after x years can be represented by the function y 6000 1 25 How much is the painting worth after 6 years to the nearest dollar O 22 888 7 169 O 36 241

19 4 B 20 Gar D HT 10 5 O Find the composition of transformations that map ABCD to EHGF Reflect over the axis then translate x y Note Enter x or y for axis m 2 4 5 6 Enter

A person invests 8000 dollars in a bank The bank pays 5 interest compounded monthly To the nearest tenth of a year how long must the person leave the money in the bank until it reaches 14100 dollars

elect all the Identify which functions have complex roots by selecting the function names on the provided coordinate plane 8 a 6 A4 2 3 6 192 4 6 2 6 1 1 ibi d 8 X