Basic Math Questions and Answers

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

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

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

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 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

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

Dylan plotted the points W 2 5 X 6 3 Y 2 1 and a fourth point Z to create rhombus WXYZ What is the area of rhombus WXYZ in square units O More information is needed to answer the question 08 04 016

Use a graphical method to solve the following equation 2x 3 x 3 0 The solution set is Round to the nearest hundredth

The graph given shows the number of minutes it takes a baker to decorate cupcakes Time minutes 33727 30 24 21 18 15 12 0636 9 0 5 15 10 20 25 Number of Cupcakes Decorated How many minutes does it take the baker to decorate each cupcake OA 0 83 minutes per cupcake B 1 2 minutes per cupcake cupcake minutes per cupcake O c 2 minutes per

You take a job as a Sales Associate and are offered one of two options to be paid Option One will pay you 500 per week plus a 6 commission on your sales Option Two will pay you 250 per week plus a 10 commission on your sales How much must be sold per week for the two options to pay the same amount

In Austin the use of landlines has been declining at a rate of 20 every year There are 51 000 landlines this year Which function can be used to determine the number of landlines after x years A f x 51 000 0 8 B f x 51 000 0 2 C f x 20 51 000 D f x 51 000 1 2

Which of these examples shows reasoning based on fact not assumption A I always greet customers at the front entrance so anyone who doesn t is just rude B Aram doesn t like filing so he probably doesn t like making copies either C Nile overheard two of his coworkers calling in sick so he offered to stay and work a double shift to help his manager D Lindsey notices that her boss leaves early when all the work is done so she does the same

Water Pollution in a January 2017 Washington Post ABC News poll online respondents were asked There is a proposal to offer nearly 140 billion dollars in tax cuts for private companies if they pay to build new roads bridges and transportation projects The companies then could charge tolls for people to use these roads bridges and transportation Do you support or oppose this proposal Do you feel that way strongly or somewhat Which question is this observational study designed to answer What proportion of voters are strongly opposed and what proportion of voters are somewhat opposed to the proposal What proportion of voters are against giving 140 billion in tax cuts to private companies What proportion of voters are against either giving 140 billion in tax cuts to private companies or against charging tolls for roads bridges and transportation

Chemicals in butter flavoring Workers in a microwave popcorn production plant in Missouri breathe chemicals that are part of the butter flavoring Are these workers at greater risk of developing lung problems To investigate this question 135 workers at the plant receive a survey but only 117 respond Researchers want to compare workers in the popcorn production area with workers who have jobs in other parts of the plant People in these other jobs are not directly exposed to the butter flavorings Of the 97 workers in the production area 30 reported experiences of shortness of breath Of the 20 workers in other jobs only 1 reported shortness of breath What can we conclude from this study Exposure to the chemicals in butter flavoring is associated with a greater incidence of lung problems such as shortness of breath The chemicals in the butter flavorings are causing shortness of breath because a much larger percentage of workers in the production area have shortness of breath

Consider the polynomials given below Determine the operation that results in the simplified expression below O A OB P x 4 3x3 2x 2 Q x x 2x2 3 x2 2 Q P P Q 5 x45x3 3x x 8

A tree has 99 400 leaves before autumn Once autumn begins the number of leaves on a tree decreases at a rate of 13 per day After t days o autumn there are fewer than 12 000 leaves on the tree Which inequality represents this situation and after how many days of autumn will the number of leaves on the tree be fewer than 12 000 OA 12 000 1 087 99 400 18 days OB 12 000 0 913 99 400 17 days O C 99 400 0 87 12 000 16 days 99 400 1 13 12 000 15 days OD

Lauren is designing a metal sculpture that contains a triangle with sides of 4 inches and 11 inches She is trying to determine possible lengths of the third side of her design Determine an inequality that shows all possible values in inches for the length of the third side of the triangle in Lauren s sculpture 7 x 15 7 x 15 11 x 15 11 x 15 ON TE

A local high school held a two day fundraiser selling lunches The equations shown represent the amount of money the school collected during the two days 12x 4y 152 32x 12y 420 In the equations x represents the cost of a chicken lunch and y represents the cost of a vegetarian lunch Which is the cost of the vegetarian lunch 9 O 11 13

Multi Step Equations Riddle Directions Solve each equation Then write the letter above the line that the answer corresponds to Who did Frankenstein s monster bring to the prom 3 R 14 p 8 E 4n 2n 4 O 6a 5a 33 N 7 4x 9 0 2 1 1 I 1 3r 2r 9 S 10 10x 1 9x G 3a 3a 16 8a 6 T L 37 3 5 x 6 2 U 23 x 3 5x D 3 4r 8 36 H a 5 5a 5 F 8 8x 6 6x 22

A new online music service has a collection of 1 500 songs It expects to triple the number of songs each year for the next few years Write an equation representing the relationship where x is time in years and y is the number of songs available 5 Jada saw a music video that her favorite artist recently posted online The equation v t 320 4 represents the number of views of the video t days since Jada saw the video a Find v 2 b What does v 2 represent in this situation

Use the dot plot to list the actual data entries What is the maximum data entry What is the minimum data entry Choose the correct actual data entries below 20 21 22 23 24 25 26 27 28 O A 121 122 123 124 125 126 127 221 222 223 225 322 323 423 523 OB 21 21 22 22 22 23 23 23 23 23 24 25 25 26 27 OC 21 22 23 24 25 26 27 OD 2 1 2 1 2 2 2 2 2 2 2 3 2 3 2 3 2 3 23 24 25 25 26 27 The maximum data entry is The minimum data entry is

Correct A swim team consists of 4 boys and 7 girls A relay team of 4 swimmers is chosen at random from the team members What is the probability that 2 boys are selected for the relay team given that the first 2 selections were girls Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth Answer How to enter your 3

29 58 13 5 A 14 5 B C B is the midpoint of AC D is the midpoint of CE and AE 29 Find BD The diagram is not drawn to scale D E

The person in the picture sights a pigeon above him If the angle the person is looking at is find in degrees Round your answer to two decimal places Ente 17 m 24 m

The amount of merchandise in millions that store A sold can be represented by A 13x 8x 3 The amount of merchandise in millions that store B sold can be represented by B 8x 3x 11 Find the total amount of merchandise that stores A and B sold 2 8

Select all the correct answers Look at the expression below 3 411 234 3 Which of the following statements are true about the expression The given expression is equal to 3 411 234 3 The given expression is equal to 3 411 234 3 The given expression is one third the value of 3 411 234 The given expression is three times the value of 3 411 234

A grain silo is constructed in the shape of an inverted cone atop a cylinder as shown belov O 18 ft What is the volume of this grain silo 10 ft F 20 ft A 1 350 cubic feet L 1 890 cubic feet 3 240 cubic feet

There are 17 books on a shelf 8 of these books are new The rest of them are used a What is the ratio of used books to all books on the shelf b What is the ratio of used books to new books X

The high speed chairlift at a ski resort transports skiers from the bottom to the top of the mountain in 12 minutes at a constant speed The times that riders are on the lift while it is operating properly are uniformly distributed The lift operator temporarily stops the lift when a skier falls from the lift at the bottom 7 What percent of the riders had been on the chairlift for less than 1 minute 8 What percent of the riders had been on the chairlift between 5 and 10 minutes when the stoppage occurred