Math Questions

Tutorial Exercise Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x axis Verify your results using the integration capabilities of a graphing utility y cos 5x y 0 X 0 X K 10 Step 1 To find the volume of a solid of revolution about the x axis use the horizontal By the washer method 7 10 The representative rectangle is shown in the figure The outer and inner radii of the solid are R x cos 5 x Cb axis of revolution X and r x 0 respectively

2 points Marissa and Tori can shovel a driveway together in 22 min If Marissa can shovel the same driveway in 70 minutes by herself how long would it take Tori by h self

2 At the local veterinarian school the number of animals treated each day over a period of 20 days was recorded 28 34 23 35 16 17 47 05 60 26 39 35 47 35 38 35 55 47 54 48 a Construct a stem plot for the data b Describe the distribution thoroughly Remember your S O C C S

University Bank pays 5 interest compounded quarterly on regular savings accounts and Rosemont Savings Bank pays 5 5 compounded semiannually Vasily and Oxana Cherchenko had 4 000 to invest for 4 years Based on the interest to be earned which bank offers the better investment

This question is designed to be answered with a calculator Water is leaking out of a tank at a rate of r t log t 2 in gallons per minute where t is the number of minutes since the tank started leaking How many gallons of water leak out of the tank between 2 and 8 minutes O 0 065 O 0 398 O 4 986 O 6 017

The shadow of a 16 ft tree is 20 ft long What is the angle of elevation from the ground to the sun Round to the nearest tenth of a degree 38 7 degrees O 25 9 degrees O 35 1 degrees 42 2 degrees

The cost in dollars to produce x litres of maple syrup for the Elmira Maple Syrup Festival is C x 75 x 10 where x 400 a What is the average cost of producing 625 L b The marginal cost is C x and the marginal revenue is R x Marginal cost at x litres is the expected change in cost if we were to produce one additional litre of syrup Similarly for marginal revenue What is the marginal cost at 1225 L c How much production is needed to achieve a marginal cost of 0 50 L

For the polynomial function f x 5x 25x2 125x 0625 find the zeros Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept x 5 cross x 5 touch x 5 touch

Sam purchased a new car for 17 930 The value of the car depreciated by 19 per year When he trades the car in after x years the car is wor no more than 1 900 Fill in the values of a b and cto complete the exponential Inequality of the form a b c that can be used to determine the number of years after which the car is worth no more than 1 900 0 101 VO 0 4 a b x c X S IV TC a A B P P E 9 P sin cos tan sin cos tan csc sec cot log logg in ZAN D U 00

Draw a point that belongs to the solution region of this system of inequalities y 1 5 4 y 6 Drawing Tools Select Point Click on a tool to begin drawing 10 8 6 2 8 6 2 Delete Undo 6 00 8 Res 10

2 Determine how many primes there are in the ranges 1 1000 1001 2000 and so on up to 9001 10000 Can you see why the Greeks might have wondered if they would run out Hint there are a number of websites that have lists of prime numbers Even easier use the Mathematica command Prime Pi k which gives the number of primes less than or equal to k

3 25H 2 25C 32 The above equation is true if Thea buys H pounds of ham slices and C pounds of cheese slices at her local deli The local deli charges 3 25 per pound of ham and 2 25 per pound of cheese According to the equation how much does Thea spend in total on both han and cheese slices

The two way frequency table below shows the preferred communication method of employees at a company based on years of employment with the company 0 to 7 years 8 or more years Total OA 44 79 OB O C OR 67 19 20 48 Text Message 36 12 48 48 84 Instant Message 49 22 71 What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication Phone Call 8 19 27 Email 21 43 64 Total 114 96 210

Suppose that you needed to make a pen for some small animals You have 13 m of fencing You decide to make a circular pen because if you wish to enclose an area using a given length of fencing then a circular fence encloses a larger area than a fence of any other shape What is the radius r of the pen Express your answer in meters to four significant figures

Drag each label to the correct location on the table A local caf serves tea coffee cookies scones and muffins They recently gathered data about their customers who purchase both a drink and a snack The given frequency table shows the results of the survey If approximately 24 of the customers surveyed have a scone with their tea and approximately 36 of the customers surveyed buy a muffin complete the column and row headings for the given table Muffin Coffee Cookie Total Tea 40 120 160 Scone 100 80 180 110 50 160 Total 250 250 500

4n 176 0 19 4n 4n START 26 Find mzC E 136 136 Find the value of b 76 64 62 440 19 Tind the value of x 16 3x 4y 1 16 4 y 60 3x 12 3 3 4 6 7 Find the value of p 2p 49 3x 4 5K 124 28 Find the value of h 130 56 59 4 9 50 116 2h find the value of g g 7 15 h 8 177 10 6 65 9 8 g 7 22 Find the value of y 25 3x 6 2 Find the value of f 72 f 30 er 5 89 3 find the value of k 18 3 6k k 10 51 9 Find mzC 119 x 187 479 61 194 119 119 669 TO FINISH 28F 611 x OMISSCRAFTYMATHIEACE

At LaGuardia Airport for a certain nightly flight the probability that it will rain is 0 07 and the probability that the flight will be delayed is o 19 The probability that it will not rain and the flight will leave on time is 0 75 What is the probability that it is raining and the flight is delayed Round your answer to the nearest thousandth

14 Three students take equivalent stress tests Which is the highest relative score meaning which has the largest z score value a A score of 144 on a test with a mean of 128 and a standard deviation of 34 b A score of 90 on a test with a mean of 86 and a standard deviation of 18 c A score of 18 on a test with a mean of 15 and a standard deviation of 5

Brownies are cut in the shape of right triangles The longest side of each brownie is 3 inches One brownie has a leg length 1 5 inches Which statement is true A All the brownies have a leg length of 1 5 inches because corresponding parts of congruent triangles are congruent B All the brownies are isosceles right triangles with leg lengths of 1 5 inches C None of the other brownies have leg lengths of 1 5 inches D You cannot make a conclusion using congruent triangles

Directions Find the rate of change slope Then predict the next interval Miles Per Hour 468 Hours 2 OP Rate of Change Slope Miles at 10 hours Miles 70 140 210 280 BOOKMARK 88 X

A sailmaker is designing a mainsail for a newly constructed sailboat The mainsail foot is 13 feet long the luff is 10 feet long and the luff makes a 50 angle at the head with the leach Luff Head Leech Foot Part A Determine the length of the leach 5 points Part B Find the area of the mainsail 5 points

5 What is the volume of a pyramid with a height of 10 units and a rectangular base with dimensions of five units by nine units OA 55 cubic units OB 150 cubic units OC 300 cubic units OD 450 cubic units

The symbol of a simple unprefixed SI unit has been left off of each measurement in the table below Fill in the missing unit symbols the mass of a US quarter how long a typical TV ad lasts the volume of gas in a car s full gas tank the length of a car 6 5 30 50 5 0

ose a table to fit in a very small space He has 5 choices and wants to choose the table with the smallest area Which of the table tops below has the smallest area Select the correct answer below O O 2 3 2 3 4 3

The drawing shows a the range of a sprinkler in the arboretum If the sprinkler reaches 3 yards what is the area covered in the green sector O square yards 3 O57 square yards O TT square yards T square yards

A piecewise function f x is defined by f x 3x 1 4 x 3x 4 x 7x 12 for x 3 for x 3 Part A Graph the piecewise function f x and determine the range 5 points Part B Determine the asymptotes of f x Show all necessary calculations 5 points Part C Describe the end behavior of f x 5 points

Based on the following calculator output determine the range of the dataset 1 Var Stats x 114 285714286 Ex 800 Ex 92018 Sx 9 91151326681 ox 9 17627820157 n 7 minX 102 Q 104 Med 115 Q3 122 maxX 128

Let R be the region bounded above by the graph of y 1 2 and below by the graph of y 22 1 for 1 1 as shaded in the figure above What is the volume of the solid generated when region R is revolved about the horizontal line y 3 A 15 C 35 12m D 16

G 0 B 1 C 1 Which of the following best describes the construction above A ray GE bisects angle FGH F H ray GE trisects angle FGH ray GE is parallel to ray GH only

Select the correct answer The depth of a pond decreases at a rate of 2 per year If the pond currently has a depth of 5 feet in approximately how many years will the depth of the pond fall below 4 feet OA 11 years OB 50 years OC 6 years OD 24 years

Question 8 of 8 Which polynomial represents the difference below 7x8 8x6 2x 9 4x 3x 3 OA 3x 5x x 2 OB 3x8 3x7 8x 2x 6 O C 11x8 11x x 2x 6 OD 3x8 3x7 8x6 2x 6

150 135 170 175 135 140 134 130 175 160 120 125 103 170 110 140 120 150 129 150 The number of calories contained in 20 randomly selected scoops of ice cream is shown above Construct a grouped frequency distribution for the data Construct the frequency distribution with five classes and let the first class begin with 103 Type your frequency distribution in the box below Note Do not worry too much about the spacing Do the best you can in the box I will figure it out

A A Which statement BEST describes Alex s construction B C f D B Alex constructed line CD parallel to line segment AB Alex constructed line CD congruent to segment AB Alex constructed line CD to be the angle bisector of segment AB Alex constructed line CD to be the perpendicular bisector of segment AE

The gas mileages in miles per gallon for 29 cars are shown in the frequency distribution Approximate the mean of the frequency distribution The approximate mean of the frequency distribution is Round to one decimal place as needed Gas Mileage in miles per gallon 27 31 32 36 37 41 42 46 Frequency 13 9 3 4

Question 8 Quadrilateral ABCD has vertices located at A 2 4 B 6 4 and C 1 6 as shown below y 9 8 7 6 3 F 2 2 G 0 0 H 3 2 4 3 2 8 7 6 5 4 3 2 1 0 1 2 2 1 3 A 7 5 3 4 5 6 789 B X Which of the following ordered pair for D would make this quadrilateral a parallelogram Answer

19 A local musician carries her portable speakers in a cylindrical container The dimensions of the container are shown in the drawing 15 in 3 in Which measurement is closest to the total surface area of the container in square inches A 424 12 in C 339 29 in B 791 68 in D 282 74 in

Let in a binomial distribution consisting of 5 independent trials probabilities of exactly 1 and 2 successes be 0 4 and 0 6 respectively Then the probability of getting exactly 3 successes is equal to O 2160 74 O 4320 74 O 4320 75 O 2160 75

16 A cylinder has a section removed in the shape of a sector with a central angle of 40 The dimensions of the cylinder are shown in the diagram G 40 117 cm What is the volume of the remaining portion of the cylinder in cubic centimeters F 104 cm H 468 cm 9 cm J T 6 5 cm 526 5 cm

11 A spinner with eight congruent sectors is spun and a fair six sided die is tossed during a game A B 1 12 4 5 What is the probability of getting an even number on the spinner and a 3 on the die 2 3 1 3 2 67 1 8 C D 48

A road crew uses the triangles shown in the diagram to measure the width of a sink hole across a highway from a safe distance away How wide is the sink hole 15 ft 13 ft 13 ft 15 ft A 18 ft B 15 ft C 13 ft D cannot be determined 18 ft

The rabbit population of Springfield Ohio was 144 000 in 2016 It is expected to decrease by 7 2 per ye Write an exponential function and use it to predict the rabbit population of Springfield in 2036 Rabbit population of Springfield in 2036 Round answer to the nearest whole number

8 J ASA Similarity Postulate AA Similarity Postulate SAS Similarity Theorem K SSS Similarity Theorem L Select the postulate or theorem that you can use to conclude that the triangles are similar P N M

Select the correct answer Each week Marcia travels to the office where she works the supermarket and a local fitness center The three locations represent the vertices of a triangle Marcia wants to move to an apartment that is equidistant from these three places Where should her new apartment be located OA the center of the inscribed circle of the triangle the center of the circumscribed circle of the triangle the point of intersection of the angle bisectors for the triangle the point of intersection of the perpendicular bisectors and the angle bisectors for the triangle B OC D Reset Next

The square pyramid shown below has a base with sides of 10 units The slant height of the pyramid is 8 units 10 The height is What is the vertical height h Round your answer to the nearest tenth 8 units

a P1 To walk from his house A to his school C Oscar has a choice of walking along the straight roads AB and BC or taking a direct shortcut AC across a field Find how much shorter his journey will be if he chooses to take the shortcut 560 m 110 b P1 The diagram shows a quadrilateral ABCD B 1200 m 9 cm 33 7 cm A C 3 marks 16 cm D a Find the perimeter of the quadrilateral 5 marks b Find the area of the quadrilateral

7 A spherical ornament is placed into a cube shaped box for shipping The surface of the ornament touches each face of the box as shown in the diagram A If the radius of the spherical ornament is 6 centimeters which measurement is closest to the remaining volume of the cube shaped box not taken up by the ornament in cubic centimeters A 1 728 cm C 823 cm 905 cm D 2 633 cm B

Julian went to the grocery store and bought bottles of soda and bottles of juice Each bottle of soda has 25 grams of sugar and each bottle of juice has 40 grams of sugar Julian purchased a total of 13 bottles of juice and soda which collectively contain 475 grams of sugar Determine the number of bottles of soda purchased and the number of bottles of juice purchased

Complete the steps to solve the equation 6x 1 6 58 Write the original equation Apply the Subtraction Property of Equality 6x 1 658 6x X Simplify your answer Apply the Division Property of Equality Simplify your answer

5 Broderick is playing a game where he must roll a number cube The faces of the number cube are labeled 1 through 6 If Broderick rolls a 6 on the number cube he must roll the cube again What is the probability that Broderick rolls a 6 on the number cube three times in a row A B 1 6 1 18 C D N2 1 216

When Cara drives to work it takes her 30 minutes to drive 15 miles On her days off she likes to drive to her favorite donut shop It takes Cara 6 minutes to drive to The Dreamy Donut Shop at the same rate How many miles away is The Dreamy Donut Shop