Basic Math Questions and Answers

Calculate the amount of money you ll have at the end of the indicated time perioc You invest 3000 in an account that pays simple interest of 6 for 30 years The amount of money you ll have at the end of 30 years is

Find the absolute change and the relative change in the following case The estimated number of refugees in a part of the world increased from 7 4 million in 2005 to 11 5 million in 2020 The absolute change is million Simplify your answer Type an integer or a decimal The relative change is Type an integer or decimal rounded to the nearest tenth as needed

Required information The following information applies to the questions displayed below Martinez Company s relevant range of production is 7 500 units to 12 500 units When it produces and sells 10 000 units its average costs per unit are as follows Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead Fixed selling expense Fixed administrative expense Sales commissions Variable administrative expense Average Cost per Unit 5 90 3 40 1 60 4 00 2 90 2 20 1 20 0 45 Required 1 For financial accounting purposes what is the total amount of product costs incurred to make 10 000 units Do not round intermediate calculations

The campus bookstore has estimated that its profit in dollars from selling x hundred basketball conference championship t shirts is given by the equation shown below P 41x 579x 528 The demand is currently 700 t shirts but euphoria over the championship is subsiding so the demand is dropping by 100 t shirts per day How is the profit changing with respect to time per day

Two friends take a 2000 mile cross country trip together but they drive their own cars Car A has a 14 gallon gas tank and averages 40 miles per gallon while car B has a 22 gallon gas tank averages 20 miles per gallon Assume both drivers pay an average of 2 35 per gallon of gas a What is the cost of one full tank of gas for car A For car B b How many tanks of gas do cars A and B each use for the trip c About how much do the drivers of cars A and B each pay for gas for the trip a The cost for car A is per tank and the cost for car B is Round to the nearest cent as needed b Car A uses tanks and car B uses Round to two decimal places as needed tanks for the trip per tank c The driver of car A pays for the trip and the driver of car B pays Round to SILE

Complete parts a through c below a A warehouse is 63 yards long 29 yards wide and 6 yards high What is the area of the warehouse floor If the warehouse is filled to half its height with tightly packed boxes what is the volum of the boxes b A room has a rectangular floor that measures 24 feet by 18 feet and a flat 6 foot ceiling What is the area of the floor and how much air does the room hold c A grain silo has a circular base with an area of 260 square feet and is 18 feet tall What is the total volume a The area of the warehouse floor is Type an integer or a decimal The volume of the boxes in the warehouse is Type an integer or a decimal b The area of the floor is Type an integer or a decimal The amount of air the room can hold is Type an integer or a decimal c The volume of the grain silo is Type an integer or a decimal GIE

Use the currency exchange rates in the table for the following question Your dinner in Tokyo cost 14 400 Japanese yen How much was it in U S dollars Your dinner cost in U S dollars Round to two decimal places as needed Currency British pound Canadian dollar European euro Japanese yen Mexican peso Dollars per Foreign 1 356 0 7828 1 225 0 009694 0 05035 Fore D 0 1 2 0 8 10 19

Elevator ride Engineers are designing a large elevator that will accommodate 56 people The maximum weight the elevator can hold safely is 11 144 pounds According to the National Health Statistics Reports the weights of adult U S men have mean 196 pounds and standard deviation 71 pounds and the weights of adult U S women have mean 169 pounds and standard deviation 80 pounds Use the TI 84 Plus calculator Part 1 of 3 a If 56 people are on the elevator and their total weight is 11 144 pounds what is their average weight The average weight is Part 2 of 3 pounds Part 3 of 3 X S b If a random sample of 56 adult men ride the elevator what is the probability that the maximum safe weight will be exceeded Round the answer to at least four decimal places The probability that the maximum safe weight will be exceeded is X c If a random sample of 56 adult women ride the elevator what is the probability that the maximum safe weight will be exceeded Round the answer to at least four decimal placer

HQ Four Quadrant Ordered Pairs 10 B E S N Write the ordered pair for each given point 8 4 9 W 11 I C 3 3 12 Z 2 2 4649 8 Tell what point is located at each ordered pair 1 3 7 3 6 4 2 8 7 4 9 7 8 5 8 9 6 3 8 13 G 14 Plot the following points on the coordinate grid 17 O 7 4 19 V 2 5 181 F 3 6 201 8 29 931 DEZ 21 Y 1 6 W 1 2 T 6 1 X FA K 7 4 4 8 1 3 15 16 X D 8 6 J 3 1 23 M 1 5

Find the slope of the line that passes through the pair of points 42 86 5 8 and 3 86 4 6 Select the correct choice below and if necessary fill in the answer box to compl O A The slope is Type an integer or a simplified fraction B The slope is undefined

4 Give the answer in the correct number of significant figures show your work 7 3 2522 33 5 0006 is the significant figure rule when adding or subtracting 6 2 What is the significant figure rule when multiplying or dividing 7 5 Find the volume of the cube 5 200 x 00235 Find the area of the rectangle A 12 0 cm 14 18cm 6362600 Find the perimeter of the shape add all the sides 10 9cm 444cm 12 0lem 5 02cm 22 322 cm 11 76 m 54 mm 2 16 cm

or more diagnoses occurring in a single patient O F05 293 0 Delirium Due to Another Medical Condition F05 293 0 Delirium Due to Multiple Etiologies

Let P n be the following proposition over P the set of positive integers a Which of the following is P 5 O A 1 2 5 5 5 1 2 OB 1 2 5 15 OC 5 5 1 OD 1 2 5 OE None of the above b Is P 5 true or false and why 1 2 n A P 5 is true because both sides of the equation equal 15 OB P 5 is false because one side equals 8 and the other side equals 15 OC Neither 1 2 5 is an expression and cannot be judged to be true or false OD P 5 is true because P 5 equals 5 5 1 OE None of the above n n 1 2 R W to go to deid FR h 1 2 Enter

1 point Given L 200 ft equal tangent parabolic curve with g1 1 25 g2 1 25 VPI station 146 00 and VPI elevation 1 895 00 ft Compute elevation at the EVC 1896 25 1895 78 1895 73 1864 04

1 point Given L 200 ft equal tangent parabolic curve with g1 1 25 g2 1 25 VPI station 146 00 and VPI elevation 1 895 00 ft Compute elevation of BVC 1896 25 1895 54 1895 00 2096 25 000

point Compute the station elevation of the BVC of an 800 ft equal tangent parabolic curve where a 2 50 grade meets a 1 75 grade at a station of 44 25 and elevation 368 96 ft 358 96 362 96 362 00 368 96

Given a railroad curve with the following parameters Do 18 00 00 2 00 00 PI Station 25 50 00 ft Compute the curve parameters Long Chord LC O 900 04

The following table lists the number of years of education past high school and the annual income of six people Determine the linear correlation coefficient for the data and also determine whether we can be 95 or 99 confident that there is significant linear correlation between the two variables Years of Education Past High School Annual Income in thousands of iClick the icon to view the table of critical values for the linear correlation coefficient n 4 5 6 7 8 9 10 11 Table of critical values 12 13 14 15 16 17 18 19 20 05 950 878 811 1 25 754 707 666 632 602 576 553 532 514 497 482 468 456 444 3 34 01 999 959 917 875 834 798 765 735 708 684 661 641 623 606 590 575 561 2 36 4 35 X 5 43 6 54 D The correlation coefficient between the two variables is r Round to four decimal places as needed

Given a railroad curve with the following parameters D 2 00 00 1 18 00 00 PI Station 25 50 00 ft Compute the curve parameters the station PT 34 78 12 O 47 69 42 O 65 43 21

Given a railroad curve with the following parameters Dc 2 00 00 1 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Middle Ordinate M

K Use the given xy pairs to complete parts a through d a Identify the problem solving method to be used b Plot the xy pairs in a scatterplot c Estimate the linear correlation coefficient between the two data sets d Calculate the linear correlation coefficient 11 6 17 13 14 5 14 9 O a Choose the correct answer below A Choose Good Names for Unknowns OB The Three Way Principle C The Order Principle D Draw Pictures b Choose the correct graph below OA Ay 15 0 20 Q G B Ay 15 20 G c The value 0 75 is a reasonable estimate of the linear correlation coefficient GEXER O C Ay 15 0 20 Q O D Ay 15 0 0 20

Given a railroad curve with the following parameters D 2 00 00 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Middle Ordinate M O42 15 O 35 27 O 900 04

K a Plot the xy pairs in a scatterplot b Estimate the linear correlation coefficient between the two data sets c Calculate r the linear correlation coefficient 6 13 8 14 10 7 12 8 a Choose the correct graph below O A 30 53 24 18 12 6 0 0 e 4 8 12 16 1 0 25 Q Q 0 5 0 75 B 16 12 8 4 0 0 6 12 18 24 30 b Which of the following is the best estimate for the linear correlation coefficient T Q C 30 24 A 18 12 6 0 0 I D 4 8 12 16 Q OD 16 124 8 4 8 12 16 PANO of I 0 0 19

Given a railroad curve with the following parameters Dc 2 00 00 C 1 18 00 00 PI Station 25 50 00 ft Compute the curve parameters External Distance E O 35 71 O 453 76 107 58

Find the line of best fit for the given data 4 2 5 9 7 12 8 13 The equation of the line of best fit is y x Round to the nearest tenth as needed

Make a scatter plot for the given data Use the scatter plot to describe whether or not the variables appear to be related Graph the point 1 10 Graph the point 4 7 Graph the point 2 9 Graph the point 5 5 Graph the point 6 3 Graph the point 7 3 Do the variables appear to be related No O Yes X y 1 10 4 7 2 5 9 5 6 3 7 3 CZE

Given a railroad curve with the following parameters Dc 2 00 00 1 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Long Chord LC O 900 04 O896 35 O 148 72

Given a railroad curve with the following parameters Dc 2 00 00 18 00 00 PI Station 25 50 00 ft Compute the curve parameter Tangent length T 587 69 O872 65 420 00

Given a railroad curve with the following parameters Dc 2 00 00 C I 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Radius R O 2864 93 O 2546 32 O2798 65

A normal distribution has a mean of 13 and a standard deviation of 3 Use the 68 95 99 7 rule to find the percentage of values in the distribution below 4 What is the percentage of values in the distribution below 4 Type an integer or a decimal

1 LM X 72 X 4 2 2 2x y 4xy 2y 6 2 3 x 4x 4 x 2 4 4 4 x 4x 4 x 2

In a dinner party of 290 persons in attendance 181 of them drink malt 142 drink wine and 117 drink fruit juice and each drink at least one of the three drinks If 75 drink Malt and wine 60 drink malt and juice and 54 drink wine and juice i ii Draw a Venn diagram to illustrate this information How many people drink a b C d e f All the three items exactly two of the drinks exactly one of the drinks wine alone at most two of the drinks at least two of the drinks

Estimate the error if P2 x 1 is used to estimate the value of cos x at x 0 1 2 Error Simplify your answer Round to seven decimal places as needed

Use the logarithm change of base formula to convert each of the following logarithms to the specified base Then use a calculator to approximate the logarithm Round approximations to four decimal places Convert log20 13 from base 20 to base 5 log20 13 which is approximately equal to Convert logg 10 from base 8 to base 10 logg 10 2 which is approximately equal to Convert log15 6 from base 15 to base e log156 which is approximately equal to

6 Using a sign chart and the graph provided sketch the polynomial function P x x 2 x 4 x 6

The upper fixed and lower fixed point of a certain thermometer are marked 110 and 10 respectively What temperature on a centigrade thermometer will be four times that on this thermometer

Using a ruler and a pair of compasses only construct i a AABC with AB 7 5cm AC 13 5cm and LABC 120 B locus I of points equidistant from A and B Y locus I of points equidistant from B and C Using N the point of intersection of I and I as centre draw a circle to pass throug points A B and C

Prove the Adiabatic expression 1 and isothermal

30 0cm hydrochloric acid of concentration 6 4 dm neutralized 25 0cm of an unknown alkali XOH whose concentration was 4 85 g dm Calculate a the molar concentration of XOH b the relative atomic mass of the element X Name the element HCl 36 5

5 Kara starts tying a baby quilt at the local community center Each quilt takes 200 ties to complete Ten minutes later Julie joins Kara and both stay to finish the quilt Kara ties 6 per minute and Julie can tie 11 per minute a Write an expression to show the number of ties Kara has completed after m minutes b Using the same variable m write an expression for the number of ties Julie has completed c If you know they finished the quilt write an equation to model the situation d How many minutes did it take them to finish the quilt e How many did each of them tie f Suppose they tied the same amount How long would it take g How many did each of them tie h The next week Julie couldn t make it so her friend Susan came to help Susan can tie the ties as fast as Kara Using the same variable m write an expression for the number of ties Susan has completed 1 If you know they finished a quilt write an equation to model the situation 2h How many minutes did it take them to finish the quilt 2h How many did each of them tie

A woman bought 130kg of tomatoes for N52 000 00 She sold half of the tomatoes at a profit of 30 The rest of the tomatoes began to go bad she then reduced the selling price per kg by 12 Calculate a b the new selling price per kg the percentage profit on the entire sales if she threw away 5kg of bad tomatoes

In the following problems you will fill in the details for various proofs On exams you are expected to write out the entire proof so you should practice by writing out the proof of each statement then comparing your work with the proofs given in the problem set In this problem you will complete the details of the proof of a direct proof Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer If n is odd then n 5n is even Proof Suppose that n is odd By definition n 2k 1 for some integer k So n 5n 2k 1 5 2k 1 2m where m Since Z is closed under addition and multiplication me Z Since n 5n 2m this means that n 5n is even

Tess needs to buy shredded rubber for her children s playground The shredded rubber costs 15 per ton and there is a delivery cost of 40 with each order What types of numbers are possible in the domain O All positive rational numbers less than 40 O All rational numbers greater than 15 O All positive rational numbers All rational numbers

10 A company s 10 year bonds are yielding 7 5 percent per year Treasury bonds with the same maturity are yielding 5 2 percent per year and the real risk free rate r is 2 1 percent The average inflation premium is 2 4 percent and the maturity risk premium is estimated to be 0 1 t 1 where t number of years to maturity If the liquidity premium is 0 2 percent what is the default risk premium on the corporate bonds

In this problem you will complete the details of the proof of an indirect proof Fill in the blanks below Each blank should be filled with a polynomial involving the variables k and p Prove Let m n be integers If mn is even then m is even or n is even Proof Suppose that mn is even Assume for the sake of contradiction that it s not true that m is even or n is even By DeMorgan s Law this means that m is odd and n is odd By definition of odd m 2k 1 and n 2p 1 for some integers k and p This means that mn 2k 1 2p 1 2N 1 where N Since Z is closed under addition and multiplication NE Z Since mn 2N 1 this means that mn is odd This contradicts the fact that mn is even Therefore it must be true that m is even or n is even O

In this problem you will complete the details of an indirect proof Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer If n 17 is even then n is odd Proof Suppose that n 17 is even Assume for the sake of contradiction that n is even By definition n 2k for some integer k So n 17 2k 17 2m 1 where m Since Z is closed under addition and multiplication m e Z Since n 17 2m 1 this means that n 17 is odd However this contradicts the fact that n 17 is even Therefore n must be odd

Let P n be the following proposition over P the set of positive integers a Which of the following is P 5 5 5 1 2 5 1 6 OA 12 22 52 OB 5 5 1 2 5 1 6 OC 12 22 5 OD 12 22 52 55 OE None of the above 12 2 n b Is P 5 true or false and why O A P 5 is true because 5 5 1 2 5 1 is a correct expression O B P 5 is true because both sides of the equation equal 55 OC P 5 is true because P 5 equals 55 OD P 5 is false because one side equals 55 but the other side does not equal 55 OE None of the above n n 1 2n 1 6 c Let k be a positive integer Consider P k and P k 1 What can you add to the left hand side of P k to get to the left hand side of P x 1 Enter an expression involving k

Let P n be the following proposition over P the set of positive integers a Which of the following is P 14 OA 2 22 2 4 215 1 OB 20 2 22 23 2 4 2 5 1 OC 20 2 2 23 2 4 OD 2 22 23 2 4 214 1 1 OE 214 1 1 20 2 22 2 2 1 1 b Let k be a positive integer Consider P k and P k 1 What can you add to the left hand side of P k to get to the left hand side of P k 1 Enter an expression involving k

In this problem you will complete the details of the proof of an if and only if statement Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer Then n is even if and only if n is even We will prove the following two statements 1 If n is even then n is even 2 If n is even then n is even Direct proof of 1 Suppose that n is even By definition n 2k for some integer k So n 2k 2m where m Since Z is closed under addition and multiplication me Z Since n 2m this means that n is even Indirect proof of 2 Suppose that n is even Assume for the sake of contradiction that n is odd Since n is odd n 2k 1 for some integer k This means that n 2k 1 4k 4k 1 2p 1 where p 8 Since Z is closed under addition and multiplication p E Z Since n is of the form 2p 1 for some integer p this means that n is odd However this contradicts the fact that n is even Therefore n must be even O

In this problem we prove the following statement Let A B be sets in a universe U Then An Bc C AUB Your task is to provide justification for some of the steps Possible answers are given below Put a number into each blank with no parentheses 1 definition of union 2 definition of intersection 3 definition of subset 4 definition of set subtraction i e S T 5 definition of complement 6 DeMorgan s law of logic Proof Let a A n B Then x E A and x E B by justification Since a A this means that x A by justification Using the same reasoning a E B means that a B so x EB is true Combining these facts A EB is true Therefore EA V EB is true using justification In other words E AUB is true using justification Since AUB this means that a E AUB using justification 9 I So x A is true which is equivalent to x AUB