Basic Math Questions and Answers

Marcus finds that 3x 2y 5x 4x 12y 7x 7x 10y 2x What error did Marcus make O He combined the terms 5x and 7x incorrectly O He combined the terms 3x and 4x incorrectly O He combined the terms 2y2 and 12y2 incorrectly O He subtracted the polynomials instead of adding

The following table contains the rate of commission number of items sol and cost of each item for four different salespeople Salesperson Felix Helen Reid Sidney Rate of commision 7 25 7 50 8 25 7 75 Number of items sold 9 12 10 6 Cost of each item 60 50 40 90 Assuming that each salesperson earned commission on all items he or she

Ouse an automated teller machine at a certain bank you must enter a 5 digit code using the digits 0 9 How many 5 digit codes are possible if repetition of digits is ermitted here are possible codes

Angel took a 2 year lease on a new car and after 8 months of driving he d put 5000 miles on it The lease allows 10 000 miles per year If his driving habits stay consistent will he stay under the allotted mileage for 2 years By how much Angel Choose one stay under the allotted miles for his lease He will be mileage at the end of two years miles Choose one the allotted X 3

As the weight of purchased items increases the shipping charges increase as shown in the table below Weight in oz not more than 5 more than 5 not more than 10 more than 10 not more than 15 more than 15 not more than 20 Total Shipping Cost 9 50 13 25 17 00 20 75 Assuming only positive domain values which statement is true of the graph that represents the total cost y in dollars shipping items that weigh x ounces O The graph is discontinuous at x 5 x 10 and x 15 The range values for the set of the data are 10 14 17 and 21 For every 1 ounce increase in weight the total shipping cost increases by 3 75 The left side of each horizontal interval is a closed circle and the right side is an open circle

In a tournament a professional golfer knows that she is 200 yards from the hole A spectator is watching her play and is 140 yards away from the golfer Golfer 25 6 39 4 64 3 140 yds 65 0 Spectator If the spectator has an angle of 115 between the golfer and the hole what is the angle that the golfer has between the spectator and the hole 115 200 yds Hole

Tutorial Exercise Find the derivative of the function without using the Quotient Rule 12 13x Step 1 Rewrite the equation so the variable is not in the denominator 12 13 y

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 320 grams and a standard deviation 14 grams Find the weight that corresponds to each event Use Excel or Appendix C to calculate the z value Round your final answers to 2 decimal places a Highest 30 percent b Middle 70 percent c Highest 90 percent d Lowest 20 percent to

48 Which of the following statements best summarizes the Side Splitter Theorem If a line is perpendicular to one side of a triangle and intersects the two other sides the line divides the two sides of the triangle proportionally If a line is parallel to one side of a triangle and intersects the two other sides the line will always form a right angle If a line is parallel to one side of a triangle and intersects the two other sides the line divides the two sides of the triangle proportionally If a line is congruent to one side of a triangle and intersects the two other sides the line divides the two sides of the triangle proportionally

Given that A represents the event that someone likes dogs find P A The probability that someone does not like dogs o Write your answer in decimal form o Round to two decimal places Dogs 87 Cats 52 100

Next O Unit Pre Test Height feet Flynn is playing with a toy that is tied to his hand by a string The toy falls toward the floor then rises back toward Flynn s hand and repeats this motion following the path illustrated by given graph 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 0 5 Submit Test hxo Reader Tools 0 1 2 3 4 5 6 7 8 9 10 Time seconds Use the graph to complete the function that models the toy s height in feet above the floor tseconds after it has left Flynn s hand cost VD

Suppose that 0 9 of male professional golfers use steroids and that Max is a male professional golfer who has been randomly selected to take a drug test The test he has been asked to take has a false positive rate of 1 and a false negative rate of 10 Use Bayes rule to calculate the probability that Max actually uses steroids if he tests positive for steroid use Give your answer as a decimal precise to three decimal places

Find the sum of the areas of the shaded rectangles under the graph Round to two decimal places Hint The width of each rectangle is the difference between the x values at its base The height of each rectangle is the height of the curve at the lef edge of the rectangle y 6 4 2 y 31X 1 1 25 1 5 1 75 X 2

accurate Explain how you made your choice Weight mg 10 1 10 23 10 Student Brad Brandon Meagan Answer most 7 You and a friend are talking and he wants to know how many significant figures there are in the number 0 012012 How would you explain to your friend how many significant figures there are in the number Answer 8 Given 1 in 2 54 cm and 1 cm 10 mm how many millimeters are present in 20 0 inches Use dimensional unit analysis to find your answer Answer

Lisa s living room has new carpet of 8 meters wide and 10 5 meters long She wants to put carpet in the basement that is twice as long as the living room and a fourth wider She also has wanted to put tile in the bathroom that has an area of 10 square feet Her bedroom is currently being completed with carpet If her bedroom is 6 meters shorter in length than the living room and the width what is her bedroom s area Do not include units in answer and round to the nearest hundredth Example if answer is 19 546 m put 19 55

1 point Your grade in a class is determined by the average of three test scores You scored 73 and 87 on the first two tests To earn at least 78 for this course how much do you have to score on the third test

You are ready to spend your Christmas money You go to your favorite store and buy some jewelry They are running a sale where everything is 10 You got 130 for Christmas and don t have any more than that to spend Write an inequality to represent how many pieces of jewelry 3 you can buy Inequality

In the circle below P is the center QS is a diameter and m QR 80 Use this information to fill in the blanks R 80 S Q a Give an inscribed angle 1 0 b Give a semicircle c Give a major arc d Find mZQPR e Find m QTR X 0

What are the maximum and minimum distances that the reader could assume based on the surveyed distance and margin of error Answer 10 A company makes and sells automatic coffee machines It is important that the machines dispense the right amount of coffee such that each cup isn t too full but also not too empty Being too full or too empty affects profits and customer satisfaction

Lisa bought 3 equally priced shirts for 41 70 Her friend Anna bought 8 shirts at the same price per shirt How much did Anna pay for her purcha 111 20 O 105 14 115 60

Mark Up A standard queen bed hotel room at the Posh Inn is currently priced at 135 a day after a 17 markup to offset inflation costs What was the daily charge for the room before the increase Choose one 5 points 157 95 118 00 115 38 100 75

Barrett works at an ice cream shop The function f x represents the amount of money Barrett earns per gallon of ice cream where x is the number of gallons of ice cream he makes The function g x represents the number of gallons of ice cream Barrett makes per hour where x is the number of hours he works Show all work to find f g x and explain what f g x represents f x 2x 4 g x 3x

Find the indicated trig function Write each answer as a fraction and a decimal rounded to four decimal places Sin A A 12 Sin B 13 5 B

Sherry needs to have at least 1600 in her bank account at the end this month She works at a restaurant where she earns 18 an hour h This month she has to pay her car payment of 200 Write an inequality to represent how many hours she will need to work in order to have 1600 in her account Inequality

The table to the right is based on the assumption that 1 of breast tumors are malignant It also assumes that mammogram screening is 95 accurate Complete parts a through c below Positive Mammogram Negative Mammogram Total a Suppose a patient has a positive mammogram What is the chance that she really has cancer Type an integer or decimal rounded to the nearest tenth as needed b What is the chance of a positive mammogram given that the patient has cancer Tumor is Tumor is Malignant Benign 95 5 100 Type an integer or decimal rounded to the nearest tenth as needed c Suppose a patient has a negative mammogram What is the chance that she actually does have cancer Type an integer or decimal rounded to the nearest hundredth as needed Total 1254 1349 8646 8651 9900 10 000

Verizon offers to sell cellular phones listing for 100 24 with a chain discount of 15 10 5 Cellular Company offers to sell its cellular phones that list at 103 49 with a chain discount of 25 5 If Irene is to buy six phones how much could she save if she buys from the lower priced company Do not round intermediate calculations Round all dollar amounts to the nearest hundredth Roun your final answer to the nearest cent Amount saved This is a numeric cell so X

A political strategist surveyed 100 people asking their opinion about a new proposal The results are summarised in the contingency table A Survey of Men s and Women s Opinion of a Proposal Disapprove Neutral Men Women Total Approve 33 57 19 31 3 Find the probability that a person chosen at random is a woman who disapproves of the 9 12 Total 46 100

Let p and q represent the following statements p The fourth of July is Independence Day q The Bible was not written in 1969 Express the following statement symbolically The Bible was written in 1969 The statement written symbolically is

The path a character takes to navigate a level of a video game is given in the following graph What is the domain 0 12 x 14 14 12 10 8 6 4 20 8 0 6 x 4 6 6 x 4 x 6 0 2 O 2 4 6 12 x 14 x 6 8 8 2 4 6 8 10 12 14 16 18

and the new balance in each problem Your balance on May 20 was 189 75 and you made a 112 45 deposit on May 22 On May 29 you wrote a 75 6 check and on June 1 you made an ATM withdrawal of 50 00

4 Billy and Jane are trying to determine how far they can travel in 8 hours if they travel at a rate of 86 km h Billy determines they could travel 688 km while Jane determines they could travel 10 75 km Who is correct Use dimensional unit analysis to justify your answer Answer 5 What is the difference between accuracy and precision Provide an example to help illustrate the difference in your explanation Answer

Match the regression equation with the appropriate graph Drag each graph given below to its corresponding regression equation to the right Ay 70 60 50 40 30 20 10 Ay 30 25 20 15 104 5 5 10 15 20 25 30 1 5 10 15 20 25 30 35 40 SSU Q Q G Ay 30 25 20 15 10 S 7 2 2 3 10 14 80 10 20 30 40 50 140 120 100 60 40 20 Q Y 13 y 1 361x 21 952 14 y 2 115x 21 958 15 y 2 125x 9 588 16 y 0 705x 27 214

Members of the student government are planning a movie night on campus They have asked a random sample of students which of four movies the students would prefer Here are the results Movie Preferred Movie A Movie B Movie C Movie D Number of Students 21 49 24 46 There are 900 students total on campus Based on the above information how many students on campus would we expect to prefer Movie B Round your answer to the nearest whole number Do not round any intermediate calculations students X

The point 4 x y in the 3rd quadrant is reflected twice in a counterclockwise direction over two lines that intersect at the origin and have an angle of 90 between them What are the coordinates of A A y x B C y x OD 2 y

The area of a rectangular living room is 450 square feet The length of the room is 15 feet less than three times the width Find the equation in terms of w that could be used to find the dimensions of the living room in feet Your answer should be in the form of a polynomial equals a constant Provide your answer below

The person s income increased from 27 000 to 40 000 over the last year What is the percent change Select the correct answer below O 48 15 decrease O 32 50 increase O 48 15 increase 67 50 increase

6 Which statements describe the altitudes of triangles Select all that apply An acute triangle has altitudes inside the sides of the triangle A right triangle only has two altitudes The point of concurrency for a triangle s altitudes is called the orthocenter An obtuse triangle has altitudes along the legs of the triangle

In the figure shown below E and G lie on AC D and F lie on AB DE and FG are parallel to BC and the given lengths are in feet What is the length of AC in feet A D O O O O 8 O F 7 B C D 16 A 13 26 29 42 LL 6 B 48 E G

ANDLI A water tank can be filled using pipe A pipe B or both pipes It takes pipe A twice as long as pipe B to fill the tank when working alone When both pipes are working it takes only 8 hours This expression represents the situation Which expression also represents this situation 123

A farmers group conducted an experiment to determine which fertilizer is better for plant growth One fertilizer contains a urea supplement while the other does not contain the urea supplement For the experiment they randomly selected 20 plants of the same species growing in their area The farmers tested the urea enhanced fertilizer on 10 plants and the non urea fertilizer on the other 10 plants After three months they reported their findings as shown Plant Growth Report Number of Plants with Above Average Growth A A 3 B N Month 2 with urea supplement without urea supplement What can be concluded from the farmers data Month 1 O C O D Month 3 Both types of fertilizer are equally effective The fertilizer with the urea supplement is more effective than the fertilizer without it There is not enough information to draw any conclusions from the data The fertilizer without the urea supplement is more effective than the fertilizer with it

Select the correct answer from each drop down menu Jane bought a new rectangular placemat with an area of 126 square inches The length of the placemat is four times the quantity of nine less than half its width Complete the equation that models the area of the placemat in terms of the width of the placemat w w w The width of the placemat is inches W

The water line on a dental unit fits through a rubber tube that is lined with insulation to maintain the temperature of the water If the water line has an outside diameter of 0 1875 inches in how thick is the layer of insulation Hint Remember that the insulation is on both sides RUBBER TUBE INSULATION WATER LINE 0 1875 IN INSIDE DIAMETER 1 4 IN I OUTSIDE DIAMETER 3 4 IN

Shelly Van Doren hired a contractor to refinish her kitchen The contractor said the job would take 45 hours To date the contractor has worked the following hours Monday Tuesday Wednesday 5 Thursday Friday 34 91 Number of hours 71 10 How much longer should the job take to be completed

22 Sporting Goods For 1998 through 2005 the sales S in billions of dollars of sporting goods can be modeled by S 0 007 0 1t2 1 4x 70 analis Towin where t is the number of years since 1998 In which year were sales about 78 billion

eason that best supports Statement 3 in the give proof A Subtraction Property of Equality B Multiplication Property of Equality C Addition Property of Equality D Substitution Given m A 5 mzB and m B 20 Prove mzA 100 Statement 1 mzA 5 m B 2 m B 20 2 mzA 5 20 Reason 1 Given 2 Given 3

The time t in minutes you need to type a certain paper varies inversely with the rate r in words per minute that you can type When typing 40 words per minute you can finish in 50 minutes Find the constant of proportionality and write an equation relating t and r t

Let A a 2 x 2 be a square matrix such that Tr A 5 If f x det A xl and f A A aA 31 where I is identify matrix of order 2 then The value of Tr 3A 1 2 a 1 3A 1 31 is O 0 05 07 O10

Special Cases and Applications Progress The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer Esmerelda rents a car from a company that rents cars by the hour She has to pay an initial fee of 50 and then they charge her 8 per hour She has 150 available to spend on car rental What is the greatest number of hours for which she can rent the car The car cannot be rented for part of an hour O 12 hours O 18 hours O 13 hours 12 5 hours Question ID 120659

Which pairs of triangles appear to be congruent Check all that apply 1 3 2 4 A Triangles 3 and 4 B Triangles 2 and 3 C Triangles 2 and 4 D Triangles 1 and 3 E Triangles 1 and 2 F Triangles 1 and 4

At a bowling alley the cost of shoe rental is 2 25 and the cost per game is 4 25 If f n represents the total cost of shoe rental and n games what is the recursive equation for f n Of n 2 25 4 25n n 0 Of n 2 25 4 25 n n 0 Of n 4 25 f n 1 f 0 2 25 Of n 2 25 4 25 f n 1 f 0 2 25