Basic Math Questions and Answers

Suppose that the velocity v t in meters per second of a sky diver falling near the Earth s surface is given by the following exponential function where time is the time after diving measured in seconds v t 61 61e 0 261 How many seconds after diving will the sky diver s velocity be 43 meters per second Round your answer to the nearest tenth and do not round any intermediate computations seconds X

Use the properties of logarithms to evaluate each of the following expressions a log 48 2log 4 b 7 Ine Ine

The plane s elevation relative to the ground in meters as a function of time in seconds is graphed Elevation meters 8 000 7 000 6 000 5 000 4 000 3 000 2 000 1 000 400 800 1 200 1 600 Time seconds How long did it take the plane to land seconds

Solve the following second order determinant 4 6 3 17 A 50 B 50 C 86 D 86 Jy

Solve the following determinant 20 110 U 70 80 A 9300 B 8800 9700 8500 2

We can lease a computer for 1 000 per month or we can purchase one for 15 000 The purchased computer will also cost 40 per month for a maintenance cost At an interest rate of 5 per month how many months would I need the computer for for the purchased system to break ev Note you will need to use a 1 2 tabulated table to solve Between 14 and 15 months Between 15 16 months O Between 16 17 months More then 18 months

Yellow Pages Directory company must decide whether to compose their own ads or pay an outside firm to do them They can buy them outside for 21 00 per ad If they choose to do them insidethey will have to do the following two things 1 Buy computer hardware for 12 000 This Quipment will last 3 years and have a salvage value of 2 000 2 Hire an employee at an annual cost of 45 000 per year In addition to the two new fixed costs there will also be a 4 00 per ad variable cost if they choose to prepare their own ads At 10 interest rate how many ads do they need do annually to break even they decide to prepare the ads themselvces O 1 895 ads per year O2 895 ads per year

1 Given the following consolidation test results a Plot the e log o curve b Using Casagrande s method determine the preconsolidation pressure c Calculate the compression index Cc from the lab e log o curve e 1 21 1 195 1 15 1 06 0 98 0 925 Pressure o kN m 25 50 100 200 400 500 NOTE Show all the calculation steps

A4 A 44 24 45 29 27 f t 34 of of fo 34 34 EN 2 32 3 44 4 30 of of 44 15 4 44 54 44 a The card drawn is a 2 55 of 4 4 54 d The card drawn a diamond 54 e The card drawn is not a club 54 A card is drawn randomly from a standard 52 card deck Find the probabilities of the given events f The card drawn is a 2 or 5 69 c The card drawn is not a face card b The card drawn is a face card Jack Queen or King 60 69 g The card drawn is between and including 2 through 5

People walking into a soccer match were asked if they had eaten at a Chipotle in the past month The number of people who responded yes was 276 and no was 103 Find the probability that if a person is chosen at random they have eaten at Chipotle in the past month Round your answer to one decimal place

A fair die is rolled once Find the probabilities of the given events Leave your answer as a fraction in the simplest form a The number rolled is a 3 b The number rolled is odd c The number rolled is at least 3

A bag of Skittles has 8 red 5 orange 4 yellow and 3 green Skittles What is the probability of randomly picking each of the following Write your answer as a fraction in the simplest form If the answer is 0 or 1 you must enter 0 or 1 a An orange Skittle b A purple Skittle c An orange or yellow Skittle

B 2 5 in Prob 16 5 16 6 A wheel has an initial clockwise angular velocity of 10 rad s and a constant angular acceleration of 3 rad s Determine the number of revolutions it must undergo to acquire a clockwise angular velocity of 15 rad s What time is required 16

16 65 The pinion gear rolls on the gear racks If B is moving to the right at 8 ft s and C is moving to the left at 4 ft s determine the angular velocity of the pinion gear and the velocity of its center A www 4 ww Lanfing B A Probs 16 64 65 0 3 ft

7 1 Given that u 7 2 Calculate i u Ans i 3 3 a Given that C ii 2u iii 4u 3v 3 9 3 c Given that AB iii J and BA Find CB b Express in column notation the unit vectors parallel to BA and CE in a above BC and determine the components of AD Comment on the position of points A and D

Name Date Period Westover is hosting a fund raising carnival You are going to make a themed game with prizes to raise money Follow the steps below and let s design our game THEME AND GAME 10 Points We are going to have a theme for our game You can use whatever you want The prizes will be based on this theme You can use the same theme from past projects if you want The theme for our game is What kind of game do you want to do The only requirement is that you need a repeatable trial that only has two possible outcomes success or failure This can be anything for example hit or miss guess right or wrong knock down all the bottles or don t etc It also needs to be repeatable 10 times like shooting 10 shots guessing 10 times or knocking down the bottles 10 times Really any game can be thought of as success or failure so be creative Write what kind of game you want to do below don t worry about the details right now for example shooting a basketball 10 times or guessing something 10 times or knocking down all the pins targets 10 times You can use games from the fair as an example if you want For our game we will PRIZES 10 Points Now we need some prizes for people to win We need to know how much our prizes are worth as well For our game we will use the following prize structure O successes no prize 1 2 or 3 successes pencil with fancy eraser fitting our theme 4 5 6 or 7 successes small prize fitting our theme 8 or 9 successes large prize fitting our theme 10 successes mega prize fitting our theme The prizes for our game will be General Prize Pencil with Fancy Eraser Small Prize Specific Theme Prize made up How Much It Is Worth made up

This survey records how many times a group of people visited a supermarket in January 22 23 20 1 19 19 16 23 12 9 18 14 22 6 15 12 7 11 3 4 15 9 16 15 Score 1 5 6 10 11 15 16 20 21 25 How many people were surveyed altogether How many people visited fewer than 6 times How many people visited more than 10 times Click the tally column to tally off the data and complete the frequency table You can click the numbers above as you tally them to cross them off Tally Frequency 000 1 1 1

62 GRIDDABLE A family of 9 people is planning a trip to the movies The table shows different ticket prices at two nearby theaters Theater Central Cinemas Midway Theater Prices of Movie Tickets Adult Child 10 50 12 00 8 00 7 50 Senior 9 00 7 50 If they see a movie at Central Cinemas the total cost of their tickets will be 84 00 If they go to Midway Theater they will spend 85 50 How m many family members need an adult ticket or lo TEKS A2 3 B MP AZ A21 C

Residential staircases are usually built with a slope of 70 If the vertical distance between the first floor and the second floor is 10 feet how much horizontal space does the staircase require

Dex plans to create a rectangular raised garden bed Soil costs 5 per cubic foot and the 2 by 12 wood boards to create the walls of the bed costs on average 2 30 per linear foot If Dex has a 100 budget to create and fill the garden bed what is the largest bed that Dex can create

Find the unknown lengths for the similar triangles below 3f 19 in 3 ft 4 2 ft ft If needed round to 2 decimal place ft If needed round to 2 decimal place Question Help Video Message instructor D Post to forum

Solve 4 c 4 CI 4 c 2 1 Enter your answer s as a reduced fraction separated by commas

Find the equation C 4 3 and of the hine which passes through Line 1 2x 5 Parallel to

During an experiment the following times in seconds were recorded Find the mean 6 8 5 9 6 5 3 7 5 9 6 The mean is Round to one decimal place as needed TEE

Find the mean height of the six tallest buildings If necessary round results to one decimal place Building Building 1 Building 2 Building 3 Building 4 Height ft 1483 1483 1450 1381 Building Height ft 1283 1260 1250 1227 Building 5 Building 6 Building 7 Building 8 The mean is ft Round to one decimal place as needed

The total amount of land of some particular countries is approximately 72 000 000 square miles Use the graph to find the area of the Country B The area of the Country B is approximately square miles Country A 25 Country B 20 Country C 16 Country D 14 Country E 5 Country F 13 Country G 7

The line graph shows the goals per game average for a sporting series during the years shown Find the average number of goals per game in 1991 The average number of goals per game in 1991 was Round to the nearest tenth as needed Ave of Goals per Game Goals per Game Average 3 8 3 4 3 2 6 2 2 1 8 1979 1987 1995 2003 Year

The list shows the golf scores for an amateur golfer Use this list to complete the frequency distribution table 88 97 75 Class Interval Scores 1733 90 99 75 77 Fill in the missing information 83 98 85 109 Class Frequency Number of Games 109 86 96 108 75 85

The bar graph shows the number of major storms by month that have made landfall in a region between 1851 and 2012 Approximate the number of hurricanes that made landfall during the month of August During the month of August approximately hurricanes made landfall June July August September October November Hurricanes Making Landfall 0 10 20 30 40 50 60 70 80 90 100 110

Use the quadratic formula to solve the equation Find the exact solutions then approximate these solutions to the nearest tenth 2 x 4x 1 0 C What are the exact solutions Select the correct choice below and fill in any answer boxes in your choice A x 2 3 2 3 Simplify your answer Type each answer as a single fraction using radicals as needed Use a comma to separate answers as needed B The solution is not a real number What are the approximate solutions Select the correct choice below and fill in any answer boxes in your choice OA x Use a comma to separate answers as needed Round to the nearest tenth as needed OB The solution is not a real number

Let A 3 5 7 B 21 30 35 and C 9 3 7 Define r to be the relation from A to B defined by the following zry if and only xly Also let s be the relation from B to C given by s 30 3 30 9 21 3 35 7 Enter each answer below as a list of ordered pairs separated by commas Be sure to not repeat any ordered pairs a Find all the elements in r Answer r 4 b Find all of the elements in the composition rs

5 Graph the line with each y intercept and slope 1 a y intercept is 1 slope is b y intercept c y intercept 2 is 5 slope is 2 is 4 slope is 4 d y intercept is 0 slope is 22 3

The perimeter of the quadrilateral is 49 centimeters Find the length of each side X 4 X 7 Side one x 7 3x 2 x 2x 2 cm cm

18 Match each equation with its graph How did you decide on the equation for each graph a y 2x 1 b y 3x 1 1 c y x 1 d y 1 Graph A y 4 2 0 24 Graph C y 2 0 2 X X 2 2 2 N Graph B y Graph D y 2 2 0 2 2 X Wo that

15 a How can you use the slope intercept form of an equation y mx b to graph the horizontal line y 2 b How can you graph the vertical line x 2 Explain your answers

19 Match each equation with its graph Compare the graphs What do you notice a f x x 4 c f x x 3 Graph A f x 2 20 3 2 Graph C 0 2 f X X b f x x 1 d f x x 1 Graph B f x 4 20 Graph D f x 4 12 2 0 2 X

17 Which equation matches each given graph Justify your choice a y x 4 y 4x 1 y x 4 y 4x 1 3 b y x 1 2 y x 1 3x 1 2 y x 1 y I x y 2 3 c y x 7 3 y x I y 7x 7 5 3 5 x 7 y 4 2 y f x y 2 20 NO 2 X y h x 2 y g x 24 0 2 do A 8 x

5 Write an equation for the graph of a linear function that a has slope 7 and y intercept 16 3 b has slope and y intercept 5 7 c passes through H 0 3 and has slope 6 16 d has y intercept 8 and slope e passes through the origin and has slope 5

4 An online music site charges a one time membership fee of 20 plus 0 80 for every song that is downloaded a Write an equation for the total cost C dollars for downloading n songs b Jacques downloaded 109 songs What was the total cost c Michelle paid a total cost of 120 How many songs did she download

3 For a service call an electrician charges an 80 initial fee plus 50 for each hour she works a Write an equation to represent the total cost C dollars for thours of work b How would the equation change if the electrician charges 100 initial fee plus 40 for each hour she works

y 42 Y 15 1

Hand draw the Bode Diagram for the following transfer function Show all intermediate steps 20 points 10 s 10 H s 3s

Question 5 The expression A 0 46 204 Solution A 6 j5 3 j4 j 8 j3 10 4260 B 46 19j is equal to C 0 46 204 D None of thes 6 j5 3 j4 j 7 81 40 52 53 1 90 8 j3 102260 8 54220 6 10 260 0 464 204

Question 7 If TF 0 increases 20 dB for a 10 fold increase in o how much does it rise for just doubling o

of units sold For this month it was given that the demand is for 300 units and each sells for 65 Find the revenue in dollars for 300 units revenue price of each unit sold number of units sold 65 300 19500 19 500 Step 4 The total cost to the company was found to be 21 750 to order 435 units However the demand was only 300 units which brought in a revenue of 19 500 The profit is found by subtracting the total cost for the company to order the units from the revenue profit revenue total cost Find the profit in dollars profit revenue total cost 19 500 21 750 If the profit is positive then the company will experience a gain If the profit is negative then a loss is experienced Since the profit is Select Carolina Industries experienced a Select Submit Skip you cannot come back

The line graph to the right shows the average gasoline prices of a country from 1990 through 2015 Let p q and r represent the following simple statements p Prices peaked in 2010 q Prices remained steady from 1995 through 2000 r Prices were more than 2 75 per gallon in 2015 Write the symbolic statement p q in words Then use the information given by the graph to determine the truth value of the statement Write the symbolic statement p q in words Choose the correct sentence below O A Prices did not peak in 2010 and prices remained steady from 1995 through 2000 OB Prices peaked in 2010 and prices remained steady from 1995 through 2000 OC Prices peaked in 2010 and prices did not remain steady from 1995 through 2000 OD Prices did not peak in 2010 and prices did not remain steady from 1995 through 2000 Gallon unleaded regular Average Price pe Average Gasoline Prices 4 00 3 00 2 00 1 00 0 00 1990 2000 Year 2010 Q S

Write the following compound statement in symbolic form and construct a truth table The cheese has been sliced or the lemonade is cold p The cheese has been sliced q The lemonade is cold Determine the symbolic form of the compound statement and construct a truth table for the symbolic expression P T T LL F q T F T Next question V

Mean Median Mode New Vocabulary The standard deviation is a measure of how much the values in a data set from the mean It is a measure of the variability or spread of the data or

1A What are the mean and standard deviation of the following data set 4 12 15 9 14 16 13 6 7 6 25 3 13 17 22 4 an Standard deviation

Q 1 An aircraft is flying at an altitude of 6 km at a Mach number of 3 Find the distance behind the aircraft and the time required to travel that distance at which the disturbances created by the aircraft reach sea level Assume the average temperature between sea level and 6 km is 10 C 30 Marks