Basic Math Questions and Answers

You and your friend want to take graduation pictures with a few of your fellow computer science class mates making 10 of you in total You hired a very expensive photographer for the occasion and want to make the most of the experience You want to select four students to stand in the front of the group in a line In how many ways is it possible to take the pictures such that a you have a place at the front of the group photo b you and your friend have a place together at the front of the group photo

Sketch the graph of the function Include two full periods Use a graphing utility to verify your result y 2 sec 2x 1 I 4 U 4 3 4 2 y

Changes in the timbre or tone color in a piece of music

c Write down the minimum height of point P 1 Later the cat is tired and it takes twice as long for point P to complete one revolution at a new constant rate d Write down the new value of b

The pressures caused by pure tones on the eardrum are sinusoidal The change in pressure P in pounds per square foot on a person s eardrum from a pure tone at time t in seconds can be modeled using the equation P Asin 2xft d where f is the frequency in cycle per second and is the phase angle When P is positive there is an increase in pressure and the eardrum is pushed inward when P is negative there is a decrease in pressure and the eardrum is pushed outward A graph of a tone P t 008 sin 2x 274 42 t shown to the right Complete parts a through c below 2 274 421 is 008 Q 005 Q 008 a Determine algebraically the values of t for which P 0 over 0 005 The solution set is Round to five decimal places as needed Use a comma to separate answers as needed b From the graph and your answer in part a determine the interval for which P 0 over 0 005 Type your answer in interval notation c Would an eardrum hearing this tone be vibrating outward or inward when P 0 Outward

Irina uses a set of coordinate axes to draw her design of a window The base of the window is on the 2 axis the upper part of the window is in the form of a quadratic curve and the sides are vertical lines as shown on the diagram The curve has end points 0 10 and 8 10 and its vertex is 4 12 Distances are measured in centimetres The quadratic curve can be expressed in the form ya br c for 0 8 a Write down the value of c a ill Hence find the equation of the quadratic curve b Find the area of the shaded region In Irina s design

18 What happened to Wade the day after he completed the first task that changed his life for the better

Question 3 A baker uses the expression 5 75c 3 45p to calculate his profit when he sells c cakes and p pies What is the baker s profit in dollars when he sells 33 cakes and 42 pies

11 Find w to find the measure of the exterior angle 13 Find mZH W 68 6x 1 H 126 F G 5x 17 12 Find x to find the measure of the remote interior angle 46 134 14 Determine the measure of the indicated exterior angle in the diagram 3x 4 15 Match each angle with its corresponding measure given m21 130 and m 7 70 Indicate a match by writing the letter for the angle on the line in front of the corresponding angle measure A mz2 B m23 C m24 D m25 E mZ6 50 60 70 110 120 16 The map of France commonly used in the 1600s was significantly revised as a result of a triangulation survey The diagram shows part of the survey map Use the diagram to find the measure of ZKMJ Note that ZKMJ ZNKM LA ROCHELLE 104 Rochefort 88 48 M N

4 A polygon has an interior angle sum of 3060 How many sides must the polygon have 3080 5 Two of the angles in a triangle measure 50 and 27 Find the measure of the third angle Solve for the unknown angle measures of the polygon 6 A pentagon has angle measures of 100 105 110 and 115 Find the fifth angle measure 116 7 The measures of 13 angles of a 14 gon add up to 2014 Find the fourteenth angle measure 8 Determine the unknown angle measures for the quadrilateral in the diagram 9 The cross section of a beehive reveals it is made of regular hexagons What is the measure of each angle in the regular hexagon 22

4 Euclid Algorithm Use Euclid s algorithm to compute the following Show all your steps 1 gcd 781 994 2 gcd 67457 43521

2 Divisibility What are the quotient and remainder when 1 44 is divided by 6 2 994 is divided by 13 3 221 is divided by 16

9 In the triangle shown XY 222 272 2 22 27 cos 39 Label all the sides and angles of the triangle with their measures to the nearest tenth Y Z

7 State the number of possible triangles that can be formed using the given measuremen a m s 136 PS 14 MP 11 b BC 30 mZA 71 AB 22

Write name date and period Show all sketches and work 1 Solve for m F Round to the nearest tenth F E 107 9 7 G

About 3 2 108 people live in the United States About 3 9 x 107 people live in Canada And about 1 1 x 108 people live in Mexico About how many people live in all three countries altogether a 4 69 x 107 b 4 69 x 108 c 8 2 x 107 lt over blow 10 d 8 2 108

Bir m teri bir mal n sat fiyat nda 20 indirim yap l rsa elindeki parayla bu maldan 5 adet daha fazla al yor Buna g re m teri elindeki parayla indirimli maldan ka

4 Proof by induction Assume n is a positive integer Use induction to prove the following 1 5 9 4n 3 2n2 N

17 3 8 18 19 20 10 7 5 7 7 12 4 54 x 7 35

ement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer Which of the writing prompts below calls for an evaluative thesis O Analyze the roles of exercise and diet in a healthy lifestyle O Compare and contrast the costs and savings of buying and renting a home O Use Shakespeare s plays to argue whether comedy or drama stands the test of time better Compare and contrast vegetarian and vegan diets and summarize their nutritional concerns

b Convert the equation to vertex form algebraically using complete the square method Write the equation using function notation c Describe the transformations applied to y x2 to get the resulting equation Task 3 Analyzing the situation a Determine the zeros algebraically and explain what these mean for b Determine the vertex and explain what this means for your situation your situation

29 What was Dennis s plan when he told Jeremiah to unbuckle himself a To fight Anna b To hide from Anna c To run away from Anna d To stay near the truck

2 The amount of dry matter in tomatoes measured in grams is the amount of solid content of the fruit subtract the water content The table below shows weights of dry matter in 10 tomatoes grown in soil with different amounts of calcium Ca measured in mg cm Ca in soil mg cm x Weight of dry matter g y 12 13 15 17 18 19 21 22 23 25 2 9 31 47 4 5 47 5 3 6 1 65 62 68 a 1 ii b 1 Find the Pearson s product moment correlation coefficient r for this data 0 96 Comment on the strength of the r value found Strong Poative linear correlation Find the Spearman s rank correlation coefficient r for this data ii Comment on the strength of the r value found c In the context of this question and the data provided comment on if both correla coefficients should be considered when determining the relationships between calcium content and dry matter weight or if one should be used in favour of the

B If DE 16x 3 EF 9x 11 and DF 52 find HG E D H

a Consider the three following Hasse diagrams representing three poset relations RA RB and Rc a a b 3 4 b b C a 1 2 A B C 1 For each poset list all the ordered pairs that belong to the relation 2 For each relation provide all least minimal greatest and maximal elements b Which of the following posets are lattices Justify your work for the non lattices only 1 1 2 2 3 A B 3 2 3 3 D

In 1 m and n are direction cosine of a vector then a 12 m n 1 c 12 m n 1 2 b 12 m n 1 d 1 m n 1

f Boris recorded the number of daylight hours on the first day of each month in a northern hemisphere town This data was plotted onto a scatter diagram The points were then joined by a smooth curve with minimum point 0 8 and maximum point 6 16 as shown in the following diagram hours of daylight each day 16 12 6 9 12 month of the year Let the curve in the diagram be y f t where t is the time measured in months since Boris first recorded these values Boris thinks that f t might be modelled by a quadratic function leng a Write down one reason why a quadratic function would not be a good model for the number of hours of daylight per day across a number of years Paula thinks that a better model is f t a cos bt d t 0 for specific values of a b and d For Paula s model use the diagram to write down b the amplitude c the period d the equation of the principal axis e Hence or otherwise find the equation of this model in the form f t a cos bt d For the first year of the model find the length of time when there 10 hours and 30 minutes of daylight per day 1

Sylvia makes pizzas at an Italian restaurant A large pizza is listed on the menu as being 16 inches Sylvia wants to know how accurate she is at throwing dough to that size A coworker measures all the pizzas Sylvia throws and they randomly select 35 data points They use this data to calculate the following 95 confidence interval 15 85 16 10 Use this to recommend a strategic decision 1 point Sylvia should use more dough since the least value of the confidence interval is less than 16 inches Sylvia should use less dough since the greatest value of the confidence interval is greater than 16 inches Sylvia should continue using the same amount of dough since 16 inches is contained within the confidence interval O Sylvia should use more dough so that the entire confidence interval is greater than 16 inches

2 x 2

Classify each function as even odd or neither 101 B 8 4 2 8 10L f x 3x 4 h x 2x 3x Even Odd g x 2x 4x Odd

1 Consider the linear transformation T R3 R3 given by 21 22 2x3 T 3x2 6x3 3x12x2 4x3 a Find a basis for the subspace that consists of all ER such that T 0 Is T injective b Find a basis for the image of T Is T surjective

2 Consider the following general 3 3 matrix a b A d e f ghi a Let B be the matrix obtained from A by switching row 2 and row 3 Show via an expli calculation that det A det B b Let C be the matrix obtained from A by replacing R3 row 3 with R3 t R1 row 3 plus t tim row 1 for some scalar t Show via an explicit calculation that det A det C hint expand along its third row

Please explain to your new client the differences between servers and consumer personal computers as well as the differences between intranet or local networks and the internet WAN Provide at least four suggestions that will help keep your client s data safe and secure

1 Which number is the location of Ayer s Rock 02 03 05 9 6 7

Which of the following points is NOT a negative number W X Y Z 6 4 2 0 OW OX OY 2 6

Which integers on the number line are opposites a b 10 8 6 4 2 02 4 6 8 10 a and b Ob and c Oc and d O a and d

The amount of food needed for proper nutrition in cups C for a puppy weighing a certain aw b where a and b are amount in pounds w can be determined by the equation C constants For a puppy weighing 9 pounds the correct amount of food is 4 cups and for a puppy weighing 11 pounds the correct amount of food is 6 cups a Determine the values for a and b b Find the correct amount 2

The position of a weight attached to a spring is s t 2 cos 4 t inches after t seconds Complete parts a d belo a What is the maximum height that the weight rises above the equilibrium position in b What are the frequency and period The frequency of the oscillation is cycles per sec Type an integer or a fraction Type an exact answer using as needed The period of the oscillation is sec Type an integer or a fraction Type an exact answer using it as needed c When does the weight first reach its maximum height after sec Type an integer or a fraction Type an exact answer using as needed d Calculate and interpret s 1 2 s 1 2 Round to the nearest integer as needed Interpret s 1 2 Choose the correct answer below OA After 2 sec the weight is about 1 2 in above the equilibrium position OB After 1 2 sec the weight is about 2 in above the equilibrium position 1 OC After 1 2 sec the weight is about in above the equilibrium position

An object is attached to a coiled spring It is pulled down a distance of 4 units from its equilibrium position and then released The time for one complete oscillation is 3 seconds a Give an equation that models the position of the object at time t s t Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression b Determine the position at time t 1 82 sec units Round to the nearest hundredth as needed c Find the frequency oscillation per sec Use integers or fractions for any numbers in the expression

If mTA 42 and mMI 130 find m C C A T I M

3 Complete the chart below Assume a one year investment period Return on Investment ROI Net Profit 4 30 25 4 10 4 000 Investment 60 100 10 ROI 100 20 40

Given the following preference schedules for a class of student voters on favorite restaurants determine the plurality winner if one exists Five Guys Chic fil a Zaby s Wendy s 7 Wendy s Chic fil a Five Guys Zaxby s a Zaxby s b Five Gur 4 Zarby s Chic fil a Wendy s Five Guys 8 Chic fil a Wendy s Zaxby s Five Guys 1

Given the following preference schedules for a class of student voters on their favorite school subject determine the Condorcet Winner if one exists Math Science Electives ocial Studi Science Language Arts Electives Science Language Arts Language Arts Electives Science

Which best describes the type of Winner defined by the following The candidate that received the most votes is the winner a Sequential Run Off Winner b Condorcet Winner c Borda Count Winner d Run Off Winner el Approval Vote Winner

Which of the following best describe the Run Off Winner a Start by eliminating a single candidate with the least number of first place votes from all of the preference schedules re tally the votes and again eliminate the next candidate with the least number of first place votes Continue repeating this process until only one candidate remains and is the winner O b Assign points based on the ranking of the preference schedule Assign 1 point for each last place vote Assign 2 points for each vote that is the next place above last place and continue adding a point for each place above last place such that a first place vote receives the most points The candidate with the most points is the winner received more than half of the votes is the winner

Jim worked 2 jobs On a typical day he is a cashier at his first job and works 6 hours while being paid 11 per hour At his second job as an evening security guard he works 5 hours while being paid 22 per hour What was Jim s average rate of pay for the day a 17 00 per hour b 16 50 per hour O c 16 00 per hour d 15 50 per hour

What is the check digit d for the UPC bar code shown below O a 4 0 b 6 042 3 21721 02314 d

Homework grades 76 82 85 Quiz grades 74 80 80 Test Grades 60 68 If the teacher weights homework at 10 Quizzes at 20 Tests at 60 what is her current class average Please be careful with this one the categories don t sum to 100 because she hasn t taken her final exam yet a 69 b 81 A

Factor using a GCF 24 1 27x y 72x y

Factor each Short Trinomial 3 x 8x 9