Permutations and Combinations Questions and Answers

An exponential function f x a b passes through the points 0 2 and 3 16 What are the values of a and b a and b

Determine the values of the parameters for which the system has a unique solution and describe the solution SX 5SX 3 4x 20sx 5 7 A s 1 x1 4 s 1 and x 1x 7 OB s 1 X 20 s 1 s 1 OC S 0 1 x D s 1 X 7 4 S 1 17 4 s 1 12 5s 20s s 1 and x and x 12 5s 20 S 1 s 1 12 5s and x2 20s S 1 12 5s 20s s 1

24 cm 37 ORP 65 n dia teacherma n 2oxtan 22 2cm I me 38 m opp n hyp 2 ado 24 37

Choose ALL correct statements if more than one are correct Let vectors i 1 1 3 2 2 5 and w 3 3 9 Which of the following statements are correct A Vector 3 3 10 is a linear combination of u and 7 B Vector 3 5 7 is a linear combination of u and 7 OC The space spanned by u 7 and has dimension 2 D Vectors and are linearly independent E Vectors and are parallel F None of the above

Sketch the graph of the piecewise defined function see belov f x 2 x 1 x 1 x 1

Solve the quadratic equation by completing the square x 8x 3 0 First choose the appropriate form and fill in the blanks with the correct numbers Then solve the equation If there is more than one solution separate them with comma Form x C D D Solution X 0 6 0 0

Question 20 1 point In a small fishing village outside of St John s Newfoundland the tides can be modeled by the function H t 2 5 cos 2 4 With H t measured in metres and f measured in hours after midnight What is the height of the tide at midnight a Om b 2 5 m Od 2m Od 4m

Question 16 1 point A function of the form f x cos a c passes through the point A 5 1 The function is O al f z cos z 0 5 Ob f z cos z 1 Od f 2 cos 2 Od f z cos z 0 5

4 Listen For f x 3 sin z 1 what are the maximum and minimum values a 4 and 2 b 4 and 4 Oc 3 and 2 d 0 and 6 Question 2 1 point Listen

Suppose that 6000 is placed in an account that pays 6 interest compounded each year Assume that no withdrawals are made from the account Follow the instructions below Do not do any rounding a Find the amount in the account at the end of 1 year 0 b Find the amount in the account at the end of 2 years 0

Solve for x logg1 x 4 Simplify your answer as much as possible x 0 log Olog O

A farmer finds that if she plants 65 trees per acre each tree will yield 50 bushels of fruit She estimates that for each additional tree planted per acre the yield of each tree will decrease by 3 bushels How many trees should she plant per acre to maximize her harvest trees Give your answer rounded to the nearest whole number

Find the present value of an annuity of 3 200 paid at the end of each quarter for 5 years after being deferred for 3 years if money is worth 8 compounded quarterly

Exercise 7 65 Suppose A a b c d a cd b What is A

Solve the proportion for x x 2 2 2 21 1 2 48 4 Points

For the equation what is the slope y 4 x 4 Points

Write an equation of a line that is parallel to the given line and passes through the point 8 6 4 Points y x 5

Find the angle in degrees rounded to one decimal D 6 5

Determine if the given point satisfies the system 5x 4y 17 4x 5y 17 OC O Yes No 5 3

Given that the system of linear equations Ax b is as follows find the least squares solution 2 121111 X1 1 1 34 1 3 7 1 X2 m 2 7

The solution of the system X Select the correct answer Seleccione una O a x O b x 1 X C X C1 O c none of these O d O e 3 2 2 1 XxX 4 1 0 1 1 10 X C Xis 1 0x 62 te 1 2 0 2 e le t

The function f is defined as follows 2x 3 x 1 3x 2 x21 a Find the domain of the function b Locate any intercepts c Graph the function d Based on the graph find the range 1 x a The domain of the function fis Type your answer in interval notation

Find the median of the data set below 9 7 6 13 12 7 08 07

Fill in the table using this function rule f x x 2 Simplify your answers as much as possible Click Not a real number if applicable X 7 2 6 27 f x 0 0 0 0

2 pts The U S Constitution states that the minimum size of a congressional district is 30 000 people The U S population in 2020 was about 329 5 million If we followed the rule of each district size being 30 000 people how many house members would we have had in 2020 Round your answer to the nearest whole Note For comparison we have 435 house members today This is not the answer Don t forget to show your work

Jaxon is deciding which raise to take for his salary adding 1000 dollars at the end of the year to his salary or adding 2 of his current salary He currently makes 57 000 a year Which should he choose O Jaxon should add the 1000 to his salary O Unable to determine with the given information O Jaxon should add the 2 to his salary O Both options result in the same increase in salary it does not matter which choice he takes O Jaxon should take half of each option adding half of 1000 and half of 2

Evaluate the definite integral 12x5 3dx 01 x

Write the polar equation of a conic with focus at the origin if its directrix is the line y 6 and its eccentricity is 42 3 7 cos 81 Or OT 42 3 7 cos 0 42 OTH 3 7 sin 01 Or 3 7 sin 0

Graph the inequality 3x 2y 8 10 8 6 4 10 84 6 2 24 G 8 10 X

How many terms does the following expression have 5x 3xy 7y29 5xy

The length of a rectangle is three times the width The perimeter is 72 feet Find the length and width of the rectangle Note Enter only numbers no words in the answer boxes The length is The width is feet feet

7 Given that mSY 114 and that mDC 86 find mAB A B E S D Y C

7 Express the perimeter of a rectangle if the length 3a 6b3 and the width 5a 3b

To win the top prize at a lottery game a player must pick 4 different numbers from 1 40 Find the num ber of possibilities if a the numbers need to be selected in order b the numbers do not need to be selected in order IF RE BE

Remember that a standard deck of cards has 52 cards of four suits clubs diamonds hearts and spades Each suit has 12 cards in it What is the probability that you will be dealt 2 cards of the same suit if you are dealt 2 cards in total Express your answer as a decimal rounded to four decimal places Drouido ancier below

What is the solution to the following system 3x 2y z 20 x 4y z 10 2x y 2z 15 O 2 3 4 O 4 3 2 O 4 3 2 O 6 7 2

Factor the following expression completely 28x 7

divided by the change in x section 2 4 Example Number of Fish 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 Population P t Example C 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 time yrs b a Find the average rate of change slope in the population from t 0 to t 5 Find the average rate of change slope in the population from t 15 to t 25 C Find the average rate of change slope in the population from t 35 to t 40 d What does a large value for the slope mean about the fish Find the average rate of change of the function f x 2x 4x 5 from x 0 to x 2

4 Solve the system of equations using the Graphing Method Show all steps neatly x 6 y 3x 4y 1 64 5 4 3 2 1 54323 2 2 3 2 IN 5 3 y axis 4 5 6 x axis 5 Solve the system of equations using the Elimination Method Show all steps neat 6x 5y 1 6x 4y 10 Check Solution Solution 6 Solve the system of equations using the Substitution Method Show all steps neatly 3x 4y 7 x 7 Check Solution 7 Solve the system of equations using the Substitution Method Show all steps neatly 6x 6y 6

Question 1 2 2 points Simplify the expression Use positive exponents O 18x 12x34 Question 2 2 2 points Simplify 27ab 3a b 36 3a b 5 a b 3b 5a b 5 Question 3 2 2 points Simplify 3 2 6 12 3 24 6 2 6 9 8 6 15 9 3

Consider the quadrilateral OABC such that ZOAC 20 ZOCA 20 ZACB 45 ZBAC Find ZBOC Suggestion Show that O is the circumcenter of AABC

8 IF YOU INVEST 100 IN AN ACCOUNT THAT PAYS 1 2 ANNUAL INTEREST ROMPOUNDED MONTHLY HOW MUCH WITH THIS BE WORTH74 10 YEARS

14 You invited 56 people to your graduation party You can afford to rent 5 tables round and om rectangular each costing the same Each round table can seat 8 people and each rectangular table can seat 12 people How many round and rectangular tables should you rent

MY NOTE A fireplace arch is to be constructed in the shape of a sereise The opening is to have a height of 2 feet at the center and a witth of 10 feet ung the bus see fires The contractores the the ellipse using tacks as the foo a What are the required positions of the tacks 2 1 targer value

Draw and shade Venn diagrams that correspond to the following sets a AUBUC b AU BNC c ANB UC d AnBnC A Q OB Q Q This question 1 point s possible O C Subm Q Q

9 5 For the given matrix alculate 45 manually A 1 3 37 3 5 3 3 1 3

Find the missing side of the triangle 11 5 m 20 6 m 5 1 m 21 2 m 17 1 m X 12 6 m

Find a polynomial u with real coefficients and degree at most 5 that approximates sinx as well a possible on the interval in the sense that sinx u x dx is as small as possible Compare this result to the Taylor series approximation

Multiply x 6 x 3x 2 x 6 x 3x 2

manufacturer of skis produces two types downhill and cross country The times required for manufacturing and finishing each ski are given in the table The maximum total weekly hours availabl or manufacturing and finishing the skis are 108 hours and 72 hours respectively The profits per ski are 60 for downhill and 90 for cross country Determine how many of each kind of ski should De produced to achieve a maximum profit Manufacturing time per ski Finishing time per ski Downhill 3 hours 1 5 hours Cross country 1 5 hours 1 5 hours CITO To achieve maximum profit the manufacturer should produce downhill skis and cross country skis