Permutations and Combinations Questions and Answers

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

Polynomial Addition Simplify each sum 1 3n 8n2n n A 5n4 8n C 7n 8n 3 3x 8 2x 8 A 2x C 4x B 7n D 7n 5n B 5x D 2x 6 5 4u8u y 3u v 2u A 5u y u4 B 8u y u C 5u y 2u4 D 5u v 7 8y 3x 2x 3y A x 4y C x 3y B x 11y D x 9y 2 4 6 8 2 2n6n 5n 3n A 6n 5n4 C 3n 2n 4 4p 8 7 3p A 4p 3p 1 B 2p 4p 1 C 2p 4p 4 D 2p 3p 1 6 4m n m 7m2m n A 7m n 8m B 16m n 8m C 6m n 8m D 8m n 8m 8 56 8 5 5b4 A 3 C 3 B 3n 3n D 5n 2n B 1 D 5

12 x y 4 2 y A 4x8y 2 C 136 8x6 B D 8p6 y 1 8ry6

Write each expression in exponential form 7 10 9 2 11 8 2 10 5 12 10

Use the vectors in the figure at the right to graph the following vector 2v u 2w Select the figure with a vector that is equivalent to 2v u 2w O A Q G OB Q www O C Q O D G G

An engineer is reviewing the layout of a solar farm The solar farm shown has 4 small panels 33 medium panels and 32 large panels 6 What expression models the difference between the total area of the large solar panels and the total area of the small solar panels

Use the vertex and intercepts to sketch the graph of the quadratic function Give the equation of the parabola s axis of symmetry Use the graph to determine the domain and range of the function f x x 4 g 9 Use the graphing tool to graph the function Use the vertex and one of the intercepts when drawing the graph 6 3 The axis of symmetry is Type an equation Simplify your answer

9 9 2m n 2mm A 16m B D 512 10 10 2a 20 Za b A 9 46 B 16ba D 4q17

3 2a a b 2ab A C 418 166 3 19 166 B D 1 4 1 C 123 A 4m n I 3 4 40 5 B a m D 8

Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions Zero of 4 having multiplicity 3 f 4 64 f x Simplify your answer Use integers or fractions for any numbers in the expression

The mean cholesterol level of women age 45 59 in Ghana Nigeria and Seychelles is 5 1 mmol l and the standard deviation is 1 0 mmol l Assume that cholesterol levels are normally distributed Round the probabilities to four decimal places It is possible with rounding for a probability to be 0 0000 a State the random variable Select an answer b Find the probability that a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level of 2 7 mmol l or more c Find the probability that a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level of 7 6 mmol l or less d Find the probability that a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level between 2 7 and 7 6 mmol l e Find the probability that randomly selected woman age 45 59 in Ghana Nigeria or Seychelles has a cholesterol level that is at least 8 6 mmol l f is a cholesterol level of 8 6 mmol l unusually high for a randomly selected woman age 45 59 in Ghana Nigeria or Seychelles Why or why not Select an answer B What cholesterol level do 44 of all women age 45 59 in Ghana Nigeria and Seychelles have less than Round your answer to two decimal places in the first box Put the correct units in the second box

Which statement best reflects the solution s of the equation 1 1 2 3 3 x 2 x 3 x 3 O There are two solutions x 1 and x 3 O O There is only one solution x 1 The solution x 0 is an extraneous solution There is only one solution x 1 The solution x 3 is an extraneous solution There is only one solution x 3 The solution x 1 is an extraneous solution

Find all real zeros of f x 3x4 5x 10x 2x 4 as we have done in c Give exact answers for the zeros i e no decimal approximations

Use a calculator to write the following expression as a decimal rounded to two decimal places 23

7 m A C C 11 n 2m 3n m n 1 2m n 1 32mn A 2m n 2m n2 2m 2mn A 16m n m 4n C mon 3 m n nm 4 4 10 6 8m 16 15 B 1 2 10 n m B 8n D mm3 D B D m m 2 n n 20 m 512m 16 20 8 13 4 14 n 8 10 12 8 A 10 3 2m n 2nm A 12 C C 2m n 8 n m 2n m 40 2a 2a 4 2a b 5 466 2 aff3 A 4x8y 2 1 36 8 x6 x y 4 2 y 3 B 8m n D B 16ba 1 4a17 D 36 12 B 1 32m n 2 D 1 8ry6

3 5 Simplify Your answer should contain only positive exponents 11 a 4 12 12 4k A 16a A k 2 C 1 C 1 256a4 13 33 A 3 15 1 2v 4v A 4 1 C 2v B D D B 1 1 3 1 8 B 4 2v 14 16 4 3 4 A 4 4 C 4 14 16 X 2 x A 4x B 64k D 16k B B D 3 17 3x 2 2

3 Simplify Your answer should contain only positive exponents 12 12 4k A k 2 C 1 11 a 4 A 16a8 C 1 256a 13 3 3 4 B 9 B 1 D 3 1 1 14 4 4 A 4 4 C 4 14 B 64k D 16k6 D C IT

Simplify Your answer should contain only positive exponents 11 a 12 12 4 A 16a8 A k 2 C 1 1 256a C B D 1 12 B 64k D 16k6

6 6 4xy 2y A 6y x6 C y x5 B 24x89 D 8 xy7

Use a half angle identity to find the exact value cos 105 Which half angle formula should be used to find the exact value of cos 105 Sele Simplify your answer including any radicals Use integers or fractions for any num A cos 105 cos B cos 105 cos cos 105 cos OD cos 105 cos 210 2 2 2 2 O O 1 cos 210 2 1 cos 1 cos 1 COS 1 cos 1 cos 2 O O O O 2 3 cos 105 2 Simplify your answer including any radicals Use integers or fractions for any nur

A 25ab2a b B 50abab C 5a b 7ab

Compute the partial sums S2 S4 and S6 S S4 S6 3 3 3 3 22 32 42

Calculate S3 S4 and S and then find the sum for the telescoping series n 1 72 where S is the partial sum using the first k values of n S3 S4 S S5

11 8 points Given that given that x 2 is a zero of the polynomial p x x 2x 16x 32 use any appropriate method either division method and factoring to find the remaining zeroes of p x

10 8 points Use synthetic division to perform the indicated operation x x 4x 11 x 5

2 Tony is selling boxes of cookies He charges 7 for the box plus 2 per cookie One filled box sells for 35 How many cookies will fit in the box 3 Tiana s pool has the shape of a rectangle with the dimensions shown If the perimeter of the pool is 2 000 feet what is the value of x X 2 X 5 X 2

Evaluate each expression using the values given in the table 1 2 3 3 6 9 0 2 7 X f x g x a fog 1 d gof 0 3 2 9 6 7 2 a fog 1 1 b fog 1 1 FV 0 1 1 b fog 1 e gog 2 1 3 0 c gof 1 f fof 1

X 3 or f x x 3 and g x x 4 b gof a fog x 5 find the following composite functions and state the domain of each X 6 d gog c fof a fo ky Factor completely Simplify your answer

Find functions f and g so that fog H H x 8x 5 Choose the correct pair of functions OA f x 8x 5 g x x O B f x x g x 8x 5 O C f x x g x 5 8 O D f x X 5 8 g x x

Evaluate each expression using the graphs of y f x and y g x shown below a gof 1 b gof 0 c fog 1 d fog 4 a gof 1 Simplify your answer I y g x 6 di y f x

If H f og and H x 64 9x which of the following cannot be the component functions f and g Choose the correct answer below O A f x 64 x g x 9x OB f x x g x 64 9x OC f x 64 9x g x x OD f x 64 x g x 9x

Evaluate each expression using the values given in the table 3 2 1 2 9 6 3 6 7 2 0 2 X f x g x a fog 1 d gof 0 a fog 1 0 3 1 0 1 b fog 1 e gog 2 3 9 7 c gof 1 f fof 1

Use synthetic division and the factor theorem to determine whether x 2 is a factor of f x f x 3x 8x 7x 6 Complete the first row of the synthetic division table 2 3 8 7 6 Is x 2 a factor of f x OA No x 2 is not a factor because when f x is divided by x 2 the remainder is OB Yes x 2 is a factor because when f x is divided by x 2 the remainder is

True or False The polynomial below satisfies the given graph 3 y A 0 81 O True O False 40 3 f x x 81x 81

For the given polynomial P x and the given c use the remainder theorem to find P c 3 P x x 2x 7x 7 2 P c Simplify your answer

5 x y 3 y 1 A B D y y 4 X X

Determine whether the statement makes sense or does not make sense and explain your reasoning The graph shown below indicates that for the period from 2016 to 2019 the percentage of Americans whose educational attainment was high school graduate or more has rapidly increased of HS Graduates or More Educational Attainment in the United States 90 2 90 0 89 8 89 6 89 4 89 2 89 0 88 8 2015 2016 2017 Year 2018 2019 OU C of I Sa Choose the correct answer below OA No it does not make sense the time interval on the horizontal axis creates an overall impression of the percentage of Americans with a high school educatio or better increasing rapidly OB Yes the statement makes sense OC No it does not make sense the percentage of Americans with a high school education or better increased more rapidly during the period from 2015 2016 OD No it does not make sense the scale on the vertical axis is stretched to create an overall impression of the percentage of Americans with a high school education or better increasing rapidly

Define an exponential function f x which passes through the points 0 25 and 2 1 Enter your answer in the form a b where b 0

a 9 1 2 b 16 1 5 G 161 5

a 16 b 92 c 162

a 5 2 b 4 3 c 2 1

a 2 b 2 c 45 d 4

As of 2011 the following are the ages at which a country s presidents were inaugurated 61 49 54 56 44 52 52 46 54 43 54 48 47 50 69 54 69 63 46 62 50 60 57 65 47 66 65 64 51 60 68 55 66 57 62 48 59 48 52 57 48 52 60 43 Construct a grouped frequency distribution for the data Use 41 45 for the first class and use the same width for each subsequent class Type the frequency value for each class Frequency Age 41 45 O

When an odd number of data values are arranged in order the Fill in the blank below When an odd number of data values are arranged in order the is the middle value is the middle value

Use the graph to evaluate each expression a f g 2 b f g 3 c fg 1 d 1 f g 2 3 f g 3 7 fg 1 0 Select the correct choice below and fill in any answer boxes within your choice A OB 1 Type an integer or a simplified fraction 1 is not defined 6 C 6 TO 2 7 tv X Q G

Use the given table to evaluate each expression in parts a through d if possible a f g 2 b f g 4 c fg 2 d 0 a f g 2 7 Simplify your answer b f g 4 Simplify your answer X 2 0 2 4

f x Simplify your answer Use integers or fractions for any numbers in the expression www

For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is Type your answer in interval notation C 81 6 AY 10 6 h b 4 6 8 10

Use the properties of logarithms to condense the following logarithmic expression The solution should be a single logarithm with a coefficient of 1 Where possible evaluate logarithmic expressions log x log x 2 loga z loga z 2

8 Solve the linear systems of equations using the elimination or addition multiplication method Write none in both blanks if there is no solution 11x 8y 100 4x6y 26 x x y 9 Find the equation of a line passing through points 6 7 5 8 y x