Permutations and Combinations Questions and Answers

A table of values of a linear function is shown below X y slope 2 4 equation y intercept 1 0 6 8 1 10 Find the slope and y intercept of the function s graph and find the equation for the function 2 12 8 08 1 0 X S

Point Slope Write the point slope form of the equation of the line through the given point with the given slope 2 1 through 1 0 slope 5 A y x 1 4 B y 1 5x C y 4 x 1 D y 5 x 1 3 through 5 4 slope A y 5 x 4 B y 5 x 4 C y 4 D y 4 5 x 5 x y x 5 6 5 B y x 1 5 C y 1 3x D y x 4 2 through 5 5 A 0 x 5 C y 5 0 slope undefined B 0 x 5 D y 5 0 Write the point slope form of the equation of the line through the given points 5 5 through 0 1 and 5 4 6 6 through 5 1 and 3 5 A y 1 x 5 B y 5 x 1 C y 1 x 5 D y 5 x 1 4 through 2 1 slope 3 A y 2 x 1 B y 1 3 x 2 C y 1 x 2 3 D y 2 2 x 1

Express the given function h as a composition of two functions f and g so that h x fog x where one of the functions is 6x 9 h x 6x 9

Question 5 4 Listen What ordered pair is shown plotted on the rectangular coordinate plane bela 10 8 7 8 7 7 8 7 8 10 5 0 5 10 5 10

Question 4 2 5 points f x 4x 5 Find f 3 O Listen 17 14 9 41

2 2 points For each of the following functions Find the function s domain i e the set of all input values Find the function s image i e the set of all output values Sketch several of its level curves on one set of axes a contour plot How many level curves At least 4 for each function generally sketch however many i sufficient to get a sense of the shape of the graph of f a f x y e y x b f x y ln x y 4

6 22i 3i 6 22i 3i Simplify your answer Type your answer in the form a bi Use integers or fractions for any numbers in th

Divide Express your answer in standard form 7 1 i 7 3 0 Simplify your answer Type an integer or an improper fraction Type your answer in the form

Write the complex conjugate of the given complex number and then find the product of the complex number and its conjugate 7 18 The complex conjugate of 7 18 is is 0 Simplify your answer Type your answer in the form a bi Type an exact answer using radicals as needed

b The system from example 2 2 2 Exercise 6 6 2 What goes wrong with the LU factorization if we use the row swap elementary operation Hint Think about what the corresponding E would be in contrast with the importance of the letter L Soliste Blisa subspace of R3 by using only the definition of Show that the plane P

Add the following expressions 11 18 5 8 11 18 5 8 Simplify your answer Type your answer in the form a

Divide the following complex numbers 5 4i 4i 5 4i 4i Type your answer in the form a biUse integers or fractions for any numbers in th

Express the percent as a decimal 1 10 10 Simplify your answer

Solve the system by the substitution method x 2y 8 y 3x 4 Select the correct choice below and fill in any answer boxes in your choic OA The solution is OB There are infinitely many solutions Type an ordered pair 1 here in no solution

Given a linear programming problem in the variables n with free variables Pk mk we write the standard form variabl 1 k 1 Pk Mk Xk 1 Xn Xn 1 n s where the final s variables are the slack variables listed in the same order as their corresponding constraints The linear programming problem can be put into the standard form minimize x1 subject to x1 X1 minimize The cost for your standard form solution is Is this solution to your standard form problem feasible No answer given 3x3 2x X2 X3 1 2x2 403 4 x1 x3 0 where in the last line we enclose the comma separated list of standard form variables in square brackets Is 0 1 2 a feasible solution to the original problem No answer given The cost for this solution is A corresponding solution to the standard form problem is the vector subject to 0

5 At a restaurant the total bill and the percentage of the bill left as a tip is repres in the scatter plot percentage 32 28 24 20 16 12 8 4 8 12 16 20 24 28 32 total The best fit line is represented by the equation y 0 632x 27 1 where x represents the total bill in dollars and y represents the percentage of the bill left as a tip a What does the best fit line estimate for the percentage of the bill left as a tip when the bill is 15 Is this reasonable b What does the best fit line predict for the percentage of the bill left as a tip when the bill is 50 Is this reasonable

Question 2 2 3 13 Use a calculator to find a decimal approximation for the following trigonometric function sec 22 42 sec 22 42 Simplify your answer Type an integer or a decimal Round to seven decimal places as needed

7B HW Determine whether 18 is a solution of the equation x 12 30 Is 18 a solution O No OYes

To say that 5 4 is the same as saying z is in the closed interval A B where A is and where B is

Solution To get the sampling distribution of probability value we should first determine whether the Sample is sufficient using the following two conditions npz 10 n 1 P 10 mp 150x 0 25 37 5210 The two conditions are fulfilled We understand from the central limit theorem that the as being is roughly normally distributed with the mean up p and the standard deviation PFP along with of 7 npzlo and n 1 P 10 Therfore the 2 conditions which satisfy the proportion of sample that were normally distributed by the mean up P and the Standard deviation PCHPJJ o p Sample proportion mean is up P 0 25 The sample proportion of the sitem and deviation of op 3 0 25 0 25 150 0025 0 0625 P 1 P n J 10 1875 0 00125 150 0 035 pproximately normer MP 0 25 op 0 035 Hence is correct option

roblem 5 If a square matrix A satisfies 46 54 41 0 which of the following is equal to 4 A 51 4 B 51 46 C 41 4 D 51 4 E 51 A6 F 41 A G 51 A H 61 A Problem 5 Select v

About the sequence x keZ we have the following a x 1 B x b for each 1 to b to b MK b x 1 x1 1 to b t b k 20 k 1 c x keZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8 B x b which is given by x t lim x 1 11 b t b Thus X 1 Jim A 506 8 5 de Finally the validity of this integral equation has the following two implications X 1 xo f s x s ds x 0 x 1 x lim ff s x s ds x flim f s x s ds x f f s lim x s ds xo ff s x s ds Thus the function tx 1 satisfying the integral equation x 1 x f s x s ds for all t 16 b 1 b 2 dt 0 ff s x s ds f t X t This now proves that the curve X 1 6 82 thus obtained is a solution of the initial value problem

MATHEMATICS Proposition 3 Let x J y J be two solutions of the initial value problem dx f t x x t x dt then x t y t for all t JOJ Proof Recall that both x and y being solutions of the initial value problem satisfy the integral equations on their domain intervals x 1 x f s x s ds y 1 x ff s y s ds Therefore x 1 y 1 s x s s y s ds which implies x 0 y 0 0 S 5 x s s y s 0 Kx s y s for all t2te Applying Gronwalls result with A 0 we get 0 x 1 y 1 0 for all t t This gives the desired equality x 1 y t for all tj Towards the uniqueness of the solution of the initial value problem 3 we consider all the solutions of the initial value problem 3 Let the totality of them be denoted by x J XEA the solutions x being thus indexed by a suitable indexing set A Above we have verified that any two solutions say x and xx are equal on the overlap of their domains Therefore we patch together all the solutions to get a maximal solution is the solution defined on the largest open interval It is obtained as follows Let J U J A clearly Jis an open sub internal of I with x EJ and all the solutions x patch up to get a solution x J 2 of the initial value problem 3

Find the equation of the line with the slope 5 and the y intercept 0 8 8 The equation of the line is Type an equation Type your answer in slope intercept form Use integers or fractions for any numbers in the equatic

Find the equation of the line whose slope is 0 and y intercept is 0 12 Graph the line The equation of the line is Type an equation Type your answer in slope intercept form

Find the equation of the line whose slope is 4 and y intercept is 0 1 Graph the line The equation of the line is Type your answer in slope intercept form

Graph the line 8x 2y 4 using the slope and y intercept Step by Step Solution Step 1 Solve the equation for y to write it in slope intercept form y mx b 8x 2y 4 2y 8x 4 y V 8x 4 2 Subtract 8x from both sides Divide both sides by 2 Simplify

For the following equation find the missing value in each ordered pair x 6 a 1 a 1 b 11 c 13

Find the equation of the line described below Write the equation in slope intercept form if possible Graph the line Contains 2 8 and 3 7 Choose the correct answer below and fill in the answer box within your choice Simplify your answer Use integers or fractions for any numbers in the equation O A The equation of the line cannot be written in slope intercept form The equation of the line is OB The equation of the line in slope intercept form is

AX O A No the graphs are not equivalent Their edges are connected in different ways OB No the graphs are not equivalent One has a triangular shape and the other has a rectangular shape OC Yes the graphs are equivalent They have the same number of vertices connected to each other in the same way D Yes the graphs are equivalent Although their edges are connected in different ways they have the same numbe Watch the video and then solve the problem given below Click here to watch the video Are the two graphs equivalent Choose the correct answer below

Find the equation of the line that contains the given points Write the equation in slope intercept form if possible 1 3 and 0 6 Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Use integers or fractions for any numbers in the equation OA The equation of the line in slope intercept form is OB The equation of the line cannot be written in slope intercept form The equation of the line is

Total number of drivers 1700 To find 99 Confidence interval for the population meam of drivers that has received at least 1 ticket Solution It is given that 33 Hence P 0 33 The CI we know that CI P Zx 1 P Now Substitude values in above furmula GI 0 33 2 576 0 33 1 0 33 1700 CI survey is of 1700 drivers hence n 1700 drivers have received ticke 0 33 2 576 1 033x 0 67 1700 0 332 576 x 0 011 40 1 0 33 0 0294 Now we construct the confidence interval 0 33 0 0294 2 CI 0 33 0 0294 0 3006 CI 0 3594 CI 30 06 35 941 Answer Hence correct option is A

The theater society members are voting for the kind of play they will perform next semester a comedy C a drama D or a musical M Their votes are summarized in the following preference table Which type of play is selected using the plurality method A Number of Votes 15 12 First Choice Second Choice Third Choice is selected for next semester drama 12 M C D C M C D D M comedy 8 C D M 4 D M C 4 M D C CID

Determine an ordered pair that satisfies the following equation by substituting the given value of the variable into the equation 2x 5y 9 y 1 The ordered pair is

Part 1 of 4 Find an ordered pair that satisfies the equation 2x y 11 30 O Step by Step Solution Step 1 Choose any value for one of the variables in the equation Choose any value of x or y For example let x 3

3 Use the distance formula to show that the points 1 5 0 3 and 2 1 are collinear on a line

2x 1 f x 3 x 21 FIND f 1 Type a response x 1 1 x 5 x 5

The parent function f x 2x is transformed into the function g x 4 2 x 3 8 Identify the transformations that occurred Vertical shift Up 8 Vertical shift Down 8 Horizontal shift Left 3 Horizontal shift Right 3 X Axis Reflection Vertical Stretch narrower Vertical Compression shrink y abx h k H Shift X reflect Left Right a 1 stretch o a 1 shrink compress N Shift Up Down Horiz Asymptote y

3 Look at the data and 1 identify the independent and dependent variables 2 determine if it can be expressed as a function and if it is a function 3 is it linear or nonlinear a b C Time t 0 Position s 3 Time t 5 Position s 7 Hour Calories 5 Force Pressure 2 1200 100 200 4 1 7 6 12 6 1000 500 10 807 2 4 7 800 750 15 34 8 6 8 600 800 16 4 6 9 2 8 20 400 1000 2500 be a function of F Can F be a function of P 50

2 The annual salaries of all employees at a financial company are normally distributed with a mean of 34 000 and a standard deviation of 4 000 What is the z score of a company employee who makes an annual salary of 42 000 A 2 B 1 C 1 D 2

Solve y 6 8 y 6 7 0 Step by Step Solution Step 1 Determine the appropriate substitution and write the equation in the form au Let uay 6 y 6 8 y 6 7 0 8 1 7 0

Determine a formula for the quadratic function in vertex form that has its vertex at 7 4 and passes through the point 9 20 A y x 7 4 B y 4 x 9 20 C y 4 x 7 4 D y x 9 20 E y 4 x 7 4

The length of a rectangle is 10 yd less than three times the width and the area of the rectangle is 77 yd Find the dimensions of the rectangle Length yd Width d 010 X

Use exact numbers y x 9 8 7 6 5 4 3 2 9 876 6 6 SK 5 4 3 2 14 23 Y 2 8788 3 4 5 6 7 8 9 HE 1 2 3 4 5 6 7 8 9

5 If f x 2x 3 g x x x 21 find x when a f x 7 b g x

A jogging track has a length of 1496 yards yd How long is this in miles mi First fill in the blank on the left side of the equation using one of the ratios Then write your answer on the right side of the equation Ratios 1 ft 12 in 1496 yd 12 in 1 ft 1 mi 5280 ft 0 5280 ft 1 mi 1760 yd 1 mi 1 mi 1760 yd ft 00 X yd in S mi

olve the equation For an equation with real solutions support the answer graphically x 8x 9 ewrite the equation in factored form E x 9 x 1 0 Factor completely he solution set is Type an integer or a simplified fraction Type an exact answer using radicals and i as needed Use a c eparate answers as needed

Write the interval notation for this compound inequality Explain why parenthesis brackets etc Lesson 1 05 x 4 or x 8

Given the following function a find the vertex b determine whether there is a maximum or a minimum value and find the value c find the range and d find the intervals on which the function is increasing and the intervals on which the function is decreasing f x 4x 4x 3 a The vertex is Type an ordered pair using integers or fractions

Graph the linear function using the slope and y intercept y x 3 10