Permutations and Combinations Questions and Answers

Determine the equation of the gr

Maria deposited 4000 into an account with 5 5 interest compounded quarterly Assuming that no withdrawals are made how much will she have in the account after 4 years Do not round any intermediate computations and round your answer to the nearest cent ell

4 It is found that Jupiter aligns with Mars 21 of the time whereas the Moon is in the seventh house 67 of the time Further either Jupiter aligns with Mars or the Moon is in the Seventh House or both 68 of the time To calculate the following express each question in terms of probabilities and show the formula you used No formula no credit a What percentage of time is the Moon is in the seventh house b What percentage of time is the moon is in the Seventh House at the same time that Jupiter aligns with Mars c What percentage of time is neither Jupiter aligned with Mars nor is the Moon in the Seventh House Solution

7 Discuss As there are infinitely many whole numbers the experiment consisting of picking a whole number at random has zero modeled probability of picking any specific number But if you actually perform the experiment and pick a number at random the relative frequency of picking that number is not zero even though there is a zero probability of picking it Is this a paradox If it is explain the contradiction if not explain why there is no contradiction

6 5 4 3 2 1 f x 1 2 3 4 5 6 1 f g 5 g f 1 f f 2 X a g 0 6 5 4 3 2 1 g x 12 3 4 5 X

Question 10 8 pts Let f x 2x 3 and let g x x 3 find and simply the following whenever possible Enter in your answer as a whole number or fraction

Graph the equation and state the slope of the line if y 8

Select all the root s of the equation 3x2 5x 2 5 1 1 3 2 0 2

Graph the equation by plotting poi

If log5 3x 5 3 then what is the value of x O a 50 O b 125 O c 40 d 25

Find the perfect square trinomial whose first two terms are x X 5

The following table shows the results of a survey of authors by a fictitious publishing company HINT See Example 5 New Authors Successful Unsuccessful 8 18 17 2 Total 25 20 Consider the following events S an author is successful U an author is unsuccessful N an author is new and E an a Describe the events S n N and SUN in words Sn N is the event that an author is SUN is the event that an author is Established Authors Total 26 19 45 successful and new either new or successful Use the table to compute n S n N and n SUN n Sn N 8

Which of the statements below must be true for any sets A and B Select all that apply A ANBCA B ACANB OC AUBCA D ACAUB E A BCA OF A BCB G ACA B H BCA B

Activity In this activity you ll apply the propert Part A Keeping the properties of exponents Hint Use the property a a BIUX X 15px

5ft 10 inches centimeters Round to the nearest tenth

1 If two indistinguishable dice are rolled find the probability of the following events Show the calculation that leads to your answer in each case No calculation No credit a E 1 5 2 2 3 3 b F The numbers are different

Identify f as being linear quadratic or neither If f is quadratic identify the leading coefficient a and evaluate f 3 3 x 3 f x Select the correct choice below and if necessary fill in the answer box to complete your choice OA Quadratic a f 3 B Linear C Neither linear nor quadratic

250 pounds Kilograms Round to the nearest tenth

DICALS AND QUADRATIC EQ ing the x intercept s a intercept s and the c

6 Who must own the vehicle if purchased after the policy is in force and Financed A Our B You C Us

For f x x and g x 5x 8 find the following composite functions and state the domain of each a fog b gof c fof d gog GEOOR a fog x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain of fog is x Type an inequality Simplify your answer Use integers or fractions for any numbers in the expression OB The domain of fog is all real numbers b gof x Simplify your answer Select the correct choice below and fill in any swer boxes within your cho OA The domain of g of is x Type an inequality Simplify your answer Use integers or fractions for any numbers in the expression

es the 2 15 points For the following series determine whether the given series relevant series determine whether the given series converges absolutely converges conditionally or diverges a 4 points 8 n 1 COS

Which equation is represented by the graph 2 Oy 4 3 2 1 2 7 1 23 2 32 1 Oy 32 Oy 2 1 2 2 1 2 1y 2 1

Question 4 Use long division to divide 4x 14x 6 x 3 28 x 3 O 4x 26 4x 2

Question 2 Use long division to divide x 5x 4 x 2 0 7 11 x 2 O x 7 11 2 x 2 0 x 2x 9 42 14

Question 5 Use synthetic division to divide 12 5x 31x 24x x 3 O 5x 7x 12 5x 9x

K Find f g f g fg and Determine the domain for each function 9 f x x 9 g x 4x f g x 4x x 9 Simplify your answer What is the domain off g OA The domain off g is Use a comma to separate answers as needed B The domain of f g is 0 00 Type your answer in interval notation OC The domain off g is f g x 4x x 9 Simplify your answer What is the domain of f g A The domain of f g is B The domain off g is Oc The domain off g is fg x Simplify your answer 0 00 Type your answer in interval notation Use a comma to separate answers as needed

Assume that the function f is a one to one function a If f 3 6 find f 6 Your answer is b If f 8 Your answer is 2 find f 2

was taught Carolina is observing the launch of a Space X rocket from the command center When she first sees the rocket the angle of elevation to it is 16 degrees Later the angle of elevation is 74 degrees If the command center is 2 1 miles from the launch pad how far did the rocket travel while Carolina was watching Round to the nearest tonth of mile

Find the inverse of the one to one function State the domain and range of the inverse function Which of the following is the inverse function O Cost of Phone Call 1 16 1 64 2 12 Minutes of Phone Call 16 24 32 Minutes of Phone Call 16 24 32 O Cost of Phone Call Cost of Phone Call 1 16 1 64 2 12 1 16 1 64 2 12 Minutes of Phone Call 32 24 16

1 For f x 5x 7 and g x x 7 find fog x and gof x Then determine whether fog x gof x What is fog x fog x

Change the exponential statement to an equivalent statement involving a logarithm ex 20 The equivalent logarithmic statement is Type an equation

Suppose that f x 3 a What is f 5 When x 5 what is the point on the graph of f 1 27 b If f x 9 1 what is x When f x 27 what is the point on the graph of f a f 5 243 The point 5 243 is on the graph of f Do not use commas in any individual coordinates 1 b If f x 27 Do not use commas in any individual coordinates X The point is on the graph of f 4

What is the factored form of the following 4x 81y O 2x 9 2x 9 O 2x 9 2x 9 O 2x 9y

d 8 d 4 d 8 d 4 O d 8 d 4 2 d 12d 32

37 Mr and Mrs Smith plan to roof the cabin on 2 consecutive days Assuming that the chance of rain is independent of the day what is the probability that it will rain both days A 0 04 B 0 08 C 0 16 D 0 20 E 0 40 O 0 04 O 0 08 O 0 16 O 0 20 0 40

y 9 X 01 4 3 s 7 6 5 4 3 2 1 0 1 2 3 5 6 6 X Which equation most likely represents the line shown on the graph Feedback A y x 3 Feedback B y 3x 3 Feedback C y x 3 Feedback D y x 3

72 y 2 N 2 3 DY 4 2 51 Which best represents the equation of the line shown Feedback A y 2x 1 Feedback B y 2x 1 Feedback C y 2x 1 x

Which is the slope of the line on the graph below NY Feedback A 00 1 TO OTH D 7 6 4 3 2 8 7 6 5 4 3 2 10 1 OH NOTECTO 7 33 1 2 3 4 5 6 7 8 1 2 3 4 5 6 8 X

A pizza with a diameter of 24 inches is cut into 18 slices Find the area of 1 slice Type a response

2 Would you be interested in investing in a dividend reinvestment plan DRIP Why or why not

3 What are some pros and cons of purchasing valuable goods as an investment If you were to invest in valuable goods what would you choose Explain your choice

gebra 4 3 1 A X New tab PlayerHomework aspx homeworkid 3 sit 1 500 in a savings account that pays i

12 ACBA AHKI A 52 2x 18 3y 11 K C X y B

Divide each polynomial by the binomial 2 12z 27 z 3

Let f x and let g x x 3 find and simply the following whenever possible Enter in your answer as a whole number or fraction Use when raising a term to an exponent Use sqrt to represent a radical For Example sqrt x or 2 sqrt 2 fog x

Divide each polynomial by the monomial 5m c4 5m4c8 10mc8 C

Divide each polynomial by the monomial 15w 10w 5w

Use the table below to evaluate the following X NON 2 4 f g 0 f x 4 8 5 0 g x 2 1 4 0

Multiply each pair of conjugates 5aw 6 5aw 6