Permutations and Combinations Questions and Answers

A math textbook explains probability by showing a set of cards numbered 4 through 9 and showing the number of people who might draw each card Drawing a card between 4 and 9 xx xxx 456789 Number drawn Which number was drawn the most times

5 54 4 3 2 What is the domain of the function on the graph O all real numbers all real numbers greater than or equal to 0 all real numbers greater than or equal to 2 all real numbers greater than or equal to 3 5 4 3 1 2 3 4 5 x 23 3 4 5

What is f g a f x x 36 9 x x 2x 10 Enter your answer in standard form in the box f g x

The public university he wants to attend to estimate the cost of attending TUITION FEES 8 000 a What should Darnell estimate the total cost of one year to be ROOM POARD 9 100 DOOKS SUPPLIES TRANSPORTATION ETC 950 650 b Darnell s family can contribute 60 of the total annual expenses before financial aid and Damn estimates that he will qualify for 6 000 in scholarships and grants for his first year How much does that leave for Darnell to cover for his first year of college c If Darnell has 18 months to save how much should he save each month

2 f x x 3 g x 2x 5 Find f 3 g 3 4 f t 2t 1 g t 1 2 Find 3 10 2g 10 6 f x x 1 g x x 2 Find 2f 3 5g 3 8 g x x 3 Find g g 0

What is the length of side AB Round your answer to two decimal places B AB 6 30 C

2 Water flowing through both a small pipe and a large pipe can fill a water tank in 9 hours Water flowing through the large pipe alone can fill the tank in 17 hours Write an equation that can be used to find the amount of time t in hours it would take to fill the tank using only the small pipe

You have placed some money into an account and it is modeled by this equation Based on the information in this equations how often was it compounded monthly daily semiannually none of these choices quarterly annually continuously

5 A savings account balance is compounded continuously If the interest rate is 2 6 per year and the current balance is 1 685 00 what will the balance be 12 8 years from now 6 A savings account balance is compounded continuously If the interest rate is 3 7 per year and the current balance is 1 412 00 what will the balance be 10 5 years from now 7 A savings account balance is compounded continuously If the interest rate is 3 9 per year and the current balance is 1 553 00 what will the balance be 5 9 years from now 8 A savings account balance is compounded continuously If the interest rate is 2 2 per year and the current balance is 1 530 00 what will the balance be 7 5 years from now 9 A savings account balance is compounded continuously If the interest rate is 2 per year and the current balance is 1 919 00 what will the balance be 19 now years A 1 908 16 B 2 806 12 C 1 795 92 D 3 339 28 from 10 A savings account balance is compounded continuously If the interest rate is 4 per year and the current balance is 1 717 00 what will the balance be 13 years from now A 2 945 80 B 2 888 04 C 3 841 09 D 2 830 28

12 EVALUATE AT X 3 ANSWERS SHOULD BE ROUNDED TO 3 DECIMAL PLACES g x 3e 0 5X 5

3 You pick a card at random put it back and then pick another card at random What is th probability of picking a number less than 7 and then picking an even number Write yo answer as a fraction Independent or Dependent 678

The function g x is a polynomial with the following end behavior as z 00 f x o as o f x 0 Which of the answer choices could be an expression that represents g x x 2x 6 4x x 5 3x 4x 1 2x 7x 4x

e system by substitution y 7x y 5x 10

A11 Hans has determined the angle B and obtained a result of 60 Explain why this is not correct 5 m 30 8 m B 2 The areas of the square and the triangle are equal Give reasons

evaluate 4 3 If needed round correctl to hundredth 2 DIGITS PASSED THE DECIMAL Type a response

log y Solve 3 1 15 for x using the change of base formula log y log b 0 594316 1 405684

1 point A new drug is being tested on mice One dozen mice are given the new drug and tested while another dozen mice are not given anything and tested What kind of data collection is this Observational Study Experiment 00 Sample Survey Census

1 point There is a study on exercise and health a group of women who have been exercising regularly for 5 years are grouped and given a wellness exam and compared to a group of women who have not exercised in the past five years What kind of data collection is this Survey Observational Study Simulation Experiment

8 1 point There is a study on exercise and health a group of women who have been exercising regularly for 5 years are grouped and given a wellness exam and compared to a group of women who have not exercised in the past five years What kind of data collection is this Observational Study Experiment O O O O Survey Simulation

Convert to exponential form log a y

17 1 point Evaluate the following Exponential expression and approximate it to the nearest ten thousandth e0 3 approximately 1 3499 approximately 20 0855 approximately 1 0305 approximately 1 4529

Simplify the following radicals 360x b 24a b

Given a polynomial f x if x 2 is a factor what else must be true Of 0 2 Of 0 2 Of 2 0 Of 2 0

4 4 9 x 18 2x 5 10 4 x 3 Xx 8 16x Determine which expressions if any are 6x 2 x

3 1 point Condense the following Logarithmic expression In 6 6 ln z In y In O In 6 0 6 2 5 y In 6 v 2 In

1 2 The function h x is given below h x 3 5 5 7 6 9 10 12 12 16 Which of the following gives h x O 3 5 5 7 6 9 10 12 12 16 O 5 3 7 5 9 6 12 10 16 12 O 3 5 5 7 6 9 10 12 12 16 O 5 3 7 5 9 6 12 10 16 12

13 M 1 point 44 0000 N P R F Which two triangles are congruent AMNO APRQ OAMNO APQR OAMNO ARPQ Not congruent

A line passes through 1 3 and has slope 2 Find an equation of the line Explain your steps Step y y m x x y 3 2 x 1 y 3 2 x 1 Written Explanation Use the point slope form Substitute 1 for x 3 for y and 2 for m Simplify inside grouping symbols

TN Write an equation in point slope form of the line that passes through the given points 7 4 0 and 2 1 4 0 24 6 x 4 8 3 2 and 5 3 9 5 1 and 3 4 not matter which point you choose when writing the

Which inequality represents the solution set shown on the given number line 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Ox 8 0x 8 Ox 8 C 00

Admission to the town festival is 5 Each activity costs 2 Rema has 21 to spend at the festival She writes the inequality 5 2a 21 to represent how many activity tickets a she can purchase at the festival Which value is a solution to this inequality 08 O 10 O 12 13

1 point The number of hours that college students sleep on a week night is approximated by a normal curve with a mean of 7 hours and a standard deviation of 1 7 hours Answer the question below using a z table About what proportion of students sleep less than 5 hours on a week night round to whole number About 16 About 32 About 24 About 12 Ne

n 3 2 2 2 Additional Practice Point Slope Form Graph the line that represents each linear equation 1 y 2 2 x 3 2 y 3 2 x 1 7 4 0 and 2 1 170 1 6 Write the equation in point slope form of the line that passes through the given point with the given slope 4 2 1 m 3 6 4 11 m 3 5 3 5 m 2 2 4 Y 0 x x enVision HW Write an equation in point slope form of the line that passes through the given points 8 3 2 and 5 3 3 y 1 x 5 9 5 1 and 3 4 10 Explain why it does not matter which point you choose when writing the equation of the line in point slope form given two points 11 Members of the student council are conducting a fundraiser by selling school calendars After selling 80 calendars they had a loss of 360 After selling 200 calendars they had a profit of 600 Write an equation that describes the relation between y the profit or loss and x the number of calendars sold How much profit did they make from selling each calendar How much would they have lost if they had sold no calendars

16 1 point Which type of study contains a treatment Sample Survey Observational Study Experiment Previous

11 1 point Normal distribution models what type of variable random continuous variable random variable Odiscrete random variable discrete continuous variable Previous

12 1 point The mean of a set of normally distributed data is 600 with a standard deviation of 20 What percent of the data is between 580 and 620 95 68 DED 50

8 1 point The finishing times of two runners for several one mile races in minutes are shown in the box and whisker plots Runner 1 65 75 is Runner 2 Based on the box plots runner 1 has a faster median time True False

5 1 point What is the range of the data set 97 85 92 86 7 O 12 Q 11 5

11 3 2 m through the point 0 6