Permutations and Combinations Questions and Answers

Questi e the following system of equations using matrices row operations

A truck hauled 136 cubic feet of sand to a construction site The sand is dumped into a cone shaped pile 6 feet in height What is the approximate diameter of the pile of sand in feet

Use a tree diagram to find the number of ways 2 letters a if repetition is allowed b if no repeats are allowed c Find the number of combinations of 4 elements take a If repetition is allowed how many ways can 2 letters

A poll showed that 57 1 of Americans say they believe that Marilyn Monroe had an affair with JF What is the probability in the decimal form of the percent of randomly selecting someone who does not believe that Marilyn Monroe had an affair with JFK

2 I am thinking of buying a used vehicle I can choose from one of three types a hatchback a sedan or an SUV There are 9 hatchbacks I am considering of which 3 have antilock brakes There are 10 sedans I am considering of which 6 have antilock brakes There are 6 SUVs I am considering of which 3 have antilock brakes a If I choose at random from all of the vehicles I am considering what is the probability that the vehicle I choose will be an SUV with antilock brakes b If I first choose a type of vehicle at random and then choose a vehicle of that type at random what is the probability that the vehicle I choose will be an SUV with antilock brakes Hint for b Draw a tree Solution Y

1 Which of the following represents the solutions to x 1 x 4 7 3 x 5 22 2 x 5 11 4 x 4 13 2 The smaller root to the nearest hundredth of 2x 3x 1 0 28 3 1 78 2 0 50 4 3 47 ort of gribrobos smir tvo 2006 3 The x intercepts of y 2x 7x 30 are

Marcel needs to find the height of a parallelogram The base is nches long and Step 2 of 3 Without substitution solve the formula chosen in the previous step for the unknown variable in terms of the known variable s Answer b Correct Formula A bh

2608 2 Which of the following is not equal to 2 2 Do 1 1 4 2 4 3 0 25 4 1 2

Question 9 of 12 Step 1 of 1 Solve the following linear equation 2 2x 5 7 x 6 17 Enter your answer as an integer a simplified fraction or a decimal rounded to two decimal places AnswerHow to enter your answer opens in new window 2 Points

Chapters 14 15 16 i 02 27 15 Calculate the average daily balance assume a 30 day billing cycle Note Round your answer to the nearest cent 4 20 4 26 4 30 5 4 5 12 Billing Date Previous Balance Payment Charge Payment Cash Advance Average daily balance 700 200 400 150 180

1 pints References TB MC Qu 08 114 Static How is deprec How is depreciation expense reported in the financia Multiple Choice O Current assets section of the balance she O Long term liabilities section of the statem O Operating expenses section of the Incom

Use Bayes theorem or a tree diagram to calculate the indicated probability Round your answer to four decimal places HINT See Quick Examples on page 515 P A B 8 P B 6 P A B 4 Find P B A X P B A 0 7018

Find an equation of the line that contains the points listed in the following table XOL234 0 1 The equation of the line is y 0 Use integers or fractions for any numbers in the equation HORONY Adidas y 0 6 12 18 24 COM MAMANDO VERBOAR

Evaluate E LE for t 0 522 s 4 062 and n 8 E Round to three decimal places as needed

Graph the interval 2 1 on the number line Include the endpoints and label the graph accordingly Choose the correct graph below OA 5 OB 5 OC 1 OD 1 4 29 O 0 to 10 ww N 2 2 02 1 13 4 4 0 0 X X x 1 x 5 x 5 In

Evaluate the formula n n z 0 25 E when z 2 115 and E 0 03 Round up to the nearest whole number as needed

11 Ollie Gibson is considering investing 10 000 in a certificate of deposit for 4 years at an annual interest rate of 4 compounded daily or 4 compounded monthly Based on the annual percentage yield which one is the better investment

If a survey with a random sample of 2500 students is conducted is it possible that only 20 of the students could respond that they text during class If so how could this be possible If not why not The margin of error is a prediction of what is most likely to happen In the context of this study it is possible a random sample could give results anywhere between 0 and 100 The margin of error is a prediction of what is most likely to happen In the context of this study it

11 2b 13 15 1 11 13 15 Task 17 19 21 23 distribution 2a 17 19 Which data set card are you looking at Determine the best measure of center and measure of variability to use based on the shape of the distribution 21 distribution 2b Determine which dot plot on your card has the greatest measure of center 25 Determine which dot plot on your card has the greatest measure of variability 23 25 27 27 29 2 29 31 31 Your Answer and Explanation 33 00000 0 33

Prove The square of the sum of two consecutive integers is odd n n 1 2n 1 n 2 n odd n n 1

Find the 13th term of the geometric sequence 1 2 4

The line plot below shows the number of pets owned by 25 people who were randomly surveyed in a particular town Pets The town mayor uses the graph to claim that the town is very pet friendly Part A Find the mean of the data Show or explain each step of work 2 points

Question 8 10 points Which is the only function below that could have a range of f x 3 i e 3 00 O 5 4 3 2 1 5 4 3 2 1 32 433 4 3 2 1 f x x 3 N f x 3 x 345 1 2 3 4 5 f x x 3 4 3 2 1 1 2 3 4 5

Q1 Consider the following maximization problem max x 1 0 x 3 3 Note that f x x 1 is a continuous function and the feasible set x 0 is compact Recall in this case there must be at least one solution 2 3 1 Solve the problem graphically 2 Now set up the Lagrangian function u for x 0 and A for x 3 and find all pairs x A satisfying the KKT first order necessary conditions 3 Each pair you found in 2 provides a candidate for optimal x again at least one of them must be optimal Can you tell which one is the optimal Check if your answer is consistent with 1

5 DETAILS LARMPMT1 7 3 032 Evaluate each expression Write your ans 5 0 x 1016 2 5 x 1013 b 7 5 x 107 1 25 x 107

What is the solution of log 2t 4 log 14 3f O 18 0 2 02 O 10

Simplify a b 4a b 9a b A 5a7b8 B 5a14616 C 13a7b8 D 13a14616

Solve for u 30 3u Simplify your answer as much as possibl 0

Add Subtract and simplify the rational expression O a 22 aw 2

5 A dice is weighted so that its probability distribution of a weighted dice has the form shown in the following table so that frac 1 Price 0 999 1 000 1999 2 000 2 999 3 000 3 999 4 000 4 999 5 000 2 1 6 4 Number sold 0 1 a A painting is auctioned for between 0 and 3 999 P E Check Clear b A painting is auctioned for at least 2 000 P E Check Clear c A painting is not auctioned for between 2 000 and 4 999

a 3 coins are tossed E The result is no more than one head n S 8 Check Clear n E 4 n E 4 b A die is thrown E The result is at least 3 n S 6 Check Clear Check n E 3 Clear Check 15 Clear c A pair of distinguishable dice are thrown and the sum of the numbers facing up is noted E The result is at most 4 n S 36 Check Clear riple space 5 and of the specified event E X Check Clear d A pair of indistinguishable dice are thrown and the sum of the numbers facing up is noted E The result is greater tha X Check Clear n S

x x5 3 x5 5x 6 f x 4x3 3x 3x 2 x 1

Ex What is the domain of f x 1 x 4 Ex What is the domain of f x Ex What is the domain of f x 1 x 25 x 5 x 4 x 3

x 2x 7x 4 x 1 X 1 Simplify your answers Do not factor Question 1 3 Divide using long division State the quotient q x and the remainder r x x 2x 7x 4 x 1

Describe how you can tell the difference between the graphs of y sinx and y cos x Be sure to justify your ideas

Without using a calculator give the exact value of each expression a sin 60 d sin b cos180 cos 2 e C f tan 225 tan 3

Convert the following angles to radians b 75 a 225 c 15 d 33

Multiply and Simplify a2 4 a 3 a 2a 8 a a 6 a 2 2 3 12 a 2a 43 a 4 a 2 2 22 3 a 2 a 4 a 2 a 2 3

Multiply and Simplify 4p p 9 2 P 3 4p 9 2p 6 P 3 2p 6p p 3 1 4p 9 P 6 p 3 p 3 p 3 J

9 6x x2 5x 11 3x 5x 10 4x 10 4x 2x 1 2x 12 2 2 17

Find the inverse of the following y 2 1 O y log x 1 O y log x 1 O y log x 1 O y log x 1

R1 10k IV Procedure R2 2 2k Figure 1 1 Series Parallel Resistor Circuit R3 1k A Measuring Resistance 1 Construct the circuit shown in Figure 1 1 on your breadboard 2 Tum the range selector switch knob of your multimeter to perform the ohmmeter operation and select the x1 range Using the ohmmeter scale what is the value

Part B Convert to Vertex Form using Formulas for h and k Given standard form f x ax bx c we can find the vertex h k by using the formula h 2a and k f h 1 Convert the following into Vertex Form using the formulas for h and k a y 2x 4x 5 b y x 10x 1 c y x 4x d y 3x 6x 1

1 When the numerator and denominator are the same degree the horizontal asymptote is the line where is the leading coefficient of the numerator and is the leading term of the denominator 2 When the degree of the numerator is bigger than the degree of the denominator there is 3 When the degree of the denominator is bigger than the degree of the numerator the horizontal asymptote is

Ex Write the equation for the horizontal asymptote if any Memory Trick for Horizontal Asymptotes T

7 The batting order for nine players on a 12 person team 9 A group of 20 people are going to run a race The top three runners earn gold silver and bronze medals

A museum curator is hanging 11 paintings in a row for an exhibit There are 7 Renaissance paintings and 4 Baroque paintings From left to right all of the Renaissance paintings will be hung first followed by all of the Baroque paintings How many ways are there to hang the paintings S

Completely solve the following equation for x 2 2x 12 Ox 4 Ox 2 x 2 or x 4 Ox 4 or x 2

Let s play a game You toss a fair coin If it comes out heads you win Otherwise the turn passes on to PLAYER 2 who tosses the same coin and wins if it comes out heads If not it is PLAYER 3 s turn If she doesn t get heads either it is your turn again The game goes on until somebody gets heads What is the probability that you win O I m stuck Help O 13 01 O 12 1 1 3 33 2 3

Step 2 of 2 Find the domai Answer