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THE ALGEBRA III MIDTERM EXAM REVIEW

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This review MUST be turned in when you take the midterm exam OR you will

not be allowed to take the midterm and will receive a ZERO for the exam.

ALG III Midterm Review

Linear Programming – Review

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region.

Find the maximum and minimum values of the given function for this region.

1)𝑓(𝑥, 𝑦) = 12𝑥 + 30𝑦

𝑦 ≤ 2𝑥 + 1

𝑦 ≥ −2𝑥 + 1

𝑥 ≤ 2

2) 𝑓(𝑥, 𝑦) = 5𝑥 − 2𝑦

𝑦 ≤ 7 − 𝑥

3𝑥 − 2𝑦 ≤ 6

𝑥 ≥ 0

𝑦 ≥ 0

3) A farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres. However, he has

only $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to

plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an

acre of wheat and 2 hours to plant an acre of rye. If the profit is $500 per acre of wheat and $300 per

acre of rye, how many acres of each should be planted to maximize profits?

Let x-wheat acres and y=rye acres

What do you know about x+y?

What do you know about the amount of money to spend…. And how much to spend on wheat acres and

how much on rye acres?

What do you know about the time to plant overall, time to plant an acre of wheat, time to plant an acre

of rye.

Can you create a formula to determine profit?

Graph each of the inequalities

Determine the points of interest

Test each of the (x,y) points to see which gives the most profit.

Probability

12-1 Counting Principle

1) The Breakfast Special at the Country Pantry, customers can choose their eggs scrambled, fried, or

poached, whole wheat, or white toast, and either orange, apple, tomato or grapefruit juice. How many

different breakfast specials can a customer order?

State whether the events are independent or dependent.

2) choosing a president, secretary and treasurer for the French Club, assuming a student could only hold

one office.

3) choosing an ice-cream flavor and choosing a topping for it.

4) choosing a marble from a bag and then choosing another marble from the bag

5) rolling a die and getting a 4, then rolling the die and getting a 2

Solve:

6) The Palace of Pizza offers small, medium and large pizzas, with fourteen different toppings.

How many different one-topping pizzas do they serve?

7) Alicia brought 8 t-shirts and 6 pairs of shorts to soccer camp. How many different outfits consisting

of a t-shirt and a pair of shorts does she have?

12-2 Permutations and Combinations

nPr= n!/( n-r)! nCr= n!/ (n-r)!r! permutation/repetition= n!/p!q! Evaluate:

1a) 8P2 1b) 7P5

1c) 10C4 1d) 12C7

2) How many four-person committees can be formed from a set of 20 people? 3) Annette has rented a summer house. She wants to select four roommates from six friends. How many combinations of four friends will she have? 4) Find the number of possibilities for putting an algebra book, a geometry book, a chemistry book an English book and a health book on a shelf. 5) How many different ways can the letters in the word MISSISSIPPI be arranged? 12-3 Probability Odds of success = s:f Probability = success/total 1) Find the odds of an event given the probability a) 8/9 b) 3/8 c) 11/12 d) 4/11 2) Find the probability of an event given the odds a) 6:1 b) 1:8 c) 4:5 d) 3:7 3) Eight out of 100 males and 1 out of 1000 females have some form of color blindness. a) What are the odds of a male being color-blind? b) What are the odds of a female being color-blind?

4) Rachel has 4 male kittens and 7 female kittens. She picks up 2 kittens to give to a friend. Find the probability of each selection. a) P(2 male) b) P(2 female) c) P(1 of each)

12-4 Multiplying Probability P(A and B)= P(A) P(B) P(A and B) = P(A) P(B following A) 1)Three dice are rolled to determine the number of moves in a board game for the players. a) What is the probability of the first die being a 4, the second die a 4 and the third die not a 4? b) What is the probability of the first die being a 2, the second die a 3 and the third die a 4? 2) The 20 prizes are each listed on a chip. The contestant picks a chip from the bag. There are 11 that say laptop, 8 say trip and 1 says truck. a) Drawing at random without replacement, what is the probability of picking a laptop and then a truck? b) Drawing at random without replacement, what is the probability of picking two trips? 3) Two cards are drawn from a standard deck of cards. Find each probability if no replacement occurs. a) P(two diamonds) b) P(jack, then king) 4) A die rolled twice. Find the probability. a) P(2, then 3) b) P(two 4’s)

5) A bowl contains 4 apples and 5 pears. Max randomly selects one, puts it back and then randomly selects another. What is the probability that both selections were pears? 6) Jack’s wallet contains three$1 bills, four $5 bills, and two $10 bills. If he selects three bills in succession, then what is the probability of selecting a $10 bill, then a $5 bill, then a $1 bill if the bills are not replaced? 7) A spinner has three colors on it, red, blue and green. What is the probability of: a) spinning twice and getting red then green b) spinning twice and getting the same number both times 12-5 Adding Probability P(A or B)= P(A) + P(B) P(A or B)= P(A) + P(B) – P(A and B) 1) Determine whether the events are mutually exclusive or inclusive. Then find the probability. a) the probability of drawing a King or a diamond from a standard deck of cards b)the probability of drawing a 3 or a Jack c) the probability of drawing an Ace or a face card(jack, queen, king) 1) A die is rolled. Find the probability of a) rolling a prime b) rolling at least a 5 c) rolling at least a 3 d) rolling less than 4 e) rolling multiples of 2 or 3

3) Sophie has 9 rings in her jewelry box. Five are gold and 4 are silver. If she randomly selects 3 rings to wear to a party, find each probability. a) P(2 silver or 2 gold) b) P(all gold or all silver)

Statistics Review

12-6 statistical measure 1) A firm gives sales training to its newly hired employees. To determine how effective the training is,

the firm compared the monthly sales of a group that has completed the training with a group that has

not.

Create a stem and leaf plot from the data and compare. Does the orientation program seem to be

succeeding?

thousands of dollars of sales last month:

No Training : 19, 22, 34, 23 ,27, 43,42, 28, 32, 29, 41, 26, 28, 26 ,43, 40

Training : 29, 21, 39, 44, 41, 36, 37, 29, 43, 45, 28, 32, 28, 33, 36, 32

2) Find the mean temperature from the data?

Temperature (Fahrenheit) Frequency

52 4

53 6

54 3

55 8

56 4

57 5

3) Find the mean, median and mode of the data:

12,11,7,9,8,6,4,5,10,1,5

4) Create a box-and-whisker plot of ages of some of the presidents at inauguration.

42, 43, 46, 51, 51, 51, 52, 54, 55, 55, 56, 56, 56, 60, 61, 61, 64, 69

Z – Score calculations

1. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an

IQ of 160.

a. What is the difference between Einsteins IQ and the mean?

b. How many standard deviations is that?

c. Convert Einstein’s IQ score to a z score.

d. If we consider “usual IQ scores to be those that convert z scores between -2 and 2, is Einstein’s IQ usual or unusual?

2. Womens heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. Find the z score corresponding to a woman with a height of 70 inches and determine whether the height is unusual.

3. Three students take equivalent stress tests. Which is the highest relative score (meaning which has the largest z score value)? a. A score of 144 on a test with a mean of 128 and a standard deviation of 34.

b. A score of 90 on a test with a mean of 86 and a standard deviation of 18.

c. A score of 18 on a test with a mean of 15 and a standard deviation of 5.

4. For the numbers below, find the area between the mean and the z-score: a) z = 1.17

b) z = -1.37

5. For the z-scores below, find the percentile rank (percent of individuals scoring below):

a) -0.47

b) 2.24

6. Scores on the SAT form a normal distribution with 500 and 100 .

a) What is the minimum score necessary to be in the top 15% of the SAT distribution?

b) Find the range of values that defines the middle 80% of the distribution of SAT scores

(372 and 628).

Sampling

1) What is the difference between a sample and a population?

2) Explain why blocking is used. Give an example.

3) What is a simple random sample?

4) Give an example of undercoverage.

5) What is convenience sampling?

6) What is the difference between a study/survey and an experiment?

7) Give an example of wording bias; then correct the bias.

8) Why should you always have a control group?

9) What does it mean if an experiment is blind?

10) What is cluster sampling? Give an example.

6) Find the mean, standard deviation for the data below as a population and then as a sample:

10, 9, 6, 9, 18, 4, 8, 20

7) Find the mean, standard deviation and coefficient of variation for the data. Determine whether

coffee prices or gasoline prices were more stable in 2004.

Month Coffee $/lb. Gasoline $/gallon

Jan 2.89 1.59

Feb 2.86 1.67

Mar 2.93 1.77

Apr 2.91 1.83

May 2.83 2.01

June 2.75 2.04

July 2.88 1.94

Aug 2.87 1.90

Sept 2.84 1.89

Oct. 2.78 2.03

Nov. 2.78 2.01

Dec. 2.85 1.88

12-7 Normal distribution

8) Use the data to make a histogram. Determine if the data is positively skewed, negatively skewed or

normally distributed.

Miles run Track Team Members

0-4 3

5-9 4

10-14 7

15-19 5

20-23 2

9) The number of eggs laid per year by a particular breed of chicken is normally distributed with a mean

of 225 and a standard deviation of 10 eggs.

Use the sketch below to place the mean and the deviations in the correct locations:

About what percent of the chickens will lay between 215 and 235 eggs per year?

What percent would you expect to lay more than 245 eggs?