Finite Mathematics
7th Edition
ISBN: 9781337280426
Author: Stefan Waner, Steven Costenoble
Publisher: Cengage Learning
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Chapter 8.4, Problem 59E
To determine
To calculate: The range after tax income of approximately
| Country | United States | Canada | Switzerland | Germany | Sweden |
| Mean household Income | |||||
| Standard deviation |
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Problem1
We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
Chapter 8 Solutions
Finite Mathematics
Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 6ECh. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - In Exercises 110, classify the random variable X...
Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - Prob. 13ECh. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - The random variable X has the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - Prob. 23ECh. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - 2010 Income Distribution up to $100,000 The...Ch. 8.1 - 2003 Income Distribution up to $100,000 Repeat...Ch. 8.1 - Population Age in Mexico The following chart shows...Ch. 8.1 - Population Age in the United States Repeat...Ch. 8.1 - Sport Utility VehiclesTow Ratings The following...Ch. 8.1 - Housing Prices Going into the Real Estate Bubble...Ch. 8.1 - Stock Market Gyrations The following chart shows...Ch. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Test Scores Your scores for the 20 surprise math...Ch. 8.1 - Car Purchases To persuade his parents to...Ch. 8.1 - Car Purchases Carmines parents, not convinced of...Ch. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Highway Safety Exercises 4150 are based on the...Ch. 8.1 - Prob. 46ECh. 8.1 - Highway Safety Exercises 4150 are based on the...Ch. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Highway Safety Exercises 4150 are based on the...Ch. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Give an example of a real-life situation that can...Ch. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - Prob. 6ECh. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - Prob. 9ECh. 8.2 - In Exercises 110, you are performing five...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - Prob. 14ECh. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - In Exercises 1118, X is a binomial variable with...Ch. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - In Exercises 19 and 20, graph the histogram of the...Ch. 8.2 - In Exercises 19 and 20, graph the histogram of the...Ch. 8.2 - In Exercises 21 and 22, graph the histogram of the...Ch. 8.2 - Prob. 22ECh. 8.2 - Internet Addiction The probability that a randomly...Ch. 8.2 - Prob. 24ECh. 8.2 - 1990s Internet Stock Boom According to a July 1999...Ch. 8.2 - 1990s Internet Stock Boom According to the article...Ch. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Manufacturing Your manufacturing plant produces...Ch. 8.2 - Manufacturing Compute the probability distribution...Ch. 8.2 - Prob. 31ECh. 8.2 - Other Teenage Pastimes According to the study...Ch. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Triple Redundancy To ensure reliable performance...Ch. 8.2 - IQ Scores Mensa is a club for people who have high...Ch. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Product Testing It is known that 65% of all the...Ch. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Highway Safety According to a study,18 a male...Ch. 8.2 - Prob. 44ECh. 8.2 - Mad Cow Disease In March 2004 the U.S. Department...Ch. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Compute the mean, median, and mode of the data...Ch. 8.3 - Prob. 9ECh. 8.3 - Give a sample of five scores with mean 100 and...Ch. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - In Exercises 1116, calculate the expected value of...Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - In Exercises 1728, calculate the expected value of...Ch. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Stock Market Gyrations Following is a sample of...Ch. 8.3 - Stock Market Gyrations Following is a sample of...Ch. 8.3 - Gold The following figures show the price of gold...Ch. 8.3 - Silver The following figures show the price of...Ch. 8.3 - Supermarkets A survey of 52 U.S. supermarkets...Ch. 8.3 - Video Arcades Your company, Sonic Video, Inc., has...Ch. 8.3 - School Enrollment The following table shows the...Ch. 8.3 - School Enrollment Repeat Exercise 35, using the...Ch. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - 2010 Income Distribution up to $100,000 The...Ch. 8.3 - 2003 Income Distribution up to $100,000 Repeat...Ch. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Roulette A roulette wheel has the numbers 1...Ch. 8.3 - Roulette A roulette wheel has the numbers 1...Ch. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Spiders Your pet tarantula, Spider, has a .12...Ch. 8.3 - Exercises 51 and 52 assume familiarity with...Ch. 8.3 - Exercises 51 and 52 assume familiarity with...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Insurance The Blue Sky Flight Insurance Company...Ch. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Prob. 63ECh. 8.3 - Prob. 64ECh. 8.3 - Prob. 65ECh. 8.3 - Prob. 66ECh. 8.3 - Prob. 67ECh. 8.3 - Prob. 68ECh. 8.3 - Slim tells you that the population mean is just...Ch. 8.3 - Prob. 70ECh. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - Prob. 11ECh. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - Prob. 13ECh. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Popularity Ratings In your bid to be elected class...Ch. 8.4 - Popularity Ratings Your candidacy for elected...Ch. 8.4 - Unemployment Following is a sample of unemployment...Ch. 8.4 - Unemployment Following is a sample of unemployment...Ch. 8.4 - Stock Market Gyrations Following is a sample of...Ch. 8.4 - Stock Market Gyrations Following is a sample of...Ch. 8.4 - Sport Utility Vehicles Following are highway...Ch. 8.4 - Sport Utility Vehicles Following are the city...Ch. 8.4 - Shopping Malls A survey of all the shopping malls...Ch. 8.4 - Prob. 34ECh. 8.4 - 2010 Income Distribution up to $100,000 The...Ch. 8.4 - Prob. 36ECh. 8.4 - Hispanic Employment: Male The following table...Ch. 8.4 - Hispanic Employment: Female Repeat Exercise 37,...Ch. 8.4 - Commerce You have been told that the average life...Ch. 8.4 - Commerce You have been told that the average life...Ch. 8.4 - Batmobiles The average life span of a Batmobile is...Ch. 8.4 - Spiderman Coupes The average life span of a...Ch. 8.4 - Teenage Pastimes According to a study,51 the...Ch. 8.4 - Prob. 44ECh. 8.4 - Teenage Marketing In 2000, 22% of all teenagers in...Ch. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Video Arcades Your company, Sonic Video, Inc., has...Ch. 8.4 - Prob. 49ECh. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 51ECh. 8.4 - Prob. 52ECh. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 56ECh. 8.4 - Prob. 57ECh. 8.4 - Prob. 58ECh. 8.4 - Prob. 59ECh. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 61ECh. 8.4 - Prob. 62ECh. 8.4 - Prob. 63ECh. 8.4 - Prob. 64ECh. 8.4 - Prob. 65ECh. 8.4 - Prob. 66ECh. 8.4 - Prob. 67ECh. 8.4 - Prob. 68ECh. 8.4 - Prob. 69ECh. 8.4 - Prob. 70ECh. 8.4 - Prob. 71ECh. 8.4 - Prob. 72ECh. 8.4 - Prob. 73ECh. 8.4 - Prob. 74ECh. 8.4 - Prob. 75ECh. 8.4 - Prob. 76ECh. 8.4 - Prob. 77ECh. 8.4 - Prob. 78ECh. 8.4 - Prob. 79ECh. 8.4 - Prob. 80ECh. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Prob. 11ECh. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Prob. 13ECh. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - Find the probability that a normal variable takes...Ch. 8.5 - Find the probability that a normal variable takes...Ch. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Suppose X is a normal random variable with mean...Ch. 8.5 - Suppose X is a normal random variable with mean...Ch. 8.5 - Prob. 22ECh. 8.5 - If you roll a die 100 times, what is the...Ch. 8.5 - If you roll a die 100 times, what is the...Ch. 8.5 - If you roll a die 200 times, what is the...Ch. 8.5 - Prob. 26ECh. 8.5 - SAT Scores SAT test scores are normally...Ch. 8.5 - Prob. 28ECh. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - Prob. 31ECh. 8.5 - Prob. 32ECh. 8.5 - Prob. 33ECh. 8.5 - Prob. 34ECh. 8.5 - SAT Scores SAT test scores are normally...Ch. 8.5 - LSAT Scores LSAT test scores are normally...Ch. 8.5 - Baseball The mean batting average in major league...Ch. 8.5 - Baseball The mean batting average in major league...Ch. 8.5 - Prob. 39ECh. 8.5 - Marketing Your hot sauce company rates its sauce...Ch. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Prob. 44ECh. 8.5 - Distribution of Income If we model after-tax...Ch. 8.5 - Prob. 46ECh. 8.5 - Prob. 47ECh. 8.5 - Prob. 48ECh. 8.5 - Prob. 49ECh. 8.5 - Prob. 50ECh. 8.5 - Prob. 51ECh. 8.5 - Prob. 52ECh. 8.5 - Prob. 53ECh. 8.5 - Prob. 54ECh. 8.5 - Prob. 55ECh. 8.5 - Prob. 56ECh. 8.5 - Prob. 57ECh. 8.5 - Prob. 58ECh. 8.5 - Aviation The probability of a plane crashing on a...Ch. 8.5 - Prob. 60ECh. 8.5 - Prob. 61ECh. 8.5 - Prob. 62ECh. 8.5 - Prob. 63ECh. 8.5 - Prob. 64ECh. 8.5 - Prob. 65ECh. 8.5 - Prob. 66ECh. 8.5 - Prob. 67ECh. 8.5 - Prob. 68ECh. 8.5 - Prob. 69ECh. 8.5 - Prob. 70ECh. 8.5 - Prob. 71ECh. 8.5 - Prob. 72ECh. 8.5 - Prob. 73ECh. 8.5 - Prob. 74ECh. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - A die is constructed in such a way that rolling a...Ch. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - In Exercises 2934 the mean and standard deviation...Ch. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 1CSCh. 8 - Prob. 2CSCh. 8 - Prob. 3CSCh. 8 - Prob. 4CSCh. 8 - Which of the following lists of data would you...Ch. 8 - Prob. 6CSCh. 8 - Prob. 7CSCh. 8 - Prob. 8CS
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- 5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forward
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Publisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License