Answers for the problems at the end of Wednesday's class

Side of a triangle are 6, 11 and 8.

Scalene because all different.

6^2 + 8^2 = 100 < 11^2 = 121, so it is obtuse.

Area = 15sqrt(39)/4

Points are (2, 1) (5, 5) and (8, 9)

(2, 1) - (2, 1) = (0, 0)
(5, 5) - (2, 1) = (3, 4)
(8, 9) - (2, 1) = (6, 8)

Area =  ½| 3x8 - 6x4 | = 0

The three points are colinear.

Notes for June 16

Here are the topics we covered Monday.

Primes, composites and the unit (1)

How many factors does a number have.

1 has one factor, just itself. (Every number has itself as a factor.)
2 has two factors, 1 and 2.
3 has two factors, 1 and 3.
4 has three factors, 1, 2 and 4.

This gives us examples of the three possible cases.

A unit has exactly one factor. The only unit is the number 1.

A prime has exactly two factors, itself and 1.

Any number with more than two factors is called a composite.


Follow this link to see previous posts about Prime factorization.

If we want to check to see if a number k is prime, we have to see if any prime number less than the square root of k divides evenly into k.

Two examples.

Is 87 prime? We have to check all primes less than sqrt(87) =~ 9.327..., so that means checking 2, 3, 5 and 7.

87/2 = 43.5, so 2 doesn't work.

87/3 = 29. Now we can stop, because 87 is a composite 3 x 29.

Is 89 prime? We have to check all primes less than sqrt(89) =~ 9.44398..., so that means checking 2, 3, 5 and 7.






89/2 = 44.5, so 2 doesn't work.

89/3 = 29.666..., so 3 doesn't work.

89/5 = 17.8, so 5 doesn't work.

89/7 = 12.714..., so 7 doesn't work.

We can stop, 89 is prime.

We also were introduced to the concept of relatively prime. Numbers a and b are relatively prime if they have no primes in common in their respective prime factorizations.

If we have a fraction, we can reduce it to lowest term a/b, where a and b are relatively prime.



Follow this link for more information on Relatively prime pairs and reducing fractions to lowest terms .

Four versions of the final exam

There are four versions of the final exam. Do not begin until Prof. Hubbard has told you which one you should take. You have from 8:05 am to 10:05 am to finish. Sorry I was late.

Version a

Version b

Version c

Version d

Send the exam to mhubbard@peralta.edu with MATH 15 FINAL in the subject line.
 
Good luck!
 

PRACTICE final exam

No class on Zoom today, but here is a link to a PRACTICE final exam.

The real final will be 8:00 to 10:00 on Wednesday, May 20.

I will be in my office hour today from 12:20 to 12:50, the Zoom room number is

584-656-357

Here is a link to the answers to the practice exam. 

Answers to midterm 2

The complete list of answers can be found here. 

If you are taking the final, it will be from 8:00 to 10:00 on Wednesday, May 20 in the regular Zoom room.

In class midterm 2 due by 10:45 this morning

Here is a link to the in-class portion of the midterm.

Answers to HW 10

Link to take-home exam, due by the end of class on Wednesday, May 6

Here is the link to the .pdf version of the test.

Homework 10 is due by midnight tonight, Monday May 4.

The in-class section of the exam will be from 9:30 to 10:45 am on Wednesday, May 6.
 

Answers to quiz 6

The formula is: deaths/population x 100,000, no parentheses

State                    pop. (nearest 100,000)     deaths                  rate per 100,000

California              39,500,000                    1,809                            5      

Texas                   29,000,000                    690                               2      

Florida                  21,500,000                    1,154                            5      

New York              19,500,000                    17,638                          90     

Pennsylvania          12,800,000                    1,716                            13     

Illinois         12,700,000                    2,125                            17     

Ohio                     11,700,000                    799                               7      

Georgia                 10,600,000                    1,026                            10     

North Carolina        10,500,000                    342                               3      

Michigan               10,000,000                    3,567                            36     

(10 points) If you have the rate r, the number of years y and the amount of the loan A.

The total you will pay back is given by

Total = A * (1 + r*y)

The monthly formula is

Monthly = Total/(12 * y)

Make sure to use the parentheses.

Round answers to the nearest dollar.

If you borrow $50,000 at 5% and have a fifteen year loan, what is the total you will pay back?       Answer: $87,500

If you borrow $50,000 at 5% and have a fifteen year loan, what is the monthly payment?              Answer: $486

If you borrow $50,000 at 5% and have a ten year loan, what is the total you will pay back?  Answer: $75,000

If you borrow $50,000 at 5% and have a ten year loan, what is the monthly payment?          Answer: $625

If you know your monthly pay payment Monthly, the number of years to pay the loan back and the rate, the maximum amount you can borrow is given by

Amount = Monthly * 12 * y / (1 + r*y)

Round the answers to the nearest dollar.

If you can afford to pay $1500 a month and you can get a ten year loan at 5%, what is the largest amount you can borrow?

                                                      Amount: $120,000

If you can afford to pay $1500 a month and you can get a fifteen year loan at 5%, what is the largest amount you can borrow?

                                                      Amount: $154,286      

If you can afford to pay $1500 a month and you can get a twenty year loan at 5%, what is the largest amount you can borrow?

                                                      Amount: $180,000

If you can afford to pay $2000 a month and you can get a ten year loan at 5%, what is the largest amount you can borrow?

                                                      Amount: $160,000      

Quiz 6

Name: ___________________ 
Math for Liberal Arts – Math 15

Quiz 6                            20 points

Put answers in spaces provided.

(10 points) Here are the populations of the ten most populous states and the number of COVID-19 deaths they have reported as of April 28, according to covidtracking.com. Find the rate per 100,000, rounding to the nearest whole number.

The formula is: deaths/population x 100,000, no parentheses

State                    pop.                    deaths                  rate 

California           39,500,000          1,809                   ____

Texas                   29,000,000            690                   ____

Florida                  21,500,000           1,154                ____

New York              19,500,000           17,638             ____

Pennsylvania          12,800,000          1,716               ____

Illinois         12,700,000            2,125                   ____

Ohio                     11,700,000             799               ____

Georgia                 10,600,000             1,026          ____

North Carolina        10,500,000             342           ____

Michigan               10,000,000             3,567         ____

====

(5 points) If you have the rate r, the number of years y and the amount of the loan A.

The total you will pay back is given by

Total = A * (1 + r*y)

The monthly formula is

Monthly = Total/(12 * y)

Make sure to use the parentheses.

Round answers to the nearest dollar.

If you borrow $50,000 at 5% and have a fifteen year loan, what is the total you will pay back?

Answer: ____________________

If you borrow $50,000 at 5% and have a fifteen year loan, what is the monthly payment?

Answer: ____________________

If you borrow $50,000 at 5% and have a ten year loan, what is the total you will pay back?

Answer: ____________________

If you borrow $50,000 at 5% and have a ten year loan, what is the monthly payment?

Answer: ____________________

====

(5 points) If you know your monthly pay payment Monthly, the number of years to pay the loan back and the rate, the maximum amount you can borrow is given by

Amount = Monthly * 12 * y / (1 + r*y)

Round the answers to the nearest dollar.

If you can afford to pay $1500 a month and you can get a ten year loan at 5%, what is the largest amount you can borrow?

            Amount: _____________________        

If you can afford to pay $1500 a month and you can get a fifteen year loan at 5%, what is the largest amount you can borrow?

            Amount: _____________________        

If you can afford to pay $1500 a month and you can get a twenty year loan at 5%, what is the largest amount you can borrow?

            Amount: _____________________        

If you can afford to pay $2000 a month and you can get a ten year loan at 5%, what is the largest amount you can borrow?

            Amount: _____________________        

Changing Roman numerals to Hindu-Arabic

There are 27 patterns used to make up Roman numerals from 1 to 999. The patterns are put in order from largest to smallest as we read from left to right, which is true for Hindu-Arabic numerals as well.

1 through 9. With these patterns the first symbol is either I or V.
I = 1
II = 2
III = 3
IV = 4 (one before five)
V = 5
VI = 6
VII = 7
VIII = 8
IX = 9 (one before ten) 

10 through 90. With these patterns the first symbol is either X or L.
X = 10
XX = 20
XXX = 30
XL = 40 (ten before fifty)
L = 50
LX = 60
LXX = 70
LXXX = 80
XC = 90 (ten before hundred) 


100 through 900. With these patterns the first symbol is either C or D.
C = 100
CC = 200
CCC = 300
CD = 400 (hundred before five hundred)
D = 500
DC = 600
DCC = 700
DCC = 800
CM = 900 (hundred before thousand) 
M = 1,000, but another way to write numbers past 1,000, is to put a bar over the numbers.

For example,
__
IX = 9,000.

Change CDXCVII into Hindu-Arabic.

We start on the left and we find CDXCVII. CD = 400, the hundreds place

Then we have XCVII. XC = 90, the tens place.

VII = 7. Put them all together and we get CDXCVII = 497.

Change DIV into Hindu-Arabic.

D = 500, IV = 4, so this is 504. In Roman numerals they had no symbol for zero, so they just left that position blank.
 

Link to homework 10

Click on this link to get a copy of Homework 10. It is due on Monday, May 4.

Answers to Homework 9

Flu/pneumonia 1910: 156 per 100,000

Flu/pneumonia 1950: 32 per 100,000

Flu/pneumonia 1990: 32 per 100,000

COVID-19 deaths per 100,000 as of April 21

California: 3 per 100,000

Texas: 2 per 100,000

Florida: 4 per 100,000

New York: 76 per 100,000

Pennsylvania: 12 per 100,000

Ilinois: 12 per 100,000

Ohio: 5 per 100,000

Georgia: 8 per 100,000

North Carolina: 2 per 100,000

Michigan: 27 per 100,000

back page

$50,000 at 4% for fifteen years

Total: $80,000
Monthly: $444

$50,000 at 4% for ten years

Total: $70,000
Monthly: $583

You can afford to pay $1500 a month, ten year loan at 5%
Most you can borrow = $120,000


You can afford to pay $1500 a month, fifteen year loan at 5%
Most you can borrow = $154,286
You can afford to pay $1500 a month, twenty year loan at 5%
Most you can borrow = $180,000
You can afford to pay $2,000 a month, ten year loan at 5%
Most you can borrow = $160,000

This week's schedule

Homework 9 is due by midnight tonight.

Quiz 6 will be Wednesday in class for 20 points, based on Homework 9.

Homework 10 will be handed out on Wednesday, due next Monday.

Next week will be the second midterm. Take-home section will be handed out on Monday, due Wednesday, in class section on Wednesday.

Zoom room number is 635-591-163.
 

Link to the answers for Wednesday's quiz.
 
Quiz 5 was given in four parts over the last two weeks, you will be sent an email with your grades.

Homework 9, answers to Homework 8, quizzes for April 22

Here is the link to Homework 9, due Mon., April 27

Here is the link to the Answers for Homework 8

If you last name begins with A through H, here is your quiz to be completed by the end of class

If you last name begins with J through Z, here is your quiz to be completed by the end of class

Link to Monday's lecture

Click here to see the lecture from Monday, April 30.

Files for class on April 20

Click here for the notes I am using during the lecture.

Click here for the worksheet due by the end of class. Completing the work is worth 5 points toward the next quiz grade.

When you are finished with the worksheet, send an email with the answers to mhubbard@peralta.edu, I will send an answer sheet and grades of the students by tomorrow morning.

Answers

USA 12.3
Italy 39.1
Spain 43.7
France 30.2
UK 23.7
Belgium 49.0
Iran 6.1
Germany 5.5
China 0.3
Netherlands 21.5
 

Files for class on April 15

Link to the answers for last week's homework

Link to today's quiz. Note that there are two pages, but you only have to complete one, depending on your last name.

Link to the homework due Monday.

Class today at 9:30

Class starts today at 9:30, I will be in the room at 9:10 if you have questions. Same Zoom room number as last week, same for the rest of the term.

635-591-163

Please sign in with a name I recognize.

See you later this morning.

Here is a link to the notes.

Both lectures this week and a link to the homework

Monday's lecture

 Wednesday's lecture

Click this link for the homework

Homework is due Monday. Stay safe and I'll see you soon.
 

Link to April 8 lecture up on YouTube

Click here to get to the YouTube page

Link to Homework 7, due Monday April 13

Click on this link.

If you want to follow along with today's lecture, click here.

Link to April 6 lecture on YouTube

https://www.youtube.com/watch?v=l2RuhHv4AYI

UPDATE: Classes begin on Zoom on Monday, April 6 at 9:30

You can access Zoom on a laptop or on a cellphone. The number for the class at 9:30 is

635-591-163

The number for the 12:20 office hour is

584-656-357

Hope to see you all this Monday. 

Below is a link to my class notes for this week.

https://drive.google.com/file/d/16-F4fKvYJjHOP6HueN-9GPfDC_J0HTCT/view?usp=sharing

Face to Face classes are canceled until Wednesday, April 8

No instruction, not face to face or online, will take place for the rest of the month.

Stay Safe,
Prof. Hubbard

Face to face classes are canceled on Wednesday, March 11

Laney has canceled face-to-face classes from Wednesday, March 11 to Saturday, March 14.

If you are enrolled in Math 15 and you read this, please send me an email at mhubbard@peralta.edu and include your student ID number.
 

The biographies of six computer scientists

Short biographies of John Von Neumann, Alan Turing, Grace Hopper, Edsger Dijkstra and Donald Knuth

NASA's page about Katherine Johnson
 

Notes for Homework 5

Notes on Richter scale and the bel/decibel system

Notes on set theory and Venn Diagrams
 

Notes for Homework 4

Defining a triangle by three side lengths

Defining a triangle by three points in the plane
 

Notes for homework #3

Scientific notation

Approximating and simplifying square roots

Classifying triangles defined by three angles

Finding isosceles triangles
 

Notes for Homework #2

Notes for time conversion

Notes for converting between binary, decimal and hexadecimal

Notes on the logical operators AND (^), OR (v) and NOT (~)

Notes for Homework #1

Time addition and subtraction problems

Notes for fractions, decimals, and percents, prime factorization and finding all factors

Link to the biographies of five British logicians

Link to the biographies

Notes for Homework 11, due Mon., 11/18 (not accepted late)

Notes on statistics: mean, median and mode

Notes on the five number summary and the IQR method for finding high and low outliers