GENERALSOLUTIONS 101
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Sophia MM212 Unit 2 College Algebra Milestone
Sophia MM212 
Unit 2 College Algebra Milestone 19/20 that's 95% 
Well done! If you keep getting Milestone scores like this you'll pass the course. 
19 questions were answered correctly. 
1 question was answered incorrectly. 
 	1	 
Rob paid $50.15 for two pairs of jeans, which include a 15% discount. 
 
What was the price of one pair of jeans before the discount was added? 
 
• 
$167.17 
• 
$21.80 
• 
$59.00 
• 
$29.50 
RATIONALE 
 
 
 
 
 
CONCEPT 
Solving Problems involving Percents
- Exam (elaborations)
- • 20 pages •
Sophia MM212 
Unit 2 College Algebra Milestone 19/20 that's 95% 
Well done! If you keep getting Milestone scores like this you'll pass the course. 
19 questions were answered correctly. 
1 question was answered incorrectly. 
 	1	 
Rob paid $50.15 for two pairs of jeans, which include a 15% discount. 
 
What was the price of one pair of jeans before the discount was added? 
 
• 
$167.17 
• 
$21.80 
• 
$59.00 
• 
$29.50 
RATIONALE 
 
 
 
 
 
CONCEPT 
Solving Problems involving Percents
Sophia College Algebra Unit 5 Milestone
MATHEMATIC 107 
Sophia College Algebra Unit 5 Milestone 
17/22 that's 77% 
Well done! If you keep getting Milestone scores like this you'll pass the course. 
17 questions were answered correctly. 
5 questions were answered incorrectly. 
 	1	 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
RATIONALE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CONCEPT 
Sum of a Finite Geometric Sequence
- Exam (elaborations)
- • 28 pages •
MATHEMATIC 107 
Sophia College Algebra Unit 5 Milestone 
17/22 that's 77% 
Well done! If you keep getting Milestone scores like this you'll pass the course. 
17 questions were answered correctly. 
5 questions were answered incorrectly. 
 	1	 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
RATIONALE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
CONCEPT 
Sum of a Finite Geometric Sequence
MATH 110 Module 5 Exam.| PORTGE LEARNING
MATH 110 Module 5 Exam.| PORTGE LEARNING 
Module 5 Exam
- Exam (elaborations)
- • 4 pages •
MATH 110 Module 5 Exam.| PORTGE LEARNING 
Module 5 Exam
	MATH 110 Module 4 Exam.| PORTGE LEARNING
MATH 110 Module 4 Exam.| PORTGE LEARNING 
Module 4 Exam 
Exam Page 1 
A factory has eight safety systems. During an emergency, the probability of any one of the safety systems failing is .08. What is the probability that six or more safety systems will fail during an emergency? 
 
f(x) = ( (n!) / (x!(n-x)!) ) x ( (p^x) x ((1-p)^n-x)) ) n = 8 
x = 6, 7, 8 (number of failures) 
p = 0.08 
 
 
6	failures: 
n = 8 
x = 6 
p = 0.8 
n-x = 8-6 = 2 
( (8!) / (6!(2)!) ) x ( (0.08^6) x ((1-0.08)^2)) ) = 6.2...
- Exam (elaborations)
- • 10 pages •
MATH 110 Module 4 Exam.| PORTGE LEARNING 
Module 4 Exam 
Exam Page 1 
A factory has eight safety systems. During an emergency, the probability of any one of the safety systems failing is .08. What is the probability that six or more safety systems will fail during an emergency? 
 
f(x) = ( (n!) / (x!(n-x)!) ) x ( (p^x) x ((1-p)^n-x)) ) n = 8 
x = 6, 7, 8 (number of failures) 
p = 0.08 
 
 
6	failures: 
n = 8 
x = 6 
p = 0.8 
n-x = 8-6 = 2 
( (8!) / (6!(2)!) ) x ( (0.08^6) x ((1-0.08)^2)) ) = 6.2...
MATH 110 – Module 1 (Book Exam) Limespring.com Questions 1-18
MATH 110 – Module 1 (Book Exam) L Questions 1-18
- Exam (elaborations)
- • 7 pages •
MATH 110 – Module 1 (Book Exam) L Questions 1-18
MATH 110 Module 1 Exam.| PORTGE LEARNING
MATH 110 Module 1 Exam.| PORTGE LEARNING 
Module 1 Exam 
 
 
 
	 
2. Explain statistical inference.
- Exam (elaborations)
- • 4 pages •
MATH 110 Module 1 Exam.| PORTGE LEARNING 
Module 1 Exam 
 
 
 
	 
2. Explain statistical inference.
MATH 110 Introduction to Statistics
MATH 110 MODULE 3 EXAM 
 
Module 3 Exam 
Exam Page 1 
Suppose A and B are two events with probabilities: 
 
P(Ac )=.40,P(B)=.45,P(A∪B)=.60. 
 
 
Find the following: 
a)	P(A∩B). 
 
p(anb) = p(a) + p(b) - p(aub) p(a) = 1 - p(a^c) 
p(a^c) = 0.40 
1 - 0.40 = 0.60 
p(a) = 0.60 
 
 
0.60 + 0.45 - 0.60 = 0.45 
 
 
P(AnB) = 0.45 
 
b)	P(A). 
 
p(a) = 1 - p(a^c) p(a^c) = 0.40 
 
1 - 0.40 = 0.60 
 
 
P(A) = 0.60 
 
c)	P(Bc). 
 
p(b) = 1 - p(b^c) 
rearranged to find p(b^c) = 1 - p(b) 
 
 
1 - 0.45 = 0....
- Exam (elaborations)
- • 10 pages •
MATH 110 MODULE 3 EXAM 
 
Module 3 Exam 
Exam Page 1 
Suppose A and B are two events with probabilities: 
 
P(Ac )=.40,P(B)=.45,P(A∪B)=.60. 
 
 
Find the following: 
a)	P(A∩B). 
 
p(anb) = p(a) + p(b) - p(aub) p(a) = 1 - p(a^c) 
p(a^c) = 0.40 
1 - 0.40 = 0.60 
p(a) = 0.60 
 
 
0.60 + 0.45 - 0.60 = 0.45 
 
 
P(AnB) = 0.45 
 
b)	P(A). 
 
p(a) = 1 - p(a^c) p(a^c) = 0.40 
 
1 - 0.40 = 0.60 
 
 
P(A) = 0.60 
 
c)	P(Bc). 
 
p(b) = 1 - p(b^c) 
rearranged to find p(b^c) = 1 - p(b) 
 
 
1 - 0.45 = 0....
MATH 110 TEST 3- PORTAGE LEARNING
MATH 110 TEST 3- PORTAGE LEARNING
- Exam (elaborations)
- • 4 pages •
MATH 110 TEST 3- PORTAGE LEARNING
CHAPTER 3 MATH 110| PORTAGE LEARNING
CHAPTER 3 MATH 110| PORTAGE LEARNING 
 
 
Chapter 3 math 110
- Exam (elaborations)
- • 8 pages •
CHAPTER 3 MATH 110| PORTAGE LEARNING 
 
 
Chapter 3 math 110
MATH 110 MODULE 7 EXAM. | PORTAGE LEARNING
MATH 110 MODULE 7 EXAM. | PORTAGE LEARNING 
 
Module 7 Exam
- Exam (elaborations)
- • 6 pages •
MATH 110 MODULE 7 EXAM. | PORTAGE LEARNING 
 
Module 7 Exam