Answer:
-3
Solve for "x":
14)
3x + 7 = 2(4x –5) –2x =
3x + 7 = 8x –10 – 2x
3x + 7 = 6x – 10
-3x = -17
x
= 17/3
Answer: x =
17/3 or 5 2/3
15)
7(y –2) +4 = 3(8y + 7) =
7y – 14 + 4 = 24y + 21
7y – 10 = 24y + 21
-17y = 31
y = 31/-17
Answer: y =
- 31/17 or – 1 14/17
Counting Techniques
16)
Interpret the following:
(BA II PLUS usage)
•
12! /7! =
{12, 2
nd
, X!
/
7, 2
nd
, X!,
=}, =
95,040 (12 x 11 x 10 x 9 x 8)
•
8! /(8 - 4)! = {8, 2
nd
, X!
/
4, 2
nd
, X!,
=}, =
1,680
(8 x 7 x 6 x 5)
Intersection % Union of Sets, Venn diagrams
17)
In the rolling of a fair die, what is the probability of rolling an even number
or
a number that is
less than 3?
Solution:
Let
A
be the event that consists of observing an even number, and
B
a number that is less than 3.
P (A) = P (Even #) = P (2, 4, 6) =
½
and
P (B) = P (# < 3) = P (1, 2) =
2/6 or
1/3, thus
P (A
U
B
)
= P (A) + P (B) – P (A ∩ B) =
½
+
⅓
– 1/6 = 4/6 o
2/3
18)
Given X = {2, 5, 7} and Y = {3, 4, 5} depict these two sets as a union and an intersection, i.e., (x
U
y) =? and (x
∩
y) =?
Solution:
Union:
= {2, 3, 4, 5, 7}
Intersection:
= {5}
Depreciation Expense