Math 104
Katina4
math_midterm.docx1. Solve the equations.
(a)
2D + 3 = 9
D =
(b)
20E − 4 = 0
E =
2. Perform the given set operation. Let
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{x | x is a multiple of 2} ∪ {x is a multiple of 3}
3. Solve the inequality.
8 < 3 + y
4. Use Euler circles to check the validity of the argument.
All mathematicians are eccentrics.
All eccentrics are rich.
Therefore, all mathematicians are rich.
valid
not valid
5. From a survey of 100 college students, a marketing research company found that 70 students owned iPods, 40 owned cars, and 30 owned both cars and iPods.
(a) How many students owned either a car or an iPod (but not both)?
students
(b) How many students do not own either a car or an iPod?
Students
6. Write the ratio given as a simplified ratio.
A cement mixture calls for 60 pounds of cement for 2 gallons of water. What is the ratio of cement to water?
to 1
7. Let U = {6, 7, 8, 9, 10, 11, 12}, A = {6, 7, 8, 9}, B = {6, 7, 10, 11}, and C = {8, 10, 12}. List all the members of the given set. (Enter your answers as a comma-separated list.)
(A ∪ B) ∩ C
8. Perform the given set operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{3, 8, 10}
9. Simplify the expression.
(3x − 1)(x2 + 3x − 4)
10. If possible, completely factor the expression. (If the expression is not factorable, enter NF.)
x2 − 3x – 4
11. Perform the given set operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{1, 2, 7} ∩ {2, 7, 9}
12. If 13% of the 250 million adult Americans live in poverty, how many adult Americans live in poverty?
13. Perform the given set operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
{3, 4, 6} ∪ {4, 6, 8}
14. If you multiply a number by four and then subtract negative ten, the difference is negative fourteen. What is the number?
15. Consider the sets X and Y. Write the statement in symbols.
16. The complement of the intersection of X and Y
X ∪ Y
X ∪ Y
X ∩ Y
X ∩ Y
X ∩ Y
What is the sum of the first 50 consecutive odd numbers?
17. Solve the proportion for the item represented by a letter.
|
3 |
|
1 |
|
|
|
A |
|
5 |
18. Simplify the expression.
(x + 3y − 5z) − (x − 4y + 6z)
19. List all possible subsets of the given set.
I = {2, 3}
∅, {2}
,
{3}
,
{2, 3}
∅, {2}
,
{3}
{2}
,
{3}
,
{2, 3}
∅, {2, 3}
{2}
,
{3}
20. Specify the sets by roster.
(a) {Odd counting numbers less than 17}
(b) {Positive multiples of 4} (Enter only the first three values of this set.)
