Other Math Answers

Determine whether these statements are true or false.

a) ∅ ∈ {∅} b) ∅ ∈ {∅, {∅}}

c) {∅} ∈ {∅} d) {∅} ∈ {{∅}}

e) {∅} ⊂ {∅, {∅}} f ) {{∅}} ⊂ {∅, {∅}}

g) {{∅}} ⊂ {{∅}, {∅}}

Suppose X has an exponential distribution with mean equal to 10. Find the value of x such that 0.95

Use the Laws of Logic to prove the following equivalence and state the laws used for each step.

p → (p ⋀ q), p → q

A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $800,000, and the standard deviation is $300,000. A random sample of 100 agents is selected, and the value of the properties they sold in a year recorded.

a) What is the standard error of the sample mean?

b) What is the probability that the sample mean exceeds $825,000?

c) What is the probability that the sample mean is between $790,000 and $820,000?

One hundred sixty eight inches of string

Let A=(2,8,5)

B=(6,0,3)

C=(4,7,9)

1.Find the vectors

a.) u=⃗

BA

2. Give examples of vectors which are parallel to u, v and w respectively.

3. Find a vector which is orthogonal to

a. u and v

4. Find the angle between and determine if they are parallel(perpendicular) or not

a. u and v

5. Find the projection of

a. u onto v

6. Find Orthogonal projection of

a. u onto v

7. Find the area of the triangle with vertices A,B and C,

8. Find the area of the parallelogram formed by

a. u and v

9.. Find the volume of the parallelpiped formed by

a. u ,v and uxv

10.Define the following Terms and give example for each

a. Symmetric Matrix

b. Skew-symmetric Matrix

c. Lower-Triangular Matrix

d. Upper Triangular Matrix

11. Write as a sum of symmetric and skew-symmetric matrices.

a.)

(

2 5 0 6 8 3 4 9 )

12. Solve the system 4 x+3 y+2 z=3

2 x+5 y+z=2

2 x+ y+6 z=5

using

a. Cramer’s rule

b. Inverse method

c. Gaussian Elimination

Minimize using K map: Y=A'B'C'+A' BC'+AB' C'+AB' C+ABC'+ABC