Math Answers

How to draw a network diagram in mathematical foundations of computer science (10mark)

m is a straight line with a 1 on the right side.

n is a straight line with a number 3 & 2 in the middle but there’s a diagonal line that goes straight through both lines and the numbers 3 & 2 are in between that diagonal line.

Given: Line m is parallel to line n.

Prove: <1 is supplementary to <3

statement: reason:

S1. Line m is parallel to line n. R1. given

S2. <1 =~ <2 R2. ?

S3. m<1 =~ m<2. R3. ?

S4. <2 & <3 for a linear pair. R4. definition of linear pair

S5. <2 is supplementary to <3 R5. ?

S6. m<2 + m<3 = 180° R6. definition of supplementary

S7. ? R7. Substitution Property of Equality

S8. ? R8. Definition of supplementary

Use the Principle of Mathematical Induction to prove that "((2n) !)\/(2^n n !)" is odd for all positive integers.

1. A commercial ship is heading due North

at 12.0 km/hr but drifts westward at 5.0

km/hr. determine the magnitude and

direction of the resultant velocity of the

ship.

2. Find the resultant of the following

vectors.

A = 30 m at 30° with the x-axis

B = 20 m at 120° with the x-axis

C = 10 m at 225° with the x-axis.

Use the Chain Rule to determine an equation for the acceleration when 𝑎 = 𝑑𝑣/ 𝑑𝑡

When 𝑣 = (2𝑡² + 3)⁴

and

When 𝑣 = ln(4𝑡³ − 1)

Groups of men from three different areas of the country are to be tested for mean weight. The entries in the Table 1 are the weights for the different groups.

Group 1 : 216 , 198 , 240 , 187 , 176

Group 2 : 202 , 213 , 284 , 228 , 210

Group 3 : 170 , 165 , 182 , 197 , 201

a)What is the Sum of Squares Factor?

b)What is the Sum of Squares Error?

c)What is the df for the numerator?

d)What is the df for the denominator?

e)What is the Mean Square Factor?

f)What is the Mean Square Error?

g)What is the F statistic?

Justify whether the given operations on relevant sets are binary operations or not.

- Multiplication and Division on set of natural numbers

- Subtraction and Addition on Set of natural numbers

- Exponential operation: (x, y) → xy on Set of Natural numbers and set of Integers.

9.

A) Let U(10)={1,3,7,9} be a group under multiplication modulo 10, what is the order of group?

B) What is the order of group Z of integers under addition?

7. For each operation * given below, determine whether * is a binary operation, commutative or associative. In the event that * is not a binary operation, give justification for this.

i. On Z, a*b=a-b

ii. On Q, a*b=ab+1

iii. On Q, a*b=ab/2

iv. On Z+ , a*b= 2ab

40% of all workers of an industry are college graduates. If a sample of 200 workers is randomly selected, what is the probability that a college graduate in the sample would be

A. more than 80?

B. between 45% and 48%?