1)An aeroplane flies 125km in the direction 110°.It then changes course and flies for 170km in the direction of 160°.Find by calculation its distance from the starting point
2)Find the compound interest on ksh 21000 in 3 years at a rate of 20% p.a compounded semiannually
3)Calculate the standard deviation for the set of numbers given 4,6,12,3,9,8
4)A box contains 36 balls all of the same size and shape,if y of the balls are red,19 are white and the rest are blue.A ball is randomly picked from the box at random.If the probability that this ball is red is 1/3.Find;
a)The value of y
b)The probability that the ball picked is blue
1) To find the distance from the starting point, we can use the cosine rule:
d = √(125^2 + 170^2 - 2*125*170*cos(110°-160°))
d = √(15625 + 28900 - 42500*cos(50°))
d = √(44525 - 42500*cos(50°))
d ≈ 58.72 km
2) The compound interest can be calculated using the formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (21000)
r = Annual interest rate (20% or 0.20)
n = Number of times interest is compounded per year (2 for semiannual)
t = Number of years (3)
A = 21000(1 + 0.20/2)^(2*3)
A = 21000(1.10)^6
A ≈ 33989.42
Compound interest = A - P
Compound interest ≈ 33989.42 - 21000
Compound interest ≈ 12989.42
3) First, calculate the mean of the set: (4+6+12+3+9+8)/6 = 42/6 = 7
Then, calculate the squared differences from the mean:
(4-7)^2 = 9
(6-7)^2 = 1
(12-7)^2 = 25
(3-7)^2 = 16
(9-7)^2 = 4
(8-7)^2 = 1
Find the mean of the squared differences: (9+1+25+16+4+1)/6 = 56/6 = 9.33
Standard deviation = √9.33 ≈ 3.05
4) Let the number of red balls be y, white balls be 19, and blue balls be (36-y-19).
Given: P(red) = 1/3
P(red) = y/36
1/3 = y/36
y = 36/3
y = 12
a) The value of y is 12.
b) Probability that the ball picked is blue:
P(blue) = (36-12-19)/36
P(blue) = 5/36