1. Natasha invests £250 in a building society account. At the end of the year her account is
credited with 2% interest. How much interest had her £250 earned in the year?
Solution: Interest = 2% of £250
= 2/100 x £250
answer = £5
2. Alan invests £140 in an account that pays r% interest. After the first year he receives £4.20 interest. What is the value of r, the rate of interest?
r/100 x £140 = £4.20
r = 100 x 4.20 / 140
= 420/140
= 3%
So the interest rate is 3%
Answer:
0.6421
Step-by-step explanation:
In this case we have 3 trials and we have 2 options for each one. The driver has or hasn't been under alcohol influence. The probability that the driver has is 0.29 and the probabiility that the driver hasn't is 1 - 0.29 = 0.71
each trial is independent because we are assuming that the population of drivers in between 21 and 25 years old is very big.
The probability that one of them was under alcohol influence can be found by finding the probability that non of them was under alcohol influence because:
1 = p(x = 0) + p(x ≥ 1)
p(x ≥ 1) = 1 - p(0)
The probability that none of them was under alcohol influence is going to be:
0.71×0.71×0.71 = 0.3579
The probability of finding at least one driver that has been under alcohol influence is:
0.6421
Strange problem...
Constraints are Y <= 40 bags and X=Y in quantity. Nothing else matters. That's a bad decision unless the chicken farmer lost a poker hand to store X.
Let x be rate of boat in still water
let y be rate of current
we use this equation to relate quantities:
distance = speed · time
we have two unknowns so we might need to create a system of equationss
upstream:
speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)
time = 3 hours
distance = 144 km
downstream:
speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)
time = 2 hours
distance = 144 km (same distance upstream and downstream)
using distance = speed times time
for upstream
144 = 3(x-y)
144 = 3x - 3y
for downstream
144 = 2(x+y)
72 = x + y
system of eqns:
144 = 3x - 3y
72 = x + y
solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x
144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h
Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h
rate of boat in still water is 60 km/h
rate of the current is 12 km/h
