QUESTION:
The code for a lock consists of 5 digits (0-9). The last number cannot be 0 or 1. How many different codes are possible.
ANSWER:
Since in this particular scenario, the order of the numbers matter, we can use the Permutation Formula:–
- P(n,r) = n!/(n−r)! where n is the number of numbers in the set and r is the subset.
Since there are 10 digits to choose from, we can assume that n = 10.
Similarly, since there are 5 numbers that need to be chosen out of the ten, we can assume that r = 5.
Now, plug these values into the formula and solve:
= 10!(10−5)!
= 10!5!
= 10⋅9⋅8⋅7⋅6
= 30240.
9514 1404 393
Answer:
- 18 tomatoes: £3.02
- £4.39 ⇒ 26 tomatoes
Step-by-step explanation:
a) at 12 tomatoes per box, 18 tomatoes will require 2 boxes. Then Isla's price will be ...
2(25p) +18(14p) = 50p +252p = £3.02
18 tomatoes in 2 boxes cost £3.02.
__
b) The 3 boxes cost 3(25p) = £0.75, so the tomatoes cost ...
£4.39 -0.75 = £3.64
at 14p each, the number of tomatoes is £3.64/£0.14 = 26
There are 26 tomatoes in 3 boxes costing £4.39.
So 4's facts
we know that 4 times 2=8 and the associative property of multiplication says
a(bc)=(ab)c
so 7(8) (means 7 times 8) means 7((4)(2)) and associative say we can group them and say (7)(4)(2) so (4)((7)(2)) or 4(14) and 4 times 14=56
7 times 8=56
This is a compound interest problem so you cannot use the simple interest formula. Effectively the total amount is being compounded each year by 6%. There is a formula for compound interest but in this simple example you can work this out recursively.
year 1 = 6500
year2 = 6500*1.06 = 6890
year3 = 6890*1.06 = 7303
year4 = 7303*1.06 = 7741..
etc......
year12 = 11604*1.06 = 12338
The length of he altitude to the hypotenuse is the square root of 108
