(a) 
since 13 is prime.
(b) 
, and there are 81/3 = 27 multiples of 3 between 1 and 81, which leaves 81 - 27 = 54 numbers between 1 and 81 that are coprime to 81, so 
.
(c) 
; there are 50 multiples of 2, and 20 multiples of 5, between 1 and 100; 10 of these are counted twice (the multiples of 2*5=10), so a total of 50 + 20 - 10 = 60 distinct numbers not coprime to 100, leaving us with 
.
(d) 
; there are 51 multiples of 2, 34 multiples of 3, and 6 multiples of 17, between 1 and 102. Among these, we double-count 17 multiples of 2*3=6, 3 multiples of 2*17=34, and 2 multiples of 3*17=51; we also triple-count 1 number, 2*3*17=102. There are then 51 + 34 + 6 - (17 + 3 + 2) + 1 = 70 numbers between 1 and 102 that are not coprime to 102, and so 
.
The Given Triangle PMO is a Right Angled Triangle with m∠M = 90°
Given m∠P = 40°
We know that : Sum of Angles in a Triangle = 180°
⇒ m∠P + m∠M + m∠O = 180°
⇒ 40° + 90° + m∠O = 180°
⇒ 130° + m∠O = 180°
⇒ m∠O = 180° - 130°
⇒ m∠O = 50°
We can notice that m∠O and m∠1 form a Linear Pair (180°)
⇒ m∠O + m∠1 = 180°
⇒ 50° + m∠1 = 180°
⇒ m∠1 = 180° - 50°
⇒ m∠1 = 130°
Last Option is the Answer
Answer:
Years = natural log (Total / Principal) / Rate
Years = natural log (1,000,000 / 2,500) / .02
Years = natural log (400) / .02
Years = 5.9914645471 / .02
It would take 299.573227355 Years
Source: http://www.1728.org/rate2.htm
Step-by-step explanation:
Answer:
He will have $4491.38 after 5 years
Step-by-step explanation:
Simple Interest = (Principal × rate × time)/100
SI = (4350 × 0.65 × 5)/100
SI = 141.375
Interest after 5 years = $141.38
The total money he will have after 5 years is
$4350 + $141.38
= $4491.38
There are 151,200 possible combinations. If you'd like an explanation of my answer, please let me know.
