(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 
.
Hello:<span>
the equation is : y = ax+b
the slope is a : a×(1/2) = -1......( perpendicular to a line with a slope of 1/2) because : -2x+4y =8...y=(1/2)x+2 ) </span>
<span>
a = -2 y=(-2x+b
the line that passes through (2,1) :1 = -2(2)+b
b =5
<span> the equation is : y = -2x+5</span></span>
Answer:
The total amount of money Susan must pay if she orders 5 tickets is $235.
Step-by-step explanation:
Simply plug in the number of tickets!
45(5) + 10 = $235
Step-by-step explanation:
-4 (-x + 2) = 2 (3x - 7)
2x-4=3x-7
x=3
Answer: 180 degrees clockwise
Step-by-step explanation:
