(i) false;
Let be N = { 0, 1 , 2}; x * y = x + y => a * a = 2a ∈ { 0, 2 , 4}, which is not a( just for a = 0);
(ii) true;
b * c = c * b => a * ( b * c ) = a * ( c * b ); (1)
but, a * ( c * b ) = ( c * b ) * a; (2)
(1) and (2) => <span>a * (b * c) = (c * b) * a.</span>
I'm sorry but the solution you proposed was a bit hard to follow, so I'll just post my solution: we convert "2 and 1/2" to a single fraction:

So, we know that 5/2 gallons cost 60 dollars, which means

To find the cost of a single gallon, we have to solve the equation for g:

<u>Number of terms = 48</u>
<u>common difference = 1.5</u>
This question involves the concept of Arithmetic Progression.
- The formula for sum of an arithmetic progression series with first and last term given is;
=
(a + l)
where;
a = first term
l = last term
n = number of terms
- From the given sequence, we see that;
first term; a = 4
last term; l = 76
Sum of A.P;
= 1920
- Plugging in relevant values into the sum of an AP formula, we have;
1920 =
(4 + 76)
simplifying this gives;
1920 = 40n
n = 1920/40
n = 48
- Formula for nth term of an AP is;
=
+ (n - 1)d
where;
is first term
d is common difference
n is number of term
is the nth term in question
the 48th term is 76
Thus;
76 = 4 + (48 - 1)d
76 - 4 = 47d
72 = 47d
d = 72/47
d ≈ 1.5
Thus;
Number of terms = 48
common difference = 1.5
Read more at; brainly.com/question/16935540