You are only showing one pair of triangles
1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
<h3>
Answer: 10 metal bats</h3>
"Ratio of wooden bats to metal bats is 2 to 1" basically means "there are twice as many wooden bats (compared to metal ones)". So if we had 3 metal bats, then we'd have 2*3 = 6 wooden bats. If we had 7 metal bats, then we have 14 wooden ones (because 2*7 = 14). And so on. The basic rule is to multiply the amount of metal bats by 2 to get the amount of wooden ones.
We can go in reverse to divide the amount of wooden bats to get the amount of metal ones. So 20/2 = 10 is the amount of metal bats.
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A more formal approach is to use the proportion below to solve for x
20/x = 2/1
20*1 = x*2
20 = 2x
2x = 20
2x/2 = 20/2
x = 10
and we get the same answer.
P(A)=0.2
P(B)=0.3
P(A and B)= 0.2 x 0.3=0.06
I can’t see it, make it clearer please
