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.
No13.
Answer:
Cos(x+x)=cosx*cosx-sinx*sinx
=cos2(x)-sin2(x)
=(cosx+sinx)(cosx-sinx)
Answer: 16 is the common denominator
The number of the students in the school that have had algebra is 203
<h3>How to determine the number of students?</h3>
The given parameters in the question are
- Proportion of students taking algebra, p = 70%
- Number of students in the school, n = 290
The number of students that had algebra in the school is calculated as:
Algebra = Proportion of students taking algebra * Number of students in the school
The above equation can be represented as:
Algebra = np
Substitute values for n and p in the above equation
So, we have
Algebra = 290 * 70%
Express 70% as decimal i.e. 0.70
So, we have
Algebra = 290 * 0.70
Evaluate the product i.e. multiply 290 and 0.70
So, we have
Algebra = 203
Hence, the number of the students in the school that have had algebra is 203
Read more about expected values at:
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The answer is y^-1 :) when you have two exponents over a y in a fraction or divison, you always subtract the top from the bottom. hope this helps!
