If <em>x</em> = -1, you have
2(-1) + 3 cos(-1) + <em>e</em> ⁻¹ ≈ -0.0112136 < 0
and if <em>x</em> = 0, you have
2(0) + 3 cos(0) + <em>e</em> ⁰ = 4 > 0
The function <em>f(x)</em> = 2<em>x</em> + 3 cos(<em>x</em>) + <em>eˣ</em> is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < <em>c</em> < 0 such that <em>f(c)</em> = 0.
The probability of her being chosen is 1/24
There is 1 Annie to choose from out of a total of 24 students
The answer is 1/24
Evaluating an expression consists of just replacing the letter by its value and do the calculus.
We have the expression 14b - 513. And by hypothesis, b = 44.
So just replace b by 44.
14b - 513 = 14*44 - 513 = 616 - 513 = 103.
So 14b - 513 = 103 (answer b) when b = 44.
Hope this helps! :)
