# Tutor profile: Nikki R.

## Questions

### Subject: Basic Math

Mary has 12 candies that she has separated by color. She has 3 blue candies, 2 green candies, 5 red candies, and 2 yellow candies. What percentage of candies are yellow or green (rounded to the nearest percentage)?

First add the fractional values for yellow or green candies: $$ \frac{2}{12} + \frac{2}{12} = \frac{4}{12} = \frac{1}{3} $$ Next, use a proportion to determine the percentage value: $$ \begin{align} \frac{1}{3} &= \frac{x}{100} \\ 1\cdot100 &= 3\cdot{x} \\ 100 &= 3x \\ \frac{100}{3} &= x \\ 33.\overline{333} &= x \end{align} $$ So 33% of candies are yellow or green

### Subject: Calculus

Find the derivative of the following: $$ f(x) = 3x^2 + 2x - 1 $$

Use the power rule: $$ \begin{align} f'(x) &= 2\cdot3x^{(2-1)}+1\cdot2x^{(1-1)} \\ f'(x) &= 6x + 2 \end{align} $$

### Subject: Algebra

Solve the following equation: $$ 3x + 2(x + 3) = 4x - 3 $$

First, distribute and simplify the left-hand side: $$ \begin{align} 3x + 2(x + 3) &= 4x - 3 \\ 3x + 2x + 6 &= 4x - 3 \\ 5x + 6 &= 4x - 3 \end{align} $$ Next, collect like terms on either side of the equation: $$ \begin{align} 5x - 4x &= -3 - 6 \\ x &= -9 \end{align} $$ Last, check the solution to verify: $$ \begin{aligned} 3(-9) + 2(-9 + 3) &\stackrel{?}{=} 4(-9) - 3 \\ -27 -18 + 6 &\stackrel{?}{=} -36 -3 \\ -39 &= -39 \end{aligned} $$

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