The best way to approach this question is through POE.

According to the data in the table, the ratio of those who enjoy biology to those who enjoy chemistry is 14 to 18, which can be reduced to a ratio of 7 to 9; eliminate (A).

The ratio of those who enjoy chemistry to those who don't enjoy chemistry is 18 to 6, which can be reduced to a ratio of 3 to 1; eliminate (B).

The ratio of those who enjoy biology to those who don't enjoy chemistry is 14 to 6, which can be reduced to a ratio of 7 to 3; eliminate (C).

The ratio of those who don't enjoy biology to those who enjoy chemistry is 10 to 18, which can be reduced to a ratio of 5 to 9; this matches (D).

Since the question states that Rob is planning to bring his favorite guitar plus x additional guitars, he will have a total of x + 1 guitars.

The question states that the variable x represents the number of additional guitars, so the number 1 must represent Rob's favorite guitar, which is (B).

Whenever the question includes variables, plug in.

If m = 2, then Merry would pay the one-time enrollment fee plus 2 months' worth of monthly fees, which is 50 + 15(2) = 80.

Plug in 2 for m in the answer choices to see which answer equals the target number of 80.

In (A), 15(2) + 50 = 80. This is the target number, so leave this answer, but be sure to check the other choices just in case.

In (B), 15 + 50(2) = 115. In (C), 15(2) - 50 = -20, and in (D), (15 + 50)(2) = 130.

Since none of the other answer choices equals the target number, the correct answer is (A).

To solve this question, simply subtract y from both sides of the equation to get 2y = 2, which is (B).

The flu shot is most effective against Strain C, which is least prevalent in March.

To determine the overall efficacy of the flu shot at this time, multiply the prevalence of each strain of flu by the efficacy of the flu shot against that strain, and then add those products to get a weighted average of the efficacy of the shot: (0.23 × 0.35) + (0.25 × 0.13) + (0.13 × 0.76) + (0.39 × 0.68) = 0.477 = 47.7%, which is closest to (D).

The zero of g is the value of the variable, in this case x, when the equation is set to 0.

This is also called the root or solution of an equation.

Set the equation to 0 to get 0 = 2x² - dx - 6.

Plug 6 in for x to get 0 = 2(6²) - d(6) - 6.

Simplify the equation to get 0 = 72 - 6d - 6, or 0 = 66 - 6d.

Solve for d to get -66 = -6d, so 11 = d.

Plug 11 in for d and set the quadratic to 0 to get 0 = 2x² - 11x - 6.

Factor the equation to get 0 = (x - 6)(2x + 1).

The other zero of the equation is when 2x + 1 = 0.

Solve for x to get 2x = -1, or x = -¹⁄₂.

The correct answer is (C).

i^a = 1 when a is a multiple of 4.

Using your exponents rules, 413 + x must also be a multiple of 4.

Plug in the answers and look for what makes 413 + x a multiple of 4.

Only (D) works.

Whenever there are variables in the question and in the answers, think Plugging In.

The question states the value of g, but it is a constant and a weird one at that.

Pick numbers for all the variables that will make the math more straightforward.

If v = 4 and g = 2, then \(t = \frac{2\left (4 \right )\cdot sin \left (\theta \right )}{2} = \frac{8\cdot sin \left (\theta \right )}{2} = 4 \cdot sin \left (\theta \right )\) and \(R = \frac{\left (4 \right )^{2} \cdot sin \left (2\theta \right )}{2} = \frac{16 \cdot sin \left (2\theta \right )}{2} = 8 \cdot sin \left (2\theta \right )\).

Plug these values into the answers to see which equation works.

Choice (A) becomes \(4 = \frac{4 \cdot sin\left ( \theta \right ) \cdot sin\left ( \theta \right )}{2\left [ 8 sin\left ( 2\theta \right )sin\left ( \theta \right )\right ]}\).

Simplify the right side of the equation to get \(4 = \frac{4 \cdot sin\left ( \theta \right ) \cdot sin\left ( \theta \right )}{16 sin\left ( 2\theta \right )sin\left ( \theta \right )}\), or \(4 = \frac{sin\left ( \theta \right )}{4sin\left ( 2\theta \right )}\).

This will not simplify further, so eliminate (A).

Choice (B) becomes \(4 = \frac{2 \left [4 sin\left ( \theta \right ) \right ] sin\left ( \theta \right )}{8 sin\left ( 2\theta \right )sin\left ( \theta \right )}\).

Simplify the right side of the equation to get \(4 = \frac{8 sin\left ( \theta \right ) sin\left ( \theta \right )}{8 sin\left ( 2\theta \right )sin\left ( \theta \right )}\) or \(4 = \frac{sin\left ( \theta \right )}{sin\left ( 2\theta \right )}\).

Eliminate (B).

Choice (C) becomes \(4 = \frac{2 \left [8 sin\left ( 2\theta \right ) \right ] sin\left ( \theta \right )}{\left (4 sin\left ( 2\theta \right ) \right )\left (sin\left ( 2\theta \right ) \right )}\).

Distribute the 2 to get \(4 = \frac{16 sin\left ( 2\theta \right ) sin\left ( \theta \right )}{\left (4 sin\left ( \theta \right ) \right )\left (sin\left ( 2\theta \right ) \right )}\).

Reduce the equation to get or 4 = ¹⁶⁄₄ or 4 = 4.

The correct answer is (C).

You can start by Plugging In a value for x; try x = 4.

Because angle AOB is 120° and the triangle is isosceles, angles A and B are each 30°.

Cut triangle AOB in half to make two 30-60-90 triangles with a hypotenuse of 4 and sides of 2 and 2√3.

The side with length 2√3 lies on chord AB.

Double it to get the total length: 4√3 or just √3x, which is (B) when you put x = 4 into the answer choices.

The formula for compound interest is A = P(1 + r)^t, where P is the starting principle, r is the rate expressed as a decimal, and t is the number of times the interest is compounded.

Melanie received less than 5% interest, so you can eliminate (B) because 1.05 = 1 + 0.05, indicating she was receiving 5% interest.

You can also eliminate (C) because over the course of a year the interest is compounded 4 times, not ¹⁄₃ of a time.

Because Melanie invested $1,100 at what she thought was 5% compounded 4 times (12 months in a year ÷ 3 months per period), she expected 1,100(1 + 0.05)⁴ = $1,337.06 after a year.

Instead, she has 1,337.06 - 50 = $1,287.06 after one year.

Because t is in years in the answer choices, make t = 1 in (A) and (D) and eliminate any choice which does not equal 1,287.06.

Only (A) works.