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 ​\( \frac{1}{3} \)​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.

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 ​\( 2\sqrt[]{3} \)​. The side with length ​\( 2\sqrt[]{3} \)​ lies on chord AB. Double it to get the total length: ​\( 4\sqrt[]{3} \)​ or just ​\( \sqrt[]{3}x \)​, which is (B) when you put x = 4 into the answer choices.

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 = ​\( \frac{-1}{2} \)​. The correct answer is (C).

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).