answer:Pamela originally had 9.8 ounces of sugar. After spilling some, she was left with 4.6 ounces. To find out how much she spilled, we subtract the amount left from the original amount: 9.8 ounces (original amount) - 4.6 ounces (amount left) = 5.2 ounces (amount spilled) Pamela spilled boxed{5.2} ounces of sugar on the floor.

answer:1. **Figure A:** - The square has a side length of 4. - The circle inscribed has a diameter of 4, so the radius is 2. - Area of square is 4^2 = 16. - Area of circle is pi times 2^2 = 4pi. - Shaded area is 16 - 4pi. 2. **Figure B:** - The lengths are similar to Figure A. - There are two semicircles each with a radius of 2. - The area of one semicircle is frac{1}{2} pi 2^2 = 2pi. - Since there are two, the combined area is 4pi. - Shaded area is 16 - 4pi. 3. **Figure C:** - The side of the square and the triangle is 4. - The height of the equilateral triangle (using formula sqrt{3}/2 times side) is sqrt{3}/2 times 4 = 2sqrt{3}. - Area of triangle is (sqrt{3}/4)4^2 = 4sqrt{3}. - Shaded area is 16 - 4sqrt{3}. Since pi approx 3.14 and sqrt{3} approx 1.73, we find: - 16 - 4pi approx 16 - 12.56 = 3.44 - 16 - 4sqrt{3} approx 16 - 6.92 = 9.08 The shaded area in Figure C is the largest. Thus, the solution is textbf{(C) text{C only}}. The final answer is boxed{C) C only}

answer:For a quadratic equation ax^2 + bx + c = 0 to have two distinct real roots, the discriminant (Delta = b^2 - 4ac) must be greater than 0. Our equation is 5x^2 + 14x + k = 0, so the discriminant is: [ Delta = 14^2 - 4(5)k = 196 - 20k. ] We need this to be greater than 0: [ 196 - 20k > 0. ] Solving the inequality: [ 196 > 20k k < frac{196}{20} = 9.8. ] The largest integer less than 9.8 is 9. Thus, the positive integer values of k for which the discriminant is positive (allowing two distinct real roots) are 1, 2, 3, 4, 5, 6, 7, 8, and 9. Summing these values together: [ 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. ] Therefore, the sum of all positive integer values of k is boxed{45}.

answer:To solve this problem, we need to find the rate at which the bathtub fills with water and the rate at which it drains, then combine these rates to find the net rate of filling. First, let's find the fill rate and the drain rate: Fill rate: The bathtub takes 10 minutes to fill, so the fill rate is 1 tub/10 minutes or 1/10 tub per minute. Drain rate: The bathtub takes 12 minutes to drain, so the drain rate is 1 tub/12 minutes or 1/12 tub per minute. Now, let's find the net fill rate when the drain is open: Net fill rate = Fill rate - Drain rate Net fill rate = (1/10) - (1/12) To subtract these fractions, we need a common denominator, which is 60 (the least common multiple of 10 and 12): Net fill rate = (6/60) - (5/60) Net fill rate = 1/60 tub per minute Now that we have the net fill rate, we can find out how long it will take to fill the tub: Time to fill = 1 tub / Net fill rate Time to fill = 1 tub / (1/60) tub per minute Time to fill = 1 * (60/1) minutes Time to fill = 60 minutes So, it will take boxed{60} minutes to fill the bathtub with water if the drain stays open unnoticed.