answer:To solve this problem, we need to determine the value of x, which represents the cost of one magazine. We know that the cost of four chocolate bars is equal to the cost of eight magazines. Therefore, the cost of one chocolate bar is equal to the cost of two magazines. We are given that a dozen chocolate bars cost 24 dollars. Since a dozen is equal to 12, we can set up the equation as follows: Cost of one chocolate bar * Number of chocolate bars = Total cost of a dozen chocolate bars 2x * 12 = 24 Let's simplify and solve for x: 24x = 24 To isolate x, we divide both sides of the equation by 24: 24x / 24 = 24 / 24 x = 1 The value of x is 1. 1 The answer is: 1

answer:Since AC and BE are perpendicular, the diagonals of rectangle ABCD are perpendicular bisectors of each other. This means that AC divides rectangle ABCD into two congruent right triangles, triangle ABE and triangle CDE. Since E is the midpoint of overline{AD}, we have AE = frac{1}{2}AD. Using the Pythagorean Theorem, we can find BE in terms of AB and AE: [BE = sqrt{AB^2 - AE^2} = sqrt{100^2 - left(frac{1}{2}ADright)^2} = sqrt{100^2 - frac{1}{4}AD^2}.] Since AC and BE are perpendicular, we have AC = BE. Therefore, we have [sqrt{100^2 - frac{1}{4}AD^2} = AC = frac{1}{2}AD.] Squaring both sides, we get [100^2 - frac{1}{4}AD^2 = frac{1}{4}AD^2.] Simplifying, we find [100^2 = frac{1}{2}AD^2.] Dividing both sides by frac{1}{2}, we get [AD^2 = 2 cdot 100^2 = 2 cdot 10000 = 20000.] Taking the square root of both sides, we find [AD = sqrt{20000} approx 141.42.] Therefore, the greatest integer less than AD is boxed{141}. The answer is: 141

answer:Pat spends 5 hours hunting for sharks, so he spends 5 * 60 = 300 minutes hunting. A shark sighting occurs every 10 minutes, so Pat can take 300 / 10 = 30 photos. Pat earns 15 for every photo he takes, so he can earn 30 * 15 = 450. The boat fuel costs 50 per hour, so for 5 hours, Pat will spend 5 * 50 = 250 on fuel. The expected profit that Pat can make is 450 - 250 = 200. 200 The answer is: 200

answer:The perimeter of a rectangle is given by 2(text{length} + text{width}). So the perimeter of this room is 2(19 + 11) = 2(30) = 60 feet. The ratio of the length of the room to its perimeter is frac{19}{60}. To simplify this ratio, we divide both the numerator and the denominator by their greatest common factor, which is 1. So the simplified ratio is frac{19}{60}. Therefore, the ratio of the length of the room to its perimeter is boxed{19:60}.The answer is: 19:60