answer:To solve this problem, we need to determine the value of x, which represents the number of ounces of coffee Jack drinks every 2 days. Let's break down the information given: Batch size of cold brew coffee: 1.5 gallons Amount of coffee Jack drinks every 2 days: x ounces Time it takes to make coffee: 20 hours Time spent making coffee over 24 days: 120 hours We can set up the equation as follows: Time spent making coffee / Time it takes to make coffee = Number of batches made 120 hours / 20 hours = Number of batches made 6 batches = Number of batches made Since each batch is 1.5 gallons, the total amount of coffee made is: 6 batches * 1.5 gallons/batch = 9 gallons Since 1 gallon is equal to 128 ounces, the total amount of coffee made is: 9 gallons * 128 ounces/gallon = 1152 ounces If Jack drinks x ounces every 2 days over 24 days, the total amount of coffee he drinks is: Number of 2-day periods in 24 days = 24 days / 2 days = 12 periods Total amount of coffee Jack drinks = x ounces/period * 12 periods = 12x ounces We can set up the equation as follows: Total amount of coffee made - Total amount of coffee Jack drinks = 1152 ounces - 12x ounces Now, we know that the difference is equal to 0 because all the coffee made is consumed by Jack: 1152 ounces - 12x ounces = 0 Let's solve for x: -12x = -1152 To isolate x, we divide both sides of the equation by -12: x = -1152 / -12 x = 96 The value of x is 96. 96 The answer is: 96

answer:We can write -16i in exponential form as 16 operatorname{cis} 270^circ. To find the solutions to z^4 = -16i, we take the fourth roots of 16 operatorname{cis} 270^circ. The magnitude of 16 operatorname{cis} 270^circ is sqrt{16}=4, so the magnitude of the fourth roots is sqrt[4]{4}=2. The principal fourth root of 16 operatorname{cis} 270^circ is 2 operatorname{cis} left(frac{270}{4}right) = 2 operatorname{cis} 67.5^circ. The other three fourth roots can be found by adding multiples of 90^circ to the angle. So the four solutions are 2 operatorname{cis} 67.5^circ, 2 operatorname{cis} 157.5^circ, 2 operatorname{cis} 247.5^circ, and 2 operatorname{cis} 337.5^circ. The angles theta_1, theta_2, theta_3, and theta_4 are 67.5^circ, 157.5^circ, 247.5^circ, and 337.5^circ. The sum of these angles is 67.5^circ + 157.5^circ + 247.5^circ + 337.5^circ = boxed{810^circ}. The answer is: 810

answer:Cody read 6 books the first week. In the second week, he read x books. After the second week, he read 9 books every week. We can calculate the total number of books Cody read by adding the number of books he read in each week: 6 + x + 9w, where w represents the number of weeks after the second week. We are given that Cody read a total of 54 books, so we can write: 6 + x + 9w = 54. We are also given that it took Cody 7 weeks to read the series, so we can write: w = 7 - 2 = 5 (subtracting the first two weeks). Substituting the value of w, we get: 6 + x + 9(5) = 54. Simplifying the equation, we get: 6 + x + 45 = 54. Combining like terms, we get: x + 51 = 54. Subtracting 51 from both sides, we get: x = 3. The value of x is 3. 3 The answer is: 3

answer:Since Jillian can afford 630 per month for rent, and the rental rate is 0.90 per square foot, we can set up the equation 0.90x=630, where x is the number of square feet in the apartment. Solving for x, we find x=frac{630}{0.90}=700 square feet. Therefore, Jillian should consider apartments that are at most boxed{700} square feet in size.The answer is: 700