(40 points) consider a valleyed array a[1, 2, . . , n] with the property that the subarray has the property that a[j] > a[j+1] for 1 ≤ j < i, and the subarray has the property that a[j] < a[j + 1] for i ≤ j < n. for example, a = [16,15,10,9,7,3,6,8,17,23] is a valleyed array.

Arefrigeration system at your company uses temperature sensors fixed to read celsius (°c) values, but the system operators in your control room understand only the fahrenheit scale. you have been asked to make a fahrenheit (°f) label for the high temperature alarm, which is set to ring whenever the system temperature rises above –10°c. what fahrenheit value should you write on the label

Offering 30 if a plus b plus c equals 68 and ab plus bc plus ca equals 1121, where a, b, and c are all prime numbers, find the value of abc. the answer is 1978 but i need an explanation on how to get that.

Timmy uses 1 1 2 cups of sugar for every 2 gallons of lemonade he makes. how many cups of sugar would timmy use if he makes 13 gallons of lemonade?