Use lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (if a value does not exist, enter none.) f(x, y,z) = 3x – y – 3z; x + y – z = 0, x2 + 2z2 = 1

Robert plans to make a box-and-whisker plot of the following set of data. 27, 14, 46, 38, 32, 18, 21 find the lower quartile, the median, and the upper quartile of the set? lower quartile: 19.5; median: 29.5; upper quartile: 42 lower quartile: 14; median: 27; upper quartile: 46 lower quartile: 18; median: 27; upper quartile: 38 lower quartile: 16; median: 29.5; upper quartile: 42

Which problem would you use the following proportion to solve for? 24/x=40/100 a. what is 40% of 24? b. what percent is 24 of 40? c. twenty-four is 40% of what number? d. forty percent of 24 is what number?

47: 4 aisha changed 1.45 + 2.38 to 1.5 + 2.4 in order to estimate the sum. what estimation method did she use?