Let l: r^rightarrow r^3 be a transformation defined by l[(u_1, u_2, u_3, u_4)^t] = (u_1 + u_2, u_3 + u_4, u_1 + u_3)^t. [7 p] (a) show that l is a linear transformation. [9 b] (b) find a basis for kernel of l, ker(l), and determine its dimension. [9 p] (c) find a basis for image of r^4, l(r^4), and determine its dimension.

Haley buys 9 pounds of apples for $3. how many pounds of apples can she buy for $1?

Given: m∠ adb = m∠cdb ad ≅ dc prove: m∠ bac = m∠bca lol

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?