Seventy percent of consumers prefer to purchase electronics online. You randomly select consumers. Find the probability that the number of consumers who prefer to purchase electronics online is​ (a) exactly​ five, (b) more than​ five, and​ (c) at most five. ​(a) Find the probability that the number that prefer to purchase electronics online is exactly five.
​P(5)

​(Round to three decimal places as​ needed.)
​(b) Find the probability that the number that prefer to purchase electronics online is more than five.
​P(x​>5)

​(Round to three decimal places as​ needed.)
​(c) Find the probability that the number that prefer to purchase electronics online is at most five.
​P(x​5)

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

4. find the geometric mean of 4 and 12. 24 8

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply