A group of people were asked whether they prefer soup or salad for lunch. The table shows the probabilities of the results. Soup No soup Total Salad 0.2 0.6 0.8 No salad 0.05 0.15 0.2 Total 0.25 0.75 1.00 Let A represent having soup and B represent having salad for lunch. Which statement is true? Having soup and salad for lunch are independent events because P(A|B)≠P(A) and P(B|A)≠P(B). Having soup and salad are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B). Having soup and salad for lunch are independent events because P(A|B)=P(A) and P(B|A)=P(B). Having soup and salad for lunch are not independent events because P(A|B)=P(A) and P(B|A)=P(B).

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

the answer is two. hope this !

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)