For each of the following pairs of functions ff and gg, determine if the level curves of the functions cross at right angles, and find their gradients at the indicated point. a) f(x, y)=5x+5y,

g(x, y)=5x−5y.

Do the level curves of f and g cross at right angles? gradfientf(6,5) = ? gradient(6,5) = ?

b) f(x, y)=x^2−y,

g(x, y)=2y+ln(|x|)

Do the level curves of f and g cross at right angles? gradfientf(6,5) = ? gradient(6,5) = ?

In a sample of 2023 u. s. adults, 373 said franklin roosevelt was the best president since world war ii. two u. s. adults are selected at random from the population of all u. s. adults without replacement. assuming the sample is representative of all u. s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.

The diagonals of a quadrilaretral intersect at (-1,4). one of the sides of the quadrilateral is bounded by (2,7) and (-3,5) determine the coordinates of the other side in order for the quadrilaretral to be a square.

Find the slope of the line passing through a pair of points