Suppose a small metal object, initially at a temperature of 50 degrees, is immersed in a room which is held at the constant temperature of 80 degrees. it takes 1 minutes for the temperature of the object to reach 65 degrees. 1. calculate the heat transfer coefficient r, i. e. the constant of proportionality in the differential equation that describes newton's law of cooling. 2. suppose now that the room temperature begins to vary; i. e. troom(t) = 70 + sin(0.1 t) . use newton's law of cooling and the heat transfer coefficient you calculated in the previous step to compute the temperature of the object as a function of time. suppose that t(0) = 65.

Which of the following is the equation that says that the product of a number and ten is equal to 20 percent of that number ? a) 10n= 2.0n b) 10+n=.20n c) n+ .20n=10 d) 10n=0.20n

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.

Which of the following expressions is equal to 2x^2+8