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A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 10° F. After one-half minute the thermometer reads 50° F. What is the reading of the thermometer at t 1 min? How long will it take for the thermometer to reach 15° F?
Now suppose that our message units are digraphs in an N - Letter alphabet. Find a formula for the number of different affine enciphering transformations there are. How many are there when N = 26, 27, 29, 30?
Now suppose that our message units are digraphs in an N - Letter alphabet. Find a formula for the number of different affine enciphering transformations there are. How many are there when N = 26, 27, 29, 30?
Off-road motorbike racing can be dangerous, especially when it rains. It has been found that it rains during
18% of races. When it does not rain, there is a 5% chance that Dwayne (a rider) will get hurt. However, when it
rains, the chance that he gets hurt increases to 35%. Dwayne has just finished a race and is hurt. What is the
probability that it rained during the race?
Determine whether the following procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). If it is not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
Regarding the number of television in 20 households
The second term of an arithmetic progression is four times the fifth term, and the first term is 10. Find the common difference, and hence the sum of the first 12 terms.
Find the derivatives of each of the following functions:
a. 𝑦 = 5𝑥2+7𝑥−8
b. 𝑓(𝑥) = 7/𝑥4
c. 𝑦 = 15/√𝑥
d. 𝑓(𝑥) = 2𝑥7/2−𝑥-1/3
e. 𝑦 = (4𝑥2−7𝑥)/𝑥
f. 𝑓(𝑥) = 7𝑥3/√𝑥
Are there any values of p such that p2+48 is equal to -14p?
Differentiate with respect to 𝑥
a. (7𝑥 – 4 )3
b. √(6𝑥+4)
Find the first 3 terms, in ascending powers of 𝑥, of the binomial expansion of (2−𝑥)4 and simplify each term.
