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Recall that for a, b ∈ Z, a ≡ b (mod 8) means that a - b is divisible by 8. Use the Division Algorithm to prove that for every integer m there exists an integer r such that m ≡ r (mod 8) and 0 ≤ r < 8.
Find the 95% confidence internal for the standard deviation
Find the directional derivative at P(-2,2,-1) in the direction of Q(18,-2,4). Find the direction of maximum decrease at P. (your answer does not have to be unit vector.) What is the maximum rate of decrease?
the lenght of a steel beam is a linear function of the temperature when temperature is 40F a certain steel beam is 50 feet long and at 95 F the same beam is 50.12 feet long.what is the lenght of the beam at 70F? at what temperature is the beam 49...
Probability that a randomly selected junior prefers meat toppings. Find the indicated probability. The table shows the number of college students who prefer a given pizza topping.
Alzheimer's disease, a neurological disease, is a very costly public health problem. As the population ages, the incidence of Alzheimer's will increase. The incidence of Alzheimer's will nearly quadruple in the next 40 years. Finding a way to delay t..
Suppose V is a complex inner product space and T: V --> V a linear operator. Use the results from parts (a) and (b) to show V = im(T) + ker (T*) = im(T*) + ker(T).
Normal Approximations to Binomial Probabilities, Mathematics Study Centre was established to help students to solve mathematics and statistics problems
The size of a certain bacteria culture doubles each hour. If the number of bacteria present initially is 3000, how many would be present at the end of 6 hours?
If the probability of seeing moose in a day in a certain region of Alaska is 0.47, what is the probability of not seeing any moose in a day there?
Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x).
Probability for rolling a pair of dices, You are rolling a pair of dices, one red and one green. What is the probability of the following outcome?
Please find the 1) length and 2) direction (when defined) of 1) A X B and 2) B X A Please show all work, including the grids for the determinants. Thank you.
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