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8. Solve x
x^2y′′− 2xy′+ 2y = x^4sin(4 log x)
what is double alkali
•Construct the truth table of the converse,
contrapositive, and inverse of p→ q
•Let p, q, and r be propositions. Construct the
truth table of r→(˥p⋀q)
What is the hydronium ion concentration of 1g of acetic acid in 100 ml of water?
The probability density function for a diameter of a drilled hole in millimeters is f(x) = 10e^-10(x-5) for x > 5 mm. Although the target diameter is 5 mm, vibrations, tool wear, and other nuisances produce diameters larger than 5 mm.
a) Determine the mean and variance of the diameter of the holes. [Hint: Use integration by parts.]
b) Determine the probability that the hole exceeds 5.1 mm.
QUESTION ONE (30 Marks)
Consider a closed economy that is characterized by the following equations:
Y = C + I + G
C = 900 + 0.5(Y − T)
I = 750 − 30r
T = 800
G = 1200
Md = Ms
Ms = 1500
Mt = 0.7Y
Msp = −80r
Where Y is the GDP, C is private consumption expenditure, I is the Investment expenditure, G
is government expenditure, T is tax revenues, Ms
is money supply, Mt
is transaction demand
for money, Msp is the speculative demand for money and r is the interest rate (in % points).
a) Derive (Md⁄P) the demand for real money balances equation (where P is the aggregate price level
What weight of lactic acid must be dissolved in a liter of solution to produce a hydronium-ion concentration of 1×10^-5
Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, which is probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful is $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product. Determine:
a) the mass function of X;
b) the mean of X; and
c) the variance of X.
evaluate the likelihood of uber making an economic profit in the long run?
1000 students took an examination in Statistics and Probability. The mean score obtained is 71 and the standard deviation is 4. Assuming that the data are normally distributed, find the area and probability of students who obtained a score of:
a. at least 83
b. mean to 92
c. at most 70
