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3 A recent survey by a local municipality established that daily water usage by its households is normally distributed with a mean of 220 liters and a standard deviation of 45 liters.
(i) What percentage of households is likely to use more than 300 liters of water per day?
(ii) What is the probability of finding a household that uses less than 100 liters of water per day?
(iii) What percentage of households is likely to use between 300 to 350 liters of water per day?
A market researcher at a major company classified households by car ownership. The relative frequencies of households for each category of ownership are shown in Table 1.
Table 1. The relative frequencies of households
Number of cars House hold 0 1 2 3 4 5
Relative Frequency 0.1 0.3 0.4 0.12 0.06 0.02
Calculate the mean value and standard deviation of the random variable and interpret the result.
Prove that there are infinitely many primes
Let "p_1,p_2,\\dots,p_n" be distinct pisitive primes. Show that "(p_1p_2\\dots p_n)+1" is divisible by none of these primes.
Show that if a nd b are positive untegers, then ab=LCM(a,b)*GCD(a,b)
If there are integers a, b, s, and t such that, the sum at+bs=1, show that GCD(a,b)=1
Let "a" and "b" be two integers. If "a|b" and "b|a", them show that "a=\\pm b"
For theta -2 theta X-ray diffraction using Cu K, (lamda = 1.54 A° ) radiation from cubic crystals(a= 3.5 A°). How many diffraction peaks are in the 0°<2theta<90° range?. Give the index of the lattice for each diffraction peaks
Find x if, 2^sin²x + 2^cos²x = 3
If 3.4 mol of HI was placed in a 2.0 L container and allowed to reach equilibrium, what would the equilibrium concentrations be for H2(g), I2(g) and HI(g) if the Ke = 49? (5 marks)
H2(g) + I2(g) ⇆ 2HI(g)
#340153 on Dec 2023