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Find these values.

a) ⌈ 3/4⌉

b) ⌊ 7/8⌋

c) ⌈−3/4⌉

d) ⌊−7/8⌋

e) ⌈3⌉

f ) ⌊−1⌋

g) ⌊ 1/2 + ⌈ 3/2⌉ ⌋

h) ⌊ 1/2 ⋅ ⌊ 5/2⌋ ⌋


Find the general solution of the DE 3y( x2 - 1) dx  (x3  8y – 3x) dy = 0


A study claims tha.t on average, male high school students spend at least 3.39 hours a day playing video games with a standard deviation of 2.05 hours. A random sample of 30 teenagers were surveyed and the results showed that these teenagers spend 4.12 hours a day playing video games.



Solve for the z-score of the sample mean of 4.12 hours

find the values for x, y, and z such the matrix below is skew symmetric.

0 x 3

2 y -1

z 1 0


Describe the Hasse Diagram for the divisibility of the set A = {1, 2, 3, 5, 6 10, 15, 30}





The diameter of steel rods manufactured on two different extrusion machines are

being investigated. Two random samples of sizes "n_1" = 15 and "n_2" = 17 are selected,

and the sample means and sample variances are x̅1 = 8.73, "s_1^2" = 0.35, x̅2 =8.68, and "s_2^2" = 0.40, respectively. Assume that "\\sigma_1^2=\\sigma_2^2"

and that data are drawn from

a normal distribution. (a) Is there evidence to support the claim that the two

machines produce rods with different mean diameters? Use α = 0.05 in arriving at

this conclusion. (b) Find the P-value for the t-statistic you calculated in part (a).

[taken from Montgomery, p. 347]


Which of the expression below is the product of (x + 2y) and (2x - 3y)?


Describe the Hasse diagram for the divisibility of the set A={1,2,3,5,6,10,15,30}

Solve using basic differentiation rule


y = 2/(x ^ (1/2)) + 6/(x ^ (1/3)) - 2/(x ^ (3/2)) + 4/(x ^ (3/4))

Solve using differentiation rule


y = 2x ^ 2 * sqrt(2 - x)

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