Math Answers

A random of 200 school managers were administered a developed leadership skill test. The sample mean and standard deviation were 78 and 4.2 respectively. In the standardization of test, the mean was 73 and the standard deviation was 8. Test for significant difference using alpha = 0.05

A rectangular garden that is 3 m wide and 8 m long is to have a uniform border is the same as the area of the garden. Find the width of the border.

If the diameters of ball bearings are normally distributed with mean 0.6140 inches and standard deviation 0.0025 inches, determine the percentage of ball bearings with diameters, (a) between 0.610 and 0.618 inches inclusive (b) greater than 0.617 inches (c) Less than 0.608 inches.

Using the principle of induction, prove that 64 is a factor of 3^(2n+2)- 8n-9 ∀ n∈N

Sketch the graph of the function, f defined by

f(x)= |x-3| +[x], x∈ [2,4] where [x] denotes the greatest integer function

How far from the y-axis is the center of the curve 2x²+2y²+10x-6y-55=0

The lifetime of bulbs produced by Tariqs lightening company follows a normal distribution with a mean of 3462 hours and a standard deviation 1070 hours. What is the probability that randomly selected bulb will have a lifetime of at most 2800?

Symbolic Logic

Can you figure out the values of the following below? Why or why not

1.    (H ≡≡ A) ⊃J (G ≡≡ B)

2.    ~ (X· G)

For each of the following pairs of sentences below, indicate whether (1) is a sufficient condi[1]tion for (2), a necessary condition for (2), both, or neither

3.   (I) Amy is not a student. (2) Amy is neither a student nor a teacher.

4.   (1) John loves Mary. (2) Someone loves Mary.

Symbolic Logic

Compute the truth values of the following, given that A, B, and C are true, and X, Y, and Z are false.

1.   ~ [((A⊃J ~B) ⊃J~C) ⊃J~X]

2.  [(((A⊃J B) ⊃J X) ⊃J Z) ⊃J Y] ⊃J [((X ⊃J Z) ⊃J A) ⊃J X]

Compute the truth values of the following, using the values given in the above Exercise, but without being given the values of G, H, or f.

3. (A∨B) ≡((G∨H) ⊃A)

4.    (G ≡≡ (H· A)) ⊃J «~H V I) ⊃J (X⊃J Z))

In the study of urinary tract infection, the sample and proportion in the group of

fosfomycin / trometamol was 25, 0.92 and trimethoprim / sulfamethoxazole was

16, 0.61, respectively.

a) Find the difference in proportions. (0.5)

4

b) Standard error of difference in proportions. (0.5)

c) Compute a 95% confidence interval of difference in proportions