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You are to construct a parallel plate capacitor out of two flat plate of area 25 cm^2. You

have three dielectrics to choose from: 1 cm thick paraffin, 2 cm thick Pyrex glass, and 3 cm thick Porcelain which of the dielectric will you used to get the maximum capacitance?


The average cost per household of owning a brand new car is Php 5,000. Suppose that we randomly selected 40 households, determine the probability that the sample mean for these 40 households is more than Php 5,350. Assume that the variable is normally distributed and the standard deviation is Php 1,230.

WHAT IS THE STANDARD ERROR OF THE MEAN ?


Briefly discuss the main contributions made by Louis Pasteur and Robert Koch in the development of modern day microbiology.

Problem: Make a program that will accept 2 numbers and a choice of operation (1 = Display Sum, 2 = Display Difference, 3 = Display Product, 4 = Display Quotient, and 5 = Display All). if the choice input is not from 1 to 5, reaccept an input again. Display the selected option by the user.

Example input and output:

Enter number: 5

Enter number: 2

[1] Display Sum

[2] Display Difference

[3] Display Product

[4] Display Quotient

[5] Display All

Input choice: -1

[1] Display Sum

[2] Display Difference

[3] Display Product

[4] Display Quotient

[5] Display All

Input choice: 10

[1] Display Sum

[2] Display Difference

[3] Display Product

[4] Display Quotient

[5] Display All

Input choice: 5

Sum : 7

Difference: 3

Product: 10

Quotient: 2

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If (π‘₯, 𝑦, 𝑧) =𝑋^ 2 π‘Œ βˆ’ 2 π‘Œο»Ώ^ 2𝑍 ^3ο»Ώ, find βˆ‡π‘“ at the point (1, βˆ’1,2)


Consider the set V = R 2 . For (x1, y1),(x2, y2) ∈ R 2 and c ∈ R, define the following operations:

I. (x1, y1) + (x2, y2) = (0, y1 + y2)

II. c(x1, y1) = (0, cy1)

Is the subset a vector of R2. If not prove the axioms that makes it false.Also prove those axioms that are true.


find the value of b for which the given equation is exact, and then solve it using that value of b


(xy^(2)+bx^(2)y)dx+(x+y)x^(2)dy=0


The osmotic pressure of an aqueous solution of a nonvolatile nonelectrolyte solute is 2.17 atm at 0.0Β°C.

a. What equation will you use?

b. Identify the hypothetical value of the van’t Hoff factor.

c. Calculate for the molarity (M) of the solution.



A trapezoid has an area of 36 sq. m and an altitude of 2m. Its two bases have ratio of 4:5. Find the perimeter of the trapezoid. Find the percentage increase in the volume if its edge is increased by 1%


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