1) +-1

2) +-i

3) 0

4)all values of (a)]]>

" One microchip is being produced in three series, each series produces 18 microchips. In the first series 12 are faulty, in the second series 14 are faulty and in the third series 15 are faulty. A series is picked randomly and one microchip from that series (also randomly). It turns out that the picked microchip is faulty. The same microchip is returned to the same series it was taken from and from that series another microchip is randomly selected. What is the...

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(a) There are 6 students, Alfie, Ben, Carol, Dennis, Edward and Fenny

(i) In how many ways can these 6 students be seated in 5 chairs? (2 marks)

(ii) If Carol must sit in chair number 1, how many difference ways now? (3 marks)

(iii) If Dennis can sit anywhere except in chair no 1and Fenny must sit in chair no 3, how many difference

ways now? (4 marks)

(b) There are 6 girls and 7 boys in a club.

(i) In how many ways can we select a committee of 5 students? (2 marks)

(ii) In how...

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I am currently doing Master in data science. I came across the function PDF probability density function which is used to find cumulative probability(range) of a continuous random variable.

The PDF probability density function is plotted against probability density in y axis and Random variable in x axis.

I am not able to understand how to convert an experiments observation of continuous random variable into probability density function

Kindly help me understand with...

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I have already worked out β^2Ξ© but am confused as to how to treat the del operator outside the bracket.

Is it grad(β^2Ξ©) x F?

Or is it (β^2Ξ©) multiplied by curlF

Or something different that I haven't understood

Thanks]]>

[math]y' = 1-y[/math]

Seperation of variables:

[math]\frac{dy}{1-y} = dx[/math]

[math]\implies \int \frac{dy}{1-y} = \int dx[/math]

u-sub with [imath]u = y -1[/imath] for the left integral gives

[math]\log{|1-y|} = -x + C[/math]

Now here is where I made my error, when taking the exponential function of both sides, this gives

[imath]y-1=\tilde{C}e^{-x} \space [/imath] and NOT...

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The problem is [math]tan(2x)= -\sqrt3[/math]

Using the general solution for tanx=a the next line of working should be:

[math]2x=n\pi + arctan( -\sqrt3)[/math]

My question is what should I set [imath]arctan(-\sqrt3)[/imath] to?.. My textbook uses [imath]- \frac{\pi}{3}[/imath] however it could also be 2pi/3 or 5pi/3 if you only use positive angles. Does it matter which angle I use? - I know they will all give me the...

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Could someone tell me the equation for the amount of water I need to add do dissolve the cream down to milk?

Thanks]]>

My question is, is the sum of those factors always a multiple of 3?

For the case where 2 is one of the primes then I think so:

If 2 is one of the prime factors of x, 2 and x must be even, 1 and the other prime factor must be odd (as 2 is the only even prime). We can express all odd numbers as two times a number plus 1 e.g. 2*a +1. So the factors of x are 1...

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Whats is the n-th term of this sequence:

I think each term is multiplied by 7 then 5 is added to it.

Also what is the general formula for this type of sequences?]]>

Intro to Slope Intercept Form

The following is a Slope intercept form of linear equation

y=2x+1

The following is not a linear equation in slope-intercept form

x=4yβ7

Now the second equation can be rewritten as y = (x+7) / 4

and we know that x and y are just variables, which can be replaced by anything, say a and b or p and q.

So the question is why is y=2x+1 a slope intercept while...

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Teacher: "If I gave you 2 cats and another 2 cats and another 2, how many would you have?"

Johnny: "Seven."

Teacher: "No, listen carefully... If I gave you two cats, and another two cats and another two, how many would you have?"

Johnny: "Seven."

Teacher: "Let me put it to you differently. If I gave you two apples, and another two apples and another...

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from supplier B. 5% of the cartons of fruits supply by supplier A are spoiled and 93% of the

cartons of fruits supply by supplier B are good. Answer the following questions.

Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5

cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.

I'm not sure how to solve this, is it...

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I am to find the amplitudefunction |

I did some transforms: [math]h(n)=\delta(n)+0.9\delta(n-D)\\ H(z)=1+0.9z^{-D}\\ z=e^{j\omega}\\ H(\omega)=1+0.9e^{-j\omega D}[/math]

My thought was to factor out [math]e^{-jxD\omega}[/math] for some factor x and then use eulers formula. But the 0.9...

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