Math Is Fun Forum

I did it a little different but you get same result.

First of all I found the distance between A and C to be:

so since this is the diagonal it means that:

Since this is a square then BC and BA have to be of same length so we let u = BC = BA so it becomes

So you know that the length of the sides of the square are sqrt(20). In this way you could find points B and D knowing the distance from A and C is sqrt(20) etc....I guess I overcomplicated this but thats how I got it.

First of all you need to know what numbers are the prime numbers. For numbers 1-6, the prime numbers are 2,3 and 5. So you have 3 prime numbers with a total outcome of 6 so the probability that the first roll is a prime number is 1/2

Rolling a die is an independent event, which means that rolling the second time doesnt depend on the first roll etc. For numbers 1-6, only 4 and 6 are composite numbers which means that you have a probability of getting a composite number of 2/6 or 1/3.

If you were asking for the probability of first getting a prime number AND THEN getting a composite number on the second roll then just multiply both events together: 1/2 * 1/3 = 1/6

So theres a 1/6 probability of getting a prime number on the first roll and then a composite number on the second roll.

My professor always tells us to change the limits but for me its more work and I never do it. Besides, I have gotten a couple questions on tests wrong because I changed the limits of integration where I couldnt because of sin, cos etc. And to be honest, I really cant tell where I can change the limits or not, so I never change them and plug them in when I have converted the answer back to x (or the initial variable). Works out for me.

For part d:

Plug this in a calculator and it gives you = 0.159435246248

Does this answer part d or I missed something?

Ok so everything but the square is shaded. So it would be something like this:

Ok so what you need to do is find the area of the whole circle which is:

A = PI * radius^2 = 6.1544 cm^2

And then you find the area of the square which is:

A = l * w = 3.61 cm^2

So the area of the part that is shaded is equal to the area of the whole circle minus the area of the square inside (which is not shaded) so:

6.15 - 3.61 = 2.54 cm^2

So 2.54 is the area of the section that is shaded. To find the ratio (percentage) of the section that is shaded in respect to the circle, it would be:

2.54/6.15 = 0.413 = 41.3%

Hope that helps.

Thanks Daniel123.

So I guess Gotovina got her answer and more than she asked for....:)

Mathsy, could you tell me whats wrong with my code?

This calls for a system of equations.

So this investor has $50,000 to invest in two different ways. The regular one and the more risky.

let x = regular invesment
let y = risky investment.

You know the total of both investments is $50,000 so:

x + y = 50000

You also know how much each investment yields.

0.08x + 0.18y = 5600

That means that the 8% yield on the regular investment plus the 18% yield on the risky investment is equal to $5600. This was given to us.

So now you have 2 equations with x and y. So now just solve both variables.

0.08x + 0.18y = 5600
x + y = 50000

y = 50000 - x

0.08x + 0.18(50000 - x) = 5600
0.08 + 9000 - 0.18x = 5600
-0.1x = -3400
x = 34000

y = 50000 - x
y = 50000 - 34000
y = 16000

So now you know that this investor invested $34000 in the regular investment and $16000 in the more risky investment.

Hope I helped.

Yes that is correct. You should say that {2^(2k+1)+3^(2k+1)} is divisible by the assumption and not from the previous step. Remember that the whole point of induction is to prove that k+1 follows from k.

I had this dilemma but with math and computer science. I chose math.

You can always choose one and get a minor in the other. Which is what im doing now.

Could anyone help?

Im really confused with this Partial Fractions in Calculus.

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