Hannelore

The Black Pearl has once again sailed into Port Royal and is firing its guns at the fort. The cannons atop the fort wall have been disabled, but there remains a single cannon at sea level which must defend the town. If the gunner estimates that the ship i...

What is the probability that a 10-sided die is rolled 3 times and each time the value was unique (i.e. there are no repeating values from previous rolls)? I know I can do this with a tree diagram fairly easily, but is there a formula for it that doesn't i...

I have two relative frequencies for the same experiment done twice. A fair coin's been flipped 100 times with 56/100 as the relative frequency of Heads, and 500 more times with 252/500 as the relative frequency of heads. I'm now being asked the average re...

The point (3, 2) is rotated 30 degrees about the origin. What are the polar coordinates of this after rotation? Am I right in saying it's (root13, 30)? The angle rotated and the radius calculated as root(3^2 + 2^2)? I can convert between polar and cartesi...

A particle moves along a trajectory given by p(t) = <6t, (2 + 3t - 2t^2)>. What is the particle's displacement during the time period t [1,3]? Do we just sub in t as appropriate (e.g. 6(1), (2+3(3) - 2(3)^2)? Or am I missing something here.

On a biased coin the probability of it showing heads for a given coin toss is 0.52. In a sequence of tosses, what is the probability of getting the first tail on flip 5? I can just do a tree diagram for this and figure it out the slow way, but if I get th...

Given: |4 -2| X = 2|-4 -4| |-1 1| | 2 2| What is X? I solved this and couldn't get an answer - that is, the result was undefined/null, as it didn't like how the multiplication worked. I got this for every way I tried doing it, including by transposing the...

If you add the numbers together, you get 887569. We can round in stages here. Rounding to the nearest 10 gets you 887570. Rounding to the nearest 100 gets you 887600. 5 and up - round up! 4 and down - go down.

1648068280 1,648,068,280 (always separate from the back in groups of 3 - this number is over 1 billion!) To the nearest ten thousand is 1648070000, I believe.

Hey Scott, Having a little trouble still. 80 = (400 * 9.8) / sin(2theta) becomes sin2theta = 3920/6400, which is sin2theta = 0.6125 which is arcsin(0.6125 / 2) which is 17.83, but my homework is still marking this as incorrect. Is there something addition...

You have 550 litres of oil. 1/5 is 0.2, so you can do 550 * 0.2 with a calculator to get 110. 110 * 2 = 220, so you sold 220 litres. You also poured 110 litres out. This means in total, you lost 330 litres. 550 - 330 = 220 litres remaining.

You have 4 of the letter R, 2 of the letter B, 1 of the letter Y and 1 of the letter G. Added together, total is 8. Now, you have 4 Rs, out of 8 total letters. 4/8. But this isn't one of your answers, so how can you simplify it? 4/8 is also 2/4, isn't it?...

Have you considered looking up trigonometric derivation rules? There're a few that might be useful.

First, find 1/9th of 450. That's 50, because 450/9. So, you spent 50 on chocolate, meaning you now have 400. You spent 2/5ths on chocolate. Let's divide 400 by 5 to find 1/5 - that's 80 - then multiply that by 2 to get 2/5 - that's 160. So, you spent 50 o...

That's just negative 2 squared. -2 * -2 = 4. Not sure what you mean 'without an exponent'. (-2)^2 is usually written that way to indicate that it's -2 that's being squared, not -(2)^2, which would be -4.

Ah awesome! Any specific reason we're dividing by 1000? Just to get the right decimal?

That one works, thank you! Didn't consider actually getting the average properly, whoops.

Oh duh I'm dumb. TY!

Oooh, I forgot about inverse matrices. Thank you!