CPhill

An athletic department sold 454 tickets to a sporting event. Adults paid $3.50 per ticket, and students paid $1.00. The total tickets sales were $1,154. How many adults tickets and how many student tickets were sold to the event?

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Call the number of adult tickets sold "x" and the number of student tickets sold "y."

Then the number sold ....x + y = 454

And the revenue is equal to the cost of the adult ticket times the number of those sold plus the the cost of a student ticket times the number of those sold. In math terms, we have .....3.50x + 1.00y = 1154.....this gives the following system...

x + y = 454

3.5x + 1y = 1154    

Subtracting the first equation from the second, we have

2.5x = 700              

divide by 2.5 on each side   this gives

x = 280 = number of adult tickets sold

And the number of student tickets sold =  [454 - 280] = 174

Make sure you check these answers in both equations to see that they "work."

Lighthouse B is 8 miles east of lighthouse A. A boat Leaves A and sails 6 miles. At this time it is sighted from B. If the bearing of the boat from lighthouse B is S71W, how far from lighthouse B is the boat?

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Using the law of sines, we need to first find the angle opposite the side of 8....we have

sin 19° / 6 = sin θ / 8

(8)/(6) * sin 19° = sin θ

.434 = sin θ    to find θ, use the inverse sine

sin^-1 (.434) ≈ 25.73°

Then the third angle (opposite the side the distance the boat is from lighthouse B) =

180 - 19 - 25.73 = 135.27°   .....Then calling the distance the boat is from lighthouse B, d, we have, using the law of sines, again

d / sin 135.27° = 6 / sin 19°

d = (6) sin 135.27° / sin 19° ≈ 12.97 miles

Quite crafty, Bertie !!

#+#(4)=56 what is the mumbers

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I'm going to replace your "#" with "x"

So we have      x + x4 = 56 ....  or ... x + 4x = 56.... or..... 5x = 56

Divide both sides by 5      we have

x = 56/5 = "#"

And that's it !!

if a word count is 3,500 and the word limit is 10% over, how many words is it?

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Let the limit = x.  The (x) + (10% of x) = 3500.

In "math" form we have..

x +.10x = 3500

1.10x = 3500    divide by 1.10 on both sides

x = 3500/ 1.10

x ≈ 3182 words

how do u find the mean?

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The "mean" of a data set is just its average. An example may work better than a definition.  Let's suppose we have four test scores and we're trying to find their average.

Let's say the scores are 60, 75, 85 and 100.

I just add them up and divide the sum by the number of scores we have.

So

(60 + 75 + 85 + 100) / 4  = (320 / 4 ) = 80.

And that's their average.

if x^2+(3*sin(x))-2=0 then what is the value of x?

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This one would be difficult to solve without a solving program....although we could use some Calculus techniques to get an approximation, like Alan did. However, since you're asking a trig question, I might assume that you haven't taken Calculus, yet.

Using Wolfram, the solutions (in rads) are -2.13105 (-122.1°) and .585321 (33.54°)

I think that's it.......

Dear Anonymous,

I'm trying to do as you requested.....but I'm running into a slight problem......I'm still looking for the Roman Numeral representation for "0"  !!!  

However.....if I DO find it, I should be finished by lunchtime......or so..........

Let me add something to what kitty<3 said.

Ask youself the question.....what could "y" be ??

Notice that, if we square any positive or negative "x," we get a "positive."

And, if we square "0," we get "0."

So, as kitty<3 points out, "y" has to be equal to or greater than 0.

$${\frac{{\mathtt{4}}}{{\mathtt{7}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{49}}}{{\mathtt{36}}}}\right){\mathtt{\,-\,}}{\frac{{\mathtt{8}}}{{\mathtt{9}}}} = -{\mathtt{0.111\: \!111\: \!111\: \!111\: \!111\: \!1}}$$