All Answers 359041 Answers

17 x 40 You can try this:

10 x 40 =400

7 x 40 =280

400 + 280 =680

Results in wavelength of 76.576576 cm  (340/444)

Directly between is 200 cm  

Look at speaker 1    400 cm to speaker 2   at what point between the two is a whole number of wavelengths from EACH speaker?

Distance from speaker 2 is   400 - 76.576576 x        =   323.423        246.84684    170.270272   93.6936         17.11712

Distance from speaker 1 is    76.576576 x 1,2,3,4     =  76.576576    153.153152   229.729728  306.306304   382.88288

None of these numbers match.   The speakers are not a whole number of wavelengths apart, so I BELIEVE there will be no where on a direct line between them where there will be constructive interference.

Hi Damien!

On the Moon, the acceleration of gravity is one sixth of it's value here on earth. If a pendulum has a period of T on here on earth Earth, what will its period be on the Moon?

A.T/

B.T

C.T/6

D.T/3

E.6T

\(T= 2\pi \times \sqrt{\frac{l}{g} }\) 

\(T_{M} = 2\pi \times \sqrt{\frac{6\times l}{g} }\)

T_M = T \(\times \sqrt{6} \) = 2.45 T

A. T = T_M / \(\sqrt{6}\)

The time for one oscillation of the pendulum on the moon is 2.45 times the time of a vibration on the earth.

Greeting asinus :- )

   !

Did you check your Trig textbook?. That is, if you have one!.

You question doesn't make sense to me for the answers given. Because the period of a pendulum should vary as the square root of the gravity ratio between the Earth and the Moon. That is, if the gravity on Earth is 6 times that on the Moon, then the period on the Moon should be:

Tsqrt(6) =2.46T. But, I don't see that on your list of choices!!. Sorry, unless I'm neglecting something.

Alan should take a look at it.

Your question is rather unrealistic in the sense that a $7 share earns a dividend of $2 per share!!!.

Because $2/$7=~29%!!. Most dividends paid are in the 2-5% range!.

At any rate, if the dividend is re-invested @ 24%, then in 1 year the dividend becomes:

$2 x 1.24 =$2.48. In order for the stock to yield 25%, the price(P) of the share would have to be:

P x 25% =$2.48 divide both sides by 25%

P=$2.48 / .25

P=$9.92 The price of 1 share.

Let the orignal amount=A, then we have:

25%A=$18,000 divide both sides by 25%

A=$18,000 / .25

A=$72,000. The original amount.

DID YOU KNOW? At these densities, the total mass and size of planet Earth would be squeezed into a cube of about 600 feet on each side!!!!!. Now, that is DENSE!!.

1) In dice tossing, where the desired outcome is some sum of the dice tossed, the probability is ALWAYS equal to the coefficients of this generating series divided by 6^n, where n=number of tosses or number of dice tossed: expand [n+n^2+n^3+n^4+n^5+n^6]^2

=n^12+2 n^11+3 n^10+4 n^9+5 n^8+6 n^7+5 n^6+4 n^5+3 n^4+2 n^3+n^2
(11 terms). So the coefficient of n^4=3, and the coefficient of n^9=4.

Therefore, the total probability is: (3+4)/6^2=7/36, or =~ 19.44%.

1) 2 standard 6-sided dice are rolled. What is the probability that the sum rolled is a perfect square?

The possible perfect squares are 4 and 9

A "4"  can be obtained in 3 ways

A "9" can be obtained in  4 ways

And the total number of outcomes = 36   so.......

The probability of a perfect square being rolled  =  [ 3 + 4 ] / 36 =    7/36

Doppler effect.  Change in frequency given by:

deltaf = (343/(343-45) - 343/(343+45))*820 Hz

.

f(x)=x^2+2x-3   g(x)=x-9

f(x-9)=(x-9)^2+2(x-9)-3

f(x-9)=x^2-18-81+2x-18-3

f(x-9)=x^2-16x-102

Given A(-5,-4) and B(7, 18), find the point two-fifths of the way from A to B.

This can be found thusly :

The x coordinate is given by ;

-5 + [2/5] [ 7 - (-5)]  =   -5 + [2/5] [12]  =  -1/5  = -.2

And the y coordinate is given by :

-4 + [2/5] [ 18 - (-4) ]  =  -4 + [2/5] [22]  = 4.8  

Proof :

The total distance between the points =  2√157

And the distance between  (-5, 4)   and ( -.2, 4.8)  = √  [4.8^2 + .8^2]  ≈ 10.024

So.....10.024 / [2 √157] ≈  .4    ≈   2/5

I think you are right Chris - I didn't separate teeth from revolutions!

Two gears work together. There are 32 teeth on one gear and 36 on the other gear. The first gear makes 128 revolutions per second. How often, during a 24 hour period, will the same two teeth from each gear be together?

I saw geno do something like this one the other day......

32 = 2^5

36 = 3^2 * 2^2

The least common multiple between 36 and 32  =  3^2 * 2^5    =  288

So....... the two teeth are together when the first gear makes 288/32  = 9 revolutions   and the second gear makes 288/36 = 8 revolutions

And it takes the first gear 9/128 seconds to make 9 revolutions

And there are  60*60*24 = 86400 seconds in  a 24 hour period.......so......

In 24 hours.......the same two teeth from both gears will be together

86400  / [ 9/128] =  1,228,800   times

2sin(x)tan(x)=tan(x)+2sin(x)

\(2sin(x)tan(x)=tan(x)+2sin(x)\\ \frac{2sin^2(x)}{cos(x)}=\frac{sin(x)}{cos(x)}+\frac{2sin(x)cos(x)}{cos(x)}\\\ 2sin^2(x)=sin(x)+2sin(x)cos(x)\\ 2sin(x)-2cos(x)=1\\ 4(sin(x)-cos(x))^2=1\\ 4(sin^2(x)-2sinxcosx+cos^2(x))=1\\ sin^2(x)+cos^2(x)-2sinxcosx=0.25\\ 1-2sinxcosx=0.25\\ -2sinxcosx=\;-0.75\\ 2sinxcosx=\;0.75\\ sin(2x)=\frac{3}{4}\\ 2x\mbox{ must be in the 1st ot 2nd quadrant}\\ 2x=asin(\frac{3}{4})\\ 2x\approx 48.6^\circ,\quad 180-48.6^\circ, \quad (48.6+360)^\circ,\quad (180-48.6+360)^\circ, \quad \\ 2x\approx 48.6^\circ,\quad 131.4^\circ, \quad 408.6^\circ,\quad 491.4^\circ, \quad \\ x\approx 24.3^\circ,\quad 65.7^\circ, \quad 204.3^\circ,\quad 245.7^\circ, \quad \\ \)

I have checked these points from substitution.  Only the 2 middle ones work. It has probably got something to do with the squaring that I did as part of the working

\(x= 65.7^\circ \qquad or \qquad 204.3^\circ \qquad (\pm360n)\)

Are you SURE 30 degrees solves this equation?  I don't think it does.....

1- http://www.wolframalpha.com/input/?i=2+6-sided+dice+tossed,+total+4

2-http://www.wolframalpha.com/input/?i=2+6-sided+dice+tossed,+total+9

How are these different from your calculations? would you add them up: 1/12 + 1/9=7/36?????????.

Hi Miss Melody,

Why isn't the answer to #5 a probality of zero?  How can one ball be white If two of the black b***s are drawn? 

The $#&^#%^* network will not let me log on. 

GA

I suggest that you use Desmos for you graphs.  :)

Ok. Thank you all!

Hi Electric Pavlov,

I'm going to have a go too :)

1) 2 standard 6-sided dice are rolled. What is the probability that the sum rolled is a perfect square?
ElectricPavlov has nailed it!

2) A card is drawn at random from a standard 52-card deck. What is the probability it is an odd number or a spade?

This one can be interpreted differently so it is a bad question....

I am going to consider odd numbers to be 3,5,7,9    there are 4*4=16 of these

There are 13 spaces and there are 4 odd spades so

P=(16+13-4)/52 = 25/52

3) A penny=1, nickel=5, and dime=10 are simultaneously flipped. What is the probability that heads are showing on at least 6 cents worth of coins?

dime and any other=0.5       nickel and penny but not dime= 0.5*0.5*0.5 = 0.125

So the prob will be  0.625   or  5/8

AGAIN ElectricPavlov nailed it!   :)

4) 8 coins are simultaneously flipped. What is the probability that heads are showing on at most 2 of them?

P(none)+P(1head)+P(2heads)

\(= 8C0 * 0.5^8 + 8C1 * 0.5^8 + 8C2 * 0.5^8\\ = 1 * 0.5^8 + 8 * 0.5^8 + 28 * 0.5^8\\ = (1+8+28) * 0.5^8 \\ = 37* 0.5^8 \\\)

37*0.5^8 = 0.14453125

5) 5 white b***s and k black b***s are placed into a bin. Two of the black b***s are drawn at random. The probability that one of the drawn b***s is white and the other is black is .

\(\mbox{P(one white and one black)=}2(\frac{5}{5+k}*\frac{k}{5+k})=\frac{10k}{(5+k)^2}\)

Please ask if you would like more explanationg :)

I hope it's right then!

Thanks Alan,

That one had me stumped.   I was looking for some really complicated solution :)

Clearly a bug in the web2.0calc graphing as it has drawn the square root of the absolute value of x.