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Let the time taken by the bus =T

Then the time taken by the Mom =T - 15

Distance  =Time x Speed

42T =72(T - 15)

42T =72T - 1,080

42T - 72T = -1,080

-30T = -1,080

T = -1,080 / -30

T = 36 minutes taken by the bus

36 - 15 =21 minutes taken by the Mom.

7:18 + :36 =7:54 am - when the Mom catches up with the bus.

You're the greatest. It's well-explained, too.

However, I tried the next one, and I still cannot figure out what the answer is. The sum is 15 and the product is 63.

This is an untrue equation.

9+2*8*2-12 simplifies to 29.

This one requires some thinking. We know that a quadratic equation has 2 zeroes. One is located at \((x,0)\), and the other is located at \((y,0)\). 

Now, what do we know about the relationship of these two numbers? Well, we know that the sum of both zeroes is -15.

Since y=-15-x, we know that a zero is located at \((-15-x,0)\). We also know that, when multiplied, both  zeroes yield -54. Knowing this information, we can generate a quadratic equation.

\(x(-15-x)=-54\)

This quadratic equation has everything that we are looking for. Now, solve for the zeroes of this quadratic.

These zeroes definitely fit the criteria.

Evaluating the expression of \(\frac{\frac{3}{8}}{1\frac{7}{8}}-\frac{1}{6}\)

"The Lakers are playing the Celtics in the NBA finals. To win the NBA finals, a team must win 4 games before the other team does. If the Celtics win each game with probability 2/3 and there are no ties, what is the probability that the Lakers will win the NBA finals but that the contest will need all seven games to be decided? Express your answer as a fraction."

.

If you asked this question Jeff123 it is better that you stay anonymous.

You are not polite enough to be a proper member of this forum.

If it was not Jeff and you are polite then it would be nice if you joined up. 

That way you can track your questions much more easily and you get email notification when answers are given :)

If you get known as a polite participant of the forum answerers will give you are great deal of help and attention. :)

Find the number of ways in which letters of the word ARRANGEMENT can be arranged so that the two A‟s and two R‟s do not occur together.

AA RR NN EE G M T

I'm going to think of this as  AR NN EE G M T

How many distict ways can this be arranged.  I have treated AA and RR as just one item each.

So I think this is how many ways the letters can be arranged so that the 2Rs and 2As are together. 

\(\frac{9!}{2!2!}=\frac{9!}{4}\)   ways

Now how many ways can the original set be arranged.  

\(\frac{11!}{2!2!2!2!}= \frac{11! }{16}\)

So the number of ways that the 2As and the 2Rs are not together is   

 \(\frac{11!}{16}-\frac{9!}{4}=2494800-90720 = 2402080\)

I think. 

(4x^3y^2)3/10

Do you mean

[(4x^3y^2)^3]/10

or

(4x^3y^2)^[3/10]

Or something different again ?

Oh dear, I did not answer the exact question that was asked. Sorry :)

Thanks Chris :)

As Melody has said, "theta"  is a 4th quadrant angle

tangent  = y / x  =    -1    .... so......x = 1     and   y  =  - 1

And  r =   sqrt (x^2 + y^2)  =  sqrt [ 1^2 + (-1)^2 ]  = sqrt (2)

Sine  =  y / r  =  -1 / sqrt (2)

Cosine  =  x / r  =   1 /  sqrt(2)

LOL!!! 

So, anyone good with trig functions and the quadrants? For ex; .

\(tan​\theta= -1, sin\theta<0\)

What is sine and cosine ratios?

Well, tan is negative in the second and forth quadrants   

 (I remember this with  All Stations To Central)

Sin is negative in the third and forth quadrant.

So tan and sin are both negative only in the 4th quadrant. So that is where the answer has to lie.

Now tan(theta)=+1 when theta = 45 degrees.

So what is the 4th quadrant equivalent?

360-45 = 315 degrees.

So then answer is 

\(\theta=315^\circ+360n\qquad n \in Z\qquad (n\; is \;an\; integer)\)

OOPS...sorry.....!!!!!

I didn't look at it .....I thought it was the same question I had answered elsewhere....

My bad !!!!

Hi Chirs, I am just wondering why you blanked this one?

Has it been asked somewhere else?

A logarithm is an index (or a power)

For instance

since

\(10^2=100\\ log_{10}100=2\)

\($\frac{a+b}{a-b} + \frac{a-b}{a+b}$\)

[ (a + b)(a + b) + (a - b)(a - b) ]  / [ a^2 - b^2 ] =

 ( [ a^2 + 2ab + b^2  + a^2 - 2ab +b^2 ] / [ a^2 - b^2]  =

[ 2a^2 + 2b^2 ] / [ a^2 - b^2 ]

2 [ a^2 + b^2] / [ a^2 - b^2 ]

The smallest positive value, 2, is achieved when  b  = 0  and a is any positive integer

In every other case,  [ a^2 + b^2] / [ a^2 - b^2 ] will be > 1   and the expression will be > 2

This is the one I was actually referring to:

Here is your question posted here and the answers. Go through it in detail:

http://web2.0calc.com/questions/counting-question#r17

You still have not responded to my last answer even though I specifically requested you to.

That was 2.5 weeks ago.  Why would I bother responding to this new question?

Well, Mr. BB, Bananas are brain food. Didn’t you know?

I have read:

"Dis-moi ce que tu manges, je te dirai ce que tu es."

(Tell me what you eat and I will tell you what you are).

1826--Anthelme Brillat-Savarin

In your case, it’s easy to tell that your dietary staples consist mainly of idiot sandwiches, pork butt-roast, meatballs, and fruitcake.

Tell me, Mr. BB, What is your favorite drink?

I know several banker and Wall Street types – not enough to do a true statistic, but most of the older ones drink Scotch (usually single malt), or well-aged bourbons.   So what is it for you? I mean what was it back when you could chose something other than bathtub gin?

If the perimeter of the rectangle is 50 units......the sum of the length and width must be 25 units

The largest area will be formed when one dimension is  12 units and the other is 13

And the area  = 12 * 13  =  156 units^2

The smallest possible area is when one dimension is 1 unit  and the other is 24

And the area is  1 * 24 =   24  units^2

The difference in the areas  =  156 - 24  =  132 units^2