All Answers 356050 Answers

If a number is the multiple of 2 prime numbers it will have exactly 4 factors

eg

7*11=77    factors are   1,7,11,77

The fraction element of the calc has never worked well.  I suggest you use a different calc for fractions.

I just answered a very similar question here;

Hint:

You cannot divide by zero.  So none of the denominators can be equal to 0.

Thanks inhuman calculator, you have given a great answer          [You should give yourself a point  ]

I'll just add a little

-(3)^2 can be expanded to   -1*(3)^2    now it should be easy to see that the answer is -1*9 = -9

however

(-3)^2   is   -3 * -3  =  +9

I will admit that I do not understand the situation you have described.

But I have also, at times, been disappointed by your behaviour.

I know you do interact with people sometimes but here is an example of what I have also seen you do (or rather not do)

Alan gave you a great answer here and you did not even comment on it or give him any points.   

Find the coefficient of y^4 in the expansion of (2y - 5)^7. 

The general term in the expansion will be

\(\binom{7}{n}(-5)^n(2y)^{7-n}\)

if I rearrange  this I get

\(\binom{7}{n}(-5)^n(2)^{7-n}(y)^{7-n}\\ \)

you want y^4

so  7-n=4    gives     n=3

sub n=3 into the term and you will have your answer

\(\binom{7}{n}(-5)^n(2)^{7-n}(y)^{7-n}\\ n=3\\ \binom{7}{3}(-5)^3(2)^{7-3}(y)^{7-3}\\ \)

You can finish it.

Thanks for the feedback.  :)

You can take this one step further.

For any three dimensional object:

If you expand the lengths by a factor of y ,  [so a side of lenth 4 is epanded to length 4y]

then the area of any surface will become y^2 times bigger

and the volume will enlarge by    y^3

This is useful for many physics applications too.

I didn't realize the negative can be calculated differently. What I meant was (-2)^2. The web2.0calc calculator says -4 but my iPhone calculator says 4 so I got a little confused. I heard before that the iPhone calculator does order of operations wrong so maybe that is why.

Well, this depends. Are you asking -(2)^2 or (-2)^2? This matters because, as per the order of operations, exponents are calculated first. So, in the first situation:

-(2)^2 = -4

In the second situation, however, we are squaring the entire expression of -2. A negative squared is a positive, so (-2)^2 = 4.

Does the question look like -2^2 or (-2)^2? Because that will change the answer.

Let me know if I did anything wrong! Hope this helps.

Thanks catmg, I got it!

Make sure it is a slash(/) and not a backslash(\).

If that doesn't work, then you should refresh the tab.

if

\(x=5\)

then

\(2x=10\)

the\(\le\) sign means that it is less than or equal to.

the\(<\) sign means that it is strictly less than.

since we know that \(2x=10\), so we can have \(2x\le10\) but not \(2x<10\).

The line under the less than sign means "possibly equal."

Therefore, the comparison is between:  2x  <= 10  which means "twice x is either less than or equal to 10"  and  2x  <  10 which means that "twice x is strictly less than 10 (and never equal to 10)."

Since x = 5, 2x = 10 which makes the first inequality true and makes the second inequality false.

Volume of cylinder A = pi × radius² × height

= pi × 13² × 20 = 10,618.6 ft ( to the nearest tenth of a cubic foot).

Volume of cylinder B = pi × radius² × height

= pi × 18² × 19 = 19,339.6 ft ( to the nearest tenth of a cubic foot).

Volume of the empty portion of cylinder B = 19,339.6 - 10,618.6 = 8721.1 ft³

What do you want to know?

< Did you get anything from it? >  

Yes, I did.  It was really good.  He confirmed what I had kinda figured out – I've taken higher math than that, but my courses never addressed polygon expansion – and he presented it in an understandable way.  He repeats himself a lot, but that's better than not explaining enough.  Thanks again for the link. 

_.

FV ==PV  x  [1 + R]^N

8000 ==4000  x  [1  +  0.07]^N, solve for N

8000 ==4000  x        1.07^N

8000/4000 ==1.07^N

2 == 1.07^N

N ==Log(2) / log(1.07)

N ==10.245 - years to double your 4000 to 8000 pounds.

To get MORE than 8000 pounds, you will need about 10 years and ~4 months.

Not sure if you wanted "divisors" or "prime factors". Here are the lists of both and you decide which ones you want:

33 = (1, 3, 11, 33) > 4 (divisors)
34 = (1, 2, 17, 34) > 4 (divisors)
35 = (1, 5, 7, 35) > 4 (divisors)
38 = (1, 2, 19, 38) > 4 (divisors)
39 = (1, 3, 13, 39) > 4 (divisors)
46 = (1, 2, 23, 46) > 4 (divisors)
51 = (1, 3, 17, 51) > 4 (divisors)
55 = (1, 5, 11, 55) > 4 (divisors)
57 = (1, 3, 19, 57) > 4 (divisors)
58 = (1, 2, 29, 58) > 4 (divisors)
62 = (1, 2, 31, 62) > 4 (divisors)
65 = (1, 5, 13, 65) > 4 (divisors)
69 = (1, 3, 23, 69) > 4 (divisors)
74 = (1, 2, 37, 74) > 4 (divisors)
77 = (1, 7, 11, 77) > 4 (divisors)
82 = (1, 2, 41, 82) > 4 (divisors)
85 = (1, 5, 17, 85) > 4 (divisors)
86 = (1, 2, 43, 86) > 4 (divisors)
87 = (1, 3, 29, 87) > 4 (divisors)
91 = (1, 7, 13, 91) > 4 (divisors)
93 = (1, 3, 31, 93) > 4 (divisors)
94 = (1, 2, 47, 94) > 4 (divisors)
95 = (1, 5, 19, 95) > 4 (divisors)
106 = (1, 2, 53, 106) > 4 (divisors)
111 = (1, 3, 37, 111) > 4 (divisors)
115 = (1, 5, 23, 115) > 4 (divisors)
118 = (1, 2, 59, 118) > 4 (divisors)
119 = (1, 7, 17, 119) > 4 (divisors)
122 = (1, 2, 61, 122) > 4 (divisors)
123 = (1, 3, 41, 123) > 4 (divisors)
125 = (1, 5, 25, 125) > 4 (divisors)
129 = (1, 3, 43, 129) > 4 (divisors)
133 = (1, 7, 19, 133) > 4 (divisors)
134 = (1, 2, 67, 134) > 4 (divisors)
Total = 34 such integers

36  = 2  2  3  3 >4 (prime factors)  
40  = 2  2  2  5 >  ....................... 
54  = 2  3  3  3 >  ........................  
56  = 2  2  2  7 >  ........................  
60  = 2  2  3  5 >  ........................  
81  = 3  3  3  3 >  ........................  
84  = 2  2  3  7>  .........................  
88  = 2  2  2  11 > .......................  
90  = 2  3  3  5  >  .......................  
100  = 2  2  5  5 >  ......................  
104  = 2  2  2  13 > .....................  
126  = 2  3  3  7 > .......................  
132  = 2  2  3  11 > .....................  
135  = 3  3  3  5 >  ......................  
136  = 2  2  2  17 > .....................  
140  = 2  2  5  7 > ....................... 
Total ==16 such integers. 

2144

A certain game is won when one player gets 3 points ahead. Two players A and B are playing the game and at a particular point, A is 1 point ahead. Each player has an equal probability of winning each point. What is the probability that A wins the game?

We do not care about the number of players we only care about the number of points that A is in front.

So draw a number line.

It goes from -3 to 3   (a total of 6 units)

If the difference gets to -3 then A loses, if it gets to +3 A wins.

A starts at +1

A must go a 2 units to the right to win and 4 units to the left to lose.

So the liklihood of a win is 4/6   and the likelihood of a loss is 2/6

So he has a 2/3 chance of winning.

This is not a formal solution.  I don't know how to solve fomally but I believe this is effectively a speed test so intuition is of utmost importance.

Well, drawing a diagram will help... 

Firstly, once you draw in the angle bisector, you can use the angle bisector theorem  to get the ratio of BD to DC.

Secondly, ABD and ACD share the same altitute, so the ratio of their areas is the ratio of their bases. The angle bisector theorem states AB/AC = BD/DC. Since we are currently trying to find BD/DC, we can use AB/AC since we know what AB is and what AC is.

Thus BD/DC = 16/24 = 2/3.

Therefore, the ratio of the area of triangle ABD to the area of triangle ACD is 2/3.

 remember the angle bisector theorem, it is helpful...

You can use this formula:  P·(r/k) / (1 - (1 + r/k)^-N·k)

where:  P = original amount = 2,250,000

             r = interest rate (as a decimal) = 0.12

             k = number of times per year money is taken out = 12

             N = number of years = 40

[notice the negative sign in the exponent]

I believe that the answer is $22,691.25; an unusually large number because the interest rate is quite large.

If the difference between any two consecutive terms is the same, then it will be arithmetic.

-173 - 27  =  -200

.373 - -173  =  -200

.573 - -373  =  -200

Since these are all the same, this sequence is arithmetic.