All Answers 356371 Answers

Divide each term by 10⁶   --->   a · 10 + b  =  c   --->   10a + b  =  c   

Angles  DOB  and  COB  are supplementary   --->   angle(DOB) + angle(COB)  =  180^o.

Since  angle(DOB)  =  5 · angle(COB)   --->   5 · angle(COB) +   angle(COB)  =  180^o

--->   6 · angle(COB)  =  180^o   --->   angle(COB)  =  30^o

Since  angle(AOD)  =  angle(COB)   --->   angle(AOD)  =  30^o

The probability that all 6 are hazelnuts is:  [ ₉C₆ ·₁₀C₀ · ₅C₀ ]  /  ₂₄C₆

(found by choosing 6 of the 9 hazelnuts, 0 of the 10 almonds, and 0 of the 5 walnuts; divided by the 

number of ways to choose a set of 6 from a set of 24)

The probability that all 6 are almonds is:  [ ₉C₀ ·₁₀C₆ · ₅C₀ ]  /  ₂₄C₆

(found by choosing 0 of the 9 hazelnuts, 6 of the 10 almonds, and 0 of the 5 walnuts; divided by the 

number of ways to choose a set of 6 from a set of 24)

The probability that all 6 are walnuts is:  0  (because there aren't 6 of them.

To find the final probability add the above two probabilities.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140      add these together.....

What do you want to do with this expression?

1 - 144 mod 16==0, 144 mod 48==0, 144 mod 144==0. None of these numbers divides 72 evenly.

2 - 196 mod 7==0, 196 mod 14==0, 196 mod 28==0, 196 mod 49==0, 196 mod 98==0 and 196 mod 196==0. None of these numbers divides 72 evenly.

There are 975 such products as follows:

1116 , 1123 , 1126 , 1132 , 1134 , 1136 , 1143 , 1146 , 1156 , 1161 , 1162 , 1163 , 1164 , 1165 , 1166 , 1213 , 1216 , 1223 , 1226 , 1231 , 1232 , 1233 , 1234 , 1235 , 1236 , 1243 , 1246 , 1253 , 1256 , 1261 , 1262 , 1263 , 1264 , 1265 , 1266 , 1312 , 1314 , 1316 , 1321 , 1322 , 1323 , 1324 , 1325 , 1326 , 1332 , 1334 , 1336 , 1341 , 1342 , 1343 , 1344 , 1345 , 1346 , 1352 , 1354 , 1356 , 1361 , 1362 , 1363 , 1364 , 1365 , 1366 , 1413 , 1416 , 1423 , 1426 , 1431 , 1432 , 1433 , 1434 , 1435 , 1436 , 1443 , 1446 , 1453 , 1456 , 1461 , 1462 , 1463 , 1464 , 1465 , 1466 , 1516 , 1523 , 1526 , 1532 , 1534 , 1536 , 1543 , 1546 , 1556 , 1561 , 1562 , 1563 , 1564 , 1565 , 1566 , 1611 , 1612 , 1613 , 1614 , 1615 , 1616 , 1621 , 1622 , 1623 , 1624 , 1625 , 1626 , 1631 , 1632 , 1633 , 1634 , 1635 , 1636 , 1641 , 1642 , 1643 , 1644 , 1645 , 1646 , 1651 , 1652 , 1653 , 1654 , 1655 , 1656 , 1661 , 1662 , 1663 , 1664 , 1665 , 1666 , 2113 , 2116 , 2123 , 2126 , 2131 , 2132 , 2133 , 2134 , 2135 , 2136 , 2143 , 2146 , 2153 , 2156 , 2161 , 2162 , 2163 , 2164 , 2165 , 2166 , 2213 , 2216 , 2223 , 2226 , 2231 , 2232 , 2233 , 2234 , 2235 , 2236 , 2243 , 2246 , 2253 , 2256 , 2261 , 2262 , 2263 , 2264 , 2265 , 2266 , 2311 , 2312 , 2313 , 2314 , 2315 , 2316 , 2321 , 2322 , 2323 , 2324 , 2325 , 2326 , 2331 , 2332 , 2333 , 2334 , 2335 , 2336 , 2341 , 2342 , 2343 , 2344 , 2345 , 2346 , 2351 , 2352 , 2353 , 2354 , 2355 , 2356 , 2361 , 2362 , 2363 , 2364 , 2365 , 2366 , 2413 , 2416 , 2423 , 2426 , 2431 , 2432 , 2433 , 2434 , 2435 , 2436 , 2443 , 2446 , 2453 , 2456 , 2461 , 2462 , 2463 , 2464 , 2465 , 2466 , 2513 , 2516 , 2523 , 2526 , 2531 , 2532 , 2533 , 2534 , 2535 , 2536 , 2543 , 2546 , 2553 , 2556 , 2561 , 2562 , 2563 , 2564 , 2565 , 2566 , 2611 , 2612 , 2613 , 2614 , 2615 , 2616 , 2621 , 2622 , 2623 , 2624 , 2625 , 2626 , 2631 , 2632 , 2633 , 2634 , 2635 , 2636 , 2641 , 2642 , 2643 , 2644 , 2645 , 2646 , 2651 , 2652 , 2653 , 2654 , 2655 , 2656 , 2661 , 2662 , 2663 , 2664 , 2665 , 2666 , 3112 , 3114 , 3116 , 3121 , 3122 , 3123 , 3124 , 3125 , 3126 , 3132 , 3134 , 3136 , 3141 , 3142 , 3143 , 3144 , 3145 , 3146 , 3152 , 3154 , 3156 , 3161 , 3162 , 3163 , 3164 , 3165 , 3166 , 3211 , 3212 , 3213 , 3214 , 3215 , 3216 , 3221 , 3222 , 3223 , 3224 , 3225 , 3226 , 3231 , 3232 , 3233 , 3234 , 3235 , 3236 , 3241 , 3242 , 3243 , 3244 , 3245 , 3246 , 3251 , 3252 , 3253 , 3254 , 3255 , 3256 , 3261 , 3262 , 3263 , 3264 , 3265 , 3266 , 3312 , 3314 , 3316 , 3321 , 3322 , 3323 , 3324 , 3325 , 3326 , 3332 , 3334 , 3336 , 3341 , 3342 , 3343 , 3344 , 3345 , 3346 , 3352 , 3354 , 3356 , 3361 , 3362 , 3363 , 3364 , 3365 , 3366 , 3411 , 3412 , 3413 , 3414 , 3415 , 3416 , 3421 , 3422 , 3423 , 3424 , 3425 , 3426 , 3431 , 3432 , 3433 , 3434 , 3435 , 3436 , 3441 , 3442 , 3443 , 3444 , 3445 , 3446 , 3451 , 3452 , 3453 , 3454 , 3455 , 3456 , 3461 , 3462 , 3463 , 3464 , 3465 , 3466 , 3512 , 3514 , 3516 , 3521 , 3522 , 3523 , 3524 , 3525 , 3526 , 3532 , 3534 , 3536 , 3541 , 3542 , 3543 , 3544 , 3545 , 3546 , 3552 , 3554 , 3556 , 3561 , 3562 , 3563 , 3564 , 3565 , 3566 , 3611 , 3612 , 3613 , 3614 , 3615 , 3616 , 3621 , 3622 , 3623 , 3624 , 3625 , 3626 , 3631 , 3632 , 3633 , 3634 , 3635 , 3636 , 3641 , 3642 , 3643 , 3644 , 3645 , 3646 , 3651 , 3652 , 3653 , 3654 , 3655 , 3656 , 3661 , 3662 , 3663 , 3664 , 3665 , 3666 , 4113 , 4116 , 4123 , 4126 , 4131 , 4132 , 4133 , 4134 , 4135 , 4136 , 4143 , 4146 , 4153 , 4156 , 4161 , 4162 , 4163 , 4164 , 4165 , 4166 , 4213 , 4216 , 4223 , 4226 , 4231 , 4232 , 4233 , 4234 , 4235 , 4236 , 4243 , 4246 , 4253 , 4256 , 4261 , 4262 , 4263 , 4264 , 4265 , 4266 , 4311 , 4312 , 4313 , 4314 , 4315 , 4316 , 4321 , 4322 , 4323 , 4324 , 4325 , 4326 , 4331 , 4332 , 4333 , 4334 , 4335 , 4336 , 4341 , 4342 , 4343 , 4344 , 4345 , 4346 , 4351 , 4352 , 4353 , 4354 , 4355 , 4356 , 4361 , 4362 , 4363 , 4364 , 4365 , 4366 , 4413 , 4416 , 4423 , 4426 , 4431 , 4432 , 4433 , 4434 , 4435 , 4436 , 4443 , 4446 , 4453 , 4456 , 4461 , 4462 , 4463 , 4464 , 4465 , 4466 , 4513 , 4516 , 4523 , 4526 , 4531 , 4532 , 4533 , 4534 , 4535 , 4536 , 4543 , 4546 , 4553 , 4556 , 4561 , 4562 , 4563 , 4564 , 4565 , 4566 , 4611 , 4612 , 4613 , 4614 , 4615 , 4616 , 4621 , 4622 , 4623 , 4624 , 4625 , 4626 , 4631 , 4632 , 4633 , 4634 , 4635 , 4636 , 4641 , 4642 , 4643 , 4644 , 4645 , 4646 , 4651 , 4652 , 4653 , 4654 , 4655 , 4656 , 4661 , 4662 , 4663 , 4664 , 4665 , 4666 , 5116 , 5123 , 5126 , 5132 , 5134 , 5136 , 5143 , 5146 , 5156 , 5161 , 5162 , 5163 , 5164 , 5165 , 5166 , 5213 , 5216 , 5223 , 5226 , 5231 , 5232 , 5233 , 5234 , 5235 , 5236 , 5243 , 5246 , 5253 , 5256 , 5261 , 5262 , 5263 , 5264 , 5265 , 5266 , 5312 , 5314 , 5316 , 5321 , 5322 , 5323 , 5324 , 5325 , 5326 , 5332 , 5334 , 5336 , 5341 , 5342 , 5343 , 5344 , 5345 , 5346 , 5352 , 5354 , 5356 , 5361 , 5362 , 5363 , 5364 , 5365 , 5366 , 5413 , 5416 , 5423 , 5426 , 5431 , 5432 , 5433 , 5434 , 5435 , 5436 , 5443 , 5446 , 5453 , 5456 , 5461 , 5462 , 5463 , 5464 , 5465 , 5466 , 5516 , 5523 , 5526 , 5532 , 5534 , 5536 , 5543 , 5546 , 5556 , 5561 , 5562 , 5563 , 5564 , 5565 , 5566 , 5611 , 5612 , 5613 , 5614 , 5615 , 5616 , 5621 , 5622 , 5623 , 5624 , 5625 , 5626 , 5631 , 5632 , 5633 , 5634 , 5635 , 5636 , 5641 , 5642 , 5643 , 5644 , 5645 , 5646 , 5651 , 5652 , 5653 , 5654 , 5655 , 5656 , 5661 , 5662 , 5663 , 5664 , 5665 , 5666 , 6111 , 6112 , 6113 , 6114 , 6115 , 6116 , 6121 , 6122 , 6123 , 6124 , 6125 , 6126 , 6131 , 6132 , 6133 , 6134 , 6135 , 6136 , 6141 , 6142 , 6143 , 6144 , 6145 , 6146 , 6151 , 6152 , 6153 , 6154 , 6155 , 6156 , 6161 , 6162 , 6163 , 6164 , 6165 , 6166 , 6211 , 6212 , 6213 , 6214 , 6215 , 6216 , 6221 , 6222 , 6223 , 6224 , 6225 , 6226 , 6231 , 6232 , 6233 , 6234 , 6235 , 6236 , 6241 , 6242 , 6243 , 6244 , 6245 , 6246 , 6251 , 6252 , 6253 , 6254 , 6255 , 6256 , 6261 , 6262 , 6263 , 6264 , 6265 , 6266 , 6311 , 6312 , 6313 , 6314 , 6315 , 6316 , 6321 , 6322 , 6323 , 6324 , 6325 , 6326 , 6331 , 6332 , 6333 , 6334 , 6335 , 6336 , 6341 , 6342 , 6343 , 6344 , 6345 , 6346 , 6351 , 6352 , 6353 , 6354 , 6355 , 6356 , 6361 , 6362 , 6363 , 6364 , 6365 , 6366 , 6411 , 6412 , 6413 , 6414 , 6415 , 6416 , 6421 , 6422 , 6423 , 6424 , 6425 , 6426 , 6431 , 6432 , 6433 , 6434 , 6435 , 6436 , 6441 , 6442 , 6443 , 6444 , 6445 , 6446 , 6451 , 6452 , 6453 , 6454 , 6455 , 6456 , 6461 , 6462 , 6463 , 6464 , 6465 , 6466 , 6511 , 6512 , 6513 , 6514 , 6515 , 6516 , 6521 , 6522 , 6523 , 6524 , 6525 , 6526 , 6531 , 6532 , 6533 , 6534 , 6535 , 6536 , 6541 , 6542 , 6543 , 6544 , 6545 , 6546 , 6551 , 6552 , 6553 , 6554 , 6555 , 6556 , 6561 , 6562 , 6563 , 6564 , 6565 , 6566 , 6611 , 6612 , 6613 , 6614 , 6615 , 6616 , 6621 , 6622 , 6623 , 6624 , 6625 , 6626 , 6631 , 6632 , 6633 , 6634 , 6635 , 6636 , 6641 , 6642 , 6643 , 6644 , 6645 , 6646 , 6651 , 6652 , 6653 , 6654 , 6655 , 6656 , 6661 , 6662 , 6663 , 6664 , 6665 , 6666 , Total =  975 such numbers.

Note: Even though many of the above permutatuions are ODD, but their products are all EVEN and MULTIPLES of 3. You may test any of them such as: 6415 =6 x 4 x 1 x 5==120 - which is EVEN and MULTIPLE of 3.

Thanks Gino,

You have done a lot of work there but unfortunately, you did label  O incorrectly.

\(15^2=m^2+t^2-2mt\cdot cos\alpha\\ Cos\alpha = \frac{2t}{4m}=\frac{t}{2m}\\ so\\ 225=m^2+t^2-2mt \cdot \frac{t}{2m}\\ 225=m^2\\ m=15 \)

This means that  the hypotenuse is  60

and the sum of the other 2 sides is  112-60 =52

As guest has already told us very loudly  ,  this is impossible.

So such a triangle cannot exist.

There are 20 multiples of 9 between 100,000 and 100,185 as follows:

(100008, 100017, 100026, 100035, 100044, 100053, 100062, 100071, 100080, 100089, 100098, 100107, 100116, 100125, 100134, 100143, 100152, 100161, 100170, 100179) Total = 20 such numbers.

100th Lucas Number = 792070839848372253127 mod 20==7 - the remainder.

10,000 x [1.05]^4 ==10,000 x 1.21550625==12,155.0625==12,155 - what Joseph owes his sister.

This question is wrong!!! 

The sum of legs MUST be greater than the length of the hypotenuse!!! 

You are criticizing the echo,  but you have not commented on the real post.

Looks like someone has gone to a lot of effort for you.   Now it is your turn to interact with your answerer.

Wow!   Is there an echo in here? ....or what?    Is this answer not EXACTLY posted above????

      THAT is great....thanx,    Very helpful.....not!    

twenty

I have no idea.

Would you like to show us Alan?

In concave equilateral pentagon ABCDE, angle A = angle B = 100 degrees.  What is the degree measure of E?

Angle E = 32.34926122 degrees

This question is easy.

Add the first 4 equations together

sum of left = sum of right

 you will have 

p( ...) +q(...) +r( ...) = (...)

factorize and take it from there

Hi Textot,

What you have done looks very impressive.   

I have to think about it some more.  

3 tenths is 36

1 tenth is  12

100%   is  120

3/8*120 = 45

45+36 = 81

120-81  = 39

13 spades plus 3 other kings       16 out of 52    =    4/13

Plug the values of x, y, and z into this equation:  x + y + z = 12

w + x + y = - 2

________________

w + y + z = 19

x + y + z =  12

--------- w = x + 7  (1)

w + x + z = 4

w + y + z = 19

--------- y = x + 15   (2)

_________________

w + x + y = - 2

x = - 2 - w - y

x = - 2 - (x + 7) - (x + 15) 

x = - 8

w = - 1

y = 7

z = 13

---------------------

wx + yz = (- 1)(- 8) + 7(13) = 99