All Answers 358115 Answers

Can I have some work? How did you get this?

OK, young person! If you don't believe it, here are the 16 distinct COMBINATIONS, which you must permute as follows:

[(2, 2, 2, 2, 2), (2, 2, 2, 2, 3), (2, 2, 2, 2, 4), (2, 2, 2, 2, 7), (2, 2, 2, 2, 8), (2, 2, 2, 3, 4), (2, 2, 2, 3, 7), (2, 2, 2, 3, 8), (2, 2, 2, 4, 7), (2, 2, 2, 4, 8), (2, 2, 2, 7, 8), (2, 2, 3, 4, 7), (2, 2, 3, 4, 8), (2, 2, 3, 7, 8), (2, 2, 4, 7, 8), (2, 3, 4, 7, 8)] >>Total = 16 distinct combinations.

[1 + 5*4 + 6*20 + 4*60 + 1*120] =501 distinct permutations.

36666 , 45666 , 46566 , 46656 , 46665 , 54666 , 55566 , 55656 , 55665 , 56466 , 56556 , 56565 , 56646 , 56655 , 56664 , 63666 , 64566 , 64656 , 64665 , 65466 , 65556 , 65565 , 65646 , 65655 , 65664 , 66366 , 66456 , 66465 , 66546 , 66555 , 66564 , 66636 , 66645 , 66654 , 66663 , Total =  35 such outcomes.

A computer code calculates a total of 501 distinct permutations and begins with:

{{2, 2, 2, 2, 2}, {2, 2, 2, 2, 3}, {2, 2, 2, 2, 4}, {2, 2, 2, 2, 7}, {2, 2, 2, 2, 8}, {2, 2, 2, 3, 2}, {2, 2, 2, 3, 4}, {2, 2, 2, 3, 7}, {2, 2, 2, 3, 8}, {2, 2, 2, 4, 2}, {2, 2, 2, 4, 3}, {2, 2, 2, 4, 7}, {2, 2, 2, 4, 8}, {2, 2, 2, 7, 2}, ...........and ends with:

 {8, 4, 7, 3, 2}, {8, 7, 2, 2, 2}, {8, 7, 2, 2, 3}, {8, 7, 2, 2, 4}, {8, 7, 2, 3, 2}, {8, 7, 2, 3, 4}, {8, 7, 2, 4, 2}, {8, 7, 2, 4, 3}, {8, 7, 3, 2, 2}, {8, 7, 3, 2, 4}, {8, 7, 3, 4, 2}, {8, 7, 4, 2, 2}, {8, 7, 4, 2, 3}, {8, 7, 4, 3, 2} = 501 permutations.

_Time(Hours):    \(  1        \space  \space  \space   \space    \space    \space   2    \space   \space       \space    \space    \space  3    \space      \space    \space    \space    \space    4    \space     \space  \space    \space    \space     5    \space    \space    \space   \space    \space     6    \space   \space   \space    \space    \space     7    \space   \space    \space    \space    \space     8    \space    \space    \space    \space    \space     9      \space  \space     \space    \space    \space   10    \space     \space    \space    \space    11 \)

_{Sandra(km):       \( 90\space \space \space  180\space\space\space    270\space\space\space    360\space\space\space    450\space\space\space   540\space\space   630 \space\space\space   720  \space\space\space  810\space\space\space    900 \space\space\space    990\)}

_{Paul(km):                           \(\space \space \space110   \space \space   220   \space \space 330 \space \space \space   440   \space \space \space  550 \space \space \space    660   \space \space \space   770   \space \space \space  880  \space \space \space    990\)}

\(x(90)= [x-2](110)\)

_{Answer: \(11\space hours\)}

(5x+2)(x-3)

7744 = 88²

\(6n = 36\)

_{positive divisors:}

\(1, 2, 3, 4, 6, 9, 12, 18,36\)

_therefore:

\(n = 6\)

yep no problem! 

ps you're so smart! these problems are really hard to figure out, and yet you do them so professionally! :)

how did you get those numbers

The hypotenuse is sqrt(19^2 + 13^2)/2 = sqrt(530)/2.

f(x) = x^4 - 2x^3 + 3x^2 - x + 4.

What question are you trying to answer?!? I spent more time trying to understand your answer than to answer the question. And I still don't get it.

you're*

Sherlock Holmes and Dr. Watson recover a suitcase with a three-digit combination lock from a mathematician turned criminal. Embedded in the suitcase above the lock is the cryptic message "AT SEA BASE. SEAS EBB SEA: BASS. "

Dr. Watson comments, "This probably isn't about ocean fish. Perhaps it is an encrypted message. The colon suggests the addition problem SEAS + EBB + SEA = BASS, where each letter represents a distinct digit, and the word 'BASE' implies that the problem is in a different base."

Holmes calmly turns the combination lock and opens the suitcase. While Dr. Watson gapes in surprise, Holmes replies, "You were indeed right, and the answer was just the value of the word SEA, interpreted as decimal digits." What was the lock combination?

Here is the problem in it's entirety.

The weather forecast shows a 90% chance of rain tomorrow.
How would this affect your plans for a class picnic? Why? 

I'd go ahead and go on the picnic, but I wouldn't get too far from the bus in case we had to jump up and run.  Getting caught in the rain isn't too bad if you can get out of it real quick.   

_.

Thank you guys for you help! I appreciate it

Two right triangles have equal areas. The first triangle has a height of 5 cm and a corresponding base of 8 cm. The second triangle has a leg of length 20 cm. What is the length of the other leg of the second triangle?

5 * 8 = 20 * x

x = 2   

The length of the other leg is  2 cm

Proof:           5 * 8 / 2 = 20 cm²             2 * 20 / 2 = 20 cm²     

This was hard enough over a year ago when the entire problem was posted in entirety.  If you want to see the parts that are missing from this post, the 2019 posting is at https://web2.0calc.com/questions/tough-number-theory-riddle   I couldn't solve it then and I can't solve it now. 

_.

It's -40

\(6x +2y= 40\)

\(-7x -2y = -44\)

_add:

\(6x-7x= 40-44\)

\(-x = -4\)

_result:

\(x = 4\)

\(y = 8\)