A group of 4444 friends is playing cards. The deck has 70707070 cards. To start the game, the dealer makes a pile of 15151515 cards in the center. Then she deals the remaining cards one at a time to each player until all the cards are gone. What is the greatest number of cards any player will have after all the cards are dealt?
cards

12502 cards

Step-by-step explanation:

Given:

» total of 70707070 cards of the deck

» 15151515 cards were taken and put in a pile

Solve:

1. So, you can subtract 15151515 from 70707070 to find how many cards are left:

70707070 - 15151515 = 55555555

2. Now, there are 55555555 cards remaining in the deck since 15151515 cards were taken to put in a pile. Since the dealer deals the remaining cards to 4444 people, you can just do 55555555 divided by 4444 to find how many cards each person gets:

55555555 ÷ 4444 = 12501.25

3. 12501.25 is the exact number of cards each person gets, but you can’t have a fraction/part of a card. You have to find a specific remaining number:

0.25 is the same as , and so convert into a fraction with a denominator of 4444, but is still equivalent to : You’ll get , which is correct because it’s still equivalent to

4. So, the remaining 55555555 cards divided by 4444 people is 12501 cards and a remainder of 1111 cards. The 1111 cards can be distributed upon the players, but not everyone can get it. Since 12501 were to given to the players and after the remaining 1111 were also distributed, this means that some will have 12501 cards and others will have 12502 cards.

So, the greatest number of cards any player will have after all the cards are dealt is 12502 cards.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

step-by-step explanation:   divide the numerator by the denominator to get the decimal

it would still be 193

if divide by 100 then 1.93

i am not sure