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Delicious77 [7]
2 years ago
9

find the sum of all possible four digit numbers that can be formed using the digits 2,4,5,6,7 and 8 with no repeated digits

Mathematics
2 answers:
Debora [2.8K]2 years ago
8 0
1+1
2+2
5+0
3+3
6+2-1
4+4
r-ruslan [8.4K]2 years ago
6 0

Answer:

2133120

Step-by-step explanation:

using 6 given digits, lets create a 4 digit number:

to choose the first number, you have 6 options. to choose the second number we have 5 options left. for the third number we have 4 options left. and for the fourth number, we have 3 options left.

6*5*4*3 = 360

with no repeats, 360 numbers can be formed.

this means that each number will occur 60 times each (360/6 digits)

so to find the sum:

60*(2+4+5+6+7+8) = 1920

but, we have one more thing:

In the thousands place, our sum of digits is multiplied by 1000; in the 100’s place, by 100; in the ten’s place, by 10; and in the one’s place, by 1. so:

1920(1000+100+10+1) = 1920*1111 = 2133120

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Answer:

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Step-by-step explanation:

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Part a)

Answer: 5*sqrt(2pi)/pi

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

Work Shown:

r = sqrt(A/pi)
r = sqrt(50/pi)
r = sqrt(50)/sqrt(pi)
r = (sqrt(50)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(50pi)/pi
r = sqrt(25*2pi)/pi
r = sqrt(25)*sqrt(2pi)/pi
r = 5*sqrt(2pi)/pi

Note: the denominator is technically not able to be rationalized because of the pi there. There is no value we can multiply pi by so that we end up with a rational value. We could try 1/pi, but that will eventually lead back to having pi in the denominator. I think your teacher may have made a typo when s/he wrote "rationalize all denominators"

============================================================

Part b)

Answer: 3*sqrt(3pi)/pi

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

Work Shown:

r = sqrt(A/pi)
r = sqrt(27/pi)
r = sqrt(27)/sqrt(pi)
r = (sqrt(27)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(27pi)/pi
r = sqrt(9*3pi)/pi
r = sqrt(9)*sqrt(3pi)/pi
r = 3*sqrt(3pi)/pi

Note: the same issue comes up as before in part a)

============================================================

Part c)

Answer: sqrt(19pi)/pi

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

Work Shown:

r = sqrt(A/pi)
r = sqrt(19/pi)
r = sqrt(19)/sqrt(pi)
r = (sqrt(19)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(19pi)/pi
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gogolik [260]

Answer:

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Step-by-step explanation:

What we have here is as follows;

if there are x 3-cent stamps, then there are 4x 10-cent stamps

So the number of 2-cent stamps is 1 less than 3 cent stamps and that will be x-1 2 cent stamps

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