How many different four-digit numbers can be made using the digits 1,2,3,4,5,6 if no digit can be used more than once?
1 answer:
Answer:
360
Step-by-step explanation:
The given digits are 1,2,3,4,5,6.
So, total number of digits = 6.
We need to find the number of different ways to form four-digit numbers using the digits, without repetition.
Total ways for first place = 6
After selecting 1 digit the number of remaining digits is 5. So,
Total ways for second place = 5
Similarly,
Total ways for third place = 4
Total ways for forth place = 3
Total number of ways =
Therefore, 360 four digit numbers are possible.
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Answer:
d.
Step-by-step explanation:
The goal of course is to solve for x. Right now there are 2 of them, one on each side of the equals sign, and they are both in exponential positions. We have to get them out of that position. The way we do that is by taking the natural log of both sides. The power rule then says we can move the exponents down in front.
becomes, after following the power rule:
x ln(2) = (x + 1) ln(3). We will distribute on the right side to get
x ln(2) = x ln(3) + 1 ln(3). The goal is to solve for x, so we will get both of them on the same side:
x ln(2) - x ln(3) = ln(3). We can now factor out the common x on the left to get:
x(ln2 - ln3) = ln3. The rule that "undoes" that division is the quotient rule backwards. Before that was a subtraction problem it was a division, so we put it back that way and get:
. We can factor out the ln from the left to simplify a bit:
. Divide both sides by ln(2/3) to get the x all alone:
On your calculator, you will find that this is approximately -2.709
A hexagon has 6 even corners that are connected evenly as shown.
