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Illusion [34]
2 years ago
7

Given that 110ₓ = 40₅ , find the value of x.

Mathematics
1 answer:
MrRa [10]2 years ago
3 0

Answer:

x = 4

Step-by-step explanation:

110ₓ = 40₅    --------- change all to base ten.

<u>the system called binary</u>

1x²+1x ¹+0x⁰ = 45¹+0*5⁰

x² + x + 0 = 20

x² + x – 20 = 0

solve x using Quadratic equation

        -1 ± \sqrt{1^2 - 4* 1 (-20)}

x =  ------------------------------------

                        2 * 1

x = -5;  x = 4

therefore, x = 4

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A closet contains n pairs of shoes. If 2r shoes are chosen at random, (where 2r &lt; n), what is the probability that there will
Pie
We are choosing 2
2
r
shoes. How many ways are there to avoid a pair? The pairs represented in our sample can be chosen in (2)
(
n
2
r
)
ways. From each chosen pair, we can choose the left shoe or the right shoe. There are 22
2
2
r
ways to do this. So of the (22)
(
2
n
2
r
)
equally likely ways to choose 2
2
r
shoes, (2)22
(
n
2
r
)
2
2
r
are "favourable."

Another way: A perhaps more natural way to attack the problem is to imagine choosing the shoes one at a time. The probability that the second shoe chosen does not match the first is 2−22−1
2
n
−
2
2
n
−
1
. Given that this has happened, the probability the next shoe does not match either of the first two is 2−42−2
2
n
−
4
2
n
−
2
. Given that there is no match so far, the probability the next shoe does not match any of the first three is 2−62−3
2
n
−
6
2
n
−
3
. Continue. We get a product, which looks a little nicer if we start it with the term 22
2
n
2
n
. So an answer is
22⋅2−22−1⋅2−42−2⋅2−62−3⋯2−4+22−2+1.
2
n
2
n
⋅
2
n
−
2
2
n
−
1
⋅
2
n
−
4
2
n
−
2
⋅
2
n
−
6
2
n
−
3
⋯
2
n
−
4
r
+
2
2
n
−
2
r
+
1
.
This can be expressed more compactly in various ways.
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