The youth group is going on a trip to the state fair. The trip costs $63. Included in that price is $13 for a concert ticket and
1 answer:
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Answer:
[a,b] divides n
Step-by-step explanation:
Let us denote the least common multiple of a and b [a,b]=m.
We want to prove that m divides n, where n is a multiple of a and b.
We suppose m does not divide n, then by the Division Theorem, there exists q and r integers such that:
(1) ... n=mq+r, where 0<r<m
As n is a multiple of a and b, there exists s and t integers such that:
sa=n and tb=n
Same thing happens to m as it is the least common multiple, there exists u and v such that:
ua=m and vb=m
So (1) has the following form:
n=mq+r ⇒ sa=uaq+r ⇒sa-uaq=r⇒(s-uq)a=r and
n=mq+r ⇒ tb=vbq+r ⇒ tb-vbq=r⇒ (t-vq)b=r
So r is a multiple of a and b, but r<m which is a contradiction as, m is the least common multiple of a and b. So this concludes the proof.
So this means that is and integer.
As m= vb, then is an integer, lets say
=v; and as m=ua, then
=u.
So v=
=a, so
divides a; on the other hand,
u=
=b, so
divides b. From this we can conclude that
is a common divisor of a and b.
Answer:
7 / 16
Step-by-step explanation:
Sample space is attached below :
Theoretical Probability of any event A
P(A) = (number of required outcome / Total number of possible outcomes)
Required outcome = sum greater than 7 = 14
Total number of possible outcomes = 32
P(sum greater than 7) = 14 / 32
P(sum greater than 7) = 7 / 16
Answer:
The probability that no more than more than 11 of them need correction for their eyesight is 0.00512
No, 11 is not a significantly low low number of adults requiring eyesight correction .
Step-by-step explanation:
A survey showed that 77% of adults need correction for their eyesight.
If 22 adults are randomly selected, find the probability that no more than more than 11 of them need correction for their eyesight.
n =22
p = 0.77
q = 1-p = 1- 0.77=0.23
We are supposed to find
Formula :
Using calculator
So, The probability that no more than more than 11 of them need correction for their eyesight is 0.00512
No, 11 is not a significantly low low number of adults requiring eyesight correction .
Answer:
Step-by-step explanation:
An <em>inverse</em> function is any function that "undoes" another function. If we think of the function as some kind of machine that takes in a number
as input and produces a number
as an output, when we give inverse function
the number
as in input, we get
, our original input, as the output
We need a function that undoes , and the natural choice for undoing an exponent is with a logarithm. Here, our base is
, so we'll choose
as our inverse function. Let's see how that works:
is the power we have to raise
to to get
, which is
, so
And we have our function.