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evablogger [386]
3 years ago
10

What are some abundant numbers

Mathematics
1 answer:
topjm [15]3 years ago
3 0
An abundant number, sometimes also called an excessive number, is a positive integer n for which
s(n)=sigma(n)-n>n,
(1)
where sigma(n) is the divisor function and s(n) is the restricted divisor function. The quantity sigma(n)-2n is sometimes called the abundance.
A number which is abundant but for which all its proper divisors are deficient is called a primitive abundant number (Guy 1994, p. 46).
The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... (OEIS A005101).
Every positive integer n with (mod n)60 is abundant. Any multiple of a perfect number or an abundant number is also abundant. Prime numbers are not abundant. Every number greater than 20161 can be expressed as a sum of two abundant numbers.
There are only 21 abundant numbers less than 100, and they are all even. The first odd abundant number is
945=3^3·7·5.
(2)
That 945 is abundant can be seen by computing
s(945)=975>945.
(3)
AbundantNumberDensity
Define the density function
A(x)=lim_(n->infty)(|{k<=n:sigma(k)>=xk}|)/n
(4)
(correcting the expression in Finch 2003, p. 126) for a positive real number x where |B| gives the cardinal number of the set B, then Davenport (1933) proved that A(x) exists and is continuous for all x, and Erdős (1934) gave a simplified proof (Finch 2003). The special case A(2) then gives the asymptotic density of abundant numbers,
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Factor 3h2 – 11h - 42
Zina [86]
The answer is D
3*-42=-126
The factors of -126 that add to -11 are 7 and -18
replace -11h with 7h-18h
3h^2 + 7h - 18h - 42
Factor the first two terms and last two terms
h(3h+7) - 6(3h+7)
See how the two parentheses are the same?
THE ANSWER IS BELOW!!
(h-6)(3h+7)
the first parentheses has the terms that were outside, and the second has the original bracketed terms
This matches option D (it just multiplies the terms backwards, which gives the same result)
7 0
3 years ago
Read 2 more answers
What is the equation of the graph below?°
MAVERICK [17]

Answer:

the first formula

Step-by-step explanation:

the graph is y=cosx and cosx=sin(x+90)

8 0
3 years ago
M is proportional to the cube of r. when r=3m,m=216.when r=5 find the value of m
klio [65]

Answer:

The value of m is 1000 for r=5

Step-by-step explanation:

Given that m is proportional to the cube of r

It can be written as:

m \propto\ r^3

When the proportionality symbol is removed a proportionality constant is introduced in the equation.

Let k be the proportionality constant

m = kr^3

Given

r=3,m=216

Putting the values

216 = k(3)^3\\216 = k * 27\\k = \frac{216}{27}\\k = 8

The equation will now become

m = 8r^3

Putting r = 5

m = 8(5)^3\\m = 8 * 125\\m = 1000

Hence,

The value of m is 1000 for r=5

7 0
3 years ago
"four times the difference of a number and 9 is -30"
lesantik [10]

Answer:

4 * (x-9)=-30

not sure if u want it solved but if u do its x=6/4

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
14 + 10y ≥ 3(y + 14) <br> A. y ≥ –4<br>B. y ≥ 4 <br>C. y ≥ 8<br>D. y ≥ 6
arsen [322]

Answer:

B

Step-by-step explanation:

Given

14 + 10y ≥ 3( y + 14) ← distribute

14 + 10y ≥ 3y + 42 ( subtract 3y from both sides )

14 + 7y ≥ 42 ( subtract 14 from both sides )

7y ≥ 28 ( divide both sides by 7 )

y ≥ 4 → B

7 0
3 years ago
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