The product of multiple perfect cubes is also a perfect cube.
Proof for two:
n^3 * p^3 = nnnppp = npnpnp = (np)^3
And any integer whose exponent is a multiple of 3 is a perfect cube.
We will use this here:
Prime factorize 3240:
3240 = 405 * 2^3 = 2^3 * 3^4 * 5^1
We need to multiply this by k, to make all the exponents divisible by 3
The exponents not divisible by 3 are 4 and 1.
So let's fix that:
2^3 * 3^4 * 3*2 * 5^1 * 5^2
So, k is 3^2 * 5^2 = 225
(3240*225)^(1/3) = 90
The mode is 1 and the range is 3.22
Answer:
- Hence, 75.52 percent of the u.s. population had internet access in 2005.
- After 25 years or in the year 2015 89% have internet access.
Step-by-step explanation:
the percent p of the u.s. population with internet access is given by:
25 p-34 t=1378
where t is the number of years after 1990.
- We are asked to find what percent of the u.s. population had internet access in 2005 i.e. we need to find the value of p after 15 years i.e. t=15.
⇒ 25p-34×(15)=1378
⇒ 25p-510=1378
⇒ 25p=1378+510
⇒ 25p=1888
⇒ p=75.52
Hence, 75.52 percent of the u.s. population had internet access in 2005.
- Next we are asked to find in what year will 89% have internet access?
i.e. we have to find the value of t when we are given p=89
⇒ 25×89-34t=1378
⇒ 2225-34t=1378
⇒ 2225-1378=34t
⇒ 847=34t
⇒ or 34t=847
⇒ t=24.9112≈25
Hence after 25 years 89% will have internet access.
i.e. in the year 2015 89% will have internet access.
Answer:
23
Step-by-step explanation:
There is one solution, x=2
