Answer:
A. 1, 287 ways
B. 154,440 ways
Step-by-step explanation:
A. We want to choose 5 objects from a total 13, without considering the order in which they are chosen.
The correct way to do this is by using the combination formula since order is not considered;
Thus we have ; 13 C 5 read as 13 combination 5;
Mathematically, n C r is ; n!/(n-r)!r!
Thus, we have ;
13!/(13-8)!8! = 13!/5!8! = 1,287 ways
B. By considering order, we shall be using the permutation formula;
Mathematically n P r = n!/(n-r)!
Read as n permutation r;
Using the numbers involved, we have ; 13 P 5
= 13!/(13-5)! = 13!/8! = 154,440 ways
Answer:
The main reason it was important to study this group was:
1) If Whitehead had found that many people had drunk water from the Broad Street pump and not caught cholera, that would have been evidence against Snow's hypothesis.
Step-by-step explanation:
But Dr. John Snow was able to convince many councillors who ensured that the pump handle was removed from the Broad Street pump. Within a few days of this removal, the cholera epidemic ended. This step proved that Dr. Snow was right from the beginning. The pump handle was the means that the cholera epidemic was being spread from one person to another within Broad Street area, since many usually fetch water from the pump.
Answer: 14.97 per pair of earrings
Step-by-step explanation:
Answer:
160m/s
Step-by-step explanation:
The object can hit the ground when t = a; meaning that s(a) = s(t) = 0
So, 0 = -16a² + 400
16a² = 400
a² = 25
a = √25
a = 5 (positive 5 only because that's the only physical solution)
The instantaneous velocity is
v(a) = lim(t->a) [s(t) - s(a)]/[t-a)
Where s(t) = -16t² + 400
and s(a) = -16a² + 400
v(a) = Lim(t->a) [-16t² + 400 + 16a² - 400]/(t-a)
v(a) = Lim(t->a) (-16t² + 16a²)/(t-a)
v(a) = lim (t->a) -16(t² - a²)(t-a)
v(a) = -16lim t->a (t²-a²)(t-a)
v(a) = -16lim t->a (t-a)(t+a)/(t-a)
v(a) = -16lim t->a (t+a)
But a = t
So, we have
v(a) = -16lim t->a 2a
v(a) = -32lim t->a (a)
v(a) = -32 * 5
v(a) = -160
Velocity = 160m/s
Answer:
![-7ab\sqrt[3]{3ab^2}](https://tex.z-dn.net/?f=-7ab%5Csqrt%5B3%5D%7B3ab%5E2%7D)
Step-by-step explanation:
Remove perfect cubes from under the radical and combine like terms.
![2ab\sqrt[3]{192ab^2}-5\sqrt[3]{81a^4b^5}=2ab\sqrt[3]{4^3\cdot 3ab^2}-5\sqrt[3]{(3ab)^3\cdot 3ab^2}\\\\=(8ab -15ab)\sqrt[3]{3ab^2}=\boxed{-7ab\sqrt[3]{3ab^2} }](https://tex.z-dn.net/?f=2ab%5Csqrt%5B3%5D%7B192ab%5E2%7D-5%5Csqrt%5B3%5D%7B81a%5E4b%5E5%7D%3D2ab%5Csqrt%5B3%5D%7B4%5E3%5Ccdot%203ab%5E2%7D-5%5Csqrt%5B3%5D%7B%283ab%29%5E3%5Ccdot%203ab%5E2%7D%5C%5C%5C%5C%3D%288ab%20-15ab%29%5Csqrt%5B3%5D%7B3ab%5E2%7D%3D%5Cboxed%7B-7ab%5Csqrt%5B3%5D%7B3ab%5E2%7D%20%7D)
