To know how many gumballs will fit in the machine, the
volume of the minature and the machine should be calculated. Volume of sphere:
V = (4/3) pi* r^3
Volume of the machine r = 6 in
V = (4/3) pi* 6^3 = 904.77 in3
Volume of the miniature gumballs
V = (4/3) pi* (1/3)^3 = 0.1551 in3
Divide the two volume to get the number of gumballs that can
fill the machine
904.77 in3/ 0.1551 in3 = 5832
<span> </span>
Answer:
x=-2 y=0
Step-by-step explanation:
put the second equation in to the first one
-2x+x+2=4
-x=2
x=-2
y=-2+2=0
x=-2 y=0
Answer:
x<7/12
Step-by-step explanation:
Subtract 1/4 from both sides and since we are not dividing, the '<' wouldn't change its direction
Hope this helps! :)
324/(95+85)=1.8 It will take 1 hour and 48 minutes
Answer:
The age of the spear head to the nearest year is 1845 years
Step-by-step explanation:
We know that
half life time of C-14 is 5730 years
so, h=5730
we can use formula
![P(t)=P_0(\frac{1}{2})^{\frac{t}{h} }](https://tex.z-dn.net/?f=P%28t%29%3DP_0%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7Bh%7D%20%7D)
now, we can plug value
![P(t)=P_0(\frac{1}{2})^{\frac{t}{5730} }](https://tex.z-dn.net/?f=P%28t%29%3DP_0%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B5730%7D%20%7D)
an archaeologist in turkey discovers a spear head that contains 80% of its original amount of C-14
so,
![P(t)=0.80P_0](https://tex.z-dn.net/?f=P%28t%29%3D0.80P_0)
we can plug it
![0.80P_0=P_0(\frac{1}{2})^{\frac{t}{5730} }](https://tex.z-dn.net/?f=0.80P_0%3DP_0%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B5730%7D%20%7D)
now, we can solve for t
![0.80=(\frac{1}{2})^{\frac{t}{5730} }](https://tex.z-dn.net/?f=0.80%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B5730%7D%20%7D)
![\ln \left(0.8\right)=\ln \left(\left(\frac{1}{2}\right)^{\frac{t}{5730}}\right)](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%280.8%5Cright%29%3D%5Cln%20%5Cleft%28%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B%5Cfrac%7Bt%7D%7B5730%7D%7D%5Cright%29)
![t=-\frac{5730\ln \left(0.8\right)}{\ln \left(2\right)}](https://tex.z-dn.net/?f=t%3D-%5Cfrac%7B5730%5Cln%20%5Cleft%280.8%5Cright%29%7D%7B%5Cln%20%5Cleft%282%5Cright%29%7D)
![t=1844.647](https://tex.z-dn.net/?f=t%3D1844.647)
So,
The age of the spear head to the nearest year is 1845 years