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Hope this helps
Answer:
1 1/6
Step-by-step explanation:
2 2/3 = 2+2/3
1 1/2 = 1+1/2
So (2 2/3) - (1 1/2)=2+2/3-(1+1/2)=
2+2/3-1-1/2=1+(2/3-1/2)=1+(4-3)/6=1+1/6=
1 1/6
Answer:
Muscle strength is the ability to exert a maximal amount of force for a short period of time. ... Muscle endurance is the ability to do something over and over for an extended period of time without getting tired. In the gym, that may be doing 50 body weight squats in a row, moving to a rhythm.
Answer:
![P(t) = 100e^{0.0251t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7B0.0251t%7D)
The doubling time is of 27.65 minutes.
Step-by-step explanation:
Exponential equation of growth:
The exponential equation for population growth is given by:
![P(t) = P(0)e^{kt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Bkt%7D)
In which P(0) is the initial value and k is the growth rate.
A freshly inoculated bacterial culture of Streptococcus contains 100 cells.
This means that
. So
![P(t) = 100e^{kt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7Bkt%7D)
When the culture is checked 60 minutes later, it is determined that there are 450 cells present.
This means that
, and we use this to find k. So
![450 = 100e^{60k}](https://tex.z-dn.net/?f=450%20%3D%20100e%5E%7B60k%7D)
![e^{60k} = 4.5](https://tex.z-dn.net/?f=e%5E%7B60k%7D%20%3D%204.5)
![\ln{e^{60k}} = \ln{4.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B60k%7D%7D%20%3D%20%5Cln%7B4.5%7D)
![60k = \ln{4.5}](https://tex.z-dn.net/?f=60k%20%3D%20%5Cln%7B4.5%7D)
![k = \frac{\ln{4.5}}{60}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B%5Cln%7B4.5%7D%7D%7B60%7D)
![k = 0.0251](https://tex.z-dn.net/?f=k%20%3D%200.0251)
So
![P(t) = 100e^{0.0251t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7B0.0251t%7D)
Doubling time:
This is t for which P(t) = 2P(0) = 200. So
![200 = 100e^{0.0251t}](https://tex.z-dn.net/?f=200%20%3D%20100e%5E%7B0.0251t%7D)
![e^{0.0251t} = 2](https://tex.z-dn.net/?f=e%5E%7B0.0251t%7D%20%3D%202)
![\ln{e^{0.0251t}} = \ln{2}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B0.0251t%7D%7D%20%3D%20%5Cln%7B2%7D)
![0.0251t = \ln{2}](https://tex.z-dn.net/?f=0.0251t%20%3D%20%5Cln%7B2%7D)
![t = \frac{\ln{2}}{0.0251}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Cln%7B2%7D%7D%7B0.0251%7D)
![t = 27.65](https://tex.z-dn.net/?f=t%20%3D%2027.65)
The doubling time is of 27.65 minutes.
Answer:
m∠OPQ + (2x+16)° = 180°
Step-by-step explanation:
You need to know a couple of things about quadrilaterals.
- The sum of the internal angles is 360°
- Opposite angles of an inscribed quadrilateral total 180°.
An inscribed quadrilateral is one that has its vertices on a circle, as in the given figure.
__
To actually solve the figure (find the measures of the angles), a two-step process is involved. First, you must find the value of x. You do that by making use of the fact that angles O and Q total 180°.
After you know the value of x, you can figure the measure of angle R, and make use of the fact that angles R and P total 180°.
__
Here, you're not asked to solve the figure. Instead, you're asked how you might find angle P. You do that as described in the previous paragraph:
m∠OPQ + m∠ORQ = 180° . . . . . . . angles R and P total 180°
m∠OPQ + (2x+16)° = 180° . . . . . . . substitute (2x+16)° for m∠ORQ
This matches the first answer choice.