Answer:
<h2>The circumference is multipled by 4.</h2>
Step-by-step explanation:
The formula of an area of a circle"
![A=\pi r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
The formula of a circumference of a circle:
![C=2\pi r](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r)
The area multipled by 16:
![16A=16\pi r^2\\\\16A=\pi(4^2r^2)\\\\16A=\pi(4r)^2](https://tex.z-dn.net/?f=16A%3D16%5Cpi%20r%5E2%5C%5C%5C%5C16A%3D%5Cpi%284%5E2r%5E2%29%5C%5C%5C%5C16A%3D%5Cpi%284r%29%5E2)
The radius has increased fourfold, therefore:
![C'=2\pi(4r)=4(2\pi r)=4C](https://tex.z-dn.net/?f=C%27%3D2%5Cpi%284r%29%3D4%282%5Cpi%20r%29%3D4C)
The circumference is multipled by 4.
You can calculate the area and check the circumference:
![r=11.6\ in\\\\A=\pi(11.6)^2=132.56\pi\\\\16A=(16)(134.56\pi)=2152.96\pi\ in^2](https://tex.z-dn.net/?f=r%3D11.6%5C%20in%5C%5C%5C%5CA%3D%5Cpi%2811.6%29%5E2%3D132.56%5Cpi%5C%5C%5C%5C16A%3D%2816%29%28134.56%5Cpi%29%3D2152.96%5Cpi%5C%20in%5E2)
Calculate the radius:
<em>divide both sides by π</em>
![r^2=2152.96\to r=\sqrt{2152.96}\\\\r=46.4\ in](https://tex.z-dn.net/?f=r%5E2%3D2152.96%5Cto%20r%3D%5Csqrt%7B2152.96%7D%5C%5C%5C%5Cr%3D46.4%5C%20in)
Calculate the circumference of both circles:
![r=11.6\ in\\\\C=2\pi(11.6)=23.2\pi\ in](https://tex.z-dn.net/?f=r%3D11.6%5C%20in%5C%5C%5C%5CC%3D2%5Cpi%2811.6%29%3D23.2%5Cpi%5C%20in)
![r=46.4\ in\\\\C'=2\pi(46.4)=92.8\pi\ in](https://tex.z-dn.net/?f=r%3D46.4%5C%20in%5C%5C%5C%5CC%27%3D2%5Cpi%2846.4%29%3D92.8%5Cpi%5C%20in)
![\dfrac{C'}{C}=\dfrac{92.8\pi}{23.2\pi}=4\to C'=4C](https://tex.z-dn.net/?f=%5Cdfrac%7BC%27%7D%7BC%7D%3D%5Cdfrac%7B92.8%5Cpi%7D%7B23.2%5Cpi%7D%3D4%5Cto%20C%27%3D4C)
Answer: The car travels 97.5 miles in 1.5 hour.
Step-by-step explanation:
Given: A car is traveling down a highway at a constant speed, described by the equation , described by the equation
, where represents the distance, in miles, that the car travels at this speed in<em> t</em> hours.
To find : Number of miles car travel in 1.5 hour.
Simply put t= 1.5 in the given expression , we get
65(1.5)= 97.5
That means , the car travels 97.5 miles in 1.5 hour.
Answer:
C. One can be 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66
Step-by-step explanation:
Given that the confidence interval is a term that defines a range of values with the probability to contain a population value that has an actual degree of confidence.
This is represented in a situation where population means falls in between upper and lower intervals.
Hence, in this case, the correct interpretation is option C: One can be 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66
Answer:
log (16)=2 in base 3x-5
==>16=2^(3x-5)
==>2^4=2^(3x-5)
==>4=3x-5
==>3x=9
==>x=3
Step-by-step explanation: