Answer:
The model for the temperature of the drink can be written as
Step-by-step explanation:
For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.
We can model that in this way
If we rearrange and integrate
We know that at time 0, the temperature of the drink was 52°F. Then we have:
We also know that at t=2, T=55°F
The model for the temperature of the drink can be written as
if the diameter of a circle is 15, its radius is half that or 7.5.
![\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=7.5 \end{cases} A=\pi (7.5)^2\implies A=56.25\pi \implies \stackrel{\pi =3.14}{A=176.625}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D7.5%20%5Cend%7Bcases%7D%20A%3D%5Cpi%20%287.5%29%5E2%5Cimplies%20A%3D56.25%5Cpi%20%5Cimplies%20%5Cstackrel%7B%5Cpi%20%3D3.14%7D%7BA%3D176.625%7D%20)
Answer:
a=2 and b=2...............
Answer:
a) 2.5
b) 6.25
Step-by-step explanation:
For similar figures, the ratio of any corresponding linear dimensions is the same. The ratio of areas is the square of that.
<h3>Application</h3>
The ratio of linear dimensions, larger to smaller, is ...
(30 yd)/(12 yd) = 2.5
<h3>a) Perimeter</h3>
Perimeter is a linear dimension, the sum of side lengths. The ratio of perimeters is 2.5.
<h3>b) Area</h3>
The ratio of areas, larger to smaller, is the square of the scale factor for side lengths:
(2.5)² = 6.25
The ratio of the areas of the larger to smaller figure is 6.25.
Answer:
Probability of a sample that contains exactly two defective parts is .0037 or .37%
Step-by-step explanation:
As we know if P is the probability of achieving k results in n trials then probability formula is P = 
In this formula n = number of trials
k = number of success
(n-k) = number of failures
p = probability of success in one trial
q = (1-p) = probability of failure in one trial
In this sum n = 5
k = 2
number failures (n-k) = (5-2) = 3
p = 2% which can be written as .02
q = 98% Which can be written as .98
Now putting these values in the formula
P = 
P = 
= 5×4×3×2×1/3×2×1×2×1
= 5×2 =10
P = 10×(.02)²×(.98)³
= .0037 or .37%
