Answer:
The average temperature is 
Step-by-step explanation:
From the question we are told that
The temperature of the coffee after time t is ![T(t) = 25 + 72 e^{[-\frac{t}{45} ]}](https://tex.z-dn.net/?f=T%28t%29%20%3D%20%2025%20%2B%2072%20e%5E%7B%5B-%5Cfrac%7Bt%7D%7B45%7D%20%5D%7D)
Now the average temperature during the first 22 minutes i.e fro 
minutes is mathematically evaluated as
![T_{a} = \frac{1}{22-0} \int\limits^{22}_{0} {25 +72 e^{[-\frac{t}{45} ]}} \, dx](https://tex.z-dn.net/?f=T_%7Ba%7D%20%3D%20%20%5Cfrac%7B1%7D%7B22-0%7D%20%20%5Cint%5Climits%5E%7B22%7D_%7B0%7D%20%7B25%20%2B72%20e%5E%7B%5B-%5Cfrac%7Bt%7D%7B45%7D%20%5D%7D%7D%20%5C%2C%20dx)
![T_{a} = \frac{1}{22} [25 t + 72 [\frac{e^{[-\frac{t}{45} ]}}{-\frac{1}{45} } ] ] \left| 22} \atop {0}} \right.](https://tex.z-dn.net/?f=T_%7Ba%7D%20%3D%20%5Cfrac%7B1%7D%7B22%7D%20%5B25%20t%20%20%2B%20%2072%20%5B%5Cfrac%7Be%5E%7B%5B-%5Cfrac%7Bt%7D%7B45%7D%20%5D%7D%7D%7B-%5Cfrac%7B1%7D%7B45%7D%20%7D%20%5D%20%5D%20%5Cleft%7C%2022%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
![T_{a} = \frac{1}{22} [25 t - 3240e^{[-\frac{t}{45} ]} ] \left | 45} \atop {{0}} \right.](https://tex.z-dn.net/?f=T_%7Ba%7D%20%3D%20%5Cfrac%7B1%7D%7B22%7D%20%5B25%20t%20%20-%203240e%5E%7B%5B-%5Cfrac%7Bt%7D%7B45%7D%20%5D%7D%20%5D%20%5Cleft%20%7C%2045%7D%20%5Catop%20%7B%7B0%7D%7D%20%5Cright.)
![T_{a} = \frac{1}{22} [25 (22) - 3240e^{[-\frac{22}{45} ]} - (- 3240e^{0} )]](https://tex.z-dn.net/?f=T_%7Ba%7D%20%3D%20%5Cfrac%7B1%7D%7B22%7D%20%5B25%20%2822%29%20%20-%203240e%5E%7B%5B-%5Cfrac%7B22%7D%7B45%7D%20%5D%7D%20%20%20-%20%28-%203240e%5E%7B0%7D%20%29%5D)
![T_{a} = \frac{1}{22} [550 - 1987.12 + 3240]](https://tex.z-dn.net/?f=T_%7Ba%7D%20%3D%20%5Cfrac%7B1%7D%7B22%7D%20%5B550%20%20-%201987.12%20%20%2B%20%203240%5D)
Answer:
x > 125
Step-by-step explanation:
Multiply both sides of the inequality by 25:
25(x/25) > 25(5)
x > 125
_____
<em>Comment on solving inequalities</em>
In general, you solve these the same way you would an equation. The difference comes when you use an operation that changes ordering. <em>Multiplying or dividing by a negative number</em> does that, for instance.
Consider ...
2 > 1.
Multiply both sides by -1, and it is true only if you reverse the comparison:
-2 < -1
(There are other operations that change ordering, but this is the one you will likely run across most often.)
Answer:
Step-by-step explanation:
Use a distributive property.
<u>Distributive property:</u>
⇒ 6(x-4)=10
<u>First, divide by 6 from both sides.</u>
⇒ 6(x-4)/6=10/6
<u>Solve.</u>
⇒ x-4=5/3
<u>Add by 4 from both sides.</u>
⇒ x-4+4=5/3+4
<u>Solve.</u>
5/3+4
4*3/3+5/3
4*3+5/3
4*3=12
12+5=17
x=17/3
<u>Dividing is another option.</u>
17/3=5.6
<u>x=17/3=5.6</u>
- <u>Therefore, the final answer is x=17=5.6.</u>
I hope this helps you! Let me know if my answer is wrong or not.
Answer:
12.5 miles
Step-by-step explanation:
20 km / 1.6 km = 12.5
Answer: 4200? or 10 because there is a minus sign
Step-by-step explanation:
if we start with the parentheses you can see 4 x 15 = 60 and your subtracting 70 minus 60 so it would be 10
