Answer:
n + 0.08n
Step-by-step explanation:
The expression that should represent the cost of the sweatshirt involving sales tax is given below
Since it is given that the cost of the sweatshirt be n dollars
And, the sale tax is 8%
So, the expression should be
= n + n × 0.08
= n + 0.08n
Hence, the expression is n + 0.08n
The same would be considered and relevant too
Answer:
? What M? What is impossible?
The <em>linear</em> function y = 3 · w - 1 represents the number of sea shells found in each week.
The speed of the <em>driven</em> gear is 180 rounds per minute.
<h3>How to use direct and inverse relationships to analyze situations</h3>
In the first problem we have an example of <em>linear</em> progression, in which the number of sea shells is increased linearly every week. After a quick analysis, we conclude that the <em>linear</em> function y = 3 · w - 1, a kind of <em>direct</em> relationship.
In the second problem, we must an <em>inverse</em> relationship to determine the speed of the <em>driven</em> gear. Please notice that the speed of the gear is inversely proportional to the number of teeths. Then, we proceed to calculate the speed:
![\frac{v_{1}}{v_{2}} = \frac{N_{2}}{N_{1}}](https://tex.z-dn.net/?f=%5Cfrac%7Bv_%7B1%7D%7D%7Bv_%7B2%7D%7D%20%3D%20%20%5Cfrac%7BN_%7B2%7D%7D%7BN_%7B1%7D%7D)
If we know that
,
and
, then the speed of the driven gear is:
![v_{1} = v_{2}\times \frac{N_{2}}{N_{1}}](https://tex.z-dn.net/?f=v_%7B1%7D%20%3D%20v_%7B2%7D%5Ctimes%20%5Cfrac%7BN_%7B2%7D%7D%7BN_%7B1%7D%7D)
![v_{1} = 60\,rpm \times \frac{60}{20}](https://tex.z-dn.net/?f=v_%7B1%7D%20%3D%2060%5C%2Crpm%20%5Ctimes%20%5Cfrac%7B60%7D%7B20%7D)
![v_{1} = 180\,rpm](https://tex.z-dn.net/?f=v_%7B1%7D%20%3D%20180%5C%2Crpm)
The speed of the <em>driven</em> gear is 180 rounds per minute.
To learn more on inverse relationships: brainly.com/question/4147411
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A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
<h3>How to analyze a radioactive decay case</h3>
Let suppose that element X experiments a <em>simple radioactive</em> decay, that is, that the element X becomes gradually into another less radioactive stable element in time.
We know that decay behaves exponentially and follows this model:
(1)
Where:
- Initial mass, in grams- <em>t</em> - Time, in minutes
- <em>τ</em> - Time constant, in minutes
- <em>m(t)</em> - Current mass, in grams
The time constant can be described in terms of half-life (
), in minutes, through the following expression:
(2)
If we know that
,
and
, then the time needed for the decay is:
<em>τ ≈ 11.541 min</em>
![t = -\tau \cdot \ln \frac{m(t)}{m_{o}}](https://tex.z-dn.net/?f=t%20%3D%20-%5Ctau%20%5Ccdot%20%5Cln%20%5Cfrac%7Bm%28t%29%7D%7Bm_%7Bo%7D%7D)
<em>t ≈ 40.698 min</em>
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
To learn more on radioactive decay, we kindly invite to check this verified question: brainly.com/question/27156663