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Rus_ich [418]
3 years ago
5

The function given by Upper A left parenthesis t right parenthesis equals 0.0265 t cubed minus 0.444 t squared plus 1.774 t plus

8.76A(t)=0.0265t3−0.444t2+1.774t+8.76​, 0 less than or equals t less than or equals 100≤t≤10​, can be used to estimate the​ amount, in billions of​ dollars, invested by large oil companies in exploration for new reserves t years after 19951995. Find the relative extreme​ points, and sketch a graph of the function.

Mathematics
1 answer:
Bogdan [553]3 years ago
8 0
A graphing calculator shows the relative extremes to be
.. (2.606, 10.837) . . . relative maximum
.. (8.564, 8.033) . . . . relative minimum

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In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than on
Kazeer [188]

Answer:

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Step-by-step explanation:

We have to write the transition matrix M for the population.

We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.

We can write the transition matrix, in which the rows are the actual state and the columns are the future state.

- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. <em>Then, the probability of staying in the same state is 90%.</em>

-  For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. <em>Then, the probability of staying in the same state is 80%.</em>

- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. <em>Then, the probability of staying in the same state is 82%.</em>

<em />

The transition matrix becomes:

\begin{vmatrix} &NS&P1&PM\\NS&  0.90&0.08&0.02 \\  P1&0.10&0.80 &0.10 \\  PM& 0.08 &0.10&0.82 \end{vmatrix}

The actual state matrix is

\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right]

We can calculate the next month state by multupling the actual state matrix and the transition matrix:

\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right]

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:

\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right]

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:

\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right]

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

3 0
3 years ago
Zack and Noah jogged 2/5 of a mile and walked another 1/4 of a mile. How far did they go in all?
Basile [38]
Find a common denominator. The lowest one would come from you multiplying 2/5 by 4 on each side and 1/4 by 5 on each side. You are left with 8/20 and 5/20, added together would be 13/20.
3 0
2 years ago
Select the expression that is equal and o (9x+3) - (5x-7)
MArishka [77]

Answer: D

Step-by-step explanation:

4 0
2 years ago
Nikki works at a store that sells consumer electronics. She earns $12 per hour, plus a commission of 5% of her total sales amoun
Mazyrski [523]

Answer:

See below.

Step-by-step explanation:

So, Nikki earns $12 per hour.

And she also earns a 5% or 0.05 commission of her total sales each day.

On Saturday, she worked eight hours and she earned $139. In other words, she earned 8(12) or $96 from working her hours and another $43 (139-96) from her commission.

Thus:

139=96+0.05x

Where x represents Nikki's total sales on Saturday.

Further notes:

To solve, subtract 96 from both sides and divide by 0.05:

139=96+0.05x\\43=0.05x\\x=\$860

Thus, her total sales that day were $860.

6 0
3 years ago
When the sum of 24 and 7 is multiplied by the difference of 18 and six what is the product?
Aloiza [94]
Alright! In order to solve this problem you need to know your keywords:

Sum = To add
Difference = Subtract 
Product = To multiply

So! When it asks for the sum of 24 and 7 you add them:

24 + 7 = 31

The difference of 18 and 6:

18 - 6 = 12

The find the product of these two you simply multiply:

12 x 31 = 372!
8 0
3 years ago
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