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Vesna [10]
3 years ago
11

Find the 98th term for the arithmetic sequence 3,4.2,5.4,6.6,7.8,...

Mathematics
1 answer:
prisoha [69]3 years ago
6 0
A₁ = 3
a₂ = 4.2

d = a₂ - a₁
   = 4.2 - 3
   = 1.2

a₉₈ = a₁ + d(n-1)
      = 3 + 1.2(98-1)
      = 3 + 1.2×97
      = 3 + 116.4
      = 119.4
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The snack shop makes 3 mixes of nuts in the following proportions.
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Answer:

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B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}

Step-by-step explanation:

It is given that the snack shop makes 3 mixes of nuts in the following proportions.

Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.

Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.

Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.

they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.

We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.

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peanuts             6                  5                    3

cashews            2                  3                    4

pecans              2                   2                    2

A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}

B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}

The product of both matrices is

AB=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}

AB=\begin{bmatrix}6\cdot \:25+5\cdot \:18+3\cdot \:35\\ 2\cdot \:25+3\cdot \:18+4\cdot \:35\\ 2\cdot \:25+2\cdot \:18+3\cdot \:35\end{bmatrix}

AB=\begin{bmatrix}345\\ 244\\ 191\end{bmatrix}

Therefore matrix AB gives the total number of lbs of each nut required to fill the order.

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Answer:

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<u>Given </u><u>:</u><u>-</u><u> </u>

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→ Cost = $ 0.22 × 6

→ Cost = $ 1.32

<h3>Hence the cost of an order of sticks is $ 1.32 </h3>
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