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jasenka [17]
3 years ago
13

Write an equation of the line in slope-intercept form that passes through (-3,5) and is perpendicular to y = -3x- 1

Mathematics
1 answer:
inna [77]3 years ago
6 0

9514 1404 393

Answer:

  y = 1/3x +6

Step-by-step explanation:

The slope of the given line is the coefficient of x, -3. The slope of the perpendicular line will be the opposite reciprocal of that:

  -1/(-3) = 1/3

The point-slope equation is then ...

  y -k = m(x -h) . . . . . for line of slope m through point (h, k)

Here, we have m = 1/3, (h, k) = (-3, 5), so the point-slope equation is ...

  y -5 = 1/3(x +3)

  y = 1/3x + 1 + 5 . . . . eliminate parentheses, add 5

  y = 1/3x +6 . . . . slope-intercept equation of the line

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Wholemark is an internet order business that sells one popular New Year greeting card once a year. The cost of the paper on the
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Answer:

The optimal production quantity is 9,322 cards.

Step-by-step explanation:

The information provided is:

Cost of the paper = $0.05 per card

Cost of printing = $0.15 per card

Selling price = $2.15 per card

Number of region (n) = 4

Mean demand = 2000

Standard deviation = 500

Compute the total cost per card as follows:

Total cost per card = Cost of the paper + Cost of printing

                                = $0.05 + $0.15

                                = $0.20

Compute the total demand as follows:

Total demand = Mean × n

                       = 2000 × 4

                       = 8000

Compute the standard deviation of total demand as follows:

SD_{\text{total demand}}=\sqrt{500^{2}\times 4}=1000

Compute the profit earned per card as follows:

Profit = Selling Price - Total Cost Price

         = $2.15 - $0.20

         = $1.95

The loss incurred per card is:

Loss = Total Cost Price = $0.20

Compute the optimal probability as follows:

\text{Optimal probability}=\frac{\text{Profit}}{\text{Profit+Loss}}

                               =\frac{1.95}{1.95+0.20}\\\\=\frac{1.95}{2.15}\\\\=0.9069767\\\\\approx 0.907

Use Excel's NORMSINV{0.907} function to find the Z-score.

<em>z</em> = 1.322

Compute the optimal production quantity for the card as follows:

\text{Optimal Production Quantity}=\text{Total Demand}+(z\times SD_{\text{total demand}}) \\

                                               =8000+(1.322\times 1000)\\=8000+1322\\=9322

Thus, the optimal production quantity is 9,322 cards.

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Answer:

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Step-by-step explanation:

They are not the same shape. Thus, you cannot use a rigid transformation to get from A to B

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