10*3 = 30 feet
30 ft*12 =360 inches
2ft *12 in=24 inches
360 +24 +1=385 inches
the list S describes all possible outcomes of the event.
the fourth option
two will get choosen, and the order matters.
The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.
Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:
- 16 chairs; 24 tables
- Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552
- Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608
- 15 chairs; 18 tables
- Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450
- Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480
- 12 chairs; 28 tables
- Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564
- Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636
- 18 chairs; 20 tables
- Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516
- Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544
Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:
- 15 x 65 + 18 x 90 = X
- 975 + 1,620 = X
- 2,595 = X
Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.
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The value of y from the given trig expression is pi/3 rad
<h3>Trigonometry identity</h3>
These identities are expressed in terms of sine, cosine and tangent
Given the expression
Expand sin(x+y)
sin(x+y) = sinxcosy + cosxsiny
Compare both equations
cosy = 1/2
y = arccos(1/2)
y = 60 degrees
y = pi/3 rad
Hence the value of y from the given trig expression is pi/3 rad
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