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Dmitry [639]
3 years ago
7

Given: ∠6≅∠7 Prove: ∠5≅∠8

Mathematics
1 answer:
RideAnS [48]3 years ago
4 0

Answer:

Step-by-step explanation:

angle 6 ang angle 7 congruent (equal to ) because they are alternate interior angles and alternate interior angles are always equal.

angle 6 and angle 5 are congruent(equal to )  because they are vertically opposite angles and vertically opposite angles are always equal.

angle 7 and angle 8 are congrunt (equal ) because they are veritically opposite angles angd vertically opposite angles are always equal.

angle 5 and angle 8 are congruent(equal ) because they are alternate exterior angles and alternate exterior angles are also always equal.

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The null and alternative hypotheses are given. Determine whether the hypothesis test is​ left-tailed, right-tailed, or​ two-tail
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Answer:  The parametric is being tested here is "p" (population proportion).

The hypothesis test is​ left-tailed.

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H_0:\ p=0.2\\\\H_1:\ p

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Since the alternative hypotheses is left-tailed, so the hypothesis test is​ left-tailed.

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A furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requir
miskamm [114]

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.

Learn more in brainly.com/question/14728529

8 0
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