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DedPeter [7]
3 years ago
14

the sides of a rectangle are 25 cm and 8 cm. what is the measure, to the nearest degree, of the angle formed by the short side a

nd a diagonal of the rectangle?

Mathematics
1 answer:
ycow [4]3 years ago
8 0

Answer:

72°

Step-by-step explanation:

The lengths 25 cm and 8 cm are the sides of the rectangle.

See the attached diagram of rectangle ABCD.

Now, let us assume the diagonal AC makes x° angle with the shorter side BC i.e.∠ BCA = x°

So, using trigonometry we can write

\tan x = \frac{AB}{BC} = \frac{25}{8} = 3.123

⇒ x = \tan ^{-1} (3.125) = 72.25 degrees ≈ 72 degrees {Rounded to nearest degree} (Answer)

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Step-by-step explanation:

Step-by-step explanation:

From the question  we are told that

Sample size 100  

Instructor    Number of Failures  

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Prof. D         16

Confidence level= 0.95

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  Proportion\ of\ Failure\ P=\frac{Number\ of\ Failure\ N}{Sample\ size\ S}

  P=\frac{N}{S}

For Prof A

    P_A=\frac{N_A}{S}

    P_A=\frac{13}{100}

    P_A=0.13

For Prof B

    P_B=\frac{N_B}{S}

   P_B=\frac{0}{100}

    P_B=0

For Prof C

    P_C=\frac{N_C}{S}

    P_C=\frac{11}{100}

   P_C=0.11

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   P_D=\frac{16}{100}

   P_D=0.16

Generally the average proportional failure is mathematically given as

    P_a_v_g=\frac{0.13+0+0.11+0.16}{4}

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Therefore  having this we calculate for the control limits

Generally the upper control limit UCl is mathematically given as

Upper control limits:

  UCL =P_a_v_g +Z\sqrt{\frac{P_a_v_g(1-P_a_v_g) }{S} }

  UCL =0.1 +1.96\sqrt{\frac{0.1(1-0.1) }{100}}

  UCL =0.1 +1.96*0.03

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Generally the upper control limit UCl is mathematically given as

Lower limit control limits:

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  UCL =0.1 -1.96*0.03

  UCL =0.1 -0.0588

  UCL =0.0412

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