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LekaFEV [45]
3 years ago
15

A wheel is rotating at 3 radians/sec, and the wheel has a 42-inch diameter. To the nearest foot per minute, what is the linear s

peed of a point on the rim?
Mathematics
1 answer:
Yuki888 [10]3 years ago
3 0

A point on the rim would travel a distance equal to the circumference of the wheel. The wheel has diameter 42 in, so the circumference is 42π in.

2π radians corresponds to one complete revolution of the wheel. So the wheel has a linear speed of

(3 rad/s) * (42π/2π in/rad) = 63 in/s

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in this case, the given line has a slope 4, which is 4/1, so the perpendicular line has a slope/gradient -\frac{1}{4}
5 0
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5/8 of the staff are male. 5/12 of the staff works part time at the aquarium. What is the fraction of the staff being a female?
mestny [16]

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Step-by-step explanation:

5/8 of the staff are male.  The entire staff is represented by the fraction 8/8.  Taking 5/8 from this, what we have left is

8/8-5/8 = 3/8 of the staff are female.

5 0
3 years ago
What are the x and y-intercepts of the line described by this equation? -6x+3y=18.9?
Naddika [18.5K]

The "x" intercept is found when you plug in "0" for "y"
  -6x + 3(0) = 18.9
        -6x = 18.9  (Divide both sides by -6)
           x = - 3.15
           (-3.15, 0)  is your x-intercept

Now plug in "0" for the x
-6(0) + 3y = 18.9
          3y = 18.9  (Divide both sides by 3)
                y = 6.3
               (0, 6.3) is your y - intercept






































5 0
3 years ago
A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and
mr Goodwill [35]

Answer:

Bias for the estimator = -0.56

Mean Square Error for the estimator = 6.6311

Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

\mu = \frac{3X_{1} + 4X_{2}  }{8}

Now

Bias for the estimator = E(μ bar) - μ

                                    = E( \frac{3X_{1} + 4X_{2}  }{8}) - 4.5

                                    = \frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5

                                    = \frac{3(4.5) + 4(4.5)}{8} - 4.5

                                    = \frac{13.5 + 18}{8} - 4.5

                                    = \frac{31.5}{8} - 4.5

                                    = 3.9375 - 4.5

                                    = - 0.5625 ≈ -0.56

∴ we get

Bias for the estimator = -0.56

Now,

Mean Square Error for the estimator = E[(μ bar - μ)²]

                                                             = Var(μ bar) + [Bias(μ bar, μ)]²

                                                             = Var( \frac{3X_{1} + 4X_{2}  }{8}) + 0.3136

                                                             = \frac{1}{64} Var( {3X_{1} + 4X_{2}  }) + 0.3136

                                                             = \frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})]  }) + 0.3136

                                                             = \frac{1}{64} [{3(57.76) + 4(57.76)}]  } + 0.3136

                                                             = \frac{1}{64} [7(57.76)}]  } + 0.3136

                                                             = \frac{1}{64} [404.32]  } + 0.3136

                                                             = 6.3175 + 0.3136

                                                              = 6.6311

∴ we get

Mean Square Error for the estimator = 6.6311

6 0
3 years ago
PLZ PLZ HELP ASAP!!!PLZ PLZ HELP ASAP!!!PLZ PLZ HELP ASAP!!!PLZ PLZ HELP ASAP!!!PLZ PLZ HELP ASAP!!!PLZ PLZ HELP ASAP!!!PLZ PLZ
juin [17]

Answer:

<em>the answer is K for #9</em>

Step-by-step explanation:

6 0
3 years ago
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