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3 years ago

A train can travel at a rate of 85 miler per hour. At this rate, how many hour will it take the train to go 102 miles?

Mathematics

1 answer:

madam [21]3 years ago

5 0

Answer:

The time required is 1.2 hours

Step-by-step explanation:

The formula is

d= rt where d is the distance and r is the rate and t is time

85 miles per hour is the rate and 102 is the distance

102 = 85 miles per hour * t

Divide each side by 85

102/85 = 85t/85

1.2 = t

The time required is 1.2 hours

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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

What is the answer?

sertanlavr [38]

Answer:

A. P(3/4)

Step-by-step explanation:

7 0

3 years ago

Evaluate 62 in mathematics

Whitepunk [10]

Answer:

Step-by-step explanation:

62+7000000= 7000062 however when you divide that by its constant of the root of the sqared denominator, you get 4. THENNNN you add 3 to planks constand to get 62.

8 0

3 years ago

3x + 5y = -19<br> 5x - 2y = 16<br> solve for x and y

beks73 [17]

Step-by-step explanation:

2(3x + 5y = -19)

6x + 10y = -38

5 (5x -2y = 16)

25x - 10y = 80

19x = 42

but idk from there the rest doesn't work Soo if u can find the prob and tell me I'll fix it.

7 0

3 years ago

PLEASE HELP MEEEEeeee

skelet666 [1.2K]

Answer:

D. 2^7

Step-by-step explanation:

2^3 x 2^4 would equal 128. So, if you do the math for all of them:

A isn't correct because it equals 16.

B isn't correct because it equals 4096.

C isn't correct because it equals 16384.

D is correct because 2^7 is 128.

Hope this helped!

7 0

3 years ago

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