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3 years ago

Please help

Mathematics

2 answers:

shtirl [24]3 years ago

4 0

I think the answer is for A the explanation is that x represent the amount of time or second that you spend in an elevator and y represent the numbers of floors that the building have.

Deffense [45]3 years ago

3 0

(0,20) The elevator is on floor 20 at time = 0 ( the time you enter the lift)

(20,0) you have descended to ground floor( 0) and it has taken 20 seconds to get there.

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What is the square root of 8

miss Akunina [59]

Answer:

2.82842712475

Step-by-step explanation:

did this help you

4 0

3 years ago

Read 2 more answers

A circle has an area of 200.96 units2 and a circumference of 50.24 units. If the radius is 8 units, what can be said about the r

AleksandrR [38]

Answer:

C. The ratio of the area to the circumference is equal to half the radius.

Step-by-step explanation:

The area of a circle can be written as;

Area A = πr^2

The circumference of a circle is;

Circumference C = 2πr

Using the formula, w can derive the relationship between the two variables.

A = kC

k = A/C

Substituting the two formulas;

k = (πr^2)/(2πr) = r/2

So,

A = (r/2)C

A/C = r/2

The ratio of the area to the circumference is equal to half the radius.

Given;

Area = 200.96

Circumference = 50.24

Radius = 8

To confirm;

k = r/2 = 8/2 = 4

Also,

A/C = 200.96/50.24

A/C = 4

6 0

3 years ago

. A triangle has side lengths of 8, 7, and 14. To the nearest tenth of a degree find the measure of the angle opposite the side

4vir4ik [10]

Given:

The measure of three sides of a triangle are 8, 7 and 14.

To find:

The measure of the angle opposite the side of length 8.

Solution:

According to the Law of Cosine:

$\cos A=\dfrac{b^2+c^2-a^2}{2bc}$

Let a=8, b=7 and c=14, then by using Law of Cosine, we get

$\cos A=\dfrac{7^2+14^2-8^2}{2(7)(14)}$

$\cos A=\dfrac{49+196-64}{196}$

$\cos A=\dfrac{181}{196}$

Taking cos inverse on both sides.

$A=\cos^{-1}\dfrac{181}{196}$

$A=22.561328$

$A\approx 22.6$

Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.

7 0

3 years ago

Need help with 8-9.

ANTONII [103]

So it is 5cm to 1m or 5cm to 1000cm
So the scale is the ratio which is 5:1000. this can be reduced to 1:200

10. if the room is 15cm on one side I can say that the ratio to actual size is 15/x. and scale is 1/200 so:
15/x = 1/200
3000 = x is one side

other side:
20/x = 1/200
4000 = x

7 0

3 years ago

Let $$X_1, X_2, ...X_n$$ be uniformly distributed on the interval 0 to a. Recall that the maximum likelihood estimator of a is $

Solnce55 [7]

Answer:

a) $\hat a = max(X_i)$

For this case the value for $\hat a$ is always smaller than the value of a, assuming $X_i \sim Unif[0,a]$ So then for this case it cannot be unbiased because an unbiased estimator satisfy this property:

$E(a) - a= 0$ and that's not our case.

b) $E(\hat a) - a= \frac{na}{n+1} - a = \frac{na -an -a}{n+1}= \frac{-a}{n+1}$

Since is a negative value we can conclude that underestimate the real value a.

$\lim_{ n \to\infty} -\frac{1}{n+1}= 0$

c) $P(Y \leq y) = P(max(X_i) \leq y) = P(X_1 \leq y, X_2 \leq y, ..., X_n\leq y)$

And assuming independence we have this:

$P(Y \leq y) = P(X_1 \leq y) P(X_2 \leq y) .... P(X_n \leq y) = [P(X_1 \leq y)]^n = (\frac{y}{a})^n$

$f_Y (Y) = n (\frac{y}{a})^{n-1} * \frac{1}{a}= \frac{n}{a^n} y^{n-1} , y \in [0,a]$

e) On this case we see that the estimator $\hat a_1$ is better than $\hat a_2$ and the reason why is because:

$V(\hat a_1) > V(\hat a_2)$

$\frac{a^2}{3n}> \frac{a^2}{n(n+2)}$

$n(n+2) = n^2 + 2n > n +2n = 3n$ and that's satisfied for n>1.

Step-by-step explanation:

Part a

For this case we are assuming $X_1, X_2 , ..., X_n \sim U(0,a)$

And we are are ssuming the following estimator:

$\hat a = max(X_i)$

$E(a) - a= 0$ and that's not our case.

Part b

For this case we assume that the estimator is given by:

$E(\hat a) = \frac{na}{n+1}$

And using the definition of bias we have this:

$E(\hat a) - a= \frac{na}{n+1} - a = \frac{na -an -a}{n+1}= \frac{-a}{n+1}$

Since is a negative value we can conclude that underestimate the real value a.

And when we take the limit when n tend to infinity we got that the bias tend to 0.

$\lim_{ n \to\infty} -\frac{1}{n+1}= 0$

Part c

For this case we the followng random variable $Y = max (X_i)$ and we can find the cumulative distribution function like this:

$P(Y \leq y) = P(max(X_i) \leq y) = P(X_1 \leq y, X_2 \leq y, ..., X_n\leq y)$

And assuming independence we have this:

$P(Y \leq y) = P(X_1 \leq y) P(X_2 \leq y) .... P(X_n \leq y) = [P(X_1 \leq y)]^n = (\frac{y}{a})^n$

Since all the random variables have the same distribution.

Now we can find the density function derivating the distribution function like this:

$f_Y (Y) = n (\frac{y}{a})^{n-1} * \frac{1}{a}= \frac{n}{a^n} y^{n-1} , y \in [0,a]$

Now we can find the expected value for the random variable Y and we got this:

$E(Y) = \int_{0}^a \frac{n}{a^n} y^n dy = \frac{n}{a^n} \frac{a^{n+1}}{n+1}= \frac{an}{n+1}$

And the bias is given by:

$E(Y)-a=\frac{an}{n+1} -a=\frac{an-an-a}{n+1}= -\frac{a}{n+1}$

And again since the bias is not 0 we have a biased estimator.

Part e

For this case we have two estimators with the following variances:

$V(\hat a_1) = \frac{a^2}{3n}$

$V(\hat a_2) = \frac{a^2}{n(n+2)}$

On this case we see that the estimator $\hat a_1$ is better than $\hat a_2$ and the reason why is because:

$V(\hat a_1) > V(\hat a_2)$

$\frac{a^2}{3n}> \frac{a^2}{n(n+2)}$

$n(n+2) = n^2 + 2n > n +2n = 3n$ and that's satisfied for n>1.

8 0

3 years ago