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3 years ago

Diameter is 22.5m. Calculate the area (round your answer to 2 decimal places). Use 3.14 for Pi.

Mathematics

1 answer:

Tamiku [17]3 years ago

7 0

Answer:

because r=d/2 it will be

22.5/2=r

r=11.25m

c=2×3.14×11.25

c=70.65msquare

c=7065/1oo

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Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 40% chan

azamat

Answer:

There are a 25% probability that Christine fails the course.

Step-by-step explanation:

We have these following probabilities:

A 50% probability that Christine finds a tutor.

With a tutor, she has a 10% probability of failling.

A 50% probability that Christine does not find a tutor.

Without a tutor, she has a 40% probability of failing.

Probability that she fails:

10% of 50%(fail with a tutor) plus 40% of 50%(fail without a tutor). So

$P = 0.1*0.5 + 0.4*0.5 = 0.25$

There are a 25% probability that Christine fails the course.

6 0

3 years ago

How many solutions are there to the following system of equations?

sweet [91]

$4x-8y=0 \\
\underline{-3x+8y=-7} \\
4x-3x=0-7 \\
x=-7 \\ \\
4x-8y=0 \\
4 \times (-7)-8y=0 \\
-28-8y=0 \\
-8y=28 \\
y=\frac{28}{-8} \\
y=-\frac{7}{2} \\ \\
 \left \{ {{x=-7} \atop {y=-\frac{7}{2}}} \right.$

There is one solution to this system of equations. The answer is B.

6 0

3 years ago

Read 2 more answers

Find the value of (-1/2)³

Evgen [1.6K]

Answer:

-1/8

Step-by-step explanation:

(-1/2) ^3

(-1/2)(-1/2)(-1/2)

-1/8

6 0

2 years ago

7) -6x + 6y=6<br> -6x + 3y=-12

Gre4nikov [31]

Answer:

(5,6)

Step-by-step explanation:

-6x+6y=6

-6x + 3y =-12

Multiply the first equation by -1

6x-6y=-6

Add this to the second equation

6x-6y=-6

-6x + 3y =-12

---------------------

-3y = -18

Divide each side by -3

-3y/-3 = -18/-3

y =6

Now we need to find x

6x - 6y = -6

6x -6(6) = -6

6x -36 = -6

Add 36 to each side

6x-36+36 = -6+36

6x = 30

Divide each side by 6

6x/6 = 30/6

x =5

3 0

3 years ago

Let X1,X2......X7 denote a random sample from a population having mean μ and variance σ. Consider the following estimators of μ:

Viefleur [7K]

Answer:

a) In order to check if an estimator is unbiased we need to check this condition:

$E(\theta) = \mu$

And we can find the expected value of each estimator like this:

$E(\theta_1 ) = \frac{1}{7} E(X_1 +X_2 +... +X_7) = \frac{1}{7} [E(X_1) +E(X_2) +....+E(X_7)]= \frac{1}{7} 7\mu= \mu$

So then we conclude that $\theta_1$ is unbiased.

For the second estimator we have this:

$E(\theta_2) = \frac{1}{2} [2E(X_1) -E(X_3) +E(X_5)]=\frac{1}{2} [2\mu -\mu +\mu] = \frac{1}{2} [2\mu]= \mu$

And then we conclude that $\theta_2$ is unbiaed too.

b) For this case first we need to find the variance of each estimator:

$Var(\theta_1) = \frac{1}{49} (Var(X_1) +...+Var(X_7))= \frac{1}{49} (7\sigma^2) = \frac{\sigma^2}{7}$

And for the second estimator we have this:

$Var(\theta_2) = \frac{1}{4} (4\sigma^2 -\sigma^2 +\sigma^2)= \frac{1}{4} (4\sigma^2)= \sigma^2$

And the relative efficiency is given by:

$RE= \frac{Var(\theta_1)}{Var(\theta_2)}=\frac{\frac{\sigma^2}{7}}{\sigma^2}= \frac{1}{7}$

Step-by-step explanation:

For this case we assume that we have a random sample given by: $X_1, X_2,....,X_7$ and each $X_i \sim N (\mu, \sigma)$

Part a

In order to check if an estimator is unbiased we need to check this condition:

$E(\theta) = \mu$

And we can find the expected value of each estimator like this:

$E(\theta_1 ) = \frac{1}{7} E(X_1 +X_2 +... +X_7) = \frac{1}{7} [E(X_1) +E(X_2) +....+E(X_7)]= \frac{1}{7} 7\mu= \mu$

So then we conclude that $\theta_1$ is unbiased.

For the second estimator we have this:

$E(\theta_2) = \frac{1}{2} [2E(X_1) -E(X_3) +E(X_5)]=\frac{1}{2} [2\mu -\mu +\mu] = \frac{1}{2} [2\mu]= \mu$

And then we conclude that $\theta_2$ is unbiaed too.

Part b

For this case first we need to find the variance of each estimator:

$Var(\theta_1) = \frac{1}{49} (Var(X_1) +...+Var(X_7))= \frac{1}{49} (7\sigma^2) = \frac{\sigma^2}{7}$

And for the second estimator we have this:

$Var(\theta_2) = \frac{1}{4} (4\sigma^2 -\sigma^2 +\sigma^2)= \frac{1}{4} (4\sigma^2)= \sigma^2$

And the relative efficiency is given by:

$RE= \frac{Var(\theta_1)}{Var(\theta_2)}=\frac{\frac{\sigma^2}{7}}{\sigma^2}= \frac{1}{7}$

5 0

3 years ago

Diameter is 22.5m. Calculate the area (round your answer to 2 decimal places). Use 3.14 for Pi.​

Diameter is 22.5m. Calculate the area (round your answer to 2 decimal places). Use 3.14 for Pi.