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3 years ago

What is the exact circumference of the circle?

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

3 0

Answer:C

Step-by-step explanation:The circumference is measured by the diameter times pi which equals 3.141592653.....etc...

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On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeding drivers. Assu

LuckyWell [14K]

Answer:

a) $\lambda = 0.0666$

b) 48.62% probability of a waiting time less than 10 minutes between successive speeders

c) 18.92% probability of a waiting time in excess of 25 minutes between successive speeders

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

(a) Calculate the rate parameter λ.

Mean of 15 minutes. So

$\lambda = \mu = \frac{1}{15} = 0.0666$

(b) What is the probability of a waiting time less than 10 minutes between successive speeders?

$P(X \leq 10) = 1 - e^{-0.0666*10} = 0.4862$

48.62% probability of a waiting time less than 10 minutes between successive speeders

(c) What is the probability of a waiting time in excess of 25 minutes between successive speeders?

Either the waiting time is 25 or less, or it is in excess of 25 minutes. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 25) + P(X > 25) = 1$

We want P(X > 25). So

$P(X > 25) = 1 - P(X \leq 25) = 1 - (1 - e^{-0.0666*25}) = 0.1892$

18.92% probability of a waiting time in excess of 25 minutes between successive speeders

6 0

3 years ago

The production manager is going to present this information to the company's board of directors. Which graph should the manager

viktelen [127]

To best emphasize the number of defects. Manager should use graph 3 (refer the image shown):

If we talk about graph 1, it can also be used but usually we put the time line on the horizontal axis, for the convenience and the quantity to be measured on the y-axis. In the graph 1, the time is placed on the vertical axis (x-axis) so it would not be a good pick for the manager.

Same is the case with graph 2 again we have time on the vertical axis. So it is not a good idea to with graph 2.

Graph 3 could be the best to emphasize the number of defects because first of all time is placed on the horizontal axis and the quantity to be shown is on the vertical axis. Secondly, the range of the vertical axis is less so it is easy to observe the data set on the graph quite distinctively. Therefore, graph 3 is the best pick.

Graph 4 is placed correctly in terms of vertical and horizontal axes but the range of vertical axis is quite high due to which the dispersion or the display of the data is quite compressed and it gets hard to visualize.

3 0

4 years ago

Read 2 more answers

Nico has 3 1/2 yards of fabric.He used 2/3 yard to make a pillow cover and 1/3 yard to make a scarf.How much fabric does Nico ha

snow_tiger [21]

Answer:

2 1/2

Step-by-step explanation:

2/3 + 1/3 =1

3 1/2-1=2 1/2

8 0

3 years ago

Read 2 more answers

What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5 cents per kilowatt-hour?

Airida [17]

5 0

3 years ago

I don’t understand, HELPPP

goldenfox [79]

$\frac{-6xy^{3}z^5}{-36x^{2}y^{2}z^4}$

First cross out the -6 and -36. Six will go into 6 one time and 6 will go into -36 six times so we have the following after crossing out.

$\frac{-6xy^{3}z^5}{-36x^{2}y^{2}z^4}$
$\frac{xy^{3}z^5}{6x^{2}y^{2}z^4}$ <---After crossing out

Next cross out the x / x^2 which will give us the following:
$\frac{xy^{3}z^5}{6x^{2}y^{2}z^4}$
$\frac{y^{3}z^5}{6xy^{2}z^4}$ <---After crossing out

Now cross out the y^2 / y^3
$\frac{y^{3}z^5}{6xy^{2}z^4}$
$\frac{yz^5}{6xz^4}$ <----After crossing out

All that is left is to cross out the z^5 / z^4 and we are done.
$\frac{yz^5}{6xz^4}$
$\frac{yz}{6x}$ <----After crossing out and we are done.

$\frac{-6xy^{3}z^5}{-36x^{2}y^{2}z^4} = \frac{yz}{6x}$

8 0

3 years ago