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Ber [7]
3 years ago
7

g In R simulate a sample of size 20 from a normal distribution with mean µ = 50 and standard deviation σ = 6. Hint: Use rnorm(20

,50,6) to get one random sample of size 20. Determine the mean and standard deviation from this sample, compare these with the population mean and standard deviation.
Mathematics
1 answer:
Illusion [34]3 years ago
5 0

Answer:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

Step-by-step explanation:

For this case first we need to create the sample of size 20 for the following distribution:

X\sim N(\mu = 50, \sigma =6)

And we can use the following code: rnorm(20,50,6) and we got this output:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

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. The London Eye is a popular tourist attraction in London, England and is one of the largest Ferris Wheels in the world. It has
astra-53 [7]

Answer:

y=-67.5[cos(\frac{\pi}{15}t)-1]

Step-by-step explanation:

We can start solving this problem by doing a drawing of London Eye. (See attached picture).

From the picture, we can see that the tourists will start at the lowest point of the trajectory, which means we can make use of a -cos function. So the function will have the following shape:

y=-Acos(\omega t)+b

where:

A=amplitude

\omega = angular speed.

t= time (in minutes)

b= vertical shift.

In this case:

A= radius = 67.5 m

\omega=2\pi f

where the frequency is the number of revolutions it takes every minute, in this case:

f=\frac{1}{30} rev/min

so:

\omega=2\pi (\frac{1}{30})

\omega=\frac{\pi}{15} rad/min

and

b= radius, so

b=A

b=67.5m

so we can now build our equation:

y=-67.5cos(\frac{\pi}{15} t)+67.5

which can be factored to:

y=-67.5[cos(\frac{\pi}{15}t)-1]

You can see a graph of what the function looks like in the end on the attached picture.

3 0
3 years ago
How do I do this?’
Ostrovityanka [42]

Answer:

1,2,3,4,5,6,7,8,9,10,11,12

Step-by-step explanation:

hehhehe easy

5 0
3 years ago
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Help pls look at the picture
Alika [10]

Answer:

Option A: -\frac{4}{3} is the correct answer.

Step-by-step explanation:

Given that:

Slope of the line = \frac{3}{4}

Let,

m be the slope of the line perpendicular to the line with slope \frac{3}{4}

We know that,

The product of slopes of two perpendicular lines is equals to -1.

Therefore,

\frac{3}{4}.m=-1\\

Multiplying both sides by \frac{4}{3}

\frac{4}{3}*\frac{3}{4}m=-1*\frac{4}{3}\\

m = -\frac{4}{3}

-\frac{4}{3} is the slope of the line perpendicular to the line having slope \frac{3}{4}

Hence,

Option A: -\frac{4}{3} is the correct answer.

3 0
3 years ago
A square has 4 sides of equal length. If a diagonal of the square is 5 2 , what is the length of each side?
ivanzaharov [21]
5 .... Hope it helps, have a good rest of the day:)
8 0
3 years ago
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A store holiday sale has an item marked down by $10 with an additional discount of 25% off the
ValentinkaMS [17]

Answer:

C : $58.36

Step-by-step explanation:

Given:

A store holiday sale has an item marked down by $10.

Discount on new price = 25%

Final price was $36.27.

Question asked:

what was the original ?

Solution:

Let original price = x

New price = x - 10

Original price - marked down amount - discount amount = $36.27

x - 10 -25\% of(x - 10 ) = 36.27\\

x - 10 - \frac{25}{100} (x - 10) = 36.27\\x - 10 - 0.25(x - 10) = 36.27\\x - 10 -0.25x +2.5 = 36.27\\0.75x - 7.5 = 36.27\\

Adding both side by 7.5

0.75x = 43.77\\

Dividing both side by 0.75

x = 58.36

Therefore, the original price was $58.36

5 0
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