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svetoff [14.1K]

3 years ago

12

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

udents. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the standard error of the mean? Select one: a. 0.50 b. 6.00 c. 0.25 d. 2.00

1 answer:

vredina [299]3 years ago

4 0

Answer:

a. 0.50

Step-by-step explanation:

The standard error of the mean is the standard deviation of the population divided by the square root of the sample size.

In this problem, we have that:

Standard deviation of the population: 6 hours

Sample size: 144

Square root of 144 is 12.

So the standard error of the sample mean is 6/12 = 0.5.

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Find the area of the composite figure.

Roman55 [17]

Answer:

The Area of the composite figure would be 76.26 in^2

Step-by-step explanation:

<u>According to the Figure Given:</u>

Total Horizontal Distance = 14 in

Length = 6 in

<u>To Find :</u>

The Area of the composite figure

<u>Solution:</u>

Firstly we need to find the area of Rectangular part.

So We know that,

$\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}$

Here, Length is 6 in but the breadth is unknown.

To Find out the breadth, we’ll use this formula:

$\boxed{\rm \: Breadth = total \: distance - Radius}$

According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,

$\longrightarrow\rm \: Length \: of \: the \: circle = Radius$

Since Length = 6 in ;

$\longrightarrow \rm \: 6 \: in = radius$

Hence Radius is 6 in.

So Substitute the value of Total distance and Radius:

Total Horizontal Distance= 14
Radius = 6

$\longrightarrow\rm \: Breadth = 14-6$

$\longrightarrow\rm \: Breadth = 8 \: in$

Hence, the Breadth is 8 in.

Then, Substitute the values of Length and Breadth in the formula of Rectangle :

Length = 6
Breadth = 8

$\longrightarrow\rm \: Area \: of \: Rectangle = 6 \times 8$

$\longrightarrow \rm \: Area \: of \: Rectangle = 48 \: in {}^{2}$

Then, We need to find the area of Quarter circle :

We know that,

$\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}}$

Now Substitute their values:

r = radius = 6
π = 3.14

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4}$

Solve it.

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4}$

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4}$

$\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9$

$\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2}$

Now we can Find out the total Area of composite figure:

We know that,

$\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}$

So Substitute their values:

$\rm Area_{(rectangle)}$ = 48
$\rm Area_{(Quarter Circle)}$ = 28.26

$\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26$

Solve it.

$\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}}$

Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.

$\rule{225pt}{2pt}$

I hope this helps!

3 0

2 years ago

What is 199000/10000 as a decimal?

jek_recluse [69]

Answer:

19.9

Step-by-step explanation:

divide 199000 by 10000

=19.9

6 0

3 years ago

Hi, just asking if anyone can help/show me how to solve this problem.

SVEN [57.7K]

Both angles equal 117 so you put both angle equations together and set them equal to 117 then x= -2

Plug the -2 in for the x in both separate equations to get
M< XYW = 32°
M< WYZ = 85°

8 0

3 years ago

I have to go to a few places but my friend needs help with this specific equation!

Mrac [35]

They are adjacent and x=20

6 0

3 years ago

Read 2 more answers

Subtract the following.Write your answer in standard notation. 15 - 1.3 * 10^-3

ycow [4]

Answer:

The Final Answer would be 14.9987.

Step-by-step explanation:

Given:

$15-1.3\times 10^-3$

We need to Subtract the above number.

Since the larger number is standard Notation form and smaller number is in Scientific notation form

So first we will convert the Scientific notation Number in standard Notation form we get;

$1.3\times 10^-3 = 0.0013$

Now Subtracting the smaller Number from larger number we get;

$15-0.0013 = 14.9987$

Hence The Final Answer would be 14.9987.

5 0

3 years ago