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Leya [2.2K]
3 years ago
10

Consider the following set of sample data.

Mathematics
1 answer:
sergij07 [2.7K]3 years ago
3 0
Consider the following set of sample data.

21 29 32 38 38 45 50 64 72 100

For the given data, the mean is 48.9, the median is 41.5, and the mode is 38.

Suppose the observation 21 in the data is mistakenly recorded as 2 instead of 21. For the sample with this error, the mean is 47, the median is 41.5, and the mode is 38.

Suppose the value 21 in the original sample is inadvertently removed from the sample. For the sample with this value removed, the mean is 52, the median is 45, and the mode is 38.
You might be interested in
Whst is 15 divided by 6 2/3 equals
PolarNik [594]
First you make 15 a fraction by putting it over 1.
Then you make 6 2/3 a mixed fraction.
To do this, you multiply 6 with 3 and add 2 to it. Then you put the number over 3.
We get
6 X 3 = 18
18 +2 = 20
20/3

Now, we divide 15/1 with 20/3.
When we divide it, we actually cross multiply it. Basically, we flip the fraction and multiply it.

So we get 15/1 X 3/20 = \frac{15 X 3}{1 X 20}.

We get 45/20 which can be simplified to 9/5 which can be simplified to 2  1/4.

So the answer is 9/4 or 2  1/4.
5 0
3 years ago
Read 2 more answers
Jeremiah plans on building a 5 meter long garden walkway that is paved with square stones that measure LaTeX: \frac{5}{6}5 6 met
yan [13]

Answer:

Example 1

A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4th side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length

L.

In a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable,

W, to represent the side of fencing parallel to the 4th side or backyard fence.

Since we know we only have 80 feet of fence available, we know that

L + W + L = 80, or more simply, 2L + W = 80. This allows us to represent the width, W, in terms of L: W = 80 – 2L

Now we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so

A = LW = L(80 – 2L)

A(L) = 80L – 2L2

This formula represents the area of the fence in terms of the variable length

L.

Example 2

Returning to our backyard farmer from the beginning of the section, what dimensions should she make her garden to maximize the enclosed area?

Earlier we determined the area she could enclose with 80 feet of fencing on three sides was given by the equation

A(L) = 80L – 2L2. Notice that quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

In finding the vertex, we take care since the equation is not written in standard polynomial form with decreasing powers. But we know that

a is the coefficient on the squared term, so a = -2, b = 80, and c = 0.

Finding the vertex:

h

=

−

80

2

(

−

2

)

=

20

,

k

=

A

(

20

)

=

80

(

20

)

−

2

(

20

)

2

=

800

The maximum value of the function is an area of 800 square feet, which occurs when

L = 20 feet. When the shorter sides are 20 feet, that leaves 40 feet of fencing for the longer side. To maximize the area, she should enclose the garden so the two shorter sides have length 20 feet, and the longer side parallel to the existing fence has length 40 feet.

Example 3

A ball is thrown upwards from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation

H(t) = –16t2 + 80t + 40.

What is the maximum height of the ball?

When does the ball hit the ground?

To find the maximum height of the ball, we would need to know the vertex of the quadratic.

h

=

−

80

2

(

−

16

)

=

80

32

=

5

2

,

k

=

H

(

5

2

)

=

−

16

(

5

2

)

2

+

80

(

5

2

)

+

40

=

140

The ball reaches a maximum height of 140 feet after 2.5 seconds.

To find when the ball hits the ground, we need to determine when the height is zero—when

H(t) = 0. While we could do this using the transformation form of the quadratic, we can also use the quadratic formula:

t

=

−

80

±

√

80

2

−

4

(

−

16

)

(

40

)

2

(

−

16

)

=

−

80

s

q

r

t

8960

−

32

Since the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions:

t

=

−

80

−

s

q

r

t

8960

−

32

a

p

p

r

o

x

5.458

The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds.Step-by-step explanation:

8 0
3 years ago
The graph shows the profit per month for the 10 months during which Swanson's Restaurant has been open. Which is a valid predict
Scrat [10]

Answer:

about $4,000 - $6,000

Step-by-step explanation:

4 0
3 years ago
X 1 2 3 4<br> y 5 10 15 20<br><br><br> What's the constant?
DiKsa [7]

<u>Answer:</u>

x ---> 1

y ---> 5

<u>Step-by-step explanation:</u>

We are given paired values for two variables x and y and we are to determine the constant number by which each term is increased such that they are in a proportional relationship.

For x, we have the following paired values:

x: 1, 2, 3, 4

So here the difference between each consecutive term is 1 so the constant is 1.

And for y, we have:

y: 5, 10, 15, 20

In this case, the difference between each consecutive term is 5 so the constant is 5.

3 0
3 years ago
Look at the following figure. Copy the cross onto another piece of paper. Then, cut apart the four pieces labeled A, B, C, and D
kozerog [31]

Answer:

C should slot on top of A.

Then D should slot in next to C of the left.

Lastly B should be beneath D and on the left of A.

Hope that makes sense.

3 0
3 years ago
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