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vodomira [7]
3 years ago
7

Which statement best explains whether the table represents a linear or nonlinear function? Input (x) Output (y) 2 5 4 10 6 15 8

20

Mathematics
2 answers:
aniked [119]3 years ago
7 0

Answer:

The table represents a linear function because the rate of change is constant or all the points lie on a straight line.

Step-by-step explanation:

From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).

The slope of the line is

m=\frac{y_2-y_1}{x_2-x_1}=\frac{10-5}{4-2}=\frac{5}{2}

The slope of line is \frac{5}{2}. It means the value of y increased by 5 if the value of x increased by 2.

From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.

Since the rate of change (slope) is same for all points, therefore the table represents a linear function.

If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a  linear function.

shusha [124]3 years ago
4 0
It is linear, because when you graph all the points they are in a straight line. And because you can draw a line straight threw the middle of the points.
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6 0
3 years ago
In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 2.2 2.2​% with a standard deviation of 6.3 6.3​%.
Svet_ta [14]

Answer:

a) 0.625; b) 16.879; c) 8.442

Step-by-step explanation:

Since this is a normal distribution, we want the value of the mean, μ:  2.2; and the value of the standard deviation, σ:  6.3.

For the 40th percentile, we look in a z chart.  We want to find the value as close to 0.40 as we can get; this is 0.4013, and it corresponds to a z score of z = -0.25.

Our formula for a z score is z=\frac{X-\mu}{\sigma}.  Using our values, we have

-0.25 = (X-2.2)/6.3

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6.3(-0.25) = X-2.2

-1.575 = X-2.2

Add 2.2 to each side:

-1.575+2.2 = X-2.2+2.2

0.625 = X

For the 99th percentile, the value in the z chart closest to 0.99 is 0.9901, which corresponds to a z score of z = 2.33:

2.33 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(2.33) = X-2.2

14.679 = X-2.2

Add 2.2 to each side:

14.679+2.2 = X-2.2+2.2

16.879 = X

For the IQR, we find the values for the 75th percentile (Q3) and the 25th percentile (Q1).  The value in a z chart closest to 0.75 is 0.7486, which corresponds to a z score of z = 0.67:

0.67 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(0.67) = X-2.2

4.221 = X-2.2

Add 2.2 to each side:

4.221+2.2 = X-2.2+2.2

6.421 = X

The value in a z chart closest to 0.25 is 0.2514, which corresponds to a z score of z = -0.67:

-0.67 = (X-2.2)/6.3

Multiply both sides by 6.3:

6.3(-0.67) = X-2.2

-4.221 = X-2.2

Add 2.2 to each side:

-4.221+2.2 = X-2.2+2.2

-2.021 = X

This makes the interquartile range

6.421--2.021 = 8.442

8 0
3 years ago
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