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daser333 [38]
2 years ago
5

If points (7,a), (-5,2) and (3,6) are collinear, find a.

Mathematics
1 answer:
uysha [10]2 years ago
7 0

Answer:

The value of a is 8

Step-by-step explanation:

If the three lines are collinear, they all lie on the same line

So let us have the equation of a line that passes through the known ends

the slope will be;

m = (6-2)/(3 + 5) = 4/8 = 1/2

The general form is;

y = mx + b

so, we have

y = 1/2x + b

To get b, we use any of the two known points

6 = 3/2 + b

b = 6-3/2

b = (12-3)/2 = 9/2

So the equation of the line is;

y = 1/2x + 9/2

Multiply through by 2

2y = x + 9

So for the point , to get a , we have that

2(a) = 7 + 9

2a = 16

a = 16/2

a = 8

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Identify the outliers of the data set. Then determine if the outlier increases or decreases the value of the mean.
Juli2301 [7.4K]
<h3>Answer:  D) 76; increases</h3>

========================================================

Explanation:

The main group or cluster of values spans from 32 to 42 (inclusive).

Then off on its own is the value 76, which we consider an outlier. This value is fairly far from the group. As a rule, large outliers pull on the arithmetic mean to make it larger than it should be. Think of it like the outlier pulling on the mean as if it was done through a magnet or gravitational pull.

Similarly, small outliers pull the mean to the left to make it smaller than it should be. We don't have any small outliers in this case.

--------------

Let's consider the set

A = {32, 34, 35, 36, 37, 38, 38, 41, 42, 42, 46}

where I've sorted the values and I replaced 76 with 46.

Computing the mean of set A gets us

(32+34+35+36+37+38+38+41+42+42+46)/11 = 38.27 approximately

--------------

Now let's form this set

B = {32, 34, 35, 36, 37, 38, 38, 41, 42, 42, 76}

which is the original set your teacher gave you. It's nearly identical to set A, except that the 46 is now 76 again.

Compute the mean of set B

(32+34+35+36+37+38+38+41+42+42+76)/11 = 41

---------------

Set A has a mean of roughly 38.72 and set B has a mean of 41. We see that the mean has increased.

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