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Alchen [17]
3 years ago
7

A linear equation that passes through (-6,-5) and parallel to 2x-3y=12

Mathematics
1 answer:
kumpel [21]3 years ago
6 0

Answer:

y= 2/3x-1

Step-by-step explanation:

The general formula for linear graph is y=mx + c. Let's convert the equation of the parallel line to be same as the formula:

2x-3y= 12

-3y= 12 -2x

y= 2/3x-4

Parallel lines won't ever be met because a couple of parallel lines will have the same slope(m). We know how much m is (m=2/3), then we just need to find c. We can do it by adding the value of the coordinate that the line pass (-6, -5). The calculation will be:

y=mx + c

-5= (2/3) (-6) + c

c= -5 +4

c= -1

The equation will be:

y=mx + c

y= 2/3x-1

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https://newsela.com/read/lib-ushistory-roman-republic/id/27389/

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2 years ago
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Answer and Explanation:

Given : The random variable x has the following probability distribution.

To find :

a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

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d. Calculate the standard deviation of x.

Solution :

First we create the table as per requirements,

x      P(x)         xP(x)           x²            x²P(x)

0    0.25           0               0                0

1     0.20        0.20             1              0.20

2    0.15          0.3               4             0.6

3    0.30         0.9               9             2.7

4    0.10          0.4               16             1.6

   ∑P(x)=1     ∑xP(x)=1.8               ∑x²P(x)=5.1

a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.

\sum P(X)=0.25+0.20+0.15+0.30+0.10

\sum P(X)=1

Yes it is a probability distribution.

b) The expected value of x is defined as

E(x)=\sum xP(x)=1.8

c) The variance of x is defined as

V=\sum x^2P(x)-(\sum xP(x))^2\\V=5.1-(1.8)^2\\V=5.1-3.24\\V=1.86

d) The standard deviation of x is  defined as

\sigma=\sqrt{V}

\sigma=\sqrt{1.86}

\sigma=1.136

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