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Sladkaya [172]
3 years ago
5

Which system of equations is graphed on this coordinate plane​

Mathematics
1 answer:
Allisa [31]3 years ago
7 0

Answer:

y=(3x/2)+3 and y=(-1x/2)-1

Step-by-step explanation:

So what I did was use rise/run to find the slope of the equation. Let's focus on the line going from the bottom left to the top right corner. For this line, I would start on (-2,0) which is one of the points plotted on your number line and count how much it is away from (0,3). You should get 3 units. After this, count how much it is to the right which is 2 units. Now, use rise/run to find the slope. 3/2, therefore the slope of the line is 3x/2.  Now all we need is the y-int. For the Y int, all we have to do is see where the line touches the Y-axis which in this case is at (0,3). So your y-int would be 3. Now we can use this information to craft an equation in the form y=mx+b, m being the slope and b  being the y int. We should get y=(3x/2)+3. Now repeat this with the other line to find the equation, but be careful!!! It has a negative slope.

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Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:
Vikentia [17]

Answer:

a

   \= x  = 18.5  ,  \sigma =  5.15

b

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c

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Step-by-step explanation:

From the question we are are told that

    The  sample data is  21, 14, 13, 24, 17, 22, 25, 12

     The sample size is  n  = 8

Generally the ample mean is evaluated as

        \= x  =  \frac{\sum x  }{n}

        \= x  =  \frac{  21 + 14 + 13 + 24 + 17 + 22+ 25 + 12  }{8}

         \= x  = 18.5

Generally the standard deviation is mathematically evaluated as

         \sigma =  \sqrt{\frac{\sum (x- \=x )^2}{n}}

\sigma =  \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}

\sigma =  5.15

considering part b

Given that the confidence level is  90% then the significance level is evaluated as

         \alpha  =  100-90

         \alpha  = 10\%

         \alpha  = 0.10

Next we obtain the critical value of  \frac{ \alpha }{2}  from the normal distribution table the value is  

     Z_{\frac{ \alpha }{2} }  =  1.645

The margin of error is mathematically represented as

      E =  Z_{\frac{ \alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

=>    E =1.645  *  \frac{5.15 }{\sqrt{8} }

=>     E =  2.995

The 90% confidence interval is evaluated as

       \= x  -  E < \mu <  \= x +  E

substituting values

       18.5 -  2.995 < \mu <  18.5 +  2.995

       15.505 < \mu <  21.495

considering part c

Given that the confidence level is  95% then the significance level is evaluated as

         \alpha  =  100-95

         \alpha  = 5\%

         \alpha  = 0.05

Next we obtain the critical value of  \frac{ \alpha }{2}  from the normal distribution table the value is  

     Z_{\frac{ \alpha }{2} }  =  1.96

The margin of error is mathematically represented as

      E =  Z_{\frac{ \alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

=>    E =1.96  *  \frac{5.15 }{\sqrt{8} }

=>     E = 3.569

The 95% confidence interval is evaluated as

       \= x  -  E < \mu <  \= x +  E

substituting values

       18.5 - 3.569 < \mu <  18.5 +  3.569

       14.93 < \mu <  22.069

8 0
3 years ago
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