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Flura [38]
3 years ago
14

Help. Please. Thank You.

Mathematics
1 answer:
GenaCL600 [577]3 years ago
3 0

Answer:

(A)\ a=-6;b=4\\\\ (B)\ a=6;b=-4

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+c

Where "m" is the slope and "c" is the y-intercept.

By definition:

1. If the lines of the System of equations are parallel (whrn they have the same slope), the system has No solutions.

2. If the they are the same exact line, the System of equations has Infinite solutions.

(A) Let's solve for "y" from the first equation:

3x-2y=-1\\\\-2y=-3x-1\\\\y=\frac{3}{2}x+\frac{1}{2}

You can notice that:

m=\frac{3}{2}\\\\c=\frac{1}{2}

In order make that the System has No solutions, the slopes must be the same, but the y-intercept must not. Then, the values of "a" and "b" can be:

a=-6\\\\b=4

Substituting those values into the second equation and solving for "y", you get:

-6x+4y=-2\\\\4y=6x-2\\\\y=\frac{6}{4}x-{2}{4}\\\\y=\frac{3}{2}x-\frac{1}{2}

You can idenfity that:

m=\frac{3}{2}\\\\c=-\frac{1}{2}

Therefore, they are parallel.

(B) In order make that the System has Infinite solutions, the slopes and the y-intercepts of both equations must be the same. Then, the values of "a" and "b" can be:

a=6\\\\b=-4

If you substitute those values into the second equation and then you solve for "y", you get:

6x+(-4y)=-2\\\\-4y=-6x-2\\\\y=\frac{-6}{-4}x-\frac{2}{-4}\\\\y=\frac{3}{2}x+\frac{1}{2}

You can identify that:

m=\frac{3}{2}\\\\b=\frac{1}{2}

Therefore, they are the same line.

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Answer:

(x-2)^2+(y+3)^2=4

Step-by-step explanation:

  • A circle's equation consist on the following expression: (x-a)^2+(y-b)^2=r^2, where r is the magnitude of the radio, and (a,b) are the coordenates of the center of the circle.
  • In this case, a=2 and b= - 3, because the circle is centered in (x,y)=(2, - 3).
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5 0
3 years ago
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An environmental scientist wants to use a 95% confidence interval to estimate the mean number of hours per day her solar panel r
MissTica

Answer:

a) The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

b) The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

Step-by-step explanation:

We have the standard deviation for the sample. So we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 48 - 1 = 47

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 47 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.0117

The margin of error is:

M = T*s = 2.0117*2.3 = 4.6

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7.1 - 4.6 = 2.5 hours of sunlight per day

The upper end of the interval is the sample mean added to M. So it is 7.1 + 4.6 = 11.7 hours of sunlight per day

a) Compute the 95% confidence interval for the mean.

The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

b) Explain your confidence interval from part (a) in context.

The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

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<h3><u>✽</u></h3>

➶ Hope This Helps You!

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