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4 years ago

Find the X- and y-intercept of the line. 2x + 3y = -18

Mathematics

2 answers:

svetlana [45]4 years ago

6 0

Answer:

x-intercept = -9

y-intercept = -6

Step-by-step explanation:

The equation is

=> 2x+3y = -18

Finding x-intercept

Let's assume y = 0

The equation becomes

=> 2x = -18

Dividing both sides by 2

=> x = -9

Finding y-intercept:

Let's assume x = 0

The equation becomes

=> 3y = -18

Dividing both sides by 3

=> y = -6

Bad White [126]4 years ago

3 0

Answer: x = -9, y = -6

y = mx + b

2x + 3y = -18

Assuming x = 0

2(0) + 3y = -18

y = -6

Assuming y = 0

2x + 3(0) = -18

x = -9

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ale4655 [162]

Answer:

$6.26-2.01\frac{2.47}{\sqrt{50}}=5.56$

$6.26+2.01\frac{2.47}{\sqrt{50}}=6.96$

So on this case the 95% confidence interval would be given by (5.56;6.96)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=6.26$

The sample deviation calculated $s=2.47$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=50-1=49$

Assuming a Confidence of 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that $t_{\alpha/2}=2.01$