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3 years ago

2) Solve the linear equation 2(3x + 2) = 2x - 1+x

1 answer:

6 0

Solving for x right?
2) 6x + 4 = 3x - 1
6x - 3x = -1 - 4
3x = -5
x = - 5/3

3) x - 9 = 3/5x
5(x-9) = 3x
5x - 45 = 3x
2x = 45
x = 45/2

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What is the slope, y-intercept, and equation of a line given the points (-4, 0) and (1, 5)?

Alex Ar [27]

Answer:

$Slope: 1\\y-Intercept: 4\\Equation: y = x + 4$

Step-by-step explanation:

Given two points, we can find the equation of the line between them with the following:

$y = mx + b\\m = \frac{y_2-y_1}{x_2-x_1}$

First, we can calculate m, or slope

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{5-0}{1-(-4)} = \frac{5}{5} = 1$

Next we can use the top equation and solve for b, the y-intercept

$y = mx + b\\y = x + b\\5 = (1) + b\\b = 4\\\\y = x + 4$

$Slope: 1\\y-Intercept: 4\\Equation: y = x + 4$

3 0

3 years ago

The health of the bear population in a park is monitored by periodic measurements taken from anesthetized bears. A sample of the

Vikki [24]

Answer:

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

Step-by-step explanation:

Assuming the following dataset:

77, 349,417,349, 167 , 225, 265, 360,205

145,335,40,139, 177,108, 163, 202, 22

123,439, 125,135, 86,43, 217,49, 156

119,178, 151, 61, 350, 312, 91, 89,89

We can calculate the sample mean with the followinf formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}= 182.167$

And the sample deviation with:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}=114.05$

The sample size on this case is n =36.

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".

$\bar X=182.167$ represent the sample mean

$\mu$ population mean (variable of interest)

s=114.05 represent the sample standard deviation

n=36 represent the sample size

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

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

The point estimate of the population mean is $\hat \mu = \bar X =182.167$

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

$df=n-1=36-1=35$

Since the Confidence is 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(0.025,35)".And we see that $t_{\alpha/2}=2.03$