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3 years ago

Find the slope of a line through the points (0,0) and (2, 9). Round your

Mathematics

1 answer:

den301095 [7]3 years ago

3 0

Answer:

Slope = 4.5

Step-by-step explanation:

We need to find the slope of a line through the points (0,0) and (2, 9).

We know that, the slope of a line is given by :

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have, x₁ = 0, x₂ = 2, y₁ = 0 and y₂ = 9

Put all the values,

$m=\dfrac{9-0}{2-0}\\\\m=4.5$

So, the slope of the line is 4.5.

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Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below.

garik1379 [7]

Answer:

The 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

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".

$\bar X_1 =9.2$ represent the sample mean 1

$\bar X_2 =8.8$ represent the sample mean 2

n1=27 represent the sample 1 size

n2=30 represent the sample 2 size

$\sigma_1 =0.3$ population standard deviation for sample 1

$\sigma_2 =0.1$ population standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =9.2-8.8=0.4$

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: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$0.4-1.96\sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}=0.281$

$0.4+1.96\sqrt{\frac{6^2}{36}+\frac{7^}{49}}=0.519$

So on this case the 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

6 0

3 years ago

The additive invers of the numer <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B7%7D%20" id="TexFormula1" title=" \fr

GuDViN [60]

Answer:

$-\frac{3}{7}$

Step-by-step explanation:

The additive inverse of a number (its "opposite") is what you add to the given number to get a sum of zero.

$\frac{3}{7} + (-\frac{3}{7}) =0$

6 0

3 years ago

How do I simplify fractions and decimals?

Mila [183]

Answer:

Divide both the numerator and denominator by the largest number that divides evenly into both to simplify the fraction

In the example, divide 2 by 2, which equals 1, and divide 20 by 2, which equals 10. This leaves 1/10, which is the simplified form of the fraction with a decimal.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Which of the following employees has the greatest total employee compensation?

Elina [12.6K]

We have to choose the correct answer which of the employees has the greatest total employee compensation. We just have to subtract the job expenses from total job benefits for everyone of them. A: $49,200 - $300 = $38,900. B : $49,500 - $500 = $49,000. C : $49,800 - $700 = $41,100. D : $50,100 - $900 = $49,200. The largest sum is $49,200 ( employee D ) . Answer: The greatest total employee compensation has Employee D<span>.</span>

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3 years ago

Read 2 more answers

What is 7 8/13 rounded to the nearest whole number?

vfiekz [6]

Answer: The answer would be 8.

Step-by-step explanation: I'm going to assume you mean 7 8/13 is a mixed fraction. So you multiply the denominator, 13, multiply 7 to that, then add 8 to it and the denominator would be the same as before. That should give you 99/13. When you divide, you get around 7.6, rounding closest to 8.

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3 years ago