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2 years ago

Which variable will you choose to eliminate? How?

Mathematics

1 answer:

Inga [223]2 years ago

4 0

Answer:

Variable elimination

8x+3y=-7
3y=-8x-7
y=-8/3x-7/3

Now plug it into y
7x-16/3x-14/3=-3
5/3x-14/3=-3
5/3x=5/3
x=1

You might be interested in

The average monthly cell phone bill was reported to be $50.07 by the U.S. Wireless Industry. Random Sampling of a large cell pho

zalisa [80]

Answer:

The null and alternative hypotheses are:

$H_{0}:\mu= 50.07$

$H_{a}:\mu>50.07$

Under the null hypothesis, the test statistic is:

$t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}} }$

Where:

$\bar{x} = 52.86$ is the sample mean

$s=7.0132$ is the sample standard deviation

$n=10$ is the sample size

$\therefore t=\frac{52.86-50.07}{\frac{7.0132}{\sqrt{10}} }$

$=1.26$

Now, the right tailed t critical value at 0.05 significance level for df = n-1 = 10-1 = 9 is:

$t_{critical}=1.833$

Since the t statistic is less than the t critical value at 0.05 significance level, therefore,we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the average phone bill has increased.

4 0

3 years ago

Estimate the minimum and maximum ages for typical textbooks currently used in college courses, then use the range rule of thumb

Maksim231197 [3]

Answer:

$n=(\frac{1.64(4)}{0.25})^2 =688.537 \approx 689$

So the answer for this case would be n=689 rounded up to the nearest integer

Step-by-step explanation:

Assuming this complete question: "Suppose that the minimum and maximum ages for typical textbooks currently used in college courses are 0 and 8 years. Use the range rule of thumb to estimate the standard deviation.

Estimate the minimum and maximum ages for typical textbooks currently used in college courses, then use the range rule of thumb to estimate the standard deviation. Next, find the size of the sample required to estimate the mean age (in years) of textbooks currently used in college courses. Use a 90% confidence level and assume that the sample mean will be in error by no more than 0.25 year."

Solution for the problem

First we need ti find the estimation for the standard deviation using the Rule of thumb, with the following formula:

$s \approx \frac{R}{4}$

Where R is the range defined as :

$R = Max - Min = 8-0 = 8$

So then the deviation would be approximately:

$s \approx 4$

Important 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 (ME) 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".

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that $ME =\pm 0.25$ and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (2)

We can assume that the estimator for the population deviation from the rule of thumb is $\hat \sigma = s= 4$

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05;0;1)", and we got $z_{\alpha/2}=1.64$ , replacing into formula (2) we got:

$n=(\frac{1.64(4)}{0.25})^2 =688.537 \approx 689$

So the answer for this case would be n=689 rounded up to the nearest integer

6 0

3 years ago

Use the diagram to answer the questions

IRISSAK [1]

Answer:

1. B. BD

2. C. 15

3. A. 2

Step-by-step explanation:

1. From the figure,

∠DAB = ∠DAC

Therefore, BD is the bisector of ∠ABC.

2. From the figure, IG = GH

3x = 5x - 10

10 = 5x - 3x

2x = 10

x = 5

So, GH = 5x - 10

= 5(5) - 10

= 25 - 10

= 15

Therefore, GH = 15.

3. From the figure,

∠DAB = ∠DAC

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 2

8 0

3 years ago

NEED THIS ASAP :)

katrin [286]

Answer:

Step-by-step explanation:

Length of the y component is how far the vector reaches vertically, so in this case it's 4

3 0

3 years ago

Find a unit vector that is perpendicular to the vector 5, −4

konstantin123 [22]

$( \frac{4}{ \sqrt{41} } , \frac{5}{ \sqrt{41} } )$

7 0

3 years ago