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3 years ago

Solve this system of equations.

Mathematics

2 answers:

Dennis_Churaev [7]3 years ago

4 0

Answer:

x = -3 and y = 0

Step-by-step explanation:

It would be more direct to apply elimination in this problem, rather than substitution:

2x + 6y = -6 ⇒ 2x + 6y = -6 ⇒ 10x = - 30

+ 2(4x - 3y = -12) + 8x - 6y = -24

Now let us solve for x through simply algebra:

10x = -30,

x = -3

Substitute this value of x into the first equation to get the value of y:

2( -3 ) + 6y = -6,

-6 + 6y = -6,

6y = 0,

y = 0

nasty-shy [4]3 years ago

3 0

Answer:

-3 and 0

Step-by-step explanation:

i hope this helps :)

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The sum of 4 numbers is 1230. The average of 3 of them is 293. What is the fourth number?

OverLord2011 [107]

351 because 293 multiplied by 3 = 879, and 1230 - 879 = 351

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3 years ago

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If the mean of the data below is 3.8, find m x 1 2 3 4 5 6 f 1 4 7 m 6 3

zloy xaker [14]

Answer:

m = 1.8

Step-by-step explanation:

Given data is as follows :

x 1 2 3 4 5 6

f 1 4 7 m 6 3

We need to find the value of m if the mean of the data is 3.8.

Mean = sum of observations/no. of observations

So,

$3.8=\dfrac{1+4+7+m+6+3}{6}\\\\22.8=21+m\\\\22.8-21=m\\\\m=1.8$

So, the value of m is equal to 1.8.

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3 years ago

What is the slope of this line?

Talja [164]

Answer:

-1

Step-by-step explanation:

Slope= rise/run

Since the line is decreasing, it will be negative.

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3 years ago

Sarah is making strings of beads in the first string she uses 3 beads and she triples the number of beads in each of the next st

xenn [34]

Answer:

She uses 243 beads for the 5th string.

Step-by-step explanation:

In this problem, we can see a pattern. If she triples the number of beads in each of the next strings, that means that we just take the last number and multiply by 3. If the first string uses 3, then:

The second uses 9, 3 * 3 = 9

The third uses 27, 9 * 3 = 27

The fourth uses 81, 27 * 3 = 81

And the 5th uses 243, 81 * 3 = 243.

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3 years ago

When the sample size and the sample proportion remain the same, a 90 percent confidence interval for a population proportion p w

deff fn [24]

Answer:

A 90% confidence interval for p will be narrower than the 99% confidence interval.

Step-by-step explanation:

The formula to compute the (1 - α) % confidence interval for a population proportion is:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Here $\hat p$ is the sample proportion.

The margin of error of the confidence interval is:

$MOE= z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The MOE is dependent on:

Confidence level
Standard deviation
Sample size

The MOE is directly related to the confidence level and standard deviation.

So if any of the two increases then the MOE also increases, thus widening the confidence interval.

And the MOE is inversely related to the sample size.

So if the sample increases the MOE decreases and vice versa.

It is provided that the sample size and the sample proportion are not altered.

The critical value of z for 90% confidence level is:

$z_{\alpha/2}= z_{0.10/2}=z_{0.05}=1.645$

And the critical value of z for 99% confidence level is:

$z_{\alpha/2}= z_{0.05/2}=z_{0.05}=1.96$

So as the confidence level increases the critical value increases.

Thus, a 90% confidence interval for p will be narrower than the 99% confidence interval.

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3 years ago