Rewrite 7+ square root-121 in complex number notation

Evaluate 3x^2 – 2xy - 4y^2

kykrilka [37]

Evaluate for x=2,y=−3

3(22)−(2)(2)(−3)−4(−3)2

= C. −12

3 0

3 years ago

Solve for x.<br> Greatly appreciate all efforts :)

Lelu [443]

Answer:

x = 11

Step-by-step explanation:

ΔLKM is an equilateral because a triangle with all 3 sides that are congruent is an equilateral triangle.

Angles in an equilateral triangle are all 60°.

Thus, ∠L = 60°.

=> 3x + 27 = 60

=> 3x = 33

=> x = 11

8 0

3 years ago

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Ind the next term for the given sequence.52, 45, 38, 31,

o-na [289]

The answer is 24. To get from one term to the next, you have to find the difference. To get from 52 to 45, you minus 7. It is the same with the other terms. So 31 - 7 = 24

4 0

3 years ago

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<img src="https://tex.z-dn.net/?f=Simplify%5C%3Beach%5C%3Bof%5C%3Bthe%5C%3Bfollowing%5C%3Bequations%5C%3Bfor%5C%3B50%5C%3Bpoints

jekas [21]

Answer:

y= -12
x = 7
q = -1
x = 24

Step-by-step explanation:

1. ..............................................

6(y + 7) = 2(y - 3)
6y + 42 = 2y - 6
6y - 2y = -6 - 42
4y = -48
y = -12

2...............................................

3x + 2(x - 5) = 25
3x + 2x - 10 = 25
5x = 25 + 10
5x = 35
x = 7

3 . ..............................................

10q + 3q + 5 = 2(q - 3)
13q + 5 = 2q - 6
13q - 2q = -6 - 5
11q = -11
q = -1

4. ..............................................

1/3(x + 6) = 2/3(x - 9)
3*1/3(x+6) = 3*2/3(x - 9)
x + 6 = 2(x - 9)
x + 6 = 2x - 18
2x - x = 6 + 18
x = 24

3 0

3 years ago

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Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below. Find the 93% conf

kobusy [5.1K]

Answer:

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

And replacing we got:

$(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903$

$(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097$

And the confidence interval for the difference of means would be given by:

$0.2903 \leq \mu_1 -\mu_2 \leq 0.5097$

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".

We have the following data given:

$\bar X_1 = 9.2 , \bar X_2 = 8.8, \sigma_1= 0.3, n_1 = 27, \sigma_2 = 0.1, n_2 = 30$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 93% of confidence, our significance level would be given by $\alpha=1-0.93=0.07$ and $\alpha/2 =0.035$ . And the critical value would be given by:

$z_{\alpha/2}=-1.811, z_{1-\alpha/2}=1.811$

The confidence interval is given by:

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

And replacing we got:

$(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903$

$(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097$

And the confidence interval for the difference of means would be given by:

$0.2903 \leq \mu_1 -\mu_2 \leq 0.5097$

4 0

3 years ago