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valkas [14]
3 years ago
9

Explain the connection between ∠2 and ∠B.

Mathematics
2 answers:
liraira [26]3 years ago
7 0

Answer:

∠2 ≅ ∠B

Step-by-step explanation:

Let the triangle be ABC,

Given that,

∠A = 50°

∠C = 65°

Using angle-sum property of the triangle,

∠A + ∠B + ∠C = 180°

50° + ∠B  + 65° = 180°

∵ ∠B = 65°         ...(i)

A.T.Q.

Two horizontal lines are extended making 3 angles. Two angles out of them are 50° and 65°.

Since the adjacent angles comprising a straight line is equals to 180°.

so,

∠2 + 50° + 65° = 180°

∠2 + 115° = 180°

∠2 = 180° - 115°

∵ ∠2 = 65°   ...(ii)

Using (i) and (ii),

∠2 ≅ ∠B

Therefore, ∠2 and ∠B are congruent to one another.

Savatey [412]3 years ago
7 0

Answer: Sample Response: The sum of the measures of the interior angles of a triangle is 180°. m∠B + 50 + 65 = 180, so m∠B = 65°. The sum of adjacent angles forming a straight line is also 180°. m∠2 + 50 + 65 =180, so m∠2 = 65°. The angles are congruent.

Step-by-step explanation: its the sample response

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Answer:

C, 4e^{i(7\pi/4)}

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

e^{ix}=\cos{x}+i\sin{x}

Given the complex number 2\sqrt{2}-2i\sqrt{2}, we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression 2(\sqrt{2}-i\sqrt{2})

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression 4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right) , and <em>now </em>we have something to work with.

Looking back at Euler's formula e^{ix}=\cos{x}+i\sin{x}, we can map our expression inside the parentheses to the one on the right side of the formula, giving us \cos{x}=\frac{\sqrt2}{2} and \sin{x}=-\frac{\sqrt2}{2}, or equivalently:

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At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so x=\frac{7\pi}{4}, and we can finally replace our expression in parentheses with its exponential equivalent:

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Answer:

a) The standard deviation of this sampling distribution is 2.07.

b) The missing number is 4.14.

c) The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

Step-by-step explanation:

To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

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Central Limit Theorem:

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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\mu = 272, n = 840, \sigma = 60

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Using the Central Limit Theorem:

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The standard deviation of this sampling distribution is 2.07.

(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x⎯⎯⎯ fall within _______ on either side of the unknown mean μ. What is the missing number?

Within 2 standard deviations of the mean.

So, 2*2.07 = 4.14

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(c) What is the 95% confidence interval for the population mean score μ based on this one sample?

Within 4.14 of the mean

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272 + 4.14 = 276.14

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2 years ago
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