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kirill [66]
3 years ago
6

Which of these is the algebraic expression for the verbal expression "ten times the difference of a number and twelve?"

Mathematics
1 answer:
fredd [130]3 years ago
5 0
The answer is, A. 10(x - 12)
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72

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Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly samp
zepelin [54]

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C) There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion.

Step-by-step explanation:

Given that 20% of the residents in a certain state support an increase in the property tax.

Sample size = 400

We want the sample proportion to be within 0.04 of the true proportion (i.e., between 0.16 and 0.24)

i.e. margin of error <0.04

Std error of sample = \sqrt{\frac{pq}{n} } =\sqrt{\frac{0.2(0.8)}{400} } \\=0.02

Critical value = margin of error/ std error = \frac{0.04}{0.02} \\=2

We know z value for 95% two tailed roughly equals 2.

Hence 95% confidence is right.

C) There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion.

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3 years ago
Use trigonometry to find the value of x. Round your answer to the nearest whole degree
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8x + 20y = 20<br> 14x + 35y = k<br> For the above system of equations to be consistent, k must equal
Goshia [24]

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  35

Step-by-step explanation:

The equations will be "consistent" when they describe lines that are not parallel.

<h3>Slopes</h3>

The slope of a line whose equation is written in this form is the opposite of the ratio of the y-coefficient to the x-coefficient:

  line 1 slope = -8/20 = -2/5

  line 2 slope = -14/35 = -2/5

These lines have the same slope, so will be parallel unless they have the same y-intercept.

<h3>Y-intercept</h3>

The y-intercept of each line is the ratio of the constant to the y-coefficient:

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  line 2 y-intercept = k/35

We want these lines to have the same y-intercept so that they are not inconsistent. This requires ...

  k/35 = 1

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For the equations to be consistent, we must have k = 35.

__

<em>Additional comment</em>

Linear equations are generally categorized as "consistent" or "inconsistent," and "dependent" or "independent."

Equations are "inconsistent" if there are no values of the variables that satisfy all of the equations. They are "dependent" if they describe exactly the same relation between the variables. "Consistent" equations may be "dependent" (describing the same line, as here), or "independent" (describing lines with different slopes.)

7 0
2 years ago
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