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3 years ago

2. Solve the following equations for 0° Sx < 180°.

Mathematics

1 answer:

diamong [38]3 years ago

5 0

Answer:

See below in bold.

Step-by-step explanation:

(1) cosec ( x + 10) = 3

Now cosec x = 1/sin x so

1 / sin (x + 10) = 3

3 sin (x + 10) = 1

sin (x + 10) = 1/3

x + 10 = 19.47 , 160.53 degrees

x = 9.47, 150.53 degrees.

(ii) cot (x - 30) =0.45

cot (x - 30)= 1 /tan (x- 30) so we have

tan (x - 30) = 1 / 0.45 = 2.2222

x - 30 = 65.77 degrees

x = 95.77 degrees.

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guapka [62]

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3 years ago

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lukranit [14]

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3 years ago

In a recent poll, 370 people were asked if they liked dogs, and 7% said they did. Find the margin of error of this poll, at the

Dennis_Churaev [7]

Answer:

$ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218$

Step-by-step explanation:

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".

$p$ represent the real population proportion of interest

$\hat p=0.07$ represent the estimated proportion for the sample

n=370 is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

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

And replacing into formula (a) the values provided we got:

$ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218$

The margin of error on this case would be ME=0.0218

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4 years ago

What is 61 divided by 207.4

romanna [79]

The answer is 0.2941.

Hope this helps!!

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3 years ago

Read 2 more answers

slope-intercept form for the line that passes through (-1,-7) and is perpendicular to the graph of 3x+12y=-6

Mrac [35]

Answer:

Step-by-step explanation:

We first need to find the slope of the given line. Putting that standard form of a line into slope intercept:

12y = -3x - 6 so

$y=-\frac{1}{4}x-\frac{1}{2}$

In this form we can easily determine that our slope is -1/4. That means that the perpendicular slope, the opposite reciprocal, is +4. We will write first the point slope of the new line using our given point, then solve it for y, putting it into slope-intercept form. y - (-7) = 4(x - (-1)) and

y + 7 = 4x + 4 so

y = 4x + 4 - 7 so

y = 4x - 3

7 0

3 years ago