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3 years ago

In two or more complete sentences describe why the range of y = cos(x) is -1 ≤ y ≤ 1

Mathematics

1 answer:

galina1969 [7]3 years ago

4 0

The domain would be the x variable, which is undefined so can be any real number.

The magnitude of the term is the absolute value of the coefficient. Since the equation does not contain a coefficient, the magnitude becomes 1.

The lower bound of the range is the negative magnitude which would be -1 and the upper bound is the magnitude, which is 1.

So the range is equal to -1 ≤ y ≤ 1

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A scale drawing of Julie's living room is shown below:

stealth61 [152]

Answer:

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Step-by-step explanation:

divide the length and width by 2 so you get 3 and 4. then you proceed to Multiply both by 4 and you get 12 and 16

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Answer:

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Step-by-step explanation:

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3 years ago

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mixer [17]

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4 years ago

Read 2 more answers

Give a 98% confidence interval for one population mean, given asample of 28 data points with sample mean 30.0 and sample standar

klio [65]

We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:

$\begin{gathered} 1-\alpha=0.98 \\ \alpha=0.02 \end{gathered}$

The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:

$CI(\mu)=\lbrack x-Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}},x+Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\rbrack$

Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:

$CI(\mu)=\lbrack30.0-Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}},30.0+Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}}\rbrack$

Where (from tables):

$Z_{0.99}=2.33$

Finally, the interval at 98% confidence level is:

$CI(\mu)=\lbrack28.94,31.06\rbrack$

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1 year ago