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3 years ago

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Mathematics

1 answer:

KatRina [158]3 years ago

5 0

Answer:

The domain of the function is (-6,6]

The range of the function is [-12.6)

Step-by-step explanation:

Domain and Range of Real Functions

The domain of a function is the set of all possible inputs for the function.

The Range is the set of values the function takes when x moves into the domain.

If the graph of a real function is given, we can find both by using the rules of the horizontal or vertical lines.

If an imaginary vertical line is moved along the x-axis, it can touch or not the graph of the function. All the values of x where the line and the graph cross each other belong to the domain of the function.

The vertical line crosses the function from x=-6 (not included since there is a hollow dot there) to x=6 (included since there is a solid dot).

Thus, the domain of the function is (-6,6]

Similarly, when an imaginary horizontal line is moved along the y-axis, it touches the function from y=-12 (included) to y=6 (not included).

The range of the function is [-12.6)

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The 90% confidence interval $-49.8$

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Step-by-step explanation:

From the question we are told that

The first sample size $n_1 = 30$

The first sample mean is $\= x _1 = 323$

The first standard deviation is $s_1 = 41$

The second sample size is $n_2 = 45$

The second sample mean is $\=x_2 = 356$

The second standard deviation is $s_2 = 45$

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$Z_{\frac{\alpha }{2} } = 1.645$

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$s^2 = \frac{(n_1 - 1)s_1^2 + (n_2 -1)s_2^2 }{n_1 + n_2 -2}$

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Generally the standard error is mathematically represented as

$SE = \sqrt{\frac{s^2}{n_1} + \frac{s^2}{n_2} }$

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$E = Z_{\frac{\alpha }{2} } * SE$

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$E = 16.85$

Generally the 90% confidence interval is mathematically represented as

$\=x_1 -\=x_2 -E < \mu_1 -\mu_2 < \=x_1 -\=x_2 +E$

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The alternative hypothesis $H_a : \mu_1 < \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \=x_2 }{SE}$

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Generally the degree of freedom is mathematically represented as

$df = n_1+n_2 -2$

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There is sufficient evidence to conclude that there are more passengers riding the 8:30 train

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