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3 years ago

Which function is continuous across its domain?

Mathematics

1 answer:

Scorpion4ik [409]3 years ago

6 0

Answer:

Step-by-step explanation:

a function is continuous, if the functional values are the same at the "connection" points of the various segments (and the segments themselves are continuous).

"continuous" simply means that the graph of the function is a continuous line without any "rips". it can have corners and such, but no "interruptions".

specifically it means : for every possible y value in the defined range of the function there is an x value that causes this y.

all defined segments are continuous functions.

so, let's look at

A. the first connection point is x=-2.

-2 + 6 = 0.5×(-2)²

4 = 0.5×4 = 2

4 = 2 is wrong. => here, at this point, the function "rips" apart and is not continuous.

B. x=-2

-2 + 4 = 0.5×(-2)²

2 = 2 is correct. continuous at this point.

second connection point x=4

0.5×4² = 20 - 3×4

0.5×16 = 20 - 12

8 = 8 is correct. continuous at this point

C. x=-2

-2 - 2 = 0.5×(-2)²

-4 = 2 is wrong. not continuous

D. x=-2

-2 + 4 = 0.5×(-2)²

2 = 2 is correct. continuous here.

now for x=4

4 + 4 = 25 - 3×4

8 = 25 - 12 = 13

8 = 13 is wrong. not continuous.

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You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence

Alla [95]

Answer:

$122 \leq \mu \leq 138$

The 95% confidence interval would be given by (122;138)

And the correct interpretation for this case is:

c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

Step-by-step explanation:

Previous concepts

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 % where by 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".

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.06$