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Ivenika [448]
3 years ago
12

Evaluate the piecewise function at the indicated values from the domain:

Mathematics
1 answer:
lidiya [134]3 years ago
7 0

In this question, we given a piece-wise function, that has different definitions depending on the domain.

Evaluate the function at x = 0.

The exercise asks for us to evaluate the function at x = 0

We have to look at the definition, and see which definition includes x = 0. The equal sign at x = 0 is on the second definition, that is:

f(x) = 1, 0 \leq x < 2

Thus, at x = 0, the value of the function is 1, and the correct answer is given by option A.

For another example of evaluation of a piece-wise function, you can check brainly.com/question/17966003

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The regular price of a shirt is $15. Natalie bought it on sale for 0.9 times its regular price. Then the sale price was multipli
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Step-by-step explanation:

Assuming it is the final price Natalie paid that you want:

Selling price = 0.9 * 15

= $13.50

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= 13.5 * 1.06

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Write -0.18 as a fraction in simplest form​
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-9/50

Step-by-step explanation:

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Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain wei
yawa3891 [41]

Answer:

The result indicates that the percentage of all samples of three men that have mean brain weights within (1.24 * sampling error) of the mean is 78.50%.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.

Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.

The explanation of the answers is now provided as follows:

Based on the Central limit theorem, it possible to say that the mean of sampling distribution (μₓ) is approximately equal to the population mean (μ) as follows:

μₓ = μ = 1.20 kg …………………………. (1)

Also, the standard deviation of the sampling distribution can be written as follows:

σₓ = (σ/√N) ……………………….. (2)

Where:

σ = population standard deviation = 0.14 kg

N = Sample size = 3

Substituting the values into equation (2), we have:

σₓ = 0.14 / √3 = 0.0808

Since we are to determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, this implies that we have:

P(1.10 ≤ x ≤ 1.30)

Therefore, 1.10 and 1.30 have to be first normalized or standardized as follows:

For 1.10 kg

z = (x - μₓ) / σₓ = (1.10 - 1.20) / 0.0808 = -1.24

For 1.30 kg

z = (x - μₓ)/σₓ = (1.30 - 1.20) / 0.0808 = 1.24

The required probability can be determined when P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24).

From the normal distribution table, the following can be obtained for these probabilities:

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24) = P(z ≤ 1.24) - P(z ≤ -1.24) = 0.89251 - 0.10749 = 0.7850, or 78.50%

Therefore, the sampling error is equal to 0.0808 which is the standard deviation of the sampling distribution.

In terms of the sampling error, the result indicates that the percentage of all samples of three men that have mean brain weights within (1.24 * sampling error) of the mean is 78.50%.

3 0
3 years ago
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