Tickets to a school play cost $2 if bought in advance, and $3 if bought at the door. By selling all 400 of their tickets, $1030

The range consists of negative values. The interval for the range is. It may be beneficial to review your functions as there seems to be no available choice that aligns with this outcome. Step-by-step explanation: Given functions, we need to determine the range of. As I evaluate the domain as well to see if it alters the range. For the function, we need to avoid division by zero, meaning that the domain excludes zero. Consequently, the domain encompasses all real numbers except zero. Overall, the final conclusion remains that the range is solely negative numbers.

The three equivalent numerical expressions are:

Solutions to create three numerical expressions equivalent to (0.0004). (0.005)

Response:

It is inferred that the authors of the sonnets belong to a certain poet from the Elizabethan era.

Step-by-step breakdown:

The details provided in the question are as follows:

Population mean, μ = 8.9

Sample mean, = 10.2

Sample size, n = 6

Alpha, α = 0.05

Population standard deviation, σ = 2.5

Initially, we formulate the null hypothesis and the alternative hypothesis

To conduct this test, we utilize the One-tailed z test.

a) Equation:

By substituting in all relevant values, we determine:

Next,

b) The p-value is computed using the z-table.

P-value = 0.1003

The p-value surpasses the alpha of 0.05

c) Because the p-value exceeds the alpha threshold, there is insufficient evidence to dismiss the null hypothesis, thereby supporting the null hypothesis.

Consequently, it is concluded that the authorship of the sonnets belongs to a particular Elizabethan poet.

Answer: (97.98, 112.020)

Step-by-step explanation: We will create a 95% confidence interval for the average weight of melons.

Given the information, we determine that the critical value for the interval needs to be retrieved from a t distribution table due to the sample size being below 30 (specifically, 20), and we are provided with the sample standard deviation (s = 15 lb).

The parameters provided are:

Sample mean = x = 105 lb

Sample standard deviation = s = 15 lb

Sample size = n = 20

To establish the 95% confidence interval, we indicate that the level of significance is 5%.

The formula for the confidence interval is:

u = x + tα/2 × s/√n... for the upper limit

u = x - tα/2 × s/√n... for the lower limit.

tα/2 represents the critical value for the test (which will be determined using the t distribution table).

To derive tα/2, we look for the value based on the degrees of freedom (sample size - 1) against the significance level for a two-tailed test (α/2 = 0.025%) in a t distribution table.

For the upper limit, we calculate:

u = 105 + 2.093×15/√20

u = 105 + 2.093× (3.3541)

u = 105 + 7.020

u = 112.020.

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u = 105 - 2.093×15/√20

u = 105 - 2.093× (3.3541)

u = 105 - 7.020

u = 97.98

Confidence interval (97.98, 112.020)

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