John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that

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.

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)

∠1 and ∠8 are alternate exterior angles while ∠3 and ∠6 are alternate interior angles.

step-by-step explanation:

When transversal l intersects lines m and n, the angles formed outside each line on the opposite side of the transversal constitute alternate angles (like ∠1 and ∠8). In contrast, alternate interior angles appear on opposite sides but are located between the two lines (like ∠3 and ∠6).

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Keywords: Transversal, angles

Answer:

Step-by-step explanation:

To determine the slope, divide the rise by the run to calculate the slope.

Note that

1 ft = 12 in

Let

y ----> the rise

x ----> the run

m ----> the slope

the values are given as

substituting these values gives

Simplifying further

Here, 'a' relates to 0.

There are two scenarios for 'r' and 't'.

Scenario 1.

Both are positioned on the same side to the right of 'a'.

In this case, 'r' would equal 5, and 't' would equal 7.

The midpoint between 'r' and 't' is .

Scenario 2.

If both are found to the left of 'a'.

Then 'r' would equal -5, while 't' would equal -7.

The midpoint is .

Scenario 3.

If 'r' is right of 'a' and 't' is left of 'a'.

Thus 'r' equals 5 and 't' equals -7.

The midpoint is .

Scenario 4.

If 'r' is left of 'a' while 't' is right of 'a'.

In this case, 'r' corresponds to -5 and 't' corresponds to 7.

The midpoint is .

The potential midpoint coordinates for 'rt' are 6, -6, 1, and -1.