Caeli is designing a flag that will be in the shape of a rectangle. She has 10 square feet of fabric to use, and she wants the h

Answer:

The chance of completing the entire package installation in under 12 minutes is 0.1271.

Step-by-step explanation:

We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.

To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.

Utilizing , we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.

Given the symmetry of the standard normal distribution density function, we ascertain .

Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.

Answer:

At a confidence level of 90%, the margin of error is calculated to be 0.5133 grams.

Step-by-step explanation:

The formula for margin of error (E) is: (critical value × sample standard deviation) ÷ sqrt(n)

The sample standard deviation is 1.5 grams.

A 90% confidence level translates to 0.9.

Significance level is determined as 1 - C, which equals 1 - 0.9 resulting in 0.1 or 10%.

The sample size (n) is 25.

Degrees of freedom are calculated as n - 1, which is 25 - 1 equaling 24.

The critical value (t) for 24 degrees of freedom at a significance level of 10% is found to be 1.711.

Using these values, we calculate: E = (1.711 × 1.5) ÷ sqrt(25) = 2.5665 ÷ 5 = 0.5133 grams.

Answer:

The diameter of a large pizza from Gambino's Pizzeria is

Step-by-step explanation:

We know that

The area of a circle (circular pizza) is calculated as

we have

substitute values into the equation and resolve for the radius r

Simplify

Determine the diameter

Remember, the diameter is double the radius

Answer:

The cost for a 2,000 square foot house is

Detailed explanation:

Recall that if two variables x and y vary directly, the relationship can be written as or .

Define:

x as the house area in square feet

y as the price of the house

Given point (1500, 300000)

Calculate proportionality constant k:

Insert values:

The direct variation equation is:

For x = 2000:

Calculate y:

Replace x in equation: