In order to determine this probability, we calculate using this difference:
To obtain these probabilities, it’s possible to utilize normal standard distribution tables, a calculator, or software like Excel. The accompanying figure displays the results achieved. Here’s a detailed breakdown of the steps: Relevant concepts include the normal distribution, which describes a probability distribution that is symmetric regarding the mean, demonstrating that occurrences close to the mean are more likely than those farther away. The Z-score represents a statistical measure illustrating how far a value is from the average of a set, expressed in standard deviations.
For our analysis, let X denote the random variable representing weights in a population, with its distribution characterized by:
We’re specifically interested in this probability. The most effective approach to address this issue is through the standard normal distribution and the Z-score calculation, expressed as:
Applying this formula to our probability provides the following:
This allows us to calculate this probability with the provided difference:
We use standard distribution tables, a calculator, or Excel for determining these probabilities. The graph illustrates the resulting outcome.
An airplane flying at a speed of 950 kilometers per hour would take 0.0010526 hours to travel 1.00 kilometer.
Response:
, indicating the amount of earnings per working hours, designated as x
Detailed Explanation:
We have two distinct functions to analyze:
This function delineates the earnings based on units of x
Then the second function is
which illustrates the quantity of gallons of ice cream produced by Barrett each hour, with x representing the hours worked.
Our aim is to determine the composite function
resulting from substituting the output of 
as input for 
. Within this framework, the function signifies the amount of money accrued per number of working hours, x.
By substituting g(x) into the x variable of f(x), we obtain:
The bus's speed is calculated as: velocity (bus) = 36 miles / 40 min, which simplifies to velocity (bus) = 0.9 miles / min. Given that the car's speed is 1.5 times that of the bus, we find: velocity (car) = 1.5 * 0.9 miles / min, leading to velocity (car) = 1.35 miles / min. At the point where they meet, the total distance covered equals 36 miles. Hence: 1.35 t + 0.9 t = 36, and thus 2.25 t = 36 resulting in t = 16 min. They will converge after 16 minutes.
