Part A: Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)

Answer:

On a coordinate grid, a triangle is defined by the points R' (1, 2), S' (3, -1), T' (7, 1)

Step-by-step explanation:

We can interpret the coordinates of the triangle's vertices as...

R(-2, 1), S(1, 3), T(-1, 7)

Applying the transformation (x, y) ⇒ (y, -x), these coordinates change to...

R'(1, 2), S'(3, -1), T'(7, 1) . . . . . (this corresponds to the first option)

To calculate total earnings: 40 hours multiplied by $8.95 leads to earnings of $358. After deducting expenses, the total earnings would be $358 - ($35.24 + $24.82 + $21.33) = $276.61.

When there is one table (t=1), you can place 6 chairs (c=6) around it: 2 along the length of each side and 1 at each end.
With t=2, where the tables are positioned end to end (joined at the width), c=10, that means 4 chairs along each side of the joined tables and 1 chair at each end. Each additional table increases the number of chairs by 4, thus we can express this as c=4t+2, with the constant 2 representing the individual chair at each end. If the tables are spread apart, then c=6t.

we understand that

A fast method for estimating the total of two numbers involves rounding each number and adding the rounded results.

case a) We round to the nearest hundred

so

Round up equals

Round up equals

Calculate the estimated sum

case b) We round to the nearest ten

so

Round up equals

Round down equals

Calculate the estimated sum

Answer:

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.

Step-by-step explanation:

Prior concepts

A normal distribution is characterized as a "probability distribution that is symmetric around the mean, indicating that data close to the mean are more frequent than those further away".

The Z-score refers to "a statistical measurement that reflects the relationship of a value to the mean of a group, measured in standard deviations".

Let X denote the random variable of interest, and we identify its distribution:

Also, let signify the sample mean, whose distribution is:

In this case,

Solution to the problem

We seek this probability

Applying the Z-score formula to the probability results in:

To determine these probabilities, we can refer to normal distribution tables, use Excel, or a calculator.

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.