One square has an area that is 10 cm2 larger than another. What is a reasonable domain for the area of the larger square?

Believe this is accurate.

Given:

The temperature recorded at 10:00 am is 8 degrees Fahrenheit.

The temperature decreases by 3 degrees Fahrenheit each hour.

To find:

The temperature at 2:00 pm on the same day.

Solution:

Let y represent the temperature after x hours since 10:00 am.

The temperature at 10:00 am serves as the initial temperature.

Thus, the y-intercept of the linear equation is 8.

The temperature reduces by 3 degrees Fahrenheit every hour.

This indicates the slope of the linear equation is -3, with the negative sign indicating a decrease.

The slope-intercept form of a linear function is indicated by

where m is the slope and b is the y-intercept.

Inserting m=-3 and y=8 into the above equation gives us the required values.

From 10:00 am to 2:00 pm spans 4 hours; therefore, substitute x=4 into the above equation.

Consequently, the temperature at 2:00 pm is -4 degrees Fahrenheit.

Response:

Alan's survey aims to determine the art preferences among students at the local high school.

To conduct a thorough investigation, he needs to consider all students in the school as the target population since that is his goal.

Nevertheless, in many cases involving statistical studies, it's impractical to include the entire population. In such instances, a sample that accurately reflects the overall student body is employed.

This sample is a subset of the population and must share the same characteristics and attributes; otherwise, the findings may be skewed.

Thus, a feasible sample would consist of a specific number of students from each grade level, including freshmen, sophomores, juniors, and seniors. This approach ensures the sample accurately represents the larger population.

Area of a rectangle = length x width
For this postcard:
length = 4 in
width = (3+b) in
area = 24 in^2

Substitute into the area formula:
24 = 4 x (3+b)
24 = 12 + 4b
24 - 12 = 4b
12 = 4b
b = 3 in

Therefore:
the length of the postcard = 4 inch
the width of the postcard = b+3 = 3 + 3 = 6 inch

The total number of bills and coins is 14.

Step-by-step explanation:

To minimize the count of bills and coins, start with the largest denominations that fit within the amount.

The change due is $39.49.

Start with:

-$20 bill (largest under $39.49)

Remaining: $19.49

-$10 bill (largest under $19.49)

Remaining: $9.49

-$5 bill (largest under $9.49)

Remaining: $4.49

Then:

4 × $1 bills (to cover $4.49)

Remaining: $0.49

-$0.25 coin (quarter)

Remaining: $0.24

2 × $0.10 coins (dimes)

Remaining: $0.04

4 × $0.01 coins (pennies)

The final composition includes:

1 twenty-dollar bill

1 ten-dollar bill

1 five-dollar bill

4 one-dollar bills

1 quarter

2 dimes

4 pennies

Totaling 14 pieces.