24. analyze the area of a square is 16 square inches. what is its perimeter?
* 25. this figure shows the shape of home plate on a baseball field. what kind of a polygon is shown?
26. explain the sales - tax rate was 7%. dexter bought two items, one for $4.95 and the other for $2.79. what was the total cost of the two items including sales tax? describe how to use estimation to check whether your answer is reasonable.
27. ramila bought a sheet of 100 stamps from the post office for $9. what was the price of each stamp?
* 28. represent draw a rectangular prism. a rectangular prism has how many
a. faces?
b. edges?
c. vertices?
refer to the cube shown below to answer problems 29 and 30.
* 29. each face of a cube is a square. what is the area of each face of this cube?
* 30. find the total surface area of the cube by adding up the area of all of the faces of the cube.
early finishers math and architecture
the pentagon in washington, d.c. is the world’s largest office building. each of the five sides of the pentagon is 921 feet long. what is the perimeter of the pentagon in yards?

Question

24. analyze the area of a square is 16 square inches. what is its perimeter?
* 25. this figure shows the shape of home plate on a baseball field. what kind of a polygon is shown?
26. explain the sales - tax rate was 7%. dexter bought two items, one for $4.95 and the other for $2.79. what was the total cost of the two items including sales tax? describe how to use estimation to check whether your answer is reasonable.
27. ramila bought a sheet of 100 stamps from the post office for $9. what was the price of each stamp?
* 28. represent draw a rectangular prism. a rectangular prism has how many
    a. faces?
    b. edges?
    c. vertices?
refer to the cube shown below to answer problems 29 and 30.
* 29. each face of a cube is a square. what is the area of each face of this cube?
* 30. find the total surface area of the cube by adding up the area of all of the faces of the cube.
early finishers math and architecture
the pentagon in washington, d.c. is the world’s largest office building. each of the five sides of the pentagon is 921 feet long. what is the perimeter of the pentagon in yards?

Accepted Answer

### Problem 24:
# Explanation:
## Step 1: Find the side length of the square
The area of a square is given by the formula $ A = s^2 $, where $ A $ is the area and $ s $ is the side length. We know the area $ A = 16 $ square inches. So we solve for $ s $:
$ s^2 = 16 $
Taking the square root of both sides, $ s=\sqrt{16} = 4 $ inches.

## Step 2: Calculate the perimeter of the square
The perimeter $ P $ of a square is given by the formula $ P = 4s $. Substituting $ s = 4 $ inches:
$ P=4\times4 = 16 $ inches.

# Answer:
The perimeter of the square is 16 inches.

### Problem 26:
# Explanation:
## Step 1: Calculate the sales tax for each item
The sales - tax rate is $ 7\%=0.07 $.

For the first item costing $ \$4.95 $, the sales tax $ t_1=4.95\times0.07 = 4.95\times\frac{7}{100}=0.3465\approx0.35 $ dollars.

For the second item costing $ \$2.79 $, the sales tax $ t_2 = 2.79\times0.07=2.79\times\frac{7}{100}=0.1953\approx0.20 $ dollars.

## Step 2: Calculate the total cost of each item including tax
The total cost of the first item $ C_1=4.95 + 0.35=5.30 $ dollars.

The total cost of the second item $ C_2=2.79+0.20 = 2.99 $ dollars.

## Step 3: Calculate the total cost of the two items
The total cost $ C = C_1 + C_2=5.30+2.99 = 8.29 $ dollars.

## Step 4: Estimation check
We can also estimate the total cost before tax: $ 4.95+2.79\approx5 + 3=8 $ dollars.

The total sales tax rate - related increase: $ 7\% $ of $ 8 $ dollars is $ 8\times0.07 = 0.56 $ dollars. So the estimated total cost is $ 8 + 0.56=8.56 $. Our calculated value of $ 8.29 $ is close to the estimated value (the difference is due to the rounding of the sales - tax amounts), so the answer is reasonable.

# Answer:
The total cost of the two items including sales tax is approximately \$8.29. The estimation (rounding the prices to \$5 and \$3, total before tax \$8, tax on \$8 is \$0.56, total estimated \$8.56) and the actual calculation (\$8.29) are close, so the answer is reasonable.

### Problem 27:
# Explanation:
## Step 1: Use the formula for unit price
The total cost of 100 stamps is \$9. The unit price (price per stamp) $ p $ is given by the formula $ p=\frac{\text{Total Cost}}{\text{Number of Stamps}} $.

## Step 2: Calculate the price per stamp
Substitute the total cost $ \$9 $ and the number of stamps $ n = 100 $ into the formula:
$ p=\frac{9}{100}=0.09 $ dollars per stamp.

# Answer:
The price of each stamp is \$0.09.

### Problem 28:
# Explanation:
A rectangular prism is a three - dimensional shape.

## Part (a): Number of faces
A rectangular prism has 6 faces. These include 2 rectangular bases (top and bottom) and 4 lateral faces (front, back, left, and right).

## Part (b): Number of edges
A rectangular prism has 12 edges. Each of the 4 edges of the top rectangle, 4 edges of the bottom rectangle, and 4 vertical edges connecting the top and bottom rectangles.

## Part (c): Number of vertices
A rectangular prism has 8 vertices. Each vertex is a corner where three edges meet.

# Answer:
a. The number of faces of a rectangular prism is 6.

b. The number of edges of a rectangular prism is 12.

c. The number of vertices of a rectangular prism is 8.

### Problem 29:
# Explanation:
## Step 1: Recall the formula for the area of a square
The area of a square is given by $ A = s^2 $, where $ s $ is the side length of the square.

## Step 2: Substitute the side length
The side length of each face (which is a square) of the cube is $ s = 3 $ cm. So the area of one face $ A=3^2=9 $ square centimeters.

# Answer:
The area of each face of the cube is 9 square centimeters.

### Problem 30:
# Explanation:
## Step 1: Recall the number of faces of a cube
A cube has 6 faces, and all the faces are squares with equal area.

## Step 2: Calculate the area of one face
From problem 29, we know that the area of one face of the cube with side length $ s = 3 $ cm is $ A = 3\times3=9 $ square centimeters.

## Step 3: Calculate the total surface area
The total surface area $ SA $ of a cube is the sum of the areas of all 6 faces. So $ SA=6\times A $. Substituting $ A = 9 $ square centimeters, we get $ SA = 6\times9=54 $ square centimeters.

# Answer:
The total surface area of the cube is 54 square centimeters.

### Early Finishers Problem:
# Explanation:
## Step 1: Calculate the perimeter in feet
The Pentagon has 5 sides, and each side is 921 feet long. The perimeter $ P $ in feet is given by the formula $ P=\text{number of sides}\times\text{length of each side} $. So $ P = 5\times921=4605 $ feet.

## Step 2: Convert feet to yards
We know that 1 yard = 3 feet. To convert feet to yards, we use the conversion factor $ \frac{1\ \text{yard}}{3\ \text{feet}} $. So the perimeter in yards $ P_y=\frac{4605}{3}=1535 $ yards.

# Answer:
The perimeter of the Pentagon in yards is 1535 yards.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 24:

Step 1: Find the side length of the square

Step 2: Calculate the perimeter of the square

Step 1: Calculate the sales tax for each item

Step 2: Calculate the total cost of each item including tax

Step 3: Calculate the total cost of the two items

Step 4: Estimation check

Step 1: Use the formula for unit price

Step 2: Calculate the price per stamp

Answer:

Problem 26: