Question

Dr. Rollins is both an anthropologist and archeologist. While excavating some ruins in South America, he discovered a scale drawing of a replica of a Mayan pyramid.The scale for the drawing to the replica was 1 inch : 2 feet.The scale for the replica to the actual pyramid was 1 foot : 14 feet.If the height of the pyramid on the drawing was 3 1/2 inches, what was the height of the actual pyramid?

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to determine the height of the replica of the pyramid using the scale 1 inch : 2 feet.

3 1/2 inches on the drawing is equivalent to (7/2) * 2 = 7 feet on the replica.

Next, we need to determine the height of the actual pyramid using the scale 1 foot : 14 feet.

7 feet on the replica is equivalent to 7 * 14 = 98 feet on the actual pyramid.

Therefore, the height of the actual pyramid is 98 feet.

Answer 2

Farmer's Fred's lawn mower is broken, so he put his goat in his front yard on a stake that pivots 360°. The length of the rope from the stake to the goat's collar is 8 feet.

If the stake is the center of the circular area of yard available for the goat to eat grass, what is the area of the yard available for the goat to eat grass, to the nearest whole square foot?

Answer 3

[AI-generated answer — Bot GPT 3.5]

The area available for the goat to eat grass is a circle with radius 8 feet, as the length of the rope from the stake to the goat's collar is the radius of the circle.

The formula for the area of a circle is A = πr^2.

Given that the radius is 8 feet, the area of the yard available for the goat to eat grass is:

A = π * 8^2
A = π * 64
A ≈ 200.96 square feet

Therefore, the area of the yard available for the goat to eat grass is approximately 201 square feet to the nearest whole square foot.

Answer 4

Atenea has 2 5/6 pounds of trail mix. She makes seven 1/3 pound snack bags with the trail mix for her daily snack for the next week and gives the rest of the trail mix to her brother. How much trail mix does Atenea give to her brother?

Answer 5

[AI-generated answer — Bot GPT 3.5]

Atenea has 2 5/6 pounds of trail mix, which is the same as 17/6 pounds.

She makes 7 snack bags with 1/3 pound of trail mix each, so the total amount of trail mix used for the snack bags is 7 * 1/3 = 7/3 pounds.

The amount of trail mix left for her brother is 17/6 - 7/3 = 17/6 - 14/6 = 3/6 = 1/2 pounds.

Atenea gives her brother 1/2 pound of trail mix.

Answer 6

Mia put two gifts in a shipping box, then filled the box with styrofoam "peanuts".

The dimensions of the shipping box were 12 inches by 5 inches by 5 inches.
One gift was a puzzle cube with a side length of 4 inches.
One gift was a card game that was in a box with dimensions 6 inches by 4 inches by 4 1/2 inches.
What was the volume of the styrofoam "peanuts" in the shipping box?

Answer 7

[AI-generated answer — Bot GPT 3.5]

First, let's calculate the volume of the two gifts in the shipping box.

1. The volume of the puzzle cube: 4 inches * 4 inches * 4 inches = 64 cubic inches

2. The volume of the card game box: 6 inches * 4 inches * 4.5 inches = 108 cubic inches

Total volume of the gifts = 64 cubic inches + 108 cubic inches = 172 cubic inches

Now, let's find the volume of the shipping box.

Volume of the shipping box = 12 inches * 5 inches * 5 inches = 300 cubic inches

The volume of the styrofoam "peanuts" in the shipping box can be obtained by subtracting the volume of the gifts from the volume of the shipping box.

Volume of the styrofoam "peanuts" = 300 cubic inches - 172 cubic inches = 128 cubic inches

Therefore, the volume of the styrofoam "peanuts" in the shipping box is 128 cubic inches.

Answer 8

The local food pantry is asking for "Gobble Kit" donations - an itemized list of non-perishable food items and a $20 donation for a turkey. The food pantry will purchase the turkeys for the "Gobble Kits". Each "Gobble Kit" will include everything needed for a Thanksgiving meal and will be given to a family in need.

3 (x + 20) = 114
Stacy donated three "Gobble Kits" and spent a total of $114. The equation shown represents the situation.

What does the variable represent in Stacy's equation?

Responses
A the cost of the non-perishable food items and turkey for 1 "Gobble Kit"the cost of the non-perishable food items and turkey for 1 "Gobble Kit"
C the cost of the turkey for 1 "Gobble Kit"the cost of the turkey for 1 "Gobble Kit"
B the cost of the non-perishable food items for 1 "Gobble Kit"the cost of the non-perishable food items for 1 "Gobble Kit"
D the cost of the non-perishable food items for all 3 "Gobble Kits"

Answer 9

[AI-generated answer — Bot GPT 3.5]

The equation given is 3(x + 20) = 114, where x represents the cost of the non-perishable food items and turkey for 1 "Gobble Kit".

Therefore, the variable x represents: A - the cost of the non-perishable food items and turkey for 1 "Gobble Kit".

Answer 10

Solve Stacy's equation in Part A for x.

Answer 11

[AI-generated answer — Bot GPT 3.5]

To solve the equation 3(x + 20) = 114 for x, we need to first distribute the 3 on the left side of the equation:

3(x + 20) = 114
3x + 60 = 114

Next, we need to isolate the variable x by subtracting 60 from both sides of the equation:

3x + 60 - 60 = 114 - 60
3x = 54

Finally, divide by 3 on both sides to solve for x:

3x/3 = 54/3
x = 18

Therefore, the cost of the non-perishable food items and turkey for 1 "Gobble Kit" is $18.