Question

Find the greatest common factor of 21 and 8.
Answer
What is the surface area of the cylinder with height 6 cm and radius 5 cm? Round your answer to the nearest thousandth.
Answer
ind the surface area of a square pyramid with side length 1 ft and slant height 4 ft.
Answer
Find the surface area of a square pyramid with side length 5 cm and slant height 5 cm.
Answer
Abigail owns a small business selling bagels. She knows that in the last week 65 customers paid cash, 2 customers used a debit card, and 9 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a debit card as a fraction in simplest form.
Answer
Annabelle owns a small business selling clothing. She knows that in the last week 56 customers paid cash, 26 customers used a debit card, and 9 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a debit card as a percent to the nearest whole number.
Answered by GPT 3.5
The greatest common factor of 21 and 8 is 1, as they do not have any common factors other than 1.
Answered by GPT 3.5
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr(r+h), where r is the radius and h is the height of the cylinder.

Given that the radius (r) is 5 cm and the height (h) is 6 cm, we can plug these values into the formula:

Surface Area = 2π(5)(5+6)
Surface Area = 2π(5)(11)
Surface Area = 2π(55)
Surface Area = 110π

Now, round the answer to the nearest thousandth:
Surface Area ≈ 345.575

Therefore, the surface area of the cylinder with a height of 6 cm and a radius of 5 cm is approximately 345.575 square centimeters.
Answered by GPT 3.5
To find the surface area of a square pyramid, we need to calculate the sum of the lateral area and the base area.

Given that the side length of the base is 1 ft and the slant height is 4 ft, we first find the height of the pyramid using the Pythagorean theorem:
h = √(slant height^2 - (side length/2)^2)
h = √(4^2 - (1/2)^2) = √(16 - 1/4) = √(63/4) = √15.75 ≈ 3.965 ft

Next, we calculate the lateral area of the pyramid:
Lateral Area = 1/2 * perimeter of base * slant height
Perimeter of base = 4 * side length = 4 * 1 = 4 ft
Lateral Area = 1/2 * 4 * 4 = 8 ft^2

And the base area of the pyramid:
Base Area = side length^2 = 1^2 = 1 ft^2

Finally, we find the total surface area by summing the lateral area and the base area:
Total Surface Area = Lateral Area + Base Area
Total Surface Area = 8 + 1 = 9 ft^2

Therefore, the surface area of the square pyramid with side length 1 ft and slant height 4 ft is 9 square feet.
Answered by GPT 3.5
To find the surface area of a square pyramid, we need to calculate the sum of the lateral area and the base area.

Given that the side length of the base is 5 cm and the slant height is also 5 cm, we can proceed with the calculations.

First, we need to find the height (h) of the pyramid using the Pythagorean theorem:
h = √(slant height^2 - (side length/2)^2)
h = √(5^2 - (5/2)^2) = √(25 - 6.25) = √18.75 ≈ 4.33 cm

Next, we calculate the lateral area of the pyramid:
Lateral Area = 1/2 * perimeter of base * slant height
Perimeter of base = 4 * side length = 4 * 5 = 20 cm
Lateral Area = 1/2 * 20 * 5 = 50 cm^2

The base of the pyramid is a square, so the base area is:
Base Area = side length^2 = 5^2 = 25 cm^2

Finally, we find the total surface area by summing the lateral area and the base area:
Total Surface Area = Lateral Area + Base Area
Total Surface Area = 50 + 25 = 75 cm^2

Therefore, the surface area of the square pyramid with side length 5 cm and slant height 5 cm is 75 square centimeters.
Answered by GPT 3.5
The total number of customers in the last week is given by:
Total number of customers = 65 (cash) + 2 (debit card) + 9 (credit card) = 76 customers

To find the probability that the next customer will pay with a debit card, we need to calculate the number of customers who paid with a debit card divided by the total number of customers:
Probability = Number of customers who paid with a debit card / Total number of customers
Probability = 2 / 76
Probability = 1 / 38

Therefore, the probability that the next customer will pay with a debit card can be expressed as a fraction in simplest form as 1/38.
Answered by GPT 3.5
To find the probability that the next customer will pay with a debit card, we need to calculate the number of customers who paid with a debit card divided by the total number of customers:

Total number of customers = 56 (cash) + 26 (debit card) + 9 (credit card) = 91 customers

Probability of paying with a debit card = Number of customers who paid with a debit card / Total number of customers
Probability = 26 / 91 ≈ 0.2857

To express this probability as a percentage, we need to multiply by 100 and round to the nearest whole number:
Probability as a percentage = 0.2857 * 100 ≈ 28.57%

Therefore, the probability that the next customer will pay with a debit card is approximately 29% to the nearest whole number.