Question
What is the simplified form of (3/2b^4)^3
Answers
Answer
Find the simplified form of the expression. Give your answer in scientific notation. (3 × 10^6)(8 × 10^–4)
Answer
Radio signals travel at a rate of 3 × 10^8 meters per second. How many seconds would it take for a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height of 3.6 × 10^7 meters? (Hint: Time is distance divided by rate.) (1 point)
Answer
Does the rule y=-5x^6 represent an exponential function? (1 point) Responses
Answer
Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains 90 pounds of algae, how much algae will be in the pond after 12 hours? (1 point)
Answer
A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account? (1 point)
Answered by
GPT 3.5
The simplified form of (3/2b^4)^3 is (27/8b^12).
Answered by
GPT 3.5
To multiply the numbers in scientific notation, you multiply the coefficients and add the exponents. Therefore, (3 × 10^6)(8 × 10^–4) can be simplified as follows:
(3 × 8)(10^6 × 10^–4) = 24 × 10^(6 + -4) = 24 × 10^2 = 2400
So, the simplified form of the expression (3 × 10^6)(8 × 10^–4) is 2400 in scientific notation, which is written as 2.4 × 10^3.
(3 × 8)(10^6 × 10^–4) = 24 × 10^(6 + -4) = 24 × 10^2 = 2400
So, the simplified form of the expression (3 × 10^6)(8 × 10^–4) is 2400 in scientific notation, which is written as 2.4 × 10^3.
Answered by
GPT 3.5
To calculate the time it takes for a radio signal to travel from a satellite to the surface of Earth, we need to divide the distance by the rate. The distance is given as 3.6 × 10^7 meters and the rate is given as 3 × 10^8 meters per second.
Dividing the distance by the rate:
Time = Distance / Rate
Time = (3.6 × 10^7 meters) / (3 × 10^8 meters/second)
Now, let's simplify the expression:
Time = (3.6 / 3) × (10^7 / 10^8) seconds
Time = 1.2 × 10^(-1) seconds
Therefore, it would take a radio signal 1.2 × 10^(-1) seconds to travel from the satellite to the surface of Earth.
Dividing the distance by the rate:
Time = Distance / Rate
Time = (3.6 × 10^7 meters) / (3 × 10^8 meters/second)
Now, let's simplify the expression:
Time = (3.6 / 3) × (10^7 / 10^8) seconds
Time = 1.2 × 10^(-1) seconds
Therefore, it would take a radio signal 1.2 × 10^(-1) seconds to travel from the satellite to the surface of Earth.
Answered by
GPT 3.5
No, the rule y=-5x^6 does not represent an exponential function.
Answered by
GPT 3.5
If the amount of algae in the pond doubles every 4 hours, we can determine the amount of algae in the pond after 12 hours by repeatedly doubling the initial amount of algae.
Starting with 90 pounds of algae, after 4 hours it will double to 90 * 2 = 180 pounds.
After another 4 hours (8 hours total), it will double again to 180 * 2 = 360 pounds.
Finally, after another 4 hours (12 hours total), it will double once more to 360 * 2 = 720 pounds.
Therefore, after 12 hours, there will be 720 pounds of algae in the pond.
Starting with 90 pounds of algae, after 4 hours it will double to 90 * 2 = 180 pounds.
After another 4 hours (8 hours total), it will double again to 180 * 2 = 360 pounds.
Finally, after another 4 hours (12 hours total), it will double once more to 360 * 2 = 720 pounds.
Therefore, after 12 hours, there will be 720 pounds of algae in the pond.
Answered by
GPT 3.5
To calculate the balance after 4 years with interest compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = principal amount (initial balance)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $4,000.00, the annual interest rate (r) is 5% (0.05 as a decimal), there is one compounding per year (n = 1), and the time period (t) is 4 years.
Plugging the values into the formula:
A = 4000(1 + 0.05/1)^(1*4)
A = 4000(1 + 0.05)^4
A = 4000(1.05)^4
A ≈ 4000(1.21550625)
A ≈ 4862.03
Therefore, after 4 years, the balance in the account will be approximately $4,862.03.
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = principal amount (initial balance)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $4,000.00, the annual interest rate (r) is 5% (0.05 as a decimal), there is one compounding per year (n = 1), and the time period (t) is 4 years.
Plugging the values into the formula:
A = 4000(1 + 0.05/1)^(1*4)
A = 4000(1 + 0.05)^4
A = 4000(1.05)^4
A ≈ 4000(1.21550625)
A ≈ 4862.03
Therefore, after 4 years, the balance in the account will be approximately $4,862.03.