Suppose that the amount of algae in a pond triples every 2 hours. If the pond initially contains 80 pounds of algae, how much algae will be in the pond after 8 hours?
After 2 hours, the pond will contain 3 times 80 pounds, or 240 pounds of algae. After another 2 hours, the amount of algae will triple again, giving a total of 3 times 240 pounds, or 720 pounds. After 6 hours, the amount of algae will triple once more, giving 3 times 720 pounds, or 2160 pounds. Finally, after 8 hours, the amount of algae will triple once more, giving a total of 3 times 2160 pounds, or 6480 pounds of algae. Therefore, there will be 6480 pounds of algae in the pond after 8 hours.
What is the order of the numbers from least to greatest?
A = 6.2 × 10–5 B = 12.3 × 10–7 C = 5.2 × 103 D = 3.7 × 10–5
B, D, A, C
A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h = –5t2+ 92t + 16. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
The maximum height of the boulder occurs at the vertex of the parabolic function given by h = –5t^2 +92t +16. The t-coordinate of the vertex is given by t = –b/2a, where a = –5 and b = 92. Substituting these values, we get:
t = –92/(2 * –5) = 9.2 seconds
This means that the boulder takes 9.2 seconds to reach maximum height.
To find the maximum height, we can substitute this value of t into the given function to get:
h = –5(9.2)^2 + 92(9.2) + 16 ≈ 423.68
So the boulder's maximum height is approximately 423.68 meters.
Suppose that y varies inversely with x, and y = 2 when x = 6. What is an equation for the inverse variation?
If y varies inversely with x, then y is equal to a constant value divided by x. Let k denote this constant of proportionality. Then we have:
y = k/x
To find the value of k, we can use the initial condition given in the problem. We know that when x = 6, y = 2. Substituting these values into the equation above, we get:
2 = k/6
Simplifying this equation, we can multiply both sides by 6 to get:
k = 12
Therefore, the equation for the inverse variation is:
y = 12/x
Simplify the rational expression. State any excluded values.
3x minus 12 over x minus 4
A. x
B. 3; where x ≠ 4
C. 3; where x ≠ 3
D. 0
The given rational expression is:
(3x - 12)/(x - 4)
We can factor the numerator and simplify the expression as follows:
(3x - 12)/(x - 4) = 3(x - 4)/(x - 4)
Notice that the factor of (x - 4) appears in both the numerator and denominator, and therefore can be canceled out. This leaves us with:
3
Therefore, the simplified expression is just 3.
However, we must note that the expression (3x - 12)/(x - 4) is undefined at x = 4, since division by zero is not allowed. Therefore, the excluded value is x = 4.
The correct answer is:
A. x; where x ≠ 4
What are the minimum, first quartile, median, third quartile, and maximum of the data set?
18, 20, 11, 10, 8, 6, 12, 4