The function $A left parenthesis t right parenthesis equals 12 left parenthesis 2 right parenthesis to the power of fraction numerator t over denominator 6 end fraction end exponent$ models the number of water hyacinths in a population over time, where A(t) is the number of water hyacinths and $t$ is the time, in days since the population was measured. Which is the best interpretation of $left parenthesis 2 right parenthesis to the power of fraction numerator t over denominator 6 end fraction end exponent$ in this context?

What is the graph of the equation $y equals 2 left parenthesis 3 right parenthesis to the power of x end exponent$ ?

Two beach balls are each in the shape of a sphere. The larger beach ball has a diameter of 3x, and the smaller beach ball has a diameter of x. What is the ratio of the volume of the larger beach ball to volume of the smaller beach ball?

volume of a sphere
A sphere is a collection of points in space separated by r from the center. The quantity of space a solid in three dimensions takes up is known as its volume. The unit of volume is measured in cubic (in³, ft³, cm³, m³, et cetera). Before calculating the volume, ensure all measurements are in the same unit.
Follow the steps below to determine the volume of a given sphere:
Step 1: Compare the radius of the given sphere. If you know the diameter of the sphere, divide it by two to get the radius.
Step 2: Find the radius of r'³s cube.
Step 3: Now divide it by (4/3) π
Step 4: The volume of the sphere will be the final answer.
The volume V of a sphere is equal to four-thirds of pi times the cube of the radius.
V = 4/3πr³
A hemisphere's volume is equal to one-half that of its related sphere.

Two beach balls are each in the shape of a sphere. The larger beach ball has a diameter of 3x, and the smaller beach ball has a diameter of x. What is the ratio of the volume of the larger beach ball to volume of the smaller beach ball?

Which expression is equivalent to $left parenthesis 2 x to the power of 2 end exponent plus blank 3 x minus 2 right parenthesis minus left parenthesis 5 x to the power of 2 end exponent minus x minus 7 right parenthesis$ ?

$y greater than 4 x$
$y less than negative x$
When graphed in the xy plane, what point (x, y) is a solution to the given system of inequalities?

$x to the power of 2 end exponent minus 10 x plus y to the power of 2 end exponent plus 6 y blank equals blank 2$
The graph in the xy- plane of the equation above is a circle. What are the coordinates of the center of the circle?

If $blank x greater than 0$ , which of the following is equivalent to $fraction numerator 1 over denominator x end fraction plus fraction numerator 1 over denominator 2 x end fraction$ ?

A line in xy - plane has a slope of 1 and passes through the point (0, 2). Which is an equation of the line?

x + 7 = 3(x - 3)
What value of x satisfies the given equation?

x² + 10 = 91
What is the positive solution to the given equation?

$x squared minus 12 x plus 23 equals 0$
Which of the following is a solution to the given equation?

The graph of the function f defined by $f left parenthesis x right parenthesis equals 1 fourth left parenthesis x plus 4 right parenthesis squared minus 5$ is shown. The graph passes through the points $left parenthesis negative 10 comma a right parenthesis text and end text left parenthesis a comma b right parenthesis comma$ where a and b are constants. What is the value of b ?

$5 x minus 2 plus 3 x equals 3 left parenthesis x plus 4 right parenthesis plus 5 x minus 10$
Which of the following statements is true about the equation above?

$y equals left parenthesis x plus 5 right parenthesis squared minus 8$
The equation above can be represented by a parabola in the -plane. The parabola is then translated so that the vertex is at (0, 0). Which of the following best describes the translation?

$vertical line x plus 2 vertical line equals vertical line x minus 8 vertical line$
What is the solution to the given equation?