Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in

Assume that the number of overdue days for the library book is X, and the total fine is Y.

Liability charges a fee of $0.30 per day for lateness,

Thus, for one day late, the fee equals: 1 * $0.30

For X days late, the fee becomes: X * $0.30.

The total fee Y corresponds to being X days late, so: Y = 0.30 * X.

Next, we'll verify which possible answers satisfy the equation Y = 0.30 * X.

Options one (-3, -0.9) and two (-2.5, -0.75) are invalid since the number of late days cannot be negative, and these give negative values for X.

Option three (4.5, 1.35) is also incorrect because the library charges per whole day; 4.5 days is not an integer, so they would charge 4 or 5 days, not 4.5.

Option four (8, 2.40) matches the equation perfectly:

Y = 0.30 * X

2.40 = 0.30 * 8

2.40 = 2.40.

Therefore, the only correct answer is option four (8, 2.40).

The equation representing the circle centered at (-27, 120) that passes through the origin is:

Solution:

The general equation of a circle is expressed as:

Where,

(a, b) denotes the center of the circle

r signifies the radius

Given the center as (-27, 120)

Thus;

a = -27

b = 120

Considering it intersects the origin, meaning (x, y) = (0, 0)

Substituting (a, b) = (-27, 120) and (x, y) = (0, 0) into the equation

Input = 15129 and (a, b) = (-27, 120) into the equation

Hence, the equation characterizing the circle is determined

Solution:

Let x be the distance in miles from the house to the theater.

Total time taken for the trip

Then average speed

Terrence walks at a speed of 2 miles per hour to the theater and returns home at 40 miles per hour.

Thus, Average Speed mi/hr

Both average speeds must be equivalent. Hence, we can express this as:

Consequently, the distance from home is 13.125 miles.

Answer:

There are 9 essay questions.

Step-by-step explanation:

Let x represent the number of multiple-choice questions and y represent the number of essay questions.

Given that the total question count is 26, we can derive the equation,

Additionally, the multiple-choice and essay questions carry values of 3 points and 8 points, respectively.

The overall points available in the test equal 123.

Thus, we set up the following equations:

x+y=26...........................(1)

3x+8y=123............................(2)

If we multiply equation (1) by 3 and subtract equation (2), we obtain:

5y = 45, leading to y = 9

Consequently, from x+y=26, we find x = 26 - y, resulting in x = 17.

Hence, the counts of multiple-choice and essay questions are 17 and 9, respectively.