An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be give

In the long term, the expense of the refrigerator represented by g(x) will be the most economical. The average yearly expenditure to operate two different refrigerators over x years is expressed by two functions, f(x) = 850 + 62x and g(x) = 1004 + 51x. Equating these functions, f(x) and g(x) allows us to determine the time in years when their costs will equalize. At x = 1 year, f(1) = 850 + 62 = $912 and g(1) = 1004 + 51 = $1055, indicating f(x) is initially cheaper. To find when f(x) equals g(x), we resolve for x. At x = 14 years, the evaluation shows f(15) = 56.67 + 62 = $118.67 and g(15) = 66.93 + 51 = $117.93, thus confirming g(x) becomes more affordable beyond 14 years. Therefore, for the initial 14 years, f(x) is less than g(x), but thereafter g(x) is cheaper.

Answer:

35.7 km and 248.3 °

Step-by-step explanation:

To clarify, I will include a diagram as an image.

We begin with the cosine law formula:

y² = 42² + 28² - (2 * 42 * 25 * cos 58 °)

y² = 2389 - 1112.83 = 1276.17

y = √1276.17

y = 35.72 km

Next, to find the bearing of the surveyor from her camp, we apply the sine law:

[(Sin 58 °) / y] = [(Sin A) / 42]

Here, A = (42 * sin 58 °) / 35.72

A = sin⁻¹ (0.9971)

A = 85.7 °

The bearing from the base camp now calculates to: 270 ° - (85.7 ° - 64 °) = 248.3 °

Rotational symmetry indicates that an object appears unchanged when rotated.

Upon examining the figures, option B might seem plausible, but observe that the edges vary in length—rotating it will not align perfectly with its original position.

Options C and D are eliminated as they lack any symmetrical characteristics; no matter how they are turned, they appear different.

This leaves option A as the only choice: if you rotate this figure by 180 degrees, its appearance remains unchanged.

Consequently, the figure possessing rotational symmetry is A.

Answer:

2.1/√55

Step-by-step explanation:

standard deviation divided by the sample size

Homer made an error in step 2

When completing the square, it's necessary to apply the adjustments to both sides of the equation

Solution:

The provided equation for the circle:

First, let’s determine the center and the radius and identify where the mistake occurred

Step 1:

Group the terms

Step 2:

However, Homer’s second step is:

Thus, Homer committed an error during this step

When completing the square, the values must be added to both sides of the equation

However, Homer neglected to add 49 and 1 to the right side of the equation

Correct steps are:

By comparing with the general equation of a circle,

It follows that the center coordinates are ( 7, -1) and the radius measures 8.66