landon owns a hybrid SUV that can travel 400 miles on a 15-gallon tank of gas.Determine how many miles he can travel on a 6 gall

Response:

4.113 × 10⁴ pounds per acre = approximately 41,130 pounds per acre when rounded to the nearest whole number.

Detailed explanation:

For every 2.3 × 10⁻⁵ acre harvested, 9.46 × 10⁻¹ pounds of potatoes were produced. To find the average production per acre, we divide the total pounds of potatoes by the harvested acres: 9.46 × 10⁻¹ pounds / 2.3 × 10⁻⁵ acre = 4.113 × 10⁴ pounds per acre = 41,130 pounds per acre when rounded.

Answer:

To achieve maximum profit, the weekly production should be 200 software programs and 235 video games.

Step-by-step explanation:

Let:

x ------> represent the number of software programs

y -----> denote the count of video games

We are aware that

------> inequality A

------> inequality B

------> inequality C

Utilizing a graphing method

The feasible solutions exist in the area marked between the positive values of x and y

Refer to the attached diagram

The vertices of this area are:

(0,0),(0,300),(135,300),(200,235),(200,0)

The profit function computes as:

Plugging the x and y values from each vertex into the profit function, we get:

For (0,300) -----

For (135,300) -----

For (200,235) -----

For (200,0) -----

Consequently,

To optimize the profit, the weekly production should consist of 200 software programs and 235 video games.

This question reveals an intriguing pattern.

The rule or pattern to follow here is:

For the left side of the number compared to its predecessor: (First digit x Third digit + 1)

For the right side: (Second digit x Fourth digit -1)

For instance, consider 6447. Next, let's examine its previous number, 9876.

Now, and

that's how we arrived at 6447

Next, for the third number, 2527, let's look at its previous number, 6447

Now,

and

that's how we reached 2527

Following the same reasoning, the missing number should be 534.

This conclusion came from applying the rule of the pattern as:

and

Thus, we derived 534.

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

Since the point lies on the circle, its coordinates must be,

The distance "d" from the point to (30,40) can be calculated as,

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when is at its lowest value.

Let’s set up the equation,

We find the critical points,

Then,

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

This leads us to conclude that the closest point is (78,104)