Which graph represents a reflection of f(x) = 6(0.5)x across the x-axis?

Answer:

6 knots

Step-by-step explanation:

Let the velocity be v knots

thus, the time required to traverse 500 M is given by 500 / v hours

Fuel consumption per hour is equal to 216 plus half the cube of the speed (v^3).

Let F denote the fuel consumption for the journey

= [500/v][216 + 0.5v^3]

= 500[216/v + 0.5v^2]

The derivative of F with respect to v is: dF/dv = 500[ - 216/v^2 + v]

The second derivative, d^2F/d^2v = 500[432/v^3 + 1], indicates positivity.

Setting dF/dv to zero helps find the minimum.

500[ -216/v^2 + v] = 0

or v = 216/v^2

or v^3 = 216

By solving, we arrive at v = [216]^(1/3) = 6 knots

A line and a point.

Additional explanation

A ray consists of a segment of a line emerging from one endpoint. It represents an infinite straight path extending in one direction from a starting point, exemplified by .

The arrow indicates the direction along which the ray extends. The ray's length isn't quantifiable.

In geometry, undefined terms refer to fundamental figures that are not defined by other figures. The primary undefined terms in geometry include a point, line, and plane.

These crucial concepts cannot be precisely defined in mathematical terms using other established words.

• A point indicates a specific location without any size; it is marked with a capital letter and a dot.
• A line comprises an infinite collection of points stretching in both directions with just one dimension; it is a straight path without thickness.
• A plane represents a flat surface encompassing numerous points and lines, extending infinitely in all directions. It is two-dimensional, and any three points that are not collinear define a unique plane.

Explore more

1. Which points are both coplanar and noncollinear?
2. Definition of line segments
3. What are three collinear points on a line?

Keywords: which undefined terms define a ray, point, line, plane, endpoint, one direction, the ray's arrow

Response:

1 B

2 A

3 B

Detailed explanation:

1

The population refers to the entire sample from which part of the event is being analyzed. Essentially, in a set, the population includes everything collectively. From the provided statement, our goal is to identify the population. The population is B.

All NBA players since 1966. This selection is because it is from this set that the draft picks were chosen, ultimately narrowed down to 45% being center backs.

2

The specified attribute is A.

Being a No. 1 draft pick, as it's the central focus of the statement itself

3

B sample proportion. As mentioned earlier, the population consists of all NBA players since 1966, so a population proportion would contain a statement like this.

45% of all NBA players since 1966...

Consequently, it's a sample proportion since it pertains to the draft pick, as opposed to the NBA players

Answer:

A) The estimated proportion of women whose platelet counts fall within 2 standard deviations of the mean, or between 118.5 and 377.3, is 95%.

B) The estimated percentage of women with platelet counts ranging from 53.8 to 442.0 is 99.7%.

Step-by-step explanation:

Provided data:

mean;μ = 247.9

standard deviation;σ = 64.7

A) We seek to find the estimated percentage of women with platelet counts within 2 standard deviations from the mean, which translates to values between 118.5 and 377.3.

Based on the attached image, the empirical curve indicates that the likelihood within 1 standard deviation of the mean is (34% + 34%) = 68%.

In contrast, the likelihood within 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%

Therefore, the estimated percentage of women having platelet counts within 2 standard deviations of the mean, or ranging from 118.5 to 377.3, equals 95%

B) Next, we want to determine the estimated percentage of women with platelet counts between 53.8 and 442.0.

The values of 53.8 and 442.0 correspond to 3 standard deviations from the mean.

Let’s verify that.

Since mean;μ = 247.9

standard deviation;σ = 64.7;

μ = 247.9

σ = 64.7

μ + 3σ = 247.9 + 3(64.7) = 442

Also;

μ - 3σ = 247.9 - 3(64.7) = 53.8

From the attached empirical curve, it can be seen that at 3 standard deviations from the mean, the probability percentage is;

(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%