A set of elementary school student heights are normally distributed with a mean of 105105105 centimeters and a standard deviatio

Answer:

To identify the critical point, we set the derivative equal to zero, resulting in:

Calculating the second derivative yields:

This indicates that t = 3.4375 marks the minimum value for the function. Substituting this back into the original function gives us:

Thus, the minimum annual income is found at t = 3.43 (between the years 2008 and 2009), with a value of 25.094

Step-by-step explanation:

In this scenario, we have the function:

Where P represents the annual net income from 2007-2011, and

t is the number of years since early 2005

To discover the lowest income, we utilize the derivative given by:

Setting this derivative to zero allows us to find the critical point, leading to:

Calculating the second derivative reveals:

Therefore, we conclude that t = 3.4375 is the minimum value, substituting into the original function results in:

Thus, the minimum annual income occurs at t = 3.43 (between 2008 and 2009) with the value being 25.094

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

The diagram is not available, so I included a supplementary figure.

Response:

The segments ST and UT are equal in length.

Detailed explanation:

As seen in the additional figure

∵ ST and UT act as tangents to circle K at points S and U respectively

∵ SK and UK are the radii of circle K

- A tangent is perpendicular to the radius at the point where it touches the circle.

Thus, ST ⊥ KS at point S

Thus, m∠KST = 90°

Thus, UT ⊥ KU at point U

Thus, m∠KUT = 90°

Therefore, m∠KST = m∠KUT

In triangles KST and KUT

∵ KS = KU because they are both radii

∵ m∠KST = m∠KUT confirms the equality

∵ KT is common to both triangles

- Therefore, the triangles are congruent according to the HL criterion

∴ Δ KST ≅ KUT as per the HL criterion

- Thus, from the congruency result

∴ ST = UT

The segments ST and UT are equal in length.

x = 3

-2 | 2.2(3) - 3.3 | = -6.6

-2 | 6.6 - 3.3 | = -6.6

-2 | 3.3 | = -6.6

-2 * 3.3 = -6.6

-6.6 = -6.6