The First Lady planted rhubarb in the square bed above. Express the perimeter of the rhubarb bed in the terms of x.

Answer:

(C) 10% to 70%(

Step-by-step explanation:

Given that at least 40% of the students are learning German, the upper limit of those who might be enrolled in English but not in German is 60%. However, since a minimum of 70% study English, it leads to the conclusion that at least 10% of students must be taking both German and English.

If we consider that at least 30% of students are learning Italian, and assuming that no student is studying all three languages simultaneously, then there is a maximum of 70% of students who could potentially be registered in both English and German.

This means the possible percentage for students enrolled in both English and German ranges from 10% to 70%

The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.

a) The sequence is geometric.

b) The subsequent term is 486

c) The rule is:

The 20th term will be: a_{20}=6973568802

Step-by-step explanation:

The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.

Part a) Is this sequence arithmetic or geometric?

An arithmetic sequence has a constant difference between consecutive terms.

In the given series 6, 18, 54, 162,

18-6 = 12

54-18= 36

The differences are not constant, thus it isn’t arithmetic.

A geometric sequence maintains a constant ratio between consecutive terms.

In this series 6, 18, 54, 162,

18/6 = 3

54/18 = 3

162/54 = 3

The ratios remain constant; therefore, the sequence is geometric.

The sequence in question is geometric.

Part b) How can you determine the next number in the series?

The next number can be calculated using the following formula:

where a_n= nth term

a= first term

r= common ratio

The next number represents the 5th term of the sequence.

To find the 5th term:

Thus, the next term in the sequence is 486

Part c) What is the rule for determining the 20th week? Calculate the 20th week.

The rule for determining the 20th week is:

Here n=20

Calculating the 20th week

Triangle XYZ is an equilateral triangle, meaning the sector's central angle measures 120 degrees, which is equivalent to 2π/3 radians. To find the area of a sector corresponding to a central angle β, we use the formula A = (1/2)r²*β, where β is expressed in radians. For this sector, the area calculation is A = (1/2)*2²*(2π/3) = 4π/3 square units.

Response:

Detailed breakdown: