Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. I

The capacity is approximately 3.5 fluid ounces. In order to determine this, we need to compute the volume of a cone-shaped cup. The formula for the volume of a cone is: 1/3 * π * r^2 * h, where r equals the diameter divided by 2, which gives 1.35 inches, and h equals 3.3 inches. After substituting these values, we find the volume to be V = 1/3 * 3.14 * 1.35^2 * 3.3 = 6.3 cubic inches. To convert cubic inches to fluid ounces, we use the relationship that 1 fluid ounce is equal to 1.8 cubic inches. Therefore, x fluid ounces equal to 6.3 cubic inches leads to x = 6.3 / 1.8, which results in 3.5 fluid ounces.

The cake board’s circumference measures 35π cm. Initially, noting the cake's diameter of 30 cm, the board's diameter is established as an additional 5 cm, leading to circumference determination by applying the formula, yielding 35π cm.

Angle A =x

Angle B is represented as 4x

Angle C is expressed as 5x-30

Hence, the correct responses are A, C, and D

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

Response:

30

Detailed steps:

9r+16=pi5

9r+16=22/7*5

9r+16=15.7

16-15.7=9r

0.3=9r

9r=0.3

r=30