The equation r = 6t gives the number of albums released, r, by a record label over time in years, t. If you graph this relations

Answer:Part a)

Part b) When Jenny divides the square root of her favorite positive integer by , the result is an integer.

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For

-----> the product results in an integer

thus

The number could potentially be Jenny's favorite positive integer

2) For

-----> the product results in an integer

thus

The number could potentially be Jenny's favorite positive integer

3) For

-----> the product results in an integer

thus

The number could potentially be Jenny's favorite positive integer

Part B)

1) For

-----> the outcome is an integer

2) For

-----> the outcome is an integer

3) For

-----> the outcome is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by , she obtains an integer as a result.

Answer:

a) Ann has a 1/3 chance of winning in the first round

b) The chance of Ann winning for the first time in the fourth round is 8/81

c) The probability that Ann's first win occurs after the fourth round is 16/81

Step-by-step explanation:

a) Each strategy is played with a probability of 1/3. Given any strategy, there’s a 1/3 chance that Bill will choose the strategy that allows Ann to win. Consequently, the probability of Ann securing a victory in the first round (or any round) is

1/3 * 1/3 + 1/3 * 1/3 + 1/3 * 1/3 = 1/9 + 1/9 + 1/9 = 1/3.

Thus, the likelihood of Ann winning the initial round is 1/3.

b) The chances of Ann winning a round stand at 1/3; therefore, her chances of not winning are 2/3. This must happen three times before her first victory. Thus, the probability that Ann's first win occurs in the fourth round is

(2/3)³ * 1/3 = 8/81.

c) The first victory happens after the fourth round if she remains unsuccessful in the first four rounds, translating to a possibility of (2/3)⁴ = 16/81.

Answer:

Step-by-step explanation:

Considering the differential equation x^4(dy/dx) + x^3y = -sec(xy). We will solve it employing the method of separation of variables;

By substituting v and dv/dx into the previous equation, we acquire;

We then separate the variables:

The end expression provides the solution to the differential equation.