You are choosing between two health clubs. Club A offers membership for a fee of $ 14 $14 plus a monthly fee of $ 15. $15.  Club B offers membership for a fee of $ 18 $18 plus a monthly fee of $ 14. $14.  After how many months will the total cost of each health club be the​ same? What will be the total cost for each​ club?

The corner of a rectangle is called the vertex of the rectangle.

Joining any two adjacent vertices is the side of the rectangle.

Joining any two vertices which are opposite to each other is called a diagonal of the rectangle.

The length of both the diagonals of a rectangle is always equal.

Final answer:

A line drawn from one corner of a rectangle to the opposite corner is called a diagonal in mathematics. It's a vector contains two components: the x-component and the y-component that are parallel to the x-axis and y-axis, respectively.

Explanation:

In the field of mathematics, a line drawn from one corner of a rectangle to the opposite corner is referred to as a diagonal. This line is equivalent to a vector that encompasses two components. The x-component Ax is the side of the rectangle that is parallel to the x-axis and the y-component Ay is the side parallel to the y-axis. To visualize it, consider a rectangle with corners A, B, C, and D. Draw a line from corner A to corner C. This line is the diagonal of the rectangle.

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Answer:

3948 members

Step-by-step explanation:

SInce a is the initial amount, a = 2000. b represents growth factor, and the amount increases by 12% every year, so b = 1.12. Since you want to find the value in 6 years, x= 6. Therefore your equation is y = 2000 • 1.12 ^ 6. Plug it into your calculator and you get y =  3947.64, and since they are people you round up to 3948 members.

Answer:

The probability that fewer than 10 in a sample of 200 pills will be ineffective is 0.4364

∴ P(X<10)=0.4364

Step-by-step explanation:

Given that the total number of sample pills is 200

ie., n=200

To find  the probability that fewer than 10 in a sample of 200 pills will be ineffective:

Let us assume it success if a pill is ineffective.

The probability of success in each trial is

∴ p=0.05

We know that the total probability is p+q=1

The probability of failure is q

q=1-p

q=1-0.05

∴ q=0.95

Let X be the random variable of the number of ineffective pills in a sample of 200 pills.

Hence X has Binomial distribution with parameter n=200 and p=0.05

The formula for Mean in Binomial distribution is

Substitute the values in the above formula we get

∴

The formula for Standard deviation in Binomial distribution is

Substitute the values in the above formula we get

∴

Now we have to find the probability that fewer than 10 in a sample of 200 pills will be ineffective.

That is to find the area to the left of x=9.5

The formula is

Substitute the values in the formula we get

∴

Now P(X<10)=P(Z<-0.16)

=0.4364

∴ P(X<10)=0.4364

Therefore the probability that fewer than 10 in a sample of 200 pills will be ineffective is 0.4364

Final answer:

The probability that fewer than 10 out of 200 birth-control pills will be ineffective is approximately 0.817, or 81.7%.

Explanation:

Probability is a mathematical concept used to quantify the likelihood of an event occurring. It ranges from 0 (impossible) to 1 (certain). It plays a crucial role in statistics and decision-making, helping to predict outcomes, assess risk, and make informed choices. To find the probability that fewer than 10 in a sample of 200 birth-control pills will be ineffective, we can use the binomial probability formula:

P(X < 10) = Σ (n choose k) * p^k * (1-p)^(n-k), where:

n = sample size = 200,

k = number of ineffective pills,

p = probability of a pill being ineffective = 0.05.

Calculating this probability using the formula, we get:

P(X < 10) ≈ 0.817, or 81.7%.

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