Please help i will make brainliest

Answer:

• c = 135
• k = 0.42615

Step-by-step explanation:

We assume you want your model to be ...

  p = c·e^(kt)

Filling in (t, p) values of (3, 484) and (5, 1135), we have two equations in the two unknowns:

  484 = c·e^(3k)

  1135 = c·e^(5k)

Taking logs makes these linear equations:

  ln(484) = ln(c) +3k

  ln(1135) = ln(c) +5k

Subtracting the first equation from the second, we have ...

  ln(1135) -ln(484) = 2k

  k = ln(1135/484)/2 ≈ 0.42615

Using that value in the first equation, we find ...

  ln(484) = ln(c) +3(ln(1135/484)/2)

  ln(c) = ln(484) -(3/2)ln(1135/484)

  c = e^(ln(484) -(3/2)ln(1135/484)) ≈ 134.8

The initial number in the culture was 135, and the k-value is about 0.42615.

_____

I prefer to start with the model ...

  p = 484·(1135/484)^((t-3)/2)

Then the initial value is that obtained when t=0:

  c = 484·(1135/484)^(-3/2) = 134.778 ≈ 135

The value of k the log of the base for exponent t. It is ...

  ln((1135/484)^(1/2)) = 0.426152

This starting model matches the given numbers exactly. The transformation to c·e^(kt) requires approximations that make it difficult to match the given numbers.

__

For this model, the base of the exponent is the ratio of the two given population values. The exponent is horizontally offset by the number of days for the first count, and scaled by the number of days between counts. The multiplier of the exponential term is the first count. The model can be written directly from the given data, with no computation required.

Answer:

Mr. Johnson borrowed the money at an interest rate of 4.25%.

Step-by-step explanation:

We can use the formula for simple interest to solve this problem:

Simple Interest = Principal x Rate x Time

Where:

Principal is the amount borrowed.

Rate is the interest rate (as a decimal).

Time is the length of time the money is borrowed for.

We know that Mr. Johnson borrowed $8000 for 4 years and repaid a total of $10,320. We can use this information to set up an equation:

10,320 = 8000 + 8000 x Rate x 4

Simplifying this equation:

10,320 = 8000 + 32000 x Rate

Dividing both sides by 32000:

Rate = (10,320 - 8000) / (8000 x 4) = 0.0425 or 4.25%

Therefore, Mr. Johnson borrowed the money at an interest rate of 4.25%.

Hope this helped! Sorry if it didn't. If you need more help, ask me! :]

Answer:

a) 0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b) 0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

Poisson process with rate 2 per minute

This means that

a. What is the probability that during a given 1 min period, the first operator receives no requests?

Single operator, so we use the Poisson distribution.

This is P(X = 0).

0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests?

6 operators, so we use the binomial distribution with

Each operator has a 13.5% probability of receiving no requests during a minute, so

This is P(X = 3).

0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

The difference between the cash price and the initial deposit in hire purchase is known as .

In hire purchase transactions, buyers can acquire goods by making an initial down payment and paying the remaining amount in installments. The difference between the total cost of the item and the initial deposit is a crucial concept known as the in mathematical terms. Let's explore this in detail.

In the context of hire purchase, the total cost of the item is often referred to as the cash price. It represents the actual value of the item without considering any interest or finance charges. On the other hand, the initial deposit, also called the down payment, is the amount paid upfront by the buyer to secure the item.

Now, let's introduce some variables to help us understand this concept mathematically:

- Let CP be the cash price of the item.

- Let D be the initial deposit made by the buyer.

The difference between the cash price and the initial deposit is given by:

The Principal is the amount that remains to be paid off in installments, and it serves as the basis for calculating the subsequent monthly or periodic payments in a hire purchase agreement.

The Principal is critical because it determines the total amount the buyer will end up paying for the item. It also affects the duration of the hire purchase agreement, as the buyer's installments are typically spread over a specific number of months or years.

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