The side of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeters units

Response:

The result is $43623.50

Detailed explanation:

This query involves compound interest.

The formula for calculating compound interest is

A=P(1+r)^t

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Provided information

P= $2,500

r= 10/100= 0.1

t= 30 years

Inserting values into the compound interest formula and calculating A gives us

A=2500(1+0.1)^30

A=2500(1.1)^30

A=2500*17.449

A=$43623.50

The total amount is $43623.50

The balance in her account comes from Jenna’s (A annuity payments)

Response:

a) The average is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% likelihood that the average time of visitors falls within 15 seconds of 10 minutes.

c) 10.58 minutes.

Step-by-step clarification:

To figure this out, we must comprehend the normal probability distribution alongside the central limit theorem.

Normal Probability Distribution

Issues involving normal distributions can be resolved using the z-score formula.

For a data set with mean and standard deviation , the z-score related to a measure X is defined as:

The z-score illustrates how many standard deviations the measure is positioned from the mean. Once the z-score is calculated, we refer to the z-score table to find the p-value matching this z-score. This p-value reflects the likelihood that the measurement is less than X, which means it indicates the percentile of X. To determine the chance that the measure exceeds X, we subtract the p-value from 1.

Central Limit Theorem

The Central Limit Theorem states that for a normally distributed random variable X, defined by mean and standard deviation , the sampling distribution of sample means of size n can be approximated as a normal distribution with mean and standard deviation .

For non-normal distributions, this theorem applies if n is at least 30.

In this case, the distribution has a mean of 10 minutes and a standard deviation of 2 minutes.

This indicates that

Assuming 64 visitors independently access the site.

This implies that

a. The expected value and variance of the average time of the visitors.

Employing the Central Limit Theorem, the mean is 10 and the variance is (0.25)^2 = 0.0625.

b. The chance that the mean visit duration is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, thus between 9.75 and 10.25 seconds, which corresponds to the p-value of z when X = 10.25 minus the p-value of z when X = 9.75.

X = 10.25

Through the Central Limit Theorem

has a p-value of 0.8413.

X = 9.75

has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

0.6826 = 68.26% chance that the average visitor time is within 15 seconds of 10 minutes.

c. The value surpassed by the average visitor time with a probability of 0.01.

This corresponds to the 99th percentile, denoting X when Z equals a p-value of 0.99, hence X when Z = 2.327.

Thus, the result is 10.58 minutes.

Answer:

Step-by-step explanation:

The exponential growth formula is

Where 'a' signifies the initial population

r is the growth rate and x represents time in years

maintaining a constant population of 32,000. Thus, the initial population is 32,000

with an annual increase of 8%. The growth rate is 8%, equivalent to 0.08

a = 32000 and r = 0.08

Now, substituting all the values into the general formula