What is an example that illustates the difference between statistical significance and practical signifincance?

Answer:

200n+50x+4000=Total Salary

Step-by-step explanation:

The equation of the line in slope-intercept form is: y = 5x + 3.

If the value of the slope of a line, m, is known, and the value of its y-intercept, b, is known, the equation of the line in slope-intercept form would be written as:

y = mx + b.

Given the following:

To write the equation of the line in slope-intercept form, substitute m = 5 and b = 3:

y = 5x + 3

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Question:

A line's slope is 5, and its y -intercept is 3. What is its equation in slope-intercept form?

The family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

To compare the box of cereal price we need to know the price per ounce first. It can be written as

Price per ounce = price /  total ounces

From the text above, we know that :

large size price = $3.34

large size ounces = 15

family size price = $5.14

family size ounces = 24

By substituting the parameter we can get the price per ounce of large size and family size

Large size

Price per ounce = price /  total ounces

Price per ounce = 3.34 / 15

Price per ounce = $0.22 / ounce

Family size

Price per ounce = price /  total ounces

Price per ounce = 5.14 / 24

Price per ounce = $0.21 / ounce

Hence, the family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

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Answer:

Step-by-step explanation:

Hope this helps :)

The ogive is a line graph that plots the cumulative relative frequency distribution.

An ogive, also known as a cumulative frequency polygon, is a line graph that shows the cumulative frequency distribution of a data set. The cumulative frequency is calculated by adding up the frequencies of each value up to a certain point in the data set.

The cumulative relative frequency is calculated by dividing the cumulative frequency by the total number of observations in the data set. The ogive plots these cumulative relative frequencies against the corresponding values in the data set, usually on the x-axis.

By plotting the cumulative relative frequencies, the ogive shows how the data is distributed over the entire range of values. It can be used to identify patterns in the data, such as whether it is skewed or symmetrical. It is also useful for determining percentiles, as the percentile for a given value can be read directly from the ogive.

Overall, the ogive is a helpful tool for summarizing and visualizing the distribution of a data set, particularly when dealing with large data sets or complex distributions.

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Answer:

2

Step-by-step explanation:

I got this answer by:

1) y = 4 - 2x

2) Move 4 to the other side of the equal sign and make it negative because thats the rule

3) Divide -2 from both sides

4) Answer is 2

y-intercept =4/1

Step-by-step explanation:

As per the angle sum property, the value of x is 125°

Angle sum property:

According to the angle sum property, the sum of interior angles of a triangle is 180°.

Given,

In the given diagram, PQR and SQT are straight line.

Now we need to find the value of x.

As per the angle sum property, we know that the sum of all the angles of the triangle is 180 degrees.

While we equate the given values within this property, we get.

x° + 55° = 180°

x° = 180° - 55°

x° = 125°

Therefore, the value of x is 125°.

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There is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

So, we know that:

27 black socks.

18 grey socks.

9 navy socks.

Probability formula: P(E) = Favouravle events/Total events

Now, insert values in the formula as follows:

P(E) = Favouravle events/Total events

P(E) = 27+18/27+18+9

P(E) = 45/54

P(E) = 15/18

P(E) = 5/6

Therefore, there is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.

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Correct question:
in a pitch-black room, you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. What is the probability that you take out pairs of socks to ensure you get a pair that is not navy?

The amount of interest would be $3076.51 in the account after 4 years.

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

A = P(1+r/100)ⁿ

Where:

A = the future value of the investment or loan

P = the principal investment or loan amount

r = the interest rate (decimal)

n = the number of compound periods

Given that Rafi has $6,629 in an account that earns 10% interest compounded annually.

p = $6,629

r = 10%

t = 4 years

A = P(1+r/100)ⁿ

Substitute the values of p,r, and t in the formula,

A = 6,629 (1 + 10/100)⁴

A = 6,629 (1 + 0.10)⁴

A = 6,629 (1.1)⁴

A ≈ 9705.51

Now, C.I. = A - P

So C.I. = 9705.51 - 6,629 = $3076.51

Therefore, the amount of interest would be $3076.51 in the account after 4 years.

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The required coordinate of point p is (4,6) of line segment PS.

Given that

M(5, 7) is the midpoint of PS The coordinates of S are (6, 9).
To determine the coordinates of p.

Here,
Let the coordinate of P be (h, k)
Now, the coordinates of the midpoint is given by,
x = [x₁ + x₂] / 2                           ;     y = [y₁ + y₂] / 2
now, putting x = 5, x₁ = 6, x₂ = h;     y = 7, y₁ = 9 y₂ = k
5 = 6 + h / 2                              ;     7 = 9 + k / 2
10 - 6 = h                                  ;     14 - 9 = k    
h = 4                                         ;      k  = 5

Thus, the required coordinate of point p is (4,6).

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Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

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a) The samples are independent.

b)  statistical notation the null and alternate hypothesis what are the df and t critical value is -2.821

c) According to the hypothesis, the statistical test makes the type 1 error.

The degrees of freedom (df) for this study is calculated as (n1 + n2 - 2), where n1 is the sample size of group 1 and n2 is the sample size of group 2. For this study, the df would be (12 + 12 - 2) = 22. The t critical value for a two-tailed test with a significance level of 0.05 and 22 degrees of freedom is ±2.074.

To conduct a t-test and d-test, we first need to calculate the means, standard deviations, and sample sizes of the two groups. The table below shows the data for each group:

Group                               In-class lectures                    Online lectures

Sample Size                          12                                                 12

Mean                                      79.5                                             84.3

Standard Deviation               6.02                                            5.67

Using this data, we can calculate the t-value and d-value for this study.

The t-value is calculated as (x₁ - x₂) / (s√(1/n1 + 1/n2)), where x₁ and x₂ are the means of the two groups, s is the pooled standard deviation, and n1 and n2 are the sample sizes of the two groups. The pooled standard deviation is calculated as s = √((n1-1)s1² + (n2-1)s2²) / (n1 + n2 - 2), where s1 and s2 are the standard deviations of the two groups.

Using the data from the table above, we can calculate the t-value as follows:

t = (79.5 - 84.3) / (5.34√(1/12 + 1/12)) = -2.821

The d-value is calculated as (x₁ - x₂) / sp, where sp is the pooled standard deviation calculated as √((s1² + s2²) / 2). Using the data from the table above, we can calculate the d-value as follows:

d = (79.5 - 84.3) / √((6.02² + 5.67²) / 2) = -1.756

For the t-test, the null hypothesis (H0) is that there is no significant difference in performance on the final exam between the two groups, and the alternative hypothesis (Ha) is that there is a significant difference in performance on the final exam between the two groups.

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The probability of selecting a bag of Original is derived as;

To find the value of the linear correlation coefficient r, you need to have two variables and their corresponding data sets.

The formula for the linear correlation coefficient r is as follows:

\($$r = \frac{n\sum xy - \sum x\sum y}{\sqrt{n\sum x^2 - (\sum x)^2} \sqrt{n\sum y^2 - (\sum y)^2}}$$\)

Where n is the number of data points, x and y are the two variables, and Σ represents the sum of the data. To calculate r, you need to calculate six sums: Σx, Σy, Σxy, Σx2, Σy2, and n.Let's go through an example.

Suppose you have the following data sets for two variables x and y:

$$x: 1, 2, 3, 4, 5$$$$

y: 2, 4, 6, 8, 10$$

First, calculate the six sums:

$$\Sigma x = 1 + 2 + 3 + 4 + 5 = 15$$$$\Sigma y = 2 + 4 + 6 + 8 + 10 = 30$$$$\Sigma xy = (1)(2) + (2)(4) + (3)(6) + (4)(8) + (5)(10) = 110$$$$\Sigma x^2 = (1)^2 + (2)^2 + (3)^2 + (4)^2 + (5)^2 = 55$$$$\Sigma y^2 = (2)^2 + (4)^2 + (6)^2 + (8)^2 + (10)^2 = 220$$$$n = 5$$

Now, substitute these values into the formula for r:

$$r = \frac{(5)(110) - (15)(30)}{\sqrt{(5)(55) - (15)^2} \sqrt{(5)(220) - (30)^2}}$$

$$r = \frac{550 - 450}{\sqrt{275 - 225} \sqrt{1100 - 900}}$$

$$r = \frac{100}{\sqrt{50} \sqrt{200}}$$

$$r = \frac{100}{\sqrt{10000}}$$

$$r = \frac{100}{100}$$

$$r = 1$$

Therefore, the linear correlation coefficient r is 1.

This indicates a perfect positive linear relationship between x and y.

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To find the value of the linear correlation coefficient r, you need to first calculate the covariance and standard deviation of the two variables.

The formula for the linear correlation coefficient r is:

\($$r = \frac{\text{cov}(X,Y)}{\sigma_X \sigma_Y}$$\)

where cov(X,Y) is the covariance of X and Y, σX is the standard deviation of X, and σY is the standard deviation of Y.

Here are the steps to calculate the linear correlation coefficient r:

Step 1: Calculate the mean of X and Y.

\($$ \begin{aligned}\overline X &= \frac{1}{n}\sum_{i=1}^{n} X_i\\ \overline Y &= \frac{1}{n}\sum_{i=1}^{n} Y_i\end{aligned} $$\)

Step 2: Calculate the deviations of X and Y from their respective means. \($$\begin{aligned}d_i(X) &= X_i - \overline X\\ d_i(Y) &= Y_i - \overline Y\end{aligned}$$\)

Step 3: Calculate the sum of the products of the deviations.

\($$S_{xy} = \sum_{i=1}^{n} d_i(X) d_i(Y)$$\)

Step 4: Calculate the covariance of X and Y.

\($$ \text{cov}(X,Y) = \frac{S_{xy}}{n-1} $$\)

Step 5: Calculate the standard deviation of X and Y.

\($$ \begin{aligned}\sigma_X &= \sqrt{\frac{\sum_{i=1}^{n} (X_i - \overline X)^2}{n-1}}\\ \sigma_Y &= \sqrt{\frac{\sum_{i=1}^{n} (Y_i - \overline Y)^2}{n-1}}\end{aligned}$$\)

Step 6: Calculate the linear correlation coefficient r.

\($$r = \frac{\text{cov}(X,Y)}{\sigma_X \sigma_Y}$$\)

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The maximum value of the function f(x) = 1 + n*sin(x) with an amplitude of 4 = 5.

To find the maximum value of function f(x) = 1 + n*sin(x), we need to consider the amplitude and the function's equation.

The amplitude of a sine function is the distance from the maximum or minimum point to the midline (which is the average value of the function). In this case, the amplitude is given as 4.

Since the function is f(x) = 1 + n*sin(x), the midline is y = 1. To find the maximum value of f, we need to add the amplitude to the midline:

Maximum value of f = midline + amplitude
Maximum value of f = 1 + 4
Maximum value of f = 5

Therefore, we can state that the maximum value of the function f(x) = 1 + n*sin(x) with an amplitude of 4 is 5.

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In this case, the mean is 5.5 cm and the standard deviation is 0.1 cm. So, one standard deviation below the mean is 5.4 cm and one standard deviation above the mean is 5.6 cm. Therefore, about 68% of the data falls between 5.4 cm and 5.6 cm, which includes the range of 5.3 cm to 5.7 cm.

Your question involves a normal distribution with a mean (µ) of 5.5 cm and a standard deviation (σ) of 0.1 cm. You want to find the percentage of data between 5.3 cm and 5.7 cm.

First, we need to standardize the scores using the z-score formula: z = (x - µ) / σ

For 5.3 cm: z1 = (5.3 - 5.5) / 0.1 = -2
For 5.7 cm: z2 = (5.7 - 5.5) / 0.1 = 2

Now, referring to a standard normal distribution table or using a calculator, we find the area between these z-scores:

This can be determined using the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean
- About 95% of the data falls within two standard deviations of the mean
- About 99.7% of the data falls within three standard deviations of the mean

P(-2 < z < 2) = P(z < 2) - P(z < -2) = 0.9772 - 0.0228 = 0.9544

Converting it to a percentage, we get 95.44%, which is approximately 95%.

So, the answer is A. 95%.

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1. The absolute value of a number is always non-negative.

2. The distance between 5 and -2 is7

3. Extends indefinitely in one or both directions. It can be denoted as (-∞, a), (a, ∞), or (-∞, ∞)

4. The midpoint of the interval [2, 8] is (2 + 8) / 2 = 5.

1. Absolute Value:

The absolute value of a real number is its distance from zero on the number line. It is denoted by placing vertical bars or absolute value symbols around the number. For example, the absolute value of -5 is written as |-5| = 5, and the absolute value of 3 is written as |3| = 3. The absolute value of a number is always non-negative.

Properties of Absolute Value:

Non-Negativity: The absolute value of a number is always non-negative. |x| ≥ 0 for any real number x.

Identity: The absolute value of zero is zero. |0| = 0.

Symmetry: The absolute value of a number is equal to the absolute value of its negative. |x| = |-x|.

Triangle Inequality: For any two real numbers x and y, the absolute value of their sum is less than or equal to the sum of their absolute values. |x + y| ≤ |x| + |y|.

2. Distance between Two Numbers:

The distance between two numbers on the real number line is the absolute value of the difference between the two numbers. For example, the distance between 5 and -2 is |5 - (-2)| = |5 + 2| = 7.

3. Intervals on the Real Number Line:

Intervals are sets of real numbers that lie within a certain range or between two specific numbers. There are four types of intervals:

Closed Interval: Includes all real numbers between and including two specific numbers. It is denoted as [a, b].

Open Interval: Includes all real numbers between two specific numbers, excluding the endpoints. It is denoted as (a, b).

Half-Open or Half-Closed Interval: Includes all real numbers between two specific numbers, including one endpoint and excluding the other. It can be denoted as [a, b) or (a, b].

Unbounded Interval: Extends indefinitely in one or both directions. It can be denoted as (-∞, a), (a, ∞), or (-∞, ∞).

4. Midpoint of an Interval:

The midpoint of an interval is the value that lies exactly halfway between the two endpoints. It is calculated by taking the average of the two endpoints. For example, the midpoint of the interval [2, 8] is (2 + 8) / 2 = 5.

Intervals in Real-Life Problems:

Intervals are used to model and solve real-life problems that involve ranges or boundaries. They can represent time intervals, temperature ranges, price ranges, or any other measurable quantities. By using intervals, we can analyze and make predictions based on specific conditions or constraints within a given range.

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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The unit rate in teaspoons per pound would be 1/2 teaspoons per pound.

What is the unit rate?

A unit rate means a rate for one or something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

The number of teaspoons:

                                      \(=1\frac{3}{4}\\\\=\frac{4+3}{4}\\\\=\frac{7}{4}\)

Amount of pasta:

                              \(=3\frac{1}{2}\\\\=\frac{6+1}{2}\\\\=\frac{7}{2}\)

Now the unit rate = number of teaspoons/ amount of pasta

                             \(=\frac{7/4}{7/2}\\\\=\frac{1}{2}\\\)

Hence, the unit rate in teaspoons per pound would be 1/2 teaspoons per pound.

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Answer:

Step-by-step explanation:

1/2

The decimal number system uses nine different symbols is False as the decimal number system actually uses ten different symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These ten symbols, also known as digits, are used to represent all possible numerical values in the decimal system.

Each digit's position in a number determines its value, and the combination of digits creates unique numbers. This system is widely used in everyday life and forms the basis for arithmetic operations and mathematical calculations. Thus, the decimal number system consists of ten symbols, not nine.

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Hi there!

~

\(2+2+4+6+8+10+\frac{1}{2} +6\)

\(= 4 + 4+ 6 + 8 + 10 + \frac{1}{2} + 6\)

\(= 8 + 6 + 8 + 10 + \frac{1}{2} + 6\)

\(= 14 + 8 + 10 + \frac{1}{2} + 6\)

\(= 22 + 10 + \frac{1}{2} + 6\)

\(= 32 + \frac{1}{2} + 6\)

\(= \frac{62}{2} + 6\)

\(= \frac{77}{2}\)

Hope this helped you!

The required value(s) of y0 such that the solution has a vertical asymptote at t = 2 and a t-interval of existence −[infinity] is:

y0 < 0.

The given initial value problem:

y′=3y2, y(0)=y0.

We can solve this initial value problem by using separation of variables. That is, we can write the given equation as:

dy/y2 = 3dt

Integrating both sides, we get:

-1/y = 3t + c, where c is a constant.

Then, the general solution of the given differential equation is:

y(t) = -1/(3t + c).

We are given that the solution has a vertical asymptote at t = 2. Therefore, we have:

3t + c = 0 when t = 2, which gives c = -6.

Then, we have:

y(t) = -1/(3t - 6)

Now, we need to determine the values of y0 such that the solution has a t-interval of existence −[infinity].

From the above equation, we see that the solution has a vertical asymptote at t = 2.

Hence, the interval of existence of the solution is (−∞, 2) U (2, ∞).

Also, for t in (−∞, 2), we have:y(t) = -1/(3t - 6) < 0Therefore, for the solution to have a t-interval of existence −[infinity], we must have y0 < 0.

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Answer:

3

Step-by-step explanation:

Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site

Probability: The chance that a given event will occur. The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes

given that the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0. 40

Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey

Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site

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Answer:

Because 0.40 represents likelihood over many visits to the site in the long term, Avery's interpretation of the probability is incorrect.

Step-by-step explanation:

What does the term probability mean?

Probability: The likelihood that a specific occurrence will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely outcomes that result in a specific event

Given that there is a 0. 40 percent chance that a randomly chosen website visitor will be requested to take an online survey

Avery asserts that of the following 5 site visits, 2 will be required to complete the survey.

Because 0.40 represents chance over the long term and several visits to the site, Avery's interpretation of the probability is incorrect.

Answer:

1.= 2.5

2.= is incorrect because there should not be more than one = sign

Step-by-step explanation:

Answer:

11.5

Step-by-step explanation:

Since the derivative of a constant is always 0, we can drop the last term:
f’(x) = -21/x^4 + 4/x^3 + 1/x^2

Using the rules of differentiation, we can find the derivative of f(x) by taking the derivative of each term separately. The power rule and the constant multiple rule will come in handy here.

f(x) = 7/x^3 – 2/x^2 – 1/x + 140

f’(x) = d/dx(7/x^3) – d/dx(2/x^2) – d/dx(1/x) + d/dx(140)

To find the derivative of 7/x^3, we can use the power rule, which states that the derivative of x^n is nx^(n-1).

f’(x) = -21/x^4 – (-4/x^3) – (-1/x^2) + 0

To find the derivative of -2/x^2, we can again use the power rule:

f’(x) = -21/x^4 + 4/x^3 – (-1/x^2) + 0

To find the derivative of -1/x, we use the power rule once more:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2 + 0

And since the derivative of a constant is always 0, we can drop the last term:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2

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The number of years for the population of bacteria to reach 7569 is given by n = 7.4 years

Given data ,

To estimate when the population will exceed 7569, we can set up an inequality using the given population growth equation:

P(t) = 1600e^(0.21t) > 7569

Now we can solve for t. Here are the steps:

Divide both sides of the inequality by 1600 to isolate the exponential term:

e^(0.21t) > 7569 / 1600

Take the natural logarithm (ln) of both sides to eliminate the exponential term:

ln(e^(0.21t)) > ln(7569 / 1600)

Note: Since ln and e are inverse functions, they cancel each other out, leaving us with just the exponent.

Simplify the right-hand side using the properties of logarithms:

0.21t > ln(7569) - ln(1600)

ln(7569/1600) is equivalent to ln(4.73125), which is approximately 1.554

0.21t > 1.554

Divide both sides by 0.21 to solve for t:

t > 7.4

Hence , the estimated time when the population will exceed 7569 is t > 7.4 years, or approximately t > 7.4 years

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