A rectangle has a length of 7 millimeters and an area of 203 square millimeters. What is the​ width? What is the​ perimeter?

To calculate the cliff's elevation in 10 millennia, we need to use a little bit of math.

Since the cliff is losing elevation at a rate of 5% every millennium, we know that after one millennium, the cliff's elevation will be 95% of its current elevation. Therefore, we can use this formula to calculate the cliff's elevation after three millennia:
1,519 meters * 0.95^10 = 601.83 meters
So, after 10 millennia, the cliff's elevation will be approximately 601.83 meters. This means that the cliff will have lost approximately 917 meters of elevation over the course of 10,000 years due to erosion.

Finally, by applying the formula, we can determine the cliff's elevation in 10 millennia. After doing the calculation, we find that the final elevation will be approximately 744.29 meters.

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Since there are four places, the total number of possible PINs is 10^4 = 10,000.

Since there are four places, the total number of possible PINs is 36^4 = 1,679,616.

So, the total number of possible PINs is 26 * 36^3 = 3,030,336.

So, the total number of possible PINs is 36^5 = 60,466,176.

a. The Personal Identification Number (PIN) for your ATM card is four places long. Any number is permitted in each place. How many possible values of a PIN are there?

For each place, we have 10 possible choices (0-9).

b. Your bank has decided to allow English alphabetic characters (upper or lower case are permitted) as well as any numeric digit in your PIN. How many possible PINs are there when that change is made?

Now we have 26 alphabetic characters (upper or lower case) in addition to the 10 numeric digits. So, for each place, we have 36 possible choices.

c. In addition to b. above, your bank has decided to require that the first place of the PIN be an English upper case alphabetic character. How many possible PINs are there when that additional change is made?

With the requirement of an English upper case alphabetic character in the first place, we have 26 choices for that place. For the remaining three places, we still have 36 choices each.

d. In addition to b. and c. above, your bank has changed the PIN size to five places. Your PIN can now have numeric or English alphabetic characters (upper or lower case are allowed) in each place. How many possible PINs are there when that change is made?

With five places, each place can have 36 choices (26 alphabetic characters + 10 numeric digits).

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To solve this problem, we need to use algebra. Let x be the number of hours that have passed since Wednesday morning. Then the total snow on the ground on Wednesday morning is 3 inches, and the total snow on the ground at any time x hours later is:

3 + 2x

Similarly, the total snow on the ground on Friday morning is 5 inches, and the total snow on the ground at any time x hours later is:

5 + 1x

To find out when these two totals are equal, we can set the expressions equal to each other and solve for x:

3 + 2x = 5 + 1x

Subtracting 1x from both sides, we get:

2x = 2

Dividing both sides by 2, we get:

x = 1

Therefore, the total snow on the ground would be equal after 1 hour.

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Answer:

The thrid one

Step-by-step explanation:

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The probability of the arrow landing on section a is 1/5 since there are 5 equal sections. The probability of the coin landing on heads is 1/2 since there are only 2 possible outcomes (heads or tails) for the coin.

To find the probability of both events happening, we need to multiply the probability of the arrow landing on section a by the probability of the coin landing on heads. This gives us (1/5) * (1/2) = 1/10. So the probability that the arrow will land on the section labeled a and the coin will land on heads is 1/10. In other words, there is a 1 in 10 chance of both events happening. It is important to note that each event is independent of each other, meaning the outcome of one does not affect the other. This is because the spinner and the coin are not connected or related in any way.

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The tablet PC manufacturer would need a sample size of at least 4229 respondents to estimate the proportion of people who want to purchase tablet PCs costing more than $700 with a 90% confidence level and a confidence interval width below 0.04.

Estimating a proportion refers to the process of determining the unknown population proportion based on a sample of data. It is commonly used in statistical inference to make inferences about a population based on sample data.

To find the required sample size to yield a 90% confidence interval with a length below 0.04, we need to determine the appropriate sample size formula for estimating a proportion.

The formula to calculate the required sample size for estimating a proportion is given:

n = (z² × p × q) / (E²)

Where:

n is the required sample size

z is the z-score corresponding to the desired confidence level (representing the desired level of confidence, such as 90% or 95%)

p is the estimated proportion of interest (in this case, the proportion of people who want to purchase tablet PCs costing more than $700)

q is the complement of p (1 - p)

E is the desired margin of error (half the desired confidence interval width)

In this case, we want the confidence interval width to be below 0.04, so the margin of error (E) will be 0.04/2 = 0.02.

Substituting the values into the formula:

n = (1.645² × 0.5 × 0.5) / (0.02²)

n = (2.705025 × 0.25) / 0.0004

n ≈ 1691.265625 / 0.0004

n ≈ 4228.164

Rounding up to the nearest whole number, the required sample size to yield a 90% confidence interval with a length below 0.04 is approximately 4229.

Therefore,

The tablet PC manufacturer would need a sample size of at least 4229 respondents to estimate the proportion of people who want to purchase tablet PCs costing more than $700 with a 90% confidence level and a confidence interval width below 0.04.

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The football's greatest height is 341.33 feet

For any quadratic function of the form, at² + bt + c, the greatest point can be determined using formula:
 

greatest point = c - b²/2a

where a, b and c are constant

Since the height of the football in feet is given by h = -16t² +64t.

Thus, a = -16, b = 64 and c = 0

substituting:

greatest point = 0 - (64)²/2*(-6)

greatest point = -4096/(-12)

greatest point = 341.33 feet

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Answer:

y=6

Step-by-step explanation:

Multiply both sides by 3y-8.

2y+3=9y/2-12

Add 12 to both sides.

2y+15=9y/2

Multiply both sides by 2.

Subtract both sides by 4y.

30=5y

Divide both sides by 5.

Therefore, y=6.

Answer:

2y+3/3y-8=3/2

multiply through by 3

3(2y+3-8)= (3/2)*3

6y-5= 9/2

6y =9/2+5

6y=19/2

y= 19*6/2

y= 57

The two statements which are valid are “All squares are rhombus” and “All parallelograms are quadrilaterals”, the correct option is A and D.

We are given that;

The five statements

Now,

“All circles are congruent.” This statement is not valid because congruent figures have the same shape and size. While all circles have the same shape, they can have different sizes (diameters).

“All rectangles are squares.” This statement is not valid because while all squares are rectangles (since they have four right angles), not all rectangles are squares. A square is a special type of rectangle where all four sides have the same length.

“All trapezoids are parallelograms.” This statement is not valid because a trapezoid is defined as a quadrilateral with at least one pair of parallel sides, while a parallelogram is defined as a quadrilateral with two pairs of parallel sides. So, while all parallelograms are trapezoids, not all trapezoids are parallelograms.

Therefore, by quadrilaterals the answer will be “All squares are rhombii” and “All parallelograms are quadrilaterals”

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Answer:

Since p(x) is exactly divisible by x – 3, then p(3) = 0.

Plugging in x = 3 into p(x), we get

4(3)2 – 6(3) – m = 0

36 – 18 – m = 0

m = 18

Therefore, the value of m is 18.

Step-by-step explanation:

The correct probabilities given the sample space would be:

The number of outcomes with one tail :

HHT, HTH, THH which is 3.

The probability is :

= 3 / 8

= 0. 375

The number of outcomes with at least two tails :

HTT, THT, TTH, TTT which is 4 :

= 4 / 8

= 0. 50

The number of outcomes with at least one heads :

HHH, HHT, HTH, HTT, TTH, THT, TTH which is 7 outcomes:

= 7 / 8  

= 0. 875

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The angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees

To find the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern, we can use the concept of diffraction and the formula for the angle of the first minimum in a single-slit diffraction pattern:

sin(θ) = λ / (diameter)

where θ is the angle, λ is the wavelength of the sound, and the diameter is the diameter of the diaphragm.

First, let's convert the frequency of 15.69 kHz to the corresponding wavelength using the formula:

wavelength = speed of sound / frequency

wavelength = 1450 m/s / (15.69 kHz * 1000 Hz/kHz)

wavelength = 0.09257 meters (rounded to five decimal places)

Next, we can substitute the values into the formula to find the angle:

θ = [tex]sin^{(-1)}[/tex] (0.09257 meters / 0.5806 meters)

θ ≈ 9.43 degrees (rounded to two decimal places)

Therefore, the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees. This angle represents the bending or spreading of the sound waves as they pass through the circular hole of the diaphragm, creating the diffraction pattern.

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The value of  [tex]a^2+ b^2+ c^2[/tex] is

[tex]a^2+ b^2+ c^2[/tex][tex]=6^2+0^2+1^2[/tex] = 37

We have the information from the question:

Average is 55 miles per hour.

We know that the number of miles she drove is divisible by 5

So, a and c must either be the equal or differ by 5.

Now, According to the question:

Let the number of hours Danica drove be k.

Then we know that 100a + 10b + c + 55k = 100c + 10b + a.

Now, 99c - 99a = 55k

9c - 9a = 5k

Thus, k is divisible by 9.

k must be 9, and

Therefore c - a = 5.

Because a + b + c [tex]\leq[/tex] 7 and a [tex]\geq[/tex] 1 , a = 1, c = 6 and b = 0,

Plug all the values

[tex]a^2+ b^2+ c^2[/tex][tex]=6^2+0^2+1^2[/tex] = 37

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Therefore, there are $2^{10} = 1024$ different ways that the group of 10 Caltech students can go to lunch at Lake Street, either choosing Chipotle or Panda Express.

To solve this problem, we can use the fundamental principle of counting, also known as the multiplication principle.
For the first student, there are two choices - either Chipotle or Panda Express. Similarly, for the second student, there are two choices, and so on. Therefore, the total number of ways that the group of 10 students can go to lunch is simply the product of the number of choices for each student:
$2 \times 2 \times 2 \times \dots \times 2$ (10 times)
This can be simplified using exponential notation as $2^{10}$.
It is worth noting that if the group were to split up and some students went to Chipotle while others went to Panda Express, then the number of ways would be different and would require a different approach to solve. But since the problem specifies that each student goes to either Chipotle or Panda Express, we can use the multiplication principle to find the answer.

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The probability of a type i error for a sample of size 10 depends on the significance level (α) chosen for the hypothesis test. Assuming a standard significance level of 0.05, the probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software.

A type i error occurs when a null hypothesis is rejected when it is actually true. In hypothesis testing, the significance level (α) is the probability of rejecting the null hypothesis when it is actually true. A common significance level used in statistical analysis is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true.

The probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software. The calculation involves finding the critical value of t at the chosen significance level and degrees of freedom (df), which is equal to the sample size minus 1 (n-1). For a sample size of 10 and a significance level of 0.05, the critical value of t is approximately 2.306 (from a t-distribution table with 9 degrees of freedom).

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99 cm is the measurement that is most accurate.

A. is the answer

Accuracy is defined as the degree of closeness of a measured value to a standard or known value.

In this case, the standard or known value is 1 meter. The measurement that is closest to this value is 99 cm. Thus, 99cm is the most accurate.

The other measurements are not as accurate. 105.98 cm is too high, 90 cm is too low, and 104.5 cm is in between but not as close to 1 meter as 99 cm.

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The function operation g(f(8) in the given functions f(x) = 3x+2 and g(x) = √(x-1) is 5.

We have,

A function is simply a relationship that maps one input to one output.

Given that:

f(x) = 3x + 2

g(x) = √( x - 1 )

g(f(x)) = ?

First, set up the composite result function:

Evaluate g( 3x + 2 ) by substituting in the value of f into g.

g( 3x + 2 ) = √( ( 3x + 2 ) - 1 )

Simplify

g( 3x + 2 ) = √( 3x + 2 - 1 )

g( 3x + 2 ) = √( 3x + 1 )

Evaluate the result function by replacing the x with 8.

g( f(x) ) = √( 3(8) + 1 )

g( f(x) ) = √( 24 + 1 )

g( f(x) ) = √( 25 )

g( f(x) ) = 5

Therefore, the composite result function g( f(x) ) is 5.

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complete question;

Given f(x)=3x+2 and g(x)= √x-1, determine the following: g(f(8))=

All the solutions are as;

LJ = 18 feet

m GM = 77 deg

m QT = 142 deg

m ∠STR = 23 deg

m ST = 13 deg

m RQ = 38 deg

Now, We can formulate;

Since, KP = PL

Hence, HP = PJ

Then, Δ PKH ≅ Δ PLJ

By HL property.

As point K, L are midpoint of GH and GJ.

Then, KH ≅ LJ = 1/2(JH)

⇒ LJ = 1/2 (36) = 18 feet

As, GH ≅ GJ

Then,

m GM = 1/2 (1/2 (m GM) = 1/4 (360 - 52) = 77 deg.

As, m ∠QST = 71°,

So, m QT = 2 (m ∠QST) = 2 (71) = 142 deg

m ∠STR = 1/2 (m SR) = 1/2 (46) = 23 deg

As RT is a diameter then,

m ∠TSR = 90°

Then, m ∠SRT = 190 - 90 - m ∠STR

m ∠SRT = 67 deg

Hence, m ST = 2 m ∠SRT = 2 (67) = 134 deg

Since, m ∠RSQ = 90 - 71 = 19 deg

And, m RQ = 2 ( m ∠RSQ)

m RQ = 2 × 19 = 38 deg

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The correct answer is 9% chance that a customer selected at random insures exactly one car and it is not a sports car.

The probability that a customer selected at random insures exactly one car and it is not a sports car.

All customers insure at least one car, and 85% insure more than one car, so the probability of a customer insuring exactly one car is 1 - 0.85 = 0.15.

We also know that 23% of customers insure a sports car, and 17% insure more than one car, including a sports car. This means that 6% of customers insure a sports car and no other car (23% - 17%), while 17% - 6% = 11% of customers insure more than one car but do not insure a sports car.

The probability of a customer selected at random insuring exactly one car and it is not a sports car is:
0.15 - 0.06 = 0.09
9% chance that a customer selected at random insures exactly one car and it is not a sports car.

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To solve the system of equations using the substitution method, we first isolate one of the variables in one of the equations. Then we substitute the expression for that variable into the other equations, creating a new system of equations with one fewer variable. We repeat this process until we have a single equation with one variable, which we can solve to obtain the values of the variables.

In this case, we can solve for z in the second equation, giving us:

z = 2x - 5y + 10

We can then substitute this expression for z into the first and third equations, giving us:

-3x + 7y + 2(2x - 5y + 10) = -8

8x - 2y + 3(2x - 5y + 10) = 38

We can simplify these equations by combining like terms:

-3x + 7y + 4x - 10y + 20 = -8

8x - 2y + 6x - 15y + 30 = 38

Simplifying further:

x - 3y = -2

14x - 17y = -8

We now have a system of two equations with two variables, which we can solve using any of the methods we know. For example, we can solve for x in the first equation and substitute that expression into the second equation, giving us:

x = -2 + 3y

14(-2 + 3y) - 17y = -8

Simplifying:

-2y - 20 = -8

y = 6

We can then substitute this value of y back into one of the equations we derived earlier to solve for x and z:

x - 3y = -2

x - 3(6) = -2

x = 16

z = 2x - 5y + 10 = 2(16) - 5(6) + 10 = 17

Therefore, the solution to the system of equations is (x, y, z) = (16, 6, 17).

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The tank will be filled at 9:20 am after tap c has been closed.

Let's calculate the rate of filling for each tap. Tap a fills the tank in 30 minutes, so its rate of filling is 1/30 of the tank per minute. Similarly, tap b fills the tank at a rate of 1/20 of the tank per minute, and tap c fills at a rate of 1/10 of the tank per minute.

When all three taps are opened, their combined rate of filling is (1/30 + 1/20 + 1/10) = 1/12 of the tank per minute.

Since tap c is turned off after some time, we need to calculate how long it takes to fill the tank with the remaining two taps. This can be done by considering the combined rate of filling with taps a and b, which is (1/30 + 1/20) = 1/12 of the tank per minute.

To find the time it takes to fill the tank with the remaining two taps, we can use the formula:

Time = (Volume of the tank) / (Rate of filling)

Since we are not given the volume of the tank, we cannot determine the exact time. However, if we assume the tank has a standard volume, we can approximate that it will take 25 minutes to fill the tank with the remaining two taps. Therefore, the tank will be filled at approximately 9:20 am after tap c has been closed.

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Conditional relative frequency that a customer prefers pepperoni given that the customer is female is 0.318, or approximately 31.8%.

Conditional relative frequency that a customer is male given that he prefers veggies pizza is 0.667, or approximately 66.7%.

The conditional relative frequency that a customer prefers pepperoni given that the customer is female is calculated as follows:

P(pepperoni | female) = P(pepperoni and female) / P(female)

The number of females who prefer pepperoni is 14, so P(pepperoni and female) = 14/90. The total number of females is 44, so P(female) = 44/90.

Therefore,

P(pepperoni | female) = (14/90) / (44/90) = 14/44 = 0.318

The conditional relative frequency that a customer is male given that he prefers veggies pizza is calculated as follows:

P(male | veggies) = P(male and veggies) / P(veggies)

The number of males who prefer veggies pizza is 16, so P(male and veggies) = 16/90.

The total number of customers who prefer veggies pizza is 24, so P(veggies) = 24/90.

Therefore,

P(male | veggies) = (16/90) / (24/90) = 16/24 = 0.667

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Answer:

There are 10,000 possible lock codes.

Each digit on the lock can be any number from 0 to 9. Since the lock uses 4 different numbers, there are 10 choices for each digit. This gives us 10 x 10 x 10 x 10 = 10,000 possible combinations.

For example, some possible combinations are 0123, 4567, 8901, and 9876.

Note that the order of the digits matters. So, 1234 is a different combination from 4321.

Step-by-step explanation:

When two vectors are added, the magnitude of the resulting vector can be found using the Pythagorean theorem. The correct answer is option b, 0.

In this case, if a vector of magnitude 3 is added to a vector of magnitude 4, the resulting vector can have a magnitude of:

sqrt(3^2 + 4^2) = 5

Therefore, the magnitude 0 is not possible when a vector of magnitude 3 is added to a vector of magnitude 4, since the resulting vector must have a magnitude of at least 5.

When adding two vectors, the resulting magnitude can range from the absolute difference to the sum of the magnitudes of the individual vectors. In this case, the magnitudes are 3 and 4.

1. Calculate the absolute difference: |3 - 4| = 1
2. Calculate the sum: 3 + 4 = 7

The resulting magnitude can range from 1 to 7. Therefore, the magnitude that is not possible when a vector of magnitude 3 is added to a vector of magnitude 4 is:

b. 0

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The equation that can be used to find the total number of tiles in the box is 37 + 28 + 31.

The equation that can be used to find the total number of tiles in the box is calculated  by applying linear equation method.

Let the total number of tiles = t

Let the number of black tiles = x

Let the number of blue tiles = y

Let the number of red tiles = z

So if there were 37 black tiles and 28 blue tiles initially in the box, we will have;

t = 37 + 28

After adding 31 red tiles, the new total number of tiles becomes;

t = 37 + 28 + 31

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The test statistic for testing equality of proportions is a z-score. It is calculated by dividing the difference in sample proportions by the standard error. The resulting z-score is then compared to critical values from the standard normal distribution to determine the statistical significance of the difference in proportions.

The correct options for the test statistic for testing the equality of proportions in a multiple-select question are:

Assumes when samples are large that p1 - p2 is normally distributed.

Uses a pooled proportion to calculate the standard error.

Is a z-score.

When the samples are large, the difference between two proportions (p1 - p2) can be approximated to follow a normal distribution. This assumption is based on the Central Limit Theorem.

To calculate the standard error in this scenario, a pooled proportion is used. The pooled proportion combines the proportions from both samples to estimate the common population proportion.

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Therefore, the frame length that gives a probability of 0.1 of one landing during any given frame is about 8.61 seconds.

Since we know the average rate of arrivals, we can use the Poisson distribution to model the number of landings per minute. Let λ be the average number of arrivals per minute, then the Poisson distribution with parameter λ is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the number of arrivals in a given minute.

In this case, λ = 2. We want to find the frame length that gives a probability of 0.1 of one landing during any given frame. Let T be the frame length in minutes, then the number of arrivals during a frame follows a Poisson distribution with parameter λ*T.

We want to find T such that P(X = 1) = 0.1, where X is the number of arrivals during a frame. Substituting λ*T = 2T, we have:

P(X = 1) = (e^(-2T) * (2T)^1) / 1! = 2Te^(-2T)

Setting this equal to 0.1 and solving for T, we have:

2Te^(-2T) = 0.1

e^(-2T) = 0.05/T

Taking the natural logarithm of both sides, we have:

-2T = ln(0.05/T)

Multiplying both sides by -1/2, we have:

T = -ln(0.05/T) / 2

Using a numerical solver or a graphing calculator, we can find that T ≈ 0.1435 minutes, or about 8.61 seconds.

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The value of the area of the shaded region is,

⇒ 23.44 m²

Since, We know that;

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Sides of parallelogram = 6 m

And, Diameter of circle = 4 m

Hence, We can formulate;

The area of parallelogram is,

⇒ area of parallelogram = 6 × 6

⇒ area of parallelogram = 36 m²

And, Area of circle is,

⇒  Area of circle = πr²

⇒  Area of circle = 3.14 × 2²

⇒  Area of circle = 3.14 × 4

⇒  Area of circle = 12.56 m²

Hence, We get;

The value of the area of the shaded region is,

⇒ area of the shaded region =  36 - 12.56

⇒ area of the shaded region = 23.44 m²

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In simple interest calculations, the interest remains the same throughout the loan term, and it is calculated based on the initial principal. In this case, the interest accrued each year will be the same, amounting to $5136 over 8 years.

To calculate the total interest paid on the loan, we can use the formula for simple interest:

Interest = Principal x Rate x Time

In this case, the principal (P) is $17,700. The rate (R) is 3.625% expressed as a decimal, which is 0.03625. The time (T) is 8 years.

Using the formula, we can calculate the interest:

Interest = $17,700 x 0.03625 x 8 = $5136

Therefore, the total interest paid on the loan is $5136.

The rounding was not necessary in this case since the answer is already provided to the nearest cent, which is $5136.

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