a basketball court is 46 feet wide and 84 feet long. the court has a border that is 10 feet wide. the cost of a hardwood floor is $9 per square foot. how much will it cost to put a new floor on both the court and its border?

The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex]

Simplify the expression, then we have

[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(3)^{2/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(9)^{1/5}}\\\\\rightarrow \dfrac{1}{\sqrt[5]{3} }\\[/tex]

The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.

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The rank (m) and the nullity (n) is the Matrix A is 5 and 3 respectively according to the planes given.

The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix. And the dimension of the null space of A, also called the kernel of A.

Given null space of [tex]L_{A}[/tex] is a plane in [tex]lR^{3}[/tex] .

So nullity of matrix A is A = 2

Since the dimensions of a plane in [tex]lR^{3}[/tex] is 2.

Also the range is spanned by non-vector V in [tex]R^{5}[/tex].

So rank of matrix A is A = 1

Clearly the linear transformation is from [tex]lR^{5}[/tex] to [tex]lR^{3}[/tex],

Then the Matrix A is a = 5x3 matrix.

Therefore, Rank of the matrix A (m)= 5 and Nullity of the matrix A (n) = 3.

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The remote interior angles of ∠4 are ∠1 and ∠2.

In a triangle, the remote interior angles are the two angles that are not adjacent to the exterior angle. In this case, ∠4 is the exterior angle, so the two angles that are not adjacent to it are ∠1 and ∠2. These are the remote interior angles of ∠4.

Here is a step-by-step explanation:

1. Identify the exterior angle. In this case, it is ∠4.
2. Find the two angles that are not adjacent to the exterior angle. These are ∠1 and ∠2.
3. These two angles are the remote interior angles of ∠4.

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The linear correlation coefficient between the length of the right humerus and the length of the right tibia is 0.517.

To compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia, we will use the formula: r = (n∑xy - (∑x)(∑y)) / sqrt([(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)])

Where r is the correlation coefficient, n is the number of observations, x is the length of the right humerus, and y is the length of the right tibia.

First, we will calculate the sum of x, y, xy, x^2, and y^2:

∑x = 24.8 + 24.59 + 24.59 + 24.29 + 23.81 + 24.87 + 25.90 + 26.11 + 26.63 + 26.31 + 26.84 = 278.74

∑y = 65.05 + 35.57 + 35.57 + 34.58 + 34.20 + 34.73 + 37.38 + 37.96 + 37.46 + 37.75 + 38.50 = 428.75

∑xy = (24.8)(65.05) + (24.59)(35.57) + (24.59)(35.57) + (24.29)(34.58) + (23.81)(34.20) + (24.87)(34.73) + (25.90)(37.38) + (26.11)(37.96) + (26.63)(37.46) + (26.31)(37.75) + (26.84)(38.50) = 10659.01

∑x^2 = (24.8)^2 + (24.59)^2 + (24.59)^2 + (24.29)^2 + (23.81)^2 + (24.87)^2 + (25.90)^2 + (26.11)^2 + (26.63)^2 + (26.31)^2 + (26.84)^2 = 7221.47

∑y^2 = (65.05)^2 + (35.57)^2 + (35.57)^2 + (34.58)^2 + (34.20)^2 + (34.73)^2 + (37.38)^2 + (37.96)^2 + (37.46)^2 + (37.75)^2 + (38.50)^2 = 15738.39

Now we can plug these values into the formula and calculate the correlation coefficient:

r = (11)(10659.01) - (278.74)(428.75) / sqrt([(11)(7221.47) - (278.74)^2][(11)(15738.39) - (428.75)^2])r = 117249.11 - 119475.235 / sqrt([79436.17 - 77691.79][173122.29 - 183744.56])r = -2226.125 / sqrt([1744.38][-10622.27])r = -2226.125 / sqrt(-18525838.35)r = -2226.125 / (-4304.18)r = 0.517

Therefore, the linear correlation coefficient between the length of the right humerus and the length of the right tibia is 0.517.

Note: The question is incomplete. The complete question probably is: Research performed at NASA and led by Emily Horton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2.

Right Humerus (mm)      Right Tibia (mm)

24.8                                 65.05

24.59                               35.57

24.59                               35.57

24.29                               34.58

23.81                                34.20

24.87                               34.73

25.90                               37.38

26.11                                 37.96

26.63                               37.46

26.31                                37.75

26.84                              38.50

Compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia.

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The No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases.

In statistics, the No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases. It represents the accuracy rate that can be achieved by simply guessing the most frequent outcome without using any predictive model or variable.

The NIR is commonly used as a benchmark for evaluating the performance of classification models, as any model that performs worse than the NIR is considered to be poorly performing. Conversely, a model that performs better than the NIR is considered to have some predictive power beyond simply guessing the most frequent outcome.

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Answer:

Step-by-step explanation:

Answer:umm

There are no values of

x

that make the equation true.

No solution

Step-by-step explanation:

Answer: 1/2(10+x)

Step-by-step explanation:

"Half the sum of 10 and a number" means 1/2(10+x), where x is the unknown number.

The solution is, an equation where y is the subject that represents this proportional relationship is,  y = 4x/9.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

Edward serves 4 cups of coffee every nine minutes

now, we have to find that,

how many cups of coffee does he serve every minute ,

i.e. we get,

in 9mint. cup = 4

so, in 1 mint cup = 4/9

now, an equation where y is the subject that represents this proportional relationship is,

y = 4x/9

where, x for the amount of minutes .

Hence, The solution is, an equation where y is the subject that represents this proportional relationship is,  y = 4x/9.

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Answer:

Daniel is 8 years old now

Step-by-step explanation:

Let Kevin's age now be K and let Daniel's age now be D

"Kevin is 3 times as old as Daniel"

Translation: K = 3D

"4 years ago, Kevin was 5 times as old as Daniel"
4 years ago Kevin's age = K - 4
4 years ago Daniel's age = D - 4
4 years ago, Kevin was 5 times as old as Daniel.

Translation: K - 4 = 5(D - 4)
K - 4 = 5D - 20

Simplify this equation:
Add 4 to both sides:
K - 4 + 4 = 5D - 20 + 4

K = 5D - 16

Substitute K = #D:
3D = 5D - 16

Subtract 5D from both sides:
3D - 5D = - 16
-2D = -16

or

2D = 16   (multiply by - 1)

D = 16/2 = 8

and

K = 3D = 3 x 8 = 24

Now, Kevin is 24 years old and Daniel is 8 years old

Verify
If Kevin is 3x older than Daniel who is 8 now,
Kevin's age now = 3 x 8 = 24  Check

4 years ago, Daniel was 8 - 4 = 4 years
4 years ago, Kevin was 24 - 4 = 20
Kevin's age 4 years ago = 5 x 4 = 20 Check

The distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).

The length along a line or line segment between two points on the line or line segment.

The distance formula is Distance=√(x₂-x₁)²+(y₂-y₁)²

Equation in terms of x for the distance between (x, y) and A(-1, 5) and  y = 3x. be any point on the line

Distance=√(x+1)²+(3x-5)²

b. We need to find coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1, 5).

√(x₁+1)²+(3x₁-5)² =√74

√(x₂+1)²+(3x₂-5)² =√74

Simplifying each equation and solving for x, we get:

x₁ = -4/3 or x₁ = -2

x₂ = 2/3 or  x₂  = -4

Simplifying each equation and solving for x, we get:

x₁ = -4/3 or x₁ = -2

x₂ = 2/3 or x₂ = -4

Substituting each value of x into y = 3x, we get the coordinates of B and C:

B: (-4/3, -4)

C: (2/3, 2)

The slope of y = 3x is 3,

Slope of any line perpendicular to it is -1/3.

Using the point-slope form of a line, we get the equation of the line passing through (-1, 5) with slope -1/3:

y-5=-1/3(x+1)

The point of intersection between y = 3x and the line y = (-1/3)x + (14/3), we can set the two equations equal to each other and solve for x:

3x = (-1/3)x + (14/3)

x = 14/10 = 7/5

y = 3(7/5) = 21/5

So the point of intersection is (7/5, 21/5).

To find the area of triangle ABC, we can use the distance formula between the points B and C:

d = √2/3 - (-4/3))² + (2 - (-4))²)

d=2√10

The base of the triangle is the distance between the x-coordinates of B and C, which is 2.

The area of the triangle is:1/2×b×h

=2√10

Hence, the distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).

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The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

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Answer:

1800

7800

Step-by-step explanation:

6000x0.06 = 360 x 5 for years since its annual then you get 1800 add that to the additional 6000 add those together and you get 7800.

Answer: The first improvement cut the time by 32 * 0.08 = 2.56 minutes.

So, the new time after the first improvement is 32 - 2.56 = 29.44 minutes.

The second improvement cut the time by 29.44 * 0.05 = 1.472 minutes.

So, the final time is 29.44 - 1.472 = 27.968 minutes.

Rounding to the nearest minute, it now takes 28 minutes to manufacture the piece.

Step-by-step explanation:

The mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:

Xi = N(μi, σ²) ; i = 1, 2,......, n

And if

X = X1 + X2 +........+ Xₙ

Then, its distribution is given as:

X ≈ N (μ1 + μ2+........+ μₙ)

For this case, it's given that

Distribution of time taken for distance ran by lady is Normal distribution and had a mean handling time of = 8.8 minutes with standard divagation of = 3.3 minutes.

Distribution of time taken for distance ran by joker is Normal distribution and had a mean handling time of = 7.3 minutes with standard divagation of = 2.9 minutes.

Samples of size n = 8 are taken from both population.

Estimated sample mean = population mean

Estimated sample standard deviation = population std. dev / √n

where n = sample size

For sample of females, the distribution is

For sample of males, the distribution is

Also, if we take distribution of difference between sample means(, then it would be normal with mean = 8.8-7.3 = 1.5 minutes (as mean for  will be -7.3 but same standard deviation) as factor gets squared for affecting standard deviation and variance)

and standard deviation is:

[tex]\sqrt{s^2f + s^2m } = \sqrt{3.3^2/8 + 2.9^2/8}[/tex]

≈ 1.553 minutes.

The distribution of difference between sample means is  approximately

We need [tex]P(Xf - Xm < 0)[/tex]

Thus, the mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

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Answer: 15

Step-by-step explanation:

223 / 26

8 reminder 15

he has to put the remainder in the box

The substitution v = y^1-n transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x) is shown below.

An equation is in the form  

dy/dx +P(x)y=Q(x)yⁿ,  where P and Q are functions of x alone or constants, is called Bernoulli's equation.

The substitution using [tex]v = y^{1-n}[/tex]

Differentiate both side with respect to 'x'

[tex]v^{'} = (1-n)y^{-n}y^{'}[/tex]

[tex]\frac{dy}{dx} = \frac{1}{1-n} y^{n}v^{'}[/tex]

we get, [tex]\frac{1}{1-n} y^{n}v^{'}[/tex] + P(x)y = Q(x)yⁿ

= [tex]v^{'} + (1-n)P(x)y^{1-n} = (1-n)Q(x)[/tex]

using [tex]v = y^{1-n}[/tex]

The given equation is well expressed as:

[tex]v^{'} + (1-n)P(x)v = (1-n)Q(x)[/tex]

or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)

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The length of the guy wire is 20 feet

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can use the Pythagorean theorem to find the length of the guy wire.

Let's call the length of the guy wire "g".

Then we have a right triangle with hypotenuse g, one leg of length 7 ft, and the other leg of length 19 ft.

Using the Pythagorean theorem, we have:

g² = 7² + 19²

g² = 49 + 361

g² = 410

Take square root on both sides

g = 20.24

Therefore, the length of the guy wire is 20 feet

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The p-value can be calculated from the Z-score of the observed result using the Z-table, which is a table of values for the standard normal distribution.

The p-value is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true. It is calculated from the Z-score of the observed result, which is a measure of how many standard deviations away from the mean the observed result is. To calculate the p-value from a Z-score, you need to use the Z-table, which is a table of values for the standard normal distribution. The Z-table shows the probability of a given Z-score, or the area under the normal distribution curve to the left of the Z-score. To find the p-value associated with a given Z-score, you simply look up the probability in the Z-table, and subtract this probability from 1. This gives you the p-value, which is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true.

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Answer:

2 3/7

Step-by-step explanation:

Answer:

2^[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

2^3·1/2 = 2^[tex]\frac{3}{2}[/tex]

the image you posted is very blurry, but it looks like the answer is the last choice

The measure of the value of x in the given circle is 27

In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle.

Given that a circle D, having an inscribed angle ∠ EBC measuring 51° and an arc covered by it is arc EC measuring 5x-33, we are to find the value of x,

We know that,

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Therefore,

m ∠ EBC = 2 arc EC

5x-33 = 2×51

5x-33 = 102

5x = 135

x = 27

Hence, the measure of the value of x in the given circle is 27

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The figure is not given, the question is solved for the attached figure.

The most important part of the design cycle is the "Iteration" phase.

In this phase, the designer goes back and forth between testing and evaluating the design, making changes, and testing again until the desired outcome is achieved.

In mathematical terms, the iteration phase can be seen as an optimization process, where the designer seeks to minimize the difference between the desired and actual outcomes.

This phase is crucial because it allows the designer to identify and resolve any issues with the design, ensuring that the final product is functional and meets the desired specifications.

In conclusion, the iteration phase of the design cycle is essential for ensuring that the final design is effective, efficient, and meets all the requirements. The designer must repeat this phase multiple times to achieve the desired outcome and ultimately improve the overall design.

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The original number in the word problem is 77.

Let's call the original two-digit number "x".

Information from the problem

the sum of the digits in x is 14.

So, we can write the number as x = 10a + b,

where a and b are the tens and ones digit, respectively, and a + b = 14.

Reversing and doubling the original number gives us 2(10b + a)

= 20b + 2a.

Adding the original number, x, and the doubled, reversed number, 2(10b + a),

we have 3x = 222.

Substituting x = 10a + b

3(10a + b) = 222

30a + 3b = 222

30a = 222 - 3b

Since the sum of the digits is 14, a + b = 14, so we can substitute for a in the equation:

30(14 - b) = 222 - 3b

420 - 30b = 222 - 3b

198 = 27b

Dividing both sides by 27, we find:

b = 7

So, the original number is x = 10a + b = 10(14 - 7) + 7 = 77.

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The number that is less than 200 and have the prime factors 3, 5, and 13 is 195.

Prime factors are the prime numbers that divide a given positive integer exactly without leaving any remainder. In other words, prime factors are the building blocks of a number.

For example, the prime factors of the number 24 are 2 and 3, because 24 can be written as the product of these prime numbers: 2 × 2 × 2 × 3.

To find the numbers that have prime factors  3,5, and 13, multiply the prime factors together:

3 * 5 * 13 = 195

This is the only number less than 200 that has prime factors 3,5, and 13.

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Assuming a 40-hour workweek, 55000 per year would be approximately 26.44per hour.

Subtract 55000 from 52, the number of weeks in a year, and you get 1057.69. Subtract 1057.69 from 40, the number of hours in a workweek, to get 26.44.To the nearest dollar, round up: 26.44 = 27 Calculating how much an individual would make per hour with a yearly salary of $55,000 is a fairly straightforward process. Divide the annual income of $55,000 by the 52 weeks that make up a year. As a result, we get a score of 1057.69. After that, divide this number by the 40 hours that make up a workweek. As a result, we get a score of 26.44. The final step is to round this result up to the nearest dollar, which gives us an hourly wage of $27. 55,000 dollars a year is therefore equal to about 27 dollars per hour.

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There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.

Therefore, 2 Quarts is 1.8927059 liters, which is equal to almost 2 liters.

Quart:

A quart is an English unit of volume equal to one quarter of a gallon. Currently, there are three types of quarts: Liquid Quart and Dry Quart of the US Conventional System, and Imperial Quart of the UK Imperial System. All of them are approximately equal to 1 liter. It is subdivided into 2 pints or (in the US) 4 cups. Historically, the exact size of a quart has varied over time and with the value of a gallon across different commodities.

Liter:

A liter or liter is a metric unit of volume. A liter is defined as the volume of a cube with sides measuring 10 centimeters. In the US, it is approximately 3.785 liters gallon.

According to the Question:

The conversion factor from quarts to liters is 0.94635295. To find how many liters are in quarts, multiply the conversion factor or use the volume converter above 2 quarts equals 1.8/10 of 93 liters.

To convert 2 quarts to equivalent liter values, multiply the amount in quarts by 0.94635295 (conversion factor). In this case, you should multiply 2 quarts by 0.94635295 to get the equivalent result in liters:

2 quarts x 0.94635295 = 1. 8927059 liters

Therefore,

2 quarts equals 1.8927059 liters.

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Answer:

Step-by-step explanation:

1. Imagine a triangle with base side 36 feet and Kate at the right with the angle of elevation, 24 degrees. We can use tangent:

tan 24 = o/a ; tan(24) = o/36 ; 36(tan(24)) = o ; o = 16 feet

This is how tall the screen is.

2. We do a similar operation:

tan(74) = o/a ; tan(74) = 555/a ; a = 555/tan(74) ; a = 159.1 feet

Hope this helps!

The vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b."

So the vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b." The following is the formula for projecting "a" orthogonally onto "b": CSS Copy: p = (dot(a, b) / dot(b, b)) * b, where "dot" stands for the dot product of the two vectors.

The procedures to determine the orthogonal projection of a vector "a" onto a vector "b" are as follows:

Identify the "a" and "b" dot product.

Add "b" to itself and calculate the dot product.

Divide the intersection of "a" and "b" by the intersection of "b" and itself.

Multiply the vector "b" by the step 3 result.

Here is a MATLAB sample that shows the orthogonal projection.

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The amount of simple interest  is (c) $90

From the question, we have the following parameters that can be used in our computation:

Principal = $600

Rate = 3%

TIme = 5 years

The simple interest is calclated as

Simple interest = PRT

Substitute the known values in the above equation, so, we have the following representation

Simple interest = 600 * 3% * 5

Evaluate

Simple interest = 90

Hence, the amount is $90

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