Roland purchased a new pair of shoes online that normally sell for $125.00 but were marked down to $93.75. What is the discount rate Roland received? (1 point)
O 10%
O 13%
O 25%
75%

The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

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Answer:

x > 1.5

Step-by-step explanation:

In order to solve for x, we must isolate x on one side of the inequality.

\(4.2x > 6.3\)

x is being multiplied by 4.2 The inverse of multiplication is division. Divide both sides of the equation by 4.2

\(\frac{4.2x}{4.2} >\frac{6.3}{4.2}\)

\(x> \frac{6.3}{4.2}\)

\(x> 1.5\)

The solution to the inequality 4.2x > 6.3 is x>1.5

Answer:

\(\huge\boxed{x>1\dfrac{1}{2}\to x\in\left(1\dfrac{1}{2},\ \infty\right)}\)

Step-by-step explanation:

\(4.2x>6.3\qquad/\text{divide both sides by 4.2}\\\\\dfrac{4.2x}{4.2}>\dfrac{6.3}{4.2}\\\\x>\dfrac{6.3\cdot10}{4.2\cdot10}\\\\x>\dfrac{63:21}{42:21}\\\\x>\dfrac{3}{2}\\\\x>1\dfrac{1}{2}\)

The solution to the system of equations, using elimination, is given as follows:

x = 0.0135, y = -0.2767, z = -0.1024.

The solution to the system of equations is obtained using the elimination method, as the variables are written as functions of each other and then solved.

The system in this problem is composed by the equations presented as follows:

From the first equation, the variable z is written as function of variables x and y, as follows:

z = 5x - 3y - 1.

Replacing in the second equation, we have that:

x + 4y - 6(5x - 3y - 1) = -1

-29x + 22y = -7.

Replacing in the third equation, we have that:

2x + 3y + 4(5x - 3y - 1) = -1

22x - 9y = 3.

Hence the system is now:

Multiplying the first equation by 9 and the second by 22, we have that:

Adding the equations, the solution for x is obtained as follows:

223x = 3

x = 3/223

x = 0.0135.

Then the solution for y is obtained as follows:

-261(0.0315) + 198y = -63

y = (-63 + 261(0.0315))/198

y = -0.2767.

The solution for z is:

z = 5(0.0135) - 3(-0.2767) - 1 = -0.1024,

The problem asks to solve the system of equations using the elimination method.

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If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.

This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.

One of the most crucial concepts for pupils to understand in maths and science is the zero product property.

The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.

Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.

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The model is appropriate since there is a constant rate of change between the two variables."

On plotting the given function we can say that it is a equation of line

Also there is a constant rate of change between two variables C and m

So we can say conclude that from the given options  third option is correct.

"

Given that , Jill has a coin collection

According to the given condition she currently has 40 coins and will add 2 new coins in the collection each month

According to her the model that represents the given situation is given by the function C(m) = 40 + 2m

where is the number of coins in her collection and m is the number of months that have passed

We have to find out that which of the statements best describes the appropriateness of her model

The given options are

The model is not appropriate since the two variables are related exponentially

The model is not appropriate since the domain of the function must be integral values.

The model is appropriate since there is a constant rate of change between the two variables.

The model is appropriate since there is a constant percent rate of change between the two variables

We can graph the function

\(\rm C(m) = 40 +2m\)

On plotting the given function we can say that it is a equation of line

Also there is a constant rate of change between two variables C and m

So we can conclude that from the given options  third option is correct.

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Answer:

An altitude of a triangle is a segment from a vertex of the triangle, perpendicular to the side opposite that vertex of the triangle.

Step-by-step explanation:

To find the volume of the pyramid with a base in the plane z = -8 and sides formed by the three planes y = 0, y - x = 3, and x + 2y + z = 3, we can use a triple integral. By setting up the appropriate limits of integration and integrating the volume element, we can calculate the volume of the pyramid.

The base of the pyramid lies in the plane z = -8. The sides of the pyramid are formed by the three planes y = 0, y - x = 3, and x + 2y + z = 3.

To find the volume of the pyramid, we need to integrate the volume element dV over the region bounded by the given planes. The volume element can be expressed as dV = dz dy dx.

The limits of integration can be determined by finding the intersection points of the planes. By solving the equations of the planes, we find that the intersection points occur at y = -1, x = -4, and z = -8.

The volume of the pyramid can be calculated as follows:

Volume = ∫∫∫ dV

Integrating the volume element over the appropriate limits will give us the volume of the pyramid.

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The largest possible range of S(n) is {0, 2, 4, 6, ...}.

The difference between the greatest and smallest values in a collection of data is the result of subtracting the sample maximum and minimum. It is given in the same units as the data.

The largest possible range of the function S(n) = 2n, which represents the amount of money the café makes from selling n croissants, is the set of all real numbers greater than or equal to 0.

This is because the café can sell any non-negative integer number of croissants, and the amount of money they make will be a non-negative multiple of 2.

So, The largest possible range of S(n) is {0, 2, 4, 6, ...}.

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The solutions for the systems of inequalities are:

a) (0, -100), (0, -150), (0, -1000)

b)  (0, 50), (0, 55) , (0, 1,204).

When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.

The first one is:

y ≤ x - 8

y < -3x - 9

Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:

-100  ≤ 0 - 8 = -8

-100 < - 3*0 - 9 = -9

Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.

For the second system:

y > 5x + 1

y > 3

Let's do the same thing, x = 0 and y gets really large values, like y = 50

50 > 5*0 + 1 = 1  this is true.

50 > 3   this is true.

so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).

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A multiple of a number is the product of that number and any whole number.

For example, the multiples of 7 are 7, 14, 21, 28, 35, 42, and so on.

To find all the multiples of 7 up to 1000, we can start with 7 and repeatedly add 7 to get the next multiple. We can keep doing this until we reach a multiple that is greater than 1000.

The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, 357, 364, 371, 378, 385, 392, 399, 406, 413, 420, 427, 434, 441, 448, 455, 462, 469, 476, 483, 490, 497, 504, 511, 518, 525, 532, 539, 546, 553, 560, 567, 574, 581, 588, 595, 602, 609, 616, 623, 630, 637, 644, 651, 658, 665, 672, 679, 686, 693, 700, 707, 714, 721, 728, 735, 742, 749, 756, 763, 770, 777, 784, 791, 798, 805, 812, 819, 826, 833, 840, 847, 854, 861, 868, 875, 882, 889, 896, 903, 910, 917, 924, 931, 938, 945, 952, 959, 966, 973, 980, 987, 994.

We can see that the highest multiple of 7 that is less than 1000 is 994.

We can also use a division method to find the multiples of 7. For example, if we divide 1000 by 7, the remainder is 6. So 1000 is not a multiple of 7, but 994 is a multiple of 7.

In summary, A multiple of a number is the product of that number and any whole number. To find all the multiples of 7 up to 1000, we can start with 7 and repeatedly add 7 to get the next multiple. We can also use a division method to find the multiples of 7. The multiples of 7 are : 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, 357, 364, 371, 378, 385, 392, 399, 406, 413, 420, 427, 434, 441, 448, 455, 462, 469, 476, 483, 490, 497, 504, 511, 518, 525, 532, 539, 546, 553, 560, 567, 574,

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The answer of the given question is Integration testing.

Integration testing is a form of testing that involves linking all of the individual components together and testing them as a group to uncover any defects between individual components.

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Integration testing is a form of testing that involves linking all of the individual components together and testing them as a group to uncover any defects between individual components.

Integration testing focuses on the interactions between different components of a system. It aims to identify any issues that may arise when the components are combined, such as communication errors, data discrepancies, or incorrect functional behavior. This type of testing is typically performed after unit testing, which tests individual components in isolation, and before system testing, which evaluates the entire system's functionality.

In summary, integration testing is a crucial step in the software testing process that ensures individual components work together seamlessly, helping to identify and resolve defects that may occur when these components are connected.

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Answer:

There are 24 frames of animation in 1 second of anime.    Step-by-step explanation:    There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.

The area of the rhombus is 108 meters²

A rhombus is a type of quadrilateral with four sides of equal length. It is also known as a diamond or a lozenge.

The diagonals of a rhombus bisect each other at right angles, and they also bisect the angles of the rhombus. The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2.  

Hence, the Area of the rhombus (A) = d₁d₂/2  

Where d₁ and d₂ are lengths of diagonals

Here we have

A drawing of a rhombus with both diagonals bisecting each other at right angles. The vertical diagonal is divided into two lengths of 6 meters each and the horizontal diagonal is divided into two lengths of 9 meters each

From the given data,

Length of vertical diagonal (d₁) = 2 × 6 = 12 meters

Length of horizontal diagonal (d₂) = 2 × 9 = 18 meters  

Using the formula, Area of the rhombus (A) = d₁d₂/2

= (12)(18)/2 = 6 (18) = 108 meters²  

Therefore,

The area of the rhombus is 108 meters²  

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Answer:

$20,400.00

Step-by-step explanation:

so, they're paying 4.25% of $5,000 every month for 8 years.

well, first lets see how many payments were made.

8 x 12 = 96 payments

4.25% of 5,000 is 212.5

so 96 payments of $212.5 is...

$20,400.00

dang, that's a lot of money.

Answer:

w = 17

Step-by-step explanation:

Isolate the variable, w. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 13 from both sides of the equation:

4w + 13 (-13) = 81 (-13)

4w = 81 - 13

4w = 68

Next, divide 4 from both sides of the equation:

(4w)/4 = (68)/4

w = 68/4

w = 17

w = 17 is your answer.

~

Answer:

w=19.5

Step-by-step explanation:

4w+13=81

4w=81-13

4w=68

w=68÷4

w=17

The coordinates of line segment are (2,2)

The section formula is the method used to get the coordinates of a point on a line segment that divides it into two segments.Lets’s imagine that the line segment marked with the coordinates A (\(x_{1}\),\(y_{1}\)) and B has a point P(x,y) that splits it (\(x_{2}\),\(y_{2}\)). To find the coordinates, we use the section formula, which is described mathematically as.

P(x, y) =(\(\frac{m.x_{2}+n.x_{1} }{m+n}\),\(\frac{m.y_{2}.n.y_{1} }{m+n}\))

Given that : the point on the directed line segment from (-6,-10) to (6,8) that partitions the segment into a ratio of 2 to 1

Consider two points P(\(x_{1} ,y_{1}\)) and Q(\(x_{2},y_{2}\)).Finding the coordinates of the point R that divides PQ in the ratio m: n is necessary because \(\frac{PR}{RQ}\) = \(\frac{m}{n}\).

Here , p = (-6, -10)

Q= (6, 8)

m :n = (2,1)

x = \(\frac{m.x{2} +n.x_{1} }{m+n}\)

y = \(\frac{m.y_{2}+n.y_{1} }{m+n}\)

by putting value we get,

x= 2 , y= 2

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In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

The radius of the sphere is 5 and the center of the sphere is (-2, -2, -3).

To find the radius of the sphere, we can complete the square. First, we move the constant term to the right side of the equation:

x^2 + y^2 + z^2 + 4x + 4y + 6z = -8

Next, we group the terms with x, y, and z together:

(x^2 + 4x) + (y^2 + 4y) + (z^2 + 6z) = -8

We can complete the square by adding (half of the coefficient of x)^2 = 4 to the first group, (half of the coefficient of y)^2 = 4 to the second group, and (half of the coefficient of z)^2 = 9 to the third group.

We also add a constant term of 1 to make sure we are adding the same thing to both sides of the equation. This gives us:

(x^2 + 4x + 4) + (y^2 + 4y + 4) + (z^2 + 6z + 9) = -8 + 4 + 4 + 9

We can now factor the left side of the equation as a squared term:

(x + 2)^2 + (y + 2)^2 + (z + 3)^2 = 5

The right side of the equation is 5, which is the square of 5. This tells us that the sphere has a radius of 5.

The center of the sphere is the point (-2, -2, -3) that was subtracted from each term on the left side of the equation.

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Loan repayment: Each semiannual payment is $879.92.

Machine cost: The equivalent uniform annual cost is $6,541.34.

Loan Repayment:

1. Calculate the semiannual interest rate: Divide the annual interest rate (8%) by the number of compounding periods per year (2) to get the semiannual interest rate (4%).

2. Calculate the number of compounding periods: Since the loan is repaid in four equal semiannual payments, there are a total of eight compounding periods (4 years x 2).

3. Calculate the present value factor: Use the formula for the present value of an annuity to calculate the present value factor for eight periods at a semiannual interest rate of 4%.

4. Determine the payment amount: Divide the loan amount ($3000) by the present value factor from step 3 to find the equal semiannual payment.

Machine Cost:

1. Calculate the semiannual interest rate: Divide the annual interest rate (8%) by the number of compounding periods per year (2) to get the semiannual interest rate (4%).

2. Calculate the number of compounding periods: Since the useful life of the machine is 6 years and compounding occurs semiannually, there are a total of 12 compounding periods (6 years x 2).

3. Calculate the future value factor: Use the formula for the future value of a single sum to calculate the future value factor for 12 periods at a semiannual interest rate of 4%.

4. Determine the equivalent uniform annual cost: Subtract the future value of the machine ($9,000) from the initial cost of the machine ($30,000) and divide by the future value factor from step 3 to find the equivalent uniform annual cost.

By following these steps and performing the calculations, you will determine the semiannual payment for the loan and the equivalent uniform annual cost of the machine.

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Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.

In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.

Here,

In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.

As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.

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Answer:

the odds against Zahra climbing to the top are,

B. 4:1

Step-by-step explanation:

Since she has climbed 7 times in 28 attempts,

the probability of a successful climb is,

P = 7/28

P = 1/4

So, the odds against Zahra climbing to the top are 4:1

In a landmark Chinese case involving Coffeebux and Javabucks, the Chinese court did not find Coffeebux guilty of improper competition, and Coffeebux was not forced to pay compensation. However, Coffeebux did copy the Javabucks logo, and Javabucks did sue Coffeebux for stealing their customers and trademark violations.

In the given scenario, the Chinese court did not find Coffeebux guilty of improper competition. It is unclear whether Coffeebux engaged in any unfair competition practices, but the court did not rule in favor of Javabucks on this particular charge. However, Coffeebux did copy the Javabucks logo, which suggests trademark infringement. This action could have legal consequences and be subject to legal action.

Javabucks did sue Coffeebux for two reasons: stealing their customers and trademark violations. Javabucks accused Coffeebux of poaching their customers, which implies that Coffeebux engaged in practices that resulted in a loss of business for Javabucks. Additionally, Javabucks filed a lawsuit against Coffeebux for trademark violations, indicating that Coffeebux illegally copied or imitated their trademarked logo.

Nevertheless, it is important to note that the information provided does not indicate whether Coffeebux was forced to pay Javabucks compensation. The outcome of such a case would depend on various factors, including the evidence presented, legal arguments, and the decision of the court.

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Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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The critical value of the chi-square distribution corresponding to a sample size of 5 and a confidence level of 98% is given as follows:

0.297 and 13.277.

To obtain a critical value, we need three parameters, given as follows:

Then, with the parameters, the critical value is found using a calculator.

The parameters for this problem are given as follows:

Using a chi-square distribution calculator, the critical values are given as follows:

0.297 and 13.277.

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Answer:

if the input has more than one arrow coming from it that whole table is not a function but if it only has one its a function

Step-by-step explanation:

u can only have one arrow from input for it to work as a function but if theres mutiple arrows from the output its still a function

Answer:

1/2 pint = 1 cup; 3/4 pint = 1.5 cups; 1 pint = 2 cups; 2 pints = 4 cups ...

Step-by-step explanation:

add all pints, fluid ounces, and quarts together then turn each into cups then you need to add all cups together and you will have answer.

Answer:

24 yards = 72 feet

Step-by-step explanation:

3 feet per yard

24 x 3 = 72

Since this is a right triangle, we can use the Pythagorean Theorem.

\(\sf a^2+b^2=c^2\)

where  and  are the legs and  is the hypotenuse.

One of the legs is 30 yards, and the other is unknown. The hypotenuse is 50 yards, because it is the longest side.

\(\sf a=30 \ yd\)

\(\sf b=b\)

\(\sf c=50 \ yd\)

Substitute the values into the formula.

\(\sf (30 \ yd)^2+b^2=(50 \ yd)^2\)

Evaluate the exponents.

\(\sf 900 \ yd^2+b^2=(50 \ yd)^2\)

\(\sf 900 \ yd^2+b^2=2500 \ yd^2\)

Now, solve for b. First, subtract 900 yards squared from both sides of the equation.

\(\sf 900 \ yd^2-900 \ yd^2+b^2=2500 \ yd^2-900 \ yd^2\)

\(\sf b^2=2500 \ yd^2-900 \ yd^2\)

\(\sf b^2=1600\ yd^2\)

Finally, take the square root of each side of the equation.

\(\sf \sqrt{b^2}=\sqrt{1600 \ yd^2}\)

\(\sf b=\sqrt{1600 \ yd^2}\)

\(\sf b=40 \ yd\)

The other side of the garden is 40 yards long.

The length of the other side of the garden is 40 feet when the garden's longest side is 50 feet long. The length of one side is thirty feet.

Given that,

In Ashley's backyard, there is a right triangle garden. The garden's longest side is 50 feet long. The length of one side is thirty feet.

We have to find the length of the other side of the garden.

We know that,

The largest side of triangle is 50 feet and one side is 30 feet.

By using the Pythagoras theorem we find the third side.

The Pythagoras theorem is square of the longest side is equal to the addition of the square of the other two sides.

So,

50² = 30² + x²

x² = 2500- 900

x² = 1600

Taking square root on both sides

x = 40 feet.

Therefore, The length of the other side of the garden is 40 feet.

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