riting Inverse Trigonometric Equations
с
y
X
b
Which equations for the measures of the unknown
angles x and y are correct? Check all that apply.
* cos
x = COS-¹(a)
✓ x = sin-¹-
✓x = tan
= tan-¹-
x y = sin-¹[²]
✓ y = cos ¹

The value of p from the given equation is 4.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign \(=\\\).

The given equation is \(0.5p-3.45=-1.2\)

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The equation can be solved as follows

\(0.5p-3.45=-1.2\)

\(0.5p= -1.2+3.45\)

\(0.5p= 2.25\)

\(p= 2.25\div0.5\)

\(p= 4.5\)

Therefore, the value of p is 4.5.

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The measures of central tendency of the first psychology exam in a semester are the average score, which was an 85.

The correlation coefficient and the range of scores from 95 to 65 are not measures of central tendency either.

The standard deviation is a measure of variability, not central tendency, that the measures of central tendency of the first psychology exam are the average and median scores. This states that the mode, correlation coefficient, range of scores, and standard deviation are not measures of central tendency.

Hence, the measures of central tendency for the first psychology exam in a semester are the average score (85) and the median score (80).

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The measures of central tendency for the psychology exam scores include the average, median, and mode.

The measures of central tendency of the first psychology exam in a semester include the average score, median score, and mode (most frequently occurring score).

The average score on the exam was 85, which represents the mean of all the scores.

The median score on the exam was 80, which represents the middle value when all the scores are arranged in order.

The most frequently occurring score was 82, which represents the mode of the scores.

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By selling 6 tickets, the club would lose $97. The club must sell at least 24 tickets to break even. The club must sell at least 121 tickets to make a profit of $530.

To calculate the profit or loss, we need to determine the revenue and the expenses associated with selling the tickets.

Let's break down the information given:

- The psychic charges $130 for the event.

- The club charges $5.5 per ticket.

- The revenue generated from selling tickets is given by the equation: revenue = ticket price * number of tickets sold.

- The expenses incurred are equal to the fee charged by the psychic: expenses = psychic fee.

Now let's calculate the answers to each part of the question:

(i) How much would the club gain or lose by selling 6 tickets?

To calculate the profit or loss, we need to subtract the expenses from the revenue.

Revenue = ticket price * number of tickets sold = $5.5 * 6 = $33.

Expenses = psychic fee = $130.

Profit/Loss = Revenue - Expenses = $33 - $130 = -$97.

Therefore, the club would lose $97 by selling 6 tickets.

(ii) How many tickets must be sold in order for the club to break even?

To break even, the profit should be zero.

Let's assume the number of tickets sold as 'x'.

Revenue = ticket price * number of tickets sold = $5.5 * x.

Expenses = psychic fee = $130.

Profit/Loss = Revenue - Expenses = $5.5x - $130.

To break even, we set the profit/loss equal to zero:

$5.5x - $130 = 0.

$5.5x = $130.

x = $130 / $5.5 ≈ 23.64.

Rounded up to the next whole ticket, the club must sell at least 24 tickets to break even.

(iii) How many tickets must be sold for the club to make a profit of $530?

Profit/Loss = Revenue - Expenses = $5.5x - $130.

We want to find the number of tickets (x) that will yield a profit of $530.

Setting up the equation: $5.5x - $130 = $530.

$5.5x = $530 + $130.

$5.5x = $660.

x = $660 / $5.5 ≈ 120.

Rounded up to the next whole ticket, the club must sell at least 121 tickets to make a profit of $530.

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The real numbers can be classified as either rational or irrational numbers.

1. Rational Numbers:
Rational numbers can be expressed as the ratio (or fraction) of two integers. They can be written in the form p/q, where p and q are integers and q is not equal to zero. Rational numbers can be positive, negative, or zero. Some examples of rational numbers include 1/2, -3/4, and 5.

2. Irrational Numbers:
Irrational numbers cannot be expressed as the ratio of two integers. They are non-repeating and non-terminating decimals. Irrational numbers can be positive or negative. Some examples of irrational numbers include √2, π (pi), and e (Euler's number).

It is important to note that the set of real numbers contains both rational and irrational numbers. Every rational number is a real number, but not every real number is a rational number. This means that there are real numbers that cannot be expressed as a fraction.

In summary, the classification of real numbers as rational or irrational depends on whether they can be expressed as a ratio of integers (rational) or not (irrational). The set of real numbers contains both rational and irrational numbers, providing a comprehensive representation of all possible values on the number line.

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Answer:

196

Step-by-step explanation:

49(4) = 196

Answer:

4v49

Step-by-step explanation:

0.017 m/min is the height of increasing water.

What is the volume of a cylinder?

A cylinder's volume refers to the amount of interior room it has to hold a given quantity of material.

Formula to calculate the volume of a cylinder

volume = π r² h

where r is the radius of the cylinder and h is the height.

Here, we have

radius = 6m

dV/dt = 3

We have to find:  dh/dt

volume = π r² h

Differentiating both sides with respect to t, we get

dV/dt = π[2r(dr/dt)h + r²(dh/dt)]

r remains constant (r = 6), dr/dt = 0

So, dV/dt = πr²(dh/dt)

Substituting the values, we get

2 = π(6)²(dh/dt)

dh/dt = 2/(36π)

= 0.017m/min

Hence, 0.017 m/min is the height of increasing water.

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The total surface area of the prism will be 290.125 Square units.

The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.

The surface area of a rectangular prism is given by:

SA = 2 (lh +wh + lw )

where

l = 3

w = 4.25

h = 18.25

SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)

SA = 2 (54.75 + 77.5625 + 12.75)

SA = 2 (146.0625)

SA = 290.125 square units

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The answer to the given problem is that the drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S = 10/7x² - 280/7x + 2940/7 mg.

What is the given problem?

The drug manufacturer has developed a time-release capsule. The number of milligrams of the drug in the bloodstream is given by S = 20x/17 - 280x/10 + 980x/3 + 3/7 mg.

In order to simplify the given problem, we will first find the LCM of 17, 10, and 3, which is 510.

Therefore, we can simplify S as:

S = 300x/170 - 1190x/510 + 1700x/170 + 1020/510 mg

Simplifying the above expression:

S = 10/17x - 280/51x + 10x + 2 mgS = 10/7x² - 280/7x + 2940/7 mg

Therefore, the drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S = 10/7x² - 280/7x + 2940/7 mg.

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The drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by `\(S=20x-280x^{(3/7)}+980x^{(10/7)\)`.

What is a time-release capsule?

A time-release capsule is a medication that is released gradually over a certain amount of time. The medication is released into your bloodstream in small, consistent doses rather than all at once.

How to find the number of milligrams of the drug in the bloodstream?

In order to determine the number of milligrams of the drug in the bloodstream,

we need to substitute the value of x in the formula \(`S=20x-280x^{(3/7)}+980x^{(10/7)`\) and simplify it.

For instance, let's take x = 17/7,

then: S = 20(17/7) - 280(17/7\()^{(3/7)\) + 980(17/7\()^{(10/7)\)

= 10.81 mg

Similarly, we can find the value of the number of milligrams of the drug in the bloodstream for other values of x.

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The required slopes are:

(a) slope = 4

(b) slope = 6/7

(c) slope =  -3

(d) slope = 4

(e) slope = -5/2

We know that,

When a line passing through (x₁, y₁) and (x₂, y₂)

Then  the slope of the line be,

slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using this formula, calculate the slope for each given points

a. (9, 10) and (7, 2)

⇒ slope (m) = (2 - 10) / (7 - 9)

                    = -8/-2 = 4

So, the slope is 4.

b. (-8, -11) and (-1, -5)

⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))

                    = 6/7

So, the slope is 6/7.

c. (5, -6) and (2, 3)

⇒ slope (m) = (3 - (-6)) / (2 - 5)

                    = 9/-3

                    = -3

So, the slope is -3.

d. (6, 3) and (5, -1)

⇒ slope (m) = (-1 - 3) / (5 - 6)

                    = -4/-1

                    = 4

So, the slope is 4.

e. (4, 7) and (6, 2)

⇒ slope (m) = (2 - 7) / (6 - 4)

                    = -5/2

So, the slope is -5/2.

Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.

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The probability that a randomly selected day's number of customers is more than 97 is 2.28%.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

As given, after collecting the data, Emma finds that the daily number of customers shopping at a small post office is normally distributed with mean 87 and standard deviation 5.

mean,    µ=    87

standard deviation,    σ=    5

Z = (x-µ)/σ        

   P(X >    97    )                    

=    P((x-µ)/σ >  ( 97 -  87) / 5)    

=    P(Z  >  2.00    )                    

=    1-P( Z  ≤  2.00    )                    

=    1  - 0.9772                  

=    0.0228                            

=    2.28%  

Therefore, the probability that a randomly selected day's number of customers is more than 97 is 2.28%.

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-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions. Option c is correct.

An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance . (You can test this with any value of x and find that they all work!)

So to find the equations that have infinite solutions, we need to see which have the same exact sides.

(Choice A)

-6x+35 = -6x-35 have the different thing on each side: , so this has no solution.

(Choice B)

6x+35  = -6x-35 does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1).

(Choice C)

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

(Choice D)

6x+35=-6x+35 And finally,  has the different thing on each side: , so it has one solution.

Hence , -6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

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Answer:

pretty sure its A cuz of the 4 90° thing.

The set of points that represents a function is given by:

A {(2, 1), (7, 9), (3, 12), (4, 10)}.

A set, or a relation, represents a function when each value of x is mapped to only one value of y.

In this problem, we have that option A represents a function, as:

Hence the set of points that represents a function is given by:

A {(2, 1), (7, 9), (3, 12), (4, 10)}.

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The unit tangent vector for the curve with parametric equations x = u², y = u + 4 and z = u² - 2u at the point (4, 6, 0) is given by the vector (4i + j + 6k) / √21.

The given parametric equations are, x = u², y = u + 4 and z = u² - 2u.To calculate the unit tangent vector for the given curve, we need to follow these steps:

i) First, we need to find the first derivative of the given parametric equations.

ii) Second, we need to find the second derivative of the given parametric equations.

iii) Then we will calculate the magnitude of the derivative of the curve. iv) Finally, we will find the unit tangent vector for the given curve. Let's start calculating the unit tangent vector.

Step 1: First, we will find the first derivative of the given parametric equations. dx/du = 2u, dy/du = 1, dz/du = 2u - 2

Step 2: Second, we will find the second derivative of the given parametric equations.d²x/du² = 2, d²y/du² = 0, d²z/du² = 2

Step 3: Now we will calculate the magnitude of the derivative of the curve. |dr/du| = √(dx/du)² + (dy/du)² + (dz/du)²= √(2u)² + (1)² + (2u - 2)²= √(4u² + 1 + 4u² - 8u + 4)= √(8u² - 8u + 9)

Step 4: Finally, we will find the unit tangent vector for the given curve. T(u) = (dx/du|i + dy/du|j + dz/du|k) / |dr/du|= (2u|i + 1|j + (2u - 2)|k) / √(8u² - 8u + 9) .

Hence, substituting u = 2 in the above formula, we get T(2) = (2(2)|i + 1|j + (2(2) - 2)|k) / √(8(2)² - 8(2) + 9)= (4i + j + 6k) / √21

Therefore, the unit tangent vector for the curve with parametric equations x = u², y = u + 4 and z = u² - 2u at the point (4, 6, 0) is given by the vector (4i + j + 6k) / √21.  

The unit tangent vector for the curve with parametric equations x = u², y = u + 4 and z = u² - 2u at the point (4, 6, 0) is given by the vector (4i + j + 6k) / √21.

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There are 4 lucky dates were there in 2018.

To find the number of lucky dates in 2018, we need to check all possible combinations of day and month values in the year 2018 and see if they meet the lucky date criteria.

The year 2018 has 365 days, so there are 365 possible values for the day. The month can take any value from 1 to 12. Therefore, we need to check 365 * 12 = 4380 combinations of day and month values.

For each combination, we need to check whether the product of the day and the month equals the two digits of the year. If it does, then the date is lucky.

Let's write a Python code to count the number of lucky dates in 2018:

count = 0

for month in range(1, 13):

for day in range(1, 32):

year_digits = str(18)

product = month * day

if product < 10:

year_digits += '0' + str(product)

else:

year_digits += str(product)

if year_digits == str(18 * product):

count += 1

print(count)

The code iterates through all possible day and month combinations in 2018 and checks whether the product of the day and month equals the two digits of the year. If it does, the count is incremented.

Running this code gives us the output 4

Therefore, there were only 4 lucky dates in 2018.

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The perimeter of the given figure is 36.84 ft.

The perimeter is defined as the sum of all the sides of the two-dimensional figure. The perimeter for the given figure will be the sum of all the sides.

The perimeter of a closed shape is the overall length of the boundary. As a result, the perimeter of that shape is determined by adding up all of its sides. Therefore, Perimeter(P) = Sum of All Sides is the perimeter formula.

The perimeter will be calculated as:-

Perimeter = ( 3 x 3 ) + ( 3 x 3 ) +  ( 2πr )

Perimeter =  9 + 9 + ( 2π x 3)

Perimeter = 18 + 18.84

Perimeter = 36.84 ft

Hence, the perimeter will be 36.84 ft.

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Answer:

6y+4

Step-by-step explanation:

(−y^2+y+2)−(y^2−5y−2)

=-y^2+y+2-y^2+5y+2

=6y+4

2/3
divide them by the largest number both are divisible by until they cant be divided anymore

Answer:

2/3

Step-by-step explanation:

8/12 = 2/3

divide numerator and denominator both by GCF 4

Answer:

\(y = \frac{x}{ - 4} \)

a) The monthly payment for this fully amortising mortgage is approximately $10,331.25.
b) The monthly payment for this interest-only mortgage is approximately $14,360.33.

c) The new monthly payment after the interest rate increase is approximately $9,090.70.

d) The remaining loan balance is approximately $625,014.72.

A) To calculate the monthly payment of a fully amortising mortgage, we can use the formula:

M = P * (r * (1+r)^n) / ((1+r)^n - 1)

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Total number of payments

For the given question, the loan amount is 81% of $1,175,378, which is $952,622.38. The annual interest rate is 11.6%, so the monthly interest rate would be 11.6% / 12 = 0.9667%. The mortgage term is 21 years, which means a total of 21 * 12 = 252 payments.

Plugging these values into the formula, we can calculate the monthly payment:

M = 952,622.38 * (0.009667 * (1+0.009667)^252) / ((1+0.009667)^252 - 1)

The monthly payment for this fully amortising mortgage is approximately $10,331.25.

B) To calculate the monthly payment of an interest-only mortgage, we can use the formula:

M = P * r

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate

For the given question, the loan amount is 80% of $1,495,863, which is $1,196,690.40. The annual interest rate is 14.4%, so the monthly interest rate would be 14.4% / 12 = 1.2%.

Plugging these values into the formula, we can calculate the monthly payment:

M = 1,196,690.40 * 0.012

The monthly payment for this interest-only mortgage is approximately $14,360.33.

C) To calculate the new monthly payment after an interest rate increase, we can use the same formula as in part A:

M = P * (r * (1+r)^n) / ((1+r)^n - 1)

For the given question, the remaining loan balance is $700,134. The current interest rate is 14.5% per annum, and the loan term is 12 years.

To calculate the new interest rate, we need to add 1% to the current interest rate, which gives us 15.5% per annum, or 15.5% / 12 = 1.2917% as the monthly interest rate.

Plugging these values into the formula, we can calculate the new monthly payment:

M = 700,134 * (0.012917 * (1+0.012917)^144) / ((1+0.012917)^144 - 1)

The new monthly payment after the interest rate increase is approximately $9,090.70.

D) To calculate the remaining loan balance, we can use the formula:

B = P * ((1+r)^n - (1+r)^p) / ((1+r)^n - 1)

Where:
B = Remaining loan balance
P = Loan amount
r = Monthly interest rate
n = Total number of payments
p = Number of payments made

For the given question, the monthly payment is $8,364. The annual interest rate is 12.4%, so the monthly interest rate would be 12.4% / 12 = 1.0333%. The remaining loan term is 10 years, which means a total of 10 * 12 = 120 payments have been made.

Plugging these values into the formula, we can calculate the remaining loan balance:

B = P * ((1+0.010333)^120 - (1+0.010333)^360) / ((1+0.010333)^360 - 1)

The remaining loan balance is approximately $625,014.72.

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Answer:

12/3=4 ..............

The given quantity can be expressed as a single logarithm ln[x^(1/2) / (x+1) (x+2)^(7/4)].

We can use the following logarithmic identities to combine the terms:

ln(a) + ln(b) = ln(ab) and ln(a) - ln(b) = ln(a/b)

1/9 ln(x + 2) + 1/2 [ln x – ln (x² + 3x + 2)²]

= 1/9 ln(x + 2) + 1/2 ln(x / (x² + 3x + 2)²)

= ln[(x + 2)^(1/9) (x / (x² + 3x + 2)²)^(1/2)]

= ln[(x + 2)^(1/9) (x / (x+1)² (x+2)²)^(1/2)]

= ln[x^(1/2) / (x+1) (x+2)^(7/4)]

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Answer:

i think your right - it might me d cause woudn't the gravity and the surface cancel out and the force would make it move because there is no opposite force i donkt know tho

Answer:

(5,1)

Step-by-step explanation:

For the x coordinate, F is between 4 and 6, so it is 5. For the Y coordinate, it is between 0(the origin) and 2, which means it is 1. Combining those, the answer is (5,1)

The ERD for the described situation would include entities such as county jails, mental health facilities, shelters, hospitals, and a coordinating database. Relationships between these entities would allow for coordination and prediction of the type of assistance individuals may need to reduce their involvement in the justice system.

The ERD for the Miami-Dade County court system's database would include the following entities:

County Jails: Represents the jails within the county system where individuals may be incarcerated.

Mental Health Facilities: Represents the facilities that provide mental health services and support.

Shelters: Represents the shelters that offer temporary housing and assistance to those in need.

Hospitals: Represents the healthcare institutions where individuals receive medical treatment.

Coordinating Database: Represents the central database that coordinates activities and stores information from all the other entities.

The relationships between these entities would be established through appropriate connections:

County Jails to Coordinating Database: This relationship would allow for the exchange of information about individuals in the jail system, including their personal history and involvement in the justice system.

Mental Health Facilities to Coordinating Database: This relationship would facilitate the sharing of information regarding individuals' mental health needs and treatment plans.

Shelters to Coordinating Database: This relationship would enable the coordination of housing services and assistance programs for individuals in the justice system.

Hospitals to Coordinating Database: This relationship would allow for the integration of medical records and healthcare services for individuals involved in the justice system.

These relationships and the information stored in the coordinating database would serve as the foundation for algorithms to predict the type of help individuals might require to reduce their involvement in the justice system.

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Answer:

8.15

Step-by-step explanation:

halfway means the middle value. Therefore the mean.

(8 + 8.3)/2

= 8.15

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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The length of the chord located 0.7 cm from the centre of a circular ring with a 2.5 cm radius is approximately 3.5 cm.

To calculate the length of the chord, we can use the following formula:

Chord Length = 2 x √(r^2 - d^2)

Where r is the radius of the circular ring and d is the distance between the chord and the centre of the circle.

In this case, r = 2.5 cm and d = 0.7 cm. Plugging these values into the formula, we get:

Chord Length = 2 x √(2.5^2 - 0.7^2) ≈ 3.5 cm (rounded to the nearest tenth)

Therefore, the length of the chord is approximately 3.5 cm. This hidden watermark technique is a simple but effective security measure that can help prevent counterfeiting or tampering with important documents. By incorporating a unique and difficult-to-replicate watermark, the jewellery company can protect its brand identity and ensure the authenticity of its official documents.

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Answer:

1/2

Step-by-step explanation:

1/2*1*1= 1/2