is - 51/5 a rational or irrational number?

The residue from $0 to $82 is 44 ≡ x(mod83)

17−1≡x(mod83)

17∗17−1≡17x(mod83)      

5∗1≡5∗17=85(mod83)

5≡2x(mod83)

42∗5=210≡2∗42x=84x≡x(mod83)

44 ≡ x(mod83).

A mathematical operations that performs a calculation on two numbers is known as an arithmetic provider. They are used in everyday arithmetic, and most computer languages include a set of such operators that can be used within equations to perform a variety of sequential calculations. The following are examples of basic arithmetic operations are:

(+) Addition

Subtraction (-) (-)

() Multiplication            

() division

In programming, computers use different symbols to represent multiplication (*) and division (/). More complex operators, such as

Let's look at an ice cream multiplication example.              

There are two  groups, each has its own ice cream.

The total number of ice creams is 2x3=6    

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Answer:

(x+4)(x-3) or A

Step-by-step explanation:

I'm going to assume that you meant to write x² and not x2

which means we have

x²+x-12

and we need to factor this

to do this we need two numbers that add up to 1 (b) but mulitply to -12 (a*c)

our two numbers are

4, -3

Which means the answer is

(x+4)(x-3)

\({ \large{ \bf{f(x) = x {}^{2} + x - 12}}}\)

\({ \large{ \bf{zeros = \dfrac{ - b± \sqrt{b {}^{2} - 4ac } }{2a} }}}\)

\({ \large{ \bf{zeros = \dfrac{ - 1± \sqrt{1 {}^{} + 48 } }{2} }}}\)

\({ \large{ \bf{zeros = \dfrac{ -1± 7 }{2} }}}\)

\({ \large{ \bf{➢ \: \: zeros = - 4 \: \: and \: 3 }}} \: \: \: \: \: \: (ans)\)

We can use Green's Theorem. The theorem relates the flux of a vector field through a closed curve to the double integral of the curl of the vector field over the region enclosed by the curve.

Green's Theorem states that the outward flux of a vector field F across a closed curve C can be calculated by integrating the dot product of F and the outward unit normal vector n along the curve C. However, Green's Theorem also provides an alternative way to calculate the flux by evaluating the double integral of the curl of F over the region enclosed by the curve C.

In this case, we need to calculate the outward flux of F = (-x, 2y) across the square C. The square has sides of length 2, and its corners are (+-1, +-1). The orientation of the square is counterclockwise, and the unit normal vector points outward.

Applying Green's Theorem, we evaluate the double integral of the curl of F over the region enclosed by C. The curl of F is given by ∂F₂/∂x - ∂F₁/∂y = 2 - (-1) = 3.

The outward flux of F across C is equal to the double integral of the curl of F over the region enclosed by C, which is 3 times the area of the square. Since the square has sides of length 2, its area is 4.

Therefore, the outward flux of F across C is 3 times the area of the square, which is 3 * 4 = 12.

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Answer:

C. (x+7)(x+6)

Step-by-step explanation:

F: X*X = X^2

O: x * 6 = 6x

I: 7 * x = 7X

L: 7*^ = 42

Answer:

Neil pays 1/3 of the total bill, which is 1/3 * 72 or 24. He then tips 20% of that which is 24 * 0.2 or 4.80. So in all he paid

24+4.80 or 28.80

Answer:

the answer is 24/5

.....

A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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Answer:  It will be 3/8.   Hope that help.

Answer:

(0,1.5) (0,-3)

Step-by-step explanation:

Hope it helps :)

The prefix associated with the multiplier 0.001 is "milli-."

The International System of Units (SI) uses prefixes to denote decimal multiples and submultiples of units. The prefix "milli-" corresponds to a multiplier of 0.001. Here's a stepwise explanation of how this prefix is determined:

1. Identify the multiplier: The given multiplier is 0.001.

2. Understand the prefix: The prefix "milli-" represents a factor of 1/1000 or 0.001.

3. Determine the prefix symbol: The symbol for "milli-" is "m." It is written in lowercase.

4. Attach the prefix: To express a unit with the multiplier 0.001, you attach the prefix "milli-" to the base unit. For example, if the base unit is meter (m), the millimeter (mm) represents 0.001 meters.

5. Other examples: The milligram (mg) represents 0.001 grams, the millisecond (ms) represents 0.001 seconds, and the milliliter (mL) represents 0.001 liters.

By using the "milli-" prefix, we can conveniently express values that are a thousandth of the base unit, allowing for easier comprehension and communication in various scientific and everyday contexts.

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The distribution of intelligence test scores in the general population forms a bell-shaped pattern is known as a normal distribution.

Normal distribution, also known as Gaussian distribution, is a continuous probability distribution used in statistics. The normal distribution has a bell-shaped curve that is symmetrical about the mean (average).The normal distribution has some important properties, including that its mean, median, and mode are equal.

Furthermore, the total area under the curve is 1. A normally distributed population is one in which the majority of the data is clustered around the mean, with fewer data points further from the mean. It is a common distribution for a variety of natural phenomena, and many statistical analyses depend on it.

The normal distribution plays a critical role in statistical hypothesis testing and other statistical analyses because of its properties, and it has numerous applications in science, engineering, and finance.

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Answer:

I think positive

Step-by-step explanation:

Answer:

zero, D

Step-by-step explanation:

a horizontal line (left to right) would be zero

a verticle line (up and down) would be undifined

Answer:

The smallest number divisible by the natural numbers 1 to 12 is 1

Answer:

73.4846922835 = 73.5 and no it is not a perfect square 5400/100 = 54

To find the z-score needed to get accepted into the University of Michigan (U of M) with an ACT score of at least 31, we can use the mean and standard deviation of the ACT scores distribution from 2015 to 2017.

The mean is 20.9, and the standard deviation is 5.6.

The z-score measures how many standard deviations an individual's ACT score is above or below the mean. We can calculate the z-score using the formula: z = (x - μ) / σ, where x is the ACT score, μ is the mean, and σ is the standard deviation.

For the desired ACT score of 31, we can calculate the z-score as follows:

z = (31 - 20.9) / 5.6 ≈ 1.82

Therefore, the z-score needed to get accepted into U of M with an ACT score of at least 31 is approximately 1.82, rounded to the nearest hundredth.

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Answer:

i think it is 110

Step-by-step explanation:

sorrt if i am wrong

When 100 ft of rope is out, the rate at which the boat is approaching the dock is 0 ft/min which means the boat is not moving towards the dock at that moment.

Let x represent the horizontal distance between the boat and the dock (in feet).

Let y represent the vertical distance between the boat and the pulley (in feet).

Since the rope is attached to the front of the boat, which is 10 feet below the level of the pulley, we have y = 10 ft.

The rate of change of the length of the rope, which is related to the distance between the boat and the dock, is dx/dt = 12 ft/min.

We want to find the rate at which the boat is approaching the dock, which is the rate of change of x with respect to time (dx/dt) when 100 ft of rope is out.

Now, let's set up the similar triangles between the boat, the pulley, and the dock.

x / y = (x + 100) / 100

Now, we can differentiate both sides of this equation with respect to time t:

d(x/y)/dt = d((x + 100) / 100)/dt

To solve for dx/dt, we need to differentiate x/y and (x + 100)/100 with respect to time.

Using the quotient rule, we have:

(dx/dt × y - x × dy/dt) / (y²) = (1/100) × (dx/dt)

Substituting y = 10 and dy/dt = 0 (since the pulley is fixed), we get:

(dx/dt × 10 - x × 0) / (10²) = (1/100) × (dx/dt)

10 × dx/dt = (1/100)×(dx/dt)

10 × dx/dt - (1/100) × dx/dt = 0

(1000/100 - 1/100) × dx/dt = 0

(999/100) × dx/dt = 0

dx/dt = 0

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The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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The new function g(x) is g(x) = (x + 6) - 2.

To translate f(x) = |x| down by 2 units and to the left 6 units, we need to subtract 2 from the function and replace x with (x+6) to shift it to the left by 6 units. Thus, the new function g(x) is obtained by the following steps:

g(x) = f(x+6) - 2 (translate left by 6 units and down by 2 units)

= |x+6| - 2 (substitute f(x) = |x|)

= (x+6) - 2 (when x+6 ≥ 0, |x+6| = x+6; otherwise, |x+6| = -(x+6))

= x + 4 (simplify)

Therefore, the new function g(x) is g(x) = x + 4, which is the original function translated down by 2 units and to the left 6 units. The given answer g(x) = x - 61 - 2 is incorrect as it involves a typo, where the constant term should be -2 instead of -61.

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The set of -values that are appropriate in the given situation is known as the practical domain. Solution: F (x) = 2 x is the function's formula.

You are not accounting for or measuring any rainfall that occurred prior to the storm's onset, thus there is a total of 0 inches of precipitation at that time. Six and a half hours are spent in the storm.

Example :

Miami, Florida, experiences heavy rainfall due to a powerful hurricane. A 2 inch per hour downpour is occurring. In 6 and a half hours, the storm is over. The total amount of rain that has fallen throughout time should be modeled mathematically. The function is plotted. For this situation, identify the practical domain. The set of -values that are appropriate in the given situation is known as the practical domain.

Solution: Since there was no rain measured or included before the storm began, the function is as follows:

f(x)= 2x

There was 0 inches of rain at the moment the storm began. Six and a half hours are spent in the storm. f(6.5) = 2(6.5) = 13 inches of rain had been recorded at 6.5 hours, or so. It follows in words what the domain and range are:

Domain :

All real numbers between and including 0 and 6.5 hours.

Range :

All real numbers between and including 0 and 1.3 inches.

Domain and range can be expressed more easily with the help of some helpful notation, such as the following:

Domain { x∈R,0≤ x ≤ 6.5} [0,6.5]

Range { x∈R,0≤ x ≤ 6.13 [0,13].

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The idea of the Laffer Curve, named after economist Arthur Laffer, is expressed mathematically as a relationship between tax rates and government revenue.

The concept suggests that at a certain point, increasing tax rates will actually lead to a decrease in government revenue, as people will be discouraged from working or investing. The Laffer Curve is typically illustrated as a bell curve, with revenue on the y-axis and tax rate on the x-axis.

At lower tax rates, increasing the rate leads to an increase in revenue. However, at a certain point, increasing the rate further leads to a decrease in revenue. The optimal tax rate, where revenue is maximized, is different for each economy and can vary over time.

The Laffer Curve is often cited by those advocating for lower tax rates and fewer government regulations on businesses as a way to stimulate economic growth and increase revenue.

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Answer:

50

Step-by-step explanation:

the step

100% * 10 =10 as 100% = 1

then mulitply 10 *5 = 50

Answer:

-25

Step-by-step explanation:

\(-5^2=-25\)

By using the approximation of 62,500 inches to the mile, you can simplify and expedite various calculations involving distances and conversions between inches and miles, providing a convenient tool for numerical analysis and problem-solving

The approximation of 62,500 inches to the mile is commonly used in various calculations, especially in scenarios where conversions between inches and miles are involved. This approximation simplifies the conversion process and allows for easier calculations.

For example, if you need to convert a distance from miles to inches, you can simply multiply the number of miles by 62,500 to obtain the equivalent distance in inches. Conversely, if you have a measurement in inches and want to convert it to miles, you divide the number of inches by 62,500 to get the distance in miles.

Additionally, this approximation can be useful in other applications, such as determining the number of inches in a given number of miles, or calculating the length of a specific distance in miles based on its measurement in inches.

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.

When filled, the formula that utilizes an absolute row reference is =$B4*B6. Option (A) B4*B6 is the correct answer.

In the formula, the dollar sign before B locks the reference to column B, while the absence of a dollar sign before row number 4 allows the row reference to be adjusted when the formula is copied or filled down to other cells.

This means that when the formula is copied or filled down to the cells below, the row reference will stay the same as row 4, while the column reference will change based on the column of the new cell.

The formula =B4*B6, on the other hand, would include relative references to both the row and the column, thus when copied or filled down, both the row and column references would alter based on the new cell.

The formulas =B4/$B6 and =B$4*B6 would have an absolute column reference and a relative row reference, meaning that when copied or filled down, the column or row references, respectively, would stay the same or adjust based on the new cell.

Therefore, the formula =$B4*B6 is the one that uses an absolute row reference when filled.

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1. The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The Probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

1. The outcomes in the sample space of choosing a letter from the word THANKS are: T, H, A, N, K, S.

  The outcomes in the sample space of choosing a letter from the word STARK are: S, T, A, R, K.

2. To find the number of outcomes in the sample space, we multiply the number of outcomes for each word.

  Number of outcomes in the sample space = Number of outcomes for the first word × Number of outcomes for the second word

  Number of outcomes in the sample space = 6 (from THANKS) × 5 (from STARK) = 30.

3. The probability of choosing the letters AA would be the number of favorable outcomes (which is 0 in this case) divided by the total number of outcomes in the sample space.

  Probability of choosing AA = Number of favorable outcomes / Total number of outcomes

  Probability of choosing AA = 0 / 30 = 0.

Therefore, the probability of choosing the letters AA is 0, as there are no occurrences of the letter A in both words together.

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The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.

Two important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.

The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.

Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.

Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}

On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.

Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.

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