Each circumference is given using the ≈ symbol. What does that mean about
the circumferences? What is the approximate circumference of a circle with
diameter 1 cm?

Justin and ruby are currently sharing sweets out after school in a ratio of 1:2 respectively. after buying 20 more sweets and sharing them evenly, they now have a ratio of 3:4. So, Justin initially had 5 sweets.

Justin and Ruby initially shared sweets in a ratio of 1:2. Let's represent the number of sweets Justin had as x, and the number of sweets Ruby had as 2x. After buying 20 more sweets and sharing them evenly, the new ratio is 3:4. Now, Justin has 3y sweets and Ruby has 4y sweets.

We can write two equations based on this information:

1) x + 20/2 = 3y (because Justin received half of the 20 new sweets)
2) 2x + 20/2 = 4y (because Ruby received half of the 20 new sweets)

Simplify the equations:

1) x + 10 = 3y
2) 2x + 10 = 4y

Now, we can solve these equations simultaneously to find the value of x and y:

From equation 1, x = 3y - 10

Substitute this value of x into equation 2:

2(3y - 10) + 10 = 4y
6y - 20 + 10 = 4y
6y - 10 = 4y

Rearrange the equation to solve for y:

2y = 10
y = 5

Now that we have the value of y, we can find the value of x:

x = 3y - 10
x = 3(5) - 10
x = 15 - 10
x = 5

So, Justin initially had 5 sweets.

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The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

On input 064 the output is "290b6e3a 39155d6f".On input 132032 the output is "d6f491c5 b645c008".

According to Luby and Rackoff's result, an attacker need at least 2n 2 selected plaintexts and their matching ciphertexts to be able to differentiate the three-round construction from a randomly chosen 2n-bit function with probability close to one. This type of permutation is known as pseudorandom.

According to the Luby-Rackoff theorem, if a round function is a secure pseudorandom function, then three rounds are enough to make the block cypher a pseudorandom permutation. PRPs may be inverted, although PRFs cannot.

It's not three sequential invocations of the PRF, but rather three rounds of the Feistel structure, with the PRF serving as the round functions. It is easy to see that any number of Feistel rounds may be inverted using simply the round functions in the forward direction.

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(kinda confused of what the question is) her guess was 90 away

Please check the attached image for answer.

By Benjemin

Answer:

A=\(26cm^2\)

Step-by-step explanation:

\(h=2.5in(\frac{2.54cm}{1in})=6.35cm\\b=3.25in(\frac{2.54cm}{1in})=8.255cm\\A=\frac{1}{2}bh\\A=\frac{1}{2}(6.35cm)(8.255cm)\\A=26.21cm^2\)

To define a method computeval() that takes one integer parameter and returns the parameter plus 7, you can use the following code:

For example, if the input is 3, the output is 10:

The sοlutiοn of  the given expression is 5⁴a²/12²b²

Least Cοmmοn Multiple(LCM) is a methοd tο find the smallest cοmmοn multiple between any twο οr mοre numbers. A cοmmοn multiple is a number which is a multiple οf twο οr mοre numbers.

Tο sοlve this expressiοn, we need tο simplify the expressiοn inside the parentheses first using the least cοmmοn multiple (LCM) οf the denοminatοrs 4b and 3b.

LCM(4b, 3b) = 12b

Sο we can rewrite the expressiοn as:

Using the formula (a + b)² +  a² + b² + 2ab

Here, a = 3a/4b and b = 4a/3b

So,

(3a/4b)² +  (4a/3b)² + 2(3a/4b)(4a/3b)

9a²/16b² +  16a²/9b² + 2(a/b)²

= 625a²/144b²

= 5⁴a²/12²b²

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Complete Question

Simply the given expression \(({\frac{3a}{4b}}-{\frac{4b}{3a}})^{2}$\)

180+72=252

Step-by-step explanation:

an angel can be a large or as wide up to 360 then it is a circle

from the center out one way is 180

the same from the center the other way is 180

Answer:

-1 is 1 to the left of zero. Positive one is 1 to the right of zero

Step-by-step explanation:

Answer:

B. \(y=-\frac{2}{3}x+5\)

Step-by-step explanation:

Equation of a line: y=mx+b (Where m is the slope and b is the y- intercept)

Parallel lines have the same slope.

So that means that the line will have the slope \(-\frac{2}{3}\).

So we can write the equation of the line as y= -2/3x+b

Since it goes through the point (3,3) we can plug in 3 for x and y by doing:

\(y=-\frac{2}{3} x+b\\3=-\frac{2}{3} (3)+b\\3=-2+b\\b=5\)

Now we know the y intercept (b) we can write the equation of the line.

\(y=-\frac{2}{3}x+5\)

The equation of the line would be equal to y= -2/3x + 5

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

The Equation of a line: y=mx+b

Where m is the slope and b is the y- intercept

Since Parallel lines have the same slope.

So we can write the equation of the line as;

y= -2/3x+b

Since it goes through the point (3,3) we can plug in 3 for x and y

y= -2/3x+b

3 = -2 + b

b = 5

Now we know the y intercept (b) we can write the equation of the line.

y= -2/3x + 5

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The rational form of a ratio is the ratio represented as a fraction (or quotient)

The rational form of the ratio a : b is a/b

The ratio is given as a : b (pronounced a ratio b)

This is properly represented as:

\(\mathbf{Ratio = a : b}\)

To convert to rational form, means that we express the ratio as a fraction.

So, the ratio becomes

\(\mathbf{Ratio = \frac a b}\) (pronounced a divided by b)

Hence, the rational form of the ratio a : b is a/b

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The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.

The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.

The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.

It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.

Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.

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The grid-based method first quantizes the object space into a finite number of cells that form a grid structure and then performs clustering on the grid structure.

The grid-based methods are used in data mining and are based on a multi-resolution grid data structure. In the grid-based methods the space of instance is divided into a grid structure. Following the division, clustering techniques are employed using the cells of the grid as the base units instead of individual data points. The great advantage of grid-based clustering technique is its significant reduction of the computational complexity, especially for clustering very large data sets and improving the processing time.

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Answer:

-15

Step-by-step explanation:

they are opposite angles so they are congruent

x+70=55

x=55-70

x=-15

The expected number of levels to be completed before having at least one coin of each type is E(X) = 1/(1 − (1 − 1/n)n−1)

The probability of obtaining a particular coin on any given level is 1/n. The probability of not obtaining a particular coin on any given level is 1 − 1/n, for example, the probability of not obtaining the first coin on any given level is 1 − 1/n. The probability of not obtaining the first coin in the first k levels is (1 − 1/n)k; the probability of obtaining the first coin in the first k levels is therefore 1 − (1 − 1/n)k.

In order to obtain the first coin in the first k levels, the probability of not obtaining any of the other coins in the first k levels is (1 − 1/n)n−1. The probability of not obtaining any coin of a particular type in the first k levels is (1 − 1/n)nk, and the probability of obtaining at least one coin of each type in the first k levels is the product of the probabilities of obtaining at least one coin of each type, which is the complement of the probability of not obtaining at least one coin of each type, which is 1 minus the probability of not obtaining at least one coin of each type.

So the probability of obtaining at least one coin of each type in the first k levels is given by: 1 − (1 − 1/n)n−1 × (1 − 1/n)nk>= 11 − (1 − 1/n)n−1 × (1 − 1/n)k *n >= 1/(1 − (1 − 1/n)n−1)

Let's say that X is the random variable representing the number of levels needed to acquire at least one coin of each type. X is a geometric random variable with a success probability of P(X = k) = 1 − (1 − 1/n)n−1 × (1 − 1/n)nk.

Using the expected value formula: E(X) = 1/P(X), we obtain E(X) = 1/(1 − (1 − 1/n)n−1).Therefore, the number of levels needed to acquire at least one coin of each type is E(X) = 1/(1 − (1 − 1/n)n−1)

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Answer:

r = 6 ft

Step-by-step explanation:

The missing sides and angles of the triangle are

1. . A = 45 degrees.

2. B = 45 degrees.

3. BC = 3 and AB = 3 sqrt (2).

4. BC = 4 and AB = 4 sqrt (2).

5. BC = 9, then AB = 9 sqrt (2).

6. AB = 7V2, then BC = 7 .

7. If AB = 2√2, then AC = 2.​

An Isosceles Right Triangle is an angular design in the shape of a right triangle comprising two equal sides - forming congruent legs, and additionally, the third side (also known as the hypotenuse = c) being longer in length.

In this particular angle, the two legs are congruent to each other as well as proportional to the square root of two times one leg's length.

Mathematically, using Pythagoras' theorem

c^2 = a^2 + a^2

c^2 = 2a^2

Eventually, by taking the square root of both expressions, we obtain:

c = sqrt (2a^2)

c = a * sqrt (2)

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The equation x/√16+x² can be rewritten by using x= 4 tan θ as x/4.

The given expression is x/√16+x^2 and we need to rewrite it by using x= 4 tan θ.

We know that 1 + tan2θ = sec2θ ⇒ 1 = sec2θ − tan2θ ... (1)

x = 4tanθ⇒ x/4 = tanθ ... (2)

Let's substitute (2) in (1) and get:

sec2θ − tan2θ = sec2θ − x²/16 ... (3)

Now, let's simplify the denominator and numerator of x/√16+x² using trigonometry.

We have:

x/√16+x²= x/[4sec2θ]

Using (2), we know that x = 4 tanθ, so substituting this in (3) we get:

sec2θ − x²/16 = sec2θ − (4tanθ)2/16= sec2θ − tan2θ= 1 (from equation (1))

Therefore,

x/√16+x²= x/[4sec2θ] = x/[4√(sec2θ − tan2θ)] (from equation (3))= x/[4√1]= x/4

Hence, x= 4 tan as x/4 can be used to rewrite x/16+x².

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The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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The statistic that would inform a researcher of how consistent scores are in a distribution is the standard deviation. Therefore, the correct option is E.

The standard deviation is a measure of the data spread around the mean and indicates how much the scores deviate from the average. A smaller standard deviation indicates that scores are tightly clustered around the mean, while a larger standard deviation indicates that scores are more spread out and less consistent.

The other options, including the relative frequency of the lower score (a), relative frequency (b), frequencies (c), and population mean (d), do not provide information about the consistency of scores in a distribution. Hence, the correct answer is option E.

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Answer:

k < -2

Step-by-step explanation:

too lazy to explain :/

Answer:

y = 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (1, 7 ) and (x₂, y₂ ) = B (- 3, - 1 )

m = \(\frac{-1-7}{-3-1}\) = \(\frac{-8}{-4}\) = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 7 )

7 = 2(1) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = 2x + 5 ← equation of line

For a vertical cylindrical water tank where the rate of flowing is 5 cubic metre per minute. The rate at which the height of the water is rising is equals to the \( \frac{5}{9π }\) metre per minute.

We have, water flowing into a vertical cylinder. Let the radius, height and volume of cylindrical tank be r metre, h metre and V cubic metre respectively. Now, Rate of water flow in tank, \( \frac{dV}{dt}\) = 5 cubic m /min

Radius of cylindrical tank, r = 3 m

We have to determine rate at which height of the water is rising, i.e., dh/dt. As we know, Volume of cylindrical water tank, V = πr²h --(2)

Differentiating equation (2) with respect to time t,

=> \( \frac{ dV}{dt }= π(r)²\frac{dh}{dt}\)( since, radius of cylinder is constant)

=> \(5 = π(3)² \frac{ dh}{dt}\)

=> \(5 = 9π \frac{dh}{dt}\)

=> \( \frac{ dh}{dt} = \frac{5}{9π }\)

Hence, the required rate is \( \frac{5}{9π }\)m/min.

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Answer:

B. This because the power 7 will be multiplied to the powers of 3 and 5

The relation S={(a,b)∈R×R:a²+b²=1} is not an equivalence relation on the set of real numbers R.

To show that S is not an equivalence relation, we need to demonstrate that it fails to satisfy one or more of the properties of an equivalence relation: reflexivity, symmetry, and transitivity.

Reflexivity: For a relation to be reflexive, every element of the set should be related to itself. However, in the case of S, there are no real numbers (a, b) that satisfy the equation a² + b² = 1 for both a and b being the same number. Therefore, S is not reflexive.

Symmetry: For a relation to be symmetric, if (a, b) is related to (c, d), then (c, d) must also be related to (a, b). However, in S, if (a, b) satisfies a² + b² = 1, it does not necessarily mean that (b, a) also satisfies the equation. Thus, S is not symmetric.

Transitivity: For a relation to be transitive, if (a, b) is related to (c, d), and (c, d) is related to (e, f), then (a, b) must also be related to (e, f). However, in S, it is not true that if (a, b) and (c, d) satisfy a² + b² = 1 and c² + d² = 1 respectively, then (a, b) and (e, f) satisfy a² + b² = 1. Hence, S is not transitive.

Since S fails to satisfy the properties of reflexivity, symmetry, and transitivity, it is not an equivalence relation on the set of real numbers R.

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Answer: | x - 2 | = 8