what are the properties of rational exponents and how are they used to solve problems

The probability of point being in between B and C is 0.167

Probability is a statistic used to indicate the likelihood or potential that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.

Distance between B and C= 4 units

Total distance=24

Probability that point lie between B and C = 4/24 =1/6

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Answer: No, -0.0022 is not less that -0.022

Step-by-step explanation:

1. We know that the bigger the negative number the lesser it is ( 0.022 is a bigger number than 0.0022) but since it's a negative number it's less in value.

The amount of vanilla in the ice cream is 1/5 in the sundae that is being mad by Peter.

Peter make sundae by using mint chocolate and vanilla ice cream.

It is given to us that, the mint ice cream is 3/5 and chocolate is 1/2 of the remaining.

So, first we calculate the amount of chocolate,

Let us say that, we take the sundae as 1,

so, algebraically, the mint is,

X - 3/5 = 1

X = 2/5

Now, half of the 2/5 is,

Half of 2/5 = 2/5x1/2

Half of 2/5 = 2/10

Half of 2/5 = 1/5

So, the remaining portion after filling chocolate is 1/5

So, the vanilla ice cream will be 1/5.

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The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required to be determined is; 25.

It is evident from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Therefore, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Ultimately, it can be inferred that the greatest possible quotient as required is; 25.

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Answer:

6000.000 + 900.000 + 0 + 5 + 3/10 + 2/100 + 7/1000

six thousand nine hundred and five ones point(.) three tenths two hundredths and seven thousandths

Step-by-step explanation:

right!!!

In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.

According to question:-

How much more garlic powder than salt is in the triple batch?

Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.

How much spice mix is in the triple batch?

Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.

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Answer:

√28 and √11

Step-by-step explanation:

Note : -

Irrational number is any real number that cannot be expressed as the quotient of two integers.

Here,

√28 = 5.291.......

5.291.... is an infinite number, it keeps going, it cannot be expressed in terms of a fraction.

Similarly,

√11 = 3.316......

Hence,

√28 and √11 are irrational numbers.

Using the distributive property to rewrite the expression, gives (14 x 10) + ( 14 x 2). When evaluated, the result would be 168.

According to the distributive property, it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

This means that with the formula given, 14 (10 + 2):, the distributive property makes it:

= 14 (10 + 2)

= (14 x 10) + ( 14 x 2)

The evaluation gives :

= (14 x 10) + ( 14 x 2)

= 140 + 28

= 168

In conclusion, using the distributive property gives (14 x 10) + ( 14 x 2).

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A trader can create their own automated trading strategies in forex by writing a script or program in a programming language, such as MQL4 or Python. This script will contain instructions to execute trades according to specific criteria defined by the trader. They can then backtest the strategy to see how it performs.

1. Decide on a trading strategy. This could include things like setting entry and exit points, calculating position sizes, and setting stop losses and take profits.

2. Choose a programming language that is compatible with the trading platform you are using, such as MQL4 or Python.

3. Write the script or program that will contain the instructions for the trading platform to follow in order to execute the trading strategy.

4. Test the script or program to make sure it works properly.

5. Run a backtest to see how the trading strategy performs.

6. If the results of the backtest are satisfactory, you can deploy the trading strategy on the trading platform.

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The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, k(x) = 4 ÷ 5x - 6.

k(x) = (4/5x) - 6.

Let, y = k(x).

y =  (4/5x) - 6.

(4/5x) = y + 6.

1/x = 5(y + 6)/4.

x = 4/{5(y + 6)}.

y = 4/{5(x + 6)}.

k⁻¹(x) = 4/{5(x + 6)}.

k⁻¹(8) = 4/{5(8 + 6)}.

k⁻¹(8) = 4/{5(14)}.

k⁻¹(8) = 4/70.

k⁻¹(8) = 2/35.

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Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.

The value that consistently appears in a given set is known as the mode in statistics. The mode or modal value is the value or number that appears most frequently in a data set and has a high frequency. Along with mean and median, there are three other ways to measure central tendency. The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.

given

Example: 50th box of cereal

All cereal boxes are lined up in the population

Example Parameter: The cereal box's average weight

Population metric: The cereal on the line's average weight

Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.

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Yara's mother was 32n-5 years old 5 years ago in terms of n.

Yara's mother is 4n times older than Yara, and Yara is 8 years old, so we can set up the equation:

Mother's age = 4n * 8 years

We are also told that Yara's mother is 5 years older than she is now, so we can add 5 to the equation above:

Mother's age 5 years ago = 4n * 8 years - 5 years

Now we can simplify this equation:

Mother's age 5 years ago = 32n - 5 years

Now we can substitute the value of n to find the mother's age in terms of n.

To find the age of Yara's mother 5 years ago in terms of n, we need to know the value of n. But we don't have the value of n so we can't find the exact age but we can find it in terms of n which is 32n-5 years.

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The necessary probabilities are 3/8, 1/3, 9/64, and 37/64.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

S = { G1, G2, G3, Y1, Y2, Y3, Y4, Y5 }

G = { G1, G2, G3 }

P(G) = 3/8

E = { G2, Y2, Y4 }

P(G|E) = 1/3

P(G and E) = P(G)*P(E) = (3/8)*(3/8) = 9/64

P(G or E) = P(G) + P(E) - P(G and E) = (3/8) + (3/8) - (9/64) = (6/8) - (9/64) = (48/64) - (9/64) = 37/64

The required probability is 3/8, 1/3, 9/64 and 37/64.

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The Third side of the right triangle with two sides can be found by Pythagoras Theorem that means by adding the square of other two sides .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the , in a Right Triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

The sides of this triangle are named as Perpendicular, Base and Hypotenuse. where , the hypotenuse is longest side of the triangle , because ,  it is opposite to the angle 90°.

Therefore , the third side (longest side) of a right triangle with two sides can be found by adding the square of the other two sides .

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The second ordered pair using the terms in each sequence is B (6, 24).

The second rule says to subtract 4 from the second term of the ordered pair, starting from 28. So the second term of the second ordered pair would be 28-4 = 24.

Therefore, the second ordered pair using the terms in each sequence is B (6, 24).

This is because:

C (14,16) can be obtained by adding 4 to first term of B(6,24) which is 6+4 = 10 and subtracting 4 from second term of B(6,24) which is 24-4=20.

D (10,20) can be obtained by adding 4 to first term of C(14,16) which is 14+4 = 18 and subtracting 4 from second term of C(14,16) which is 16-4=12.

So the sequence list of ordered pair would be:

First order: A (2,28)

Second order: B(6,24)

Third order: C (14,16) D (10,20)

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Answer:

44.8

Step-by-step explanation:

44.4 - (-0.4) = 44.8

Writing the whole number in the numerator and 1 in the denominator. Fraction in simplest form is 8

How to Find the Most Basic Form

Determine the GCF of the fraction’s numerator and denominator.

Divide the created GCF by the numerator and denominator.

Fill in the blanks with the simplified fraction of the supplied fraction.

The most basic form, If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase “lowest terms” when referring to the simplest form.

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Answer:

320 grams ÷ 27% = 8.3 grams

Step-by-step explanation:

mark brainliest plss

There is no upper limit if the ratio raises x to a higher power. The limit is 0 if the ratio causes the power of x to be reduced to zero.

A ratio is an expression for an ordered pair of numbers, a and b, where b is not equal to zero and the expression is written as a/b. A ratio is created by combining two ratios. Assuming a ratio of one boy to three girls, this would suggest that 3/4 of the population is female and only 1/4 is male. A part can be an amount, a percentage, or the difference between two or more objects.

Here,

The ratio of, say, the highest-degree words serves as the upper bound as x grows.

There is no upper bound on how much the ratio can raise the power of x. The limit is 0 if the ratio causes the power of x to be reduced to zero.

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Step-by-step explanation:

credits are also on there

Answer:

Step-by-step explanation:

To find the y-intercept, we can use the slope-intercept form of a linear equation which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

Since the line passes through the points (2, -2.5) and (4, -2), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

To find the slope(m) we can use the rise over the run formula ,

m = (y2 - y1) / (x2 - x1) = (-2 - (-2.5)) / (4 - 2) = -0.5

then we can substitute the values in point-slope form

y - (-2.5) = -0.5 (x - 2)

And now we can use x = 0,

y = -0.5(0-2) -2.5 = 1.5

so the y-intercept of the line is 1.5

The options that shows expressions which are functions in the ranges they are defined are;

Option A: f(x) = 2x + 5

Option B:  f(x) = x² + 1

Real numbers are defined as the combination of rational and irrational numbers, in the number system. This means that, all the arithmetic operations can be performed on real numbers and they can be represented in the number line.

Now, integers are defined as whole numbers that can be positive, negative or zero.

a) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = 2x + 5 will yield an output that is also a real number.

b) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = x² + 1 will yield an output that is also a real number.

c) We are told that the input of real numbers must yield only real numbers. No this is not true because if we put -1 which is a real number for x in the denominator, we will get an undefined function.

d) We are told that the input of integers must yield only integers. No this is not true because if we put 1 for x which is an integer, we will get a fraction which is not an integer.

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Answer:

b and c

Step-by-step explanation:

b is basically saying flip it up and turning the whole thing left which will put it on top of pnms and c is saying rotate it where line sr and sm would be side by side then flip it right

It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.

Triangles must have equal corresponding sides and equal corresponding angles in order to be congruent.

According to the RHS congruence theorem, two right-angled triangles are congruent if their respective hypotenuses and sides are the same as those of another right-angled triangle.

Here we have

AOC and BOD are diameters of a circle and have a center O.

It is given that AOC and BOD are diameters of a circle.

From the triangles Δ AOC and ΔBOD

⇒ BD = CA  [ Diameters of the circle i.e Hypotenuse of triangles ]    

⇒ ∠BAD = ∠CDA [ Right angles in a semicircle is 90°]

⇒ AD = AD [ Common in both triangles i.e sides of triangles ]

Thus, Using RHS congruence criteria

⇒ ΔABD ≅ ΔDCA

Hence,

It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.

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Answer:

2.50 × 19 = 47.5

Therefore, she would get $47.5 if she sold 19 cups.

Answer:

Step-by-step explanation:

Find the prime factorization of 144

144 = 2 × 2 × 2 × 2 × 3 × 3

Find the prime factorization of 405

405 = 3 × 3 × 3 × 3 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 3 × 3

Answer = 9

If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.

Pythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.

The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.

Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2  

We apply the Pythagorean Theorem to determine the kite's height, h

the problem can solve if the kite is 60feet

[tex]h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80[/tex]

h =80 ft (we take the positive solution since the height can not be negative number)

The kite is 80 ft above the ground.

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Therefore , In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.

What is triangle?

Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.

A polygon is a closed two-dimensional geometric shape that has three or more straight sides. The sides of a polygon are called edges and the points where the edges meet are called vertices.

Here,

We must apply the mathematical procedure for computing an equilateral triangle's area.

An equilateral triangle's area is equal to 3/4 of each side; assume that each side is x cm long.

[3/4 (a)2] cm2 is the equilateral triangle's surface area.

In light of the information mentioned in the query,

√3/4 × (a)² = 196√3

a²/4 = 196√3/√3

a²/4 = 196

a² = 196×4

a² = 784

a = √784

a = 28

In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.

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Answer:

Answer:

Foci: (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

Hyperbola:

Write the equation of hyperbola in the form,

\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}

a

2

x

2

−

b

2

y

2

=1

9x² - 16y² = 144

Divide the entire equation by 144,

\begin{gathered}\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1\end{gathered}

144

9x

2

−

144

16y

2

=

144

144

16

x

2

−

9

y

2

=1

4

2

x

2

−

3

2

y

2

=1

a = 4 and b =3

Eccentricity: e

\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}

e=

1+

a

2

b

2

\begin{gathered}\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}\end{gathered}

=

1+

16

9

=

16

16

+

16

9

=

16

25

=

4∗4

5∗5

=

4

5

Foci:

(ae, 0) & (-ae , 0)

\begin{gathered}\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)\end{gathered}

(4∗

4

5

,0) ; (−4∗

4

5

,0)

(5,0) ; (−5,0)

Vertex of hyperbola:

The vertex of the hyperbola is a point where the hyperbola cuts the axis. (-a , 0) ; (a , 0)

Vertex : (-4 , 0) ; (4 , 0)

The parabola is open upward direction. The vertex is the minimum value of the parabola.

What is a parabola?

A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.

Given quadratic function is

f(x) = 5x² -3x

The leading term of the given function is 5x².

The sign of the leading term is positive, thus it is open upward direction.

Rewrite the given function in the form f(x) = a(x - h)² + k

f(x) = 5x² -3x

f(x) = 5( x² - 3/5 x)

f(x) = 5( x² - 3/5 x + 9/100 - 9/100)

f(x) = 5( x² - 3/5 x + 9/100) - 5 × 9/100

f(x) = 5( x -  3/10)² - 9/20

f(x) = 5( x -  3/10)² + (-9/20)

The vertex of the parabola is (3/10, -9/20).

Since the parabola opens upward direction, thus the vertex of the parabole is a minimum value.

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