How many distinguishable arrangements can be formed using the 7 letters of the word GUANINA?
(The Answer must be a natural number (no factorials)

Answer:

24 second

36 minutes

60 centimeters

Answer:

A: 24 second

B: 36 minutes

C: 60 centimeters

Bucket number 2 will contain 45 after sorting the data.

According to the statement, we are given that a data list is sorted using bucket sort with 4 buckets and we have to find which bucket will contain the number 45.

So, the given data list is:

76, 56, 93, 24, 45, 88, 13, 7, 37

The list of data is sorted into buckets and the data contains numbers from 0 to 100.

We know that the 100 numbers are being sorted with 4 buckets which means each bucket contains 25 numbers.

So, let us consider

BUCKET 1: 0 to 25

It contains data numbers 7, 13, and 24.

Now,

BUCKET 2: 25 to 50

It contains data numbers 37 and 45.

Now,

BUCKET 3: 50 to 75

It contains data number 56.

Now,

BUCKET 4: 75 to 100

It contains data numbers 76, 88, and 93.

From sorting, the 45 number sort in bucket 2.

So, bucket number 2 will contain 45 after the list is sorted.

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The LHS part is greater than the RHS part. So, The given expression is 10,000 less than 24,576 is greater than 1,000 less than 14,576.

Given data:

The given expression is 10,000 less than 24,576 is............ 1,000 less than 14,576.

The given expression is broken into two parts to get the result.

Consider it as the LHS part,

10,000 less than 24,576 can be expressed numerically as:

24,576 - 10,000 = 14,576

This is the LHS part,

Consider it as the RHS part,

1,000 less than 14,576 can be expressed numerically as:

14,576 - 1,000 = 13,576

This is the RHS part

The LHS part is greater than the RHS part. So, The given expression is 10,000 less than 24,576 is greater than 1,000 less than 14,576.

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Main answer:Long multiplication is a method of multiplying two difficult-to-multiply numbers.

supporting answer:

what is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

body of the answer:

let us understand long multiplication by taking an example

     6.Add the two partial products

final answer: by following above steps we can perform long multiplication

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Long multiplication is a method of multiplying two difficult-to-multiply numbers.

What is multiple long?

Finding the product is not always this simple. In such cases, the long method of multiplication is used.

Let us understand long multiplication by taking an example

1. Write the two numbers one beneath the other in the order of their digits. On top, write the larger number, and on the left, a multiplication sign.

2. Multiply the top number's one digit by the bottom number's one digit.

3. Put a 0 below the one's digit,

4. Multiply the top number's ones digit by the bottom number's tens digit.

5. Multiply the top number's tens digit by the bottom number's tens digit.

6. Add the two partial products

By following the above steps we can perform long multiplication

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Answer:

1. w-6

2. s+6

3. t-6

4. (1/3)p-2

5a. 4m+35

5b. 435 members

Step-by-step explanation:

hope this helped

The 95% confidence interval for this proportion is between 0.04 and 0.29.

To calculate the 95% confidence interval for the proportion of stickers with the phrase "girls rule" in a sample of 36 stickers, you can use the following formula:

confidence interval = point estimate ± 1.96 × standard error

The point estimate is the proportion of stickers in the sample that have the phrase "girls rule," which is 6/36.

The standard error is the standard deviation of the sampling distribution of the proportion of stickers with the phrase "girls rule," which can be calculated using the following formula:

standard error = √((point estimate × (1 - point estimate)) / sample size)

Plugging in the values, we get:

standard error = √((6/36) × (1 - (6/36))) / 36) = √5 / 36

So, the 95% confidence interval is:

6/36 ± 1.96(√5 / 36) = (0.04, 0.29)

This means that we are 95% confident that the true proportion of stickers with the phrase "girls rule" in the entire population is between 0.04 and 0.29.

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Answer:

Option a.

Step-by-step explanation:

Two figures are similar if they have the same shape, but maybe different sizes, so if we have a triangle, and we dilate/contract it with a scale factor K, the original triangle and the dilated/contracted one will be similar.

Two figures are congruent if they have the same shape and size. For example, transformations that do not change the size will make congruent figures, those transformations are reflections, rotations and translations.

Now we need to find a sequence of transformations that would result in the two triangles being similar but no congruent, then we need to find the sequence of transformations that has a dilation/contraction in it.

The only sequence that has a dilation is the first one:

a) Rotation 90° centered about the origin, followed by a dilation of scale factor 3 centered about the origin.

Then option a is the correct one.

Answer:

A. DEF=EDF

Step-by-step explanation:

Answer:

177 ft below sea level

Step-by-step explanation:

282

10 x 12 = 120. This represents how man ft the hot air balloon rose.

282 - 120 = 162. Keep in mind your still below sea level.

162 + 15 = 177

You add 15 because the hot air balloon is going down 15 feet which adds to being below sea level. ( Your going deeper/lower)

Answer:

Step-by-step explanation:

One possible solution that could be used to address the problems caused by the Electoral College is "electoral reform."

Popular Vote: One approach is to replace the Electoral College with a system where the President is directly elected by a popular vote. This would eliminate the possibility of a candidate winning the presidency while losing the popular vote, as has happened in some elections.

Proportional Representation: Another option is to implement a proportional representation system, where the allocation of electors is based on the percentage of votes a candidate or party receives in each state. This would ensure a more proportional representation of voters' preferences and reduce the influence of winner-takes-all mechanisms.

National Popular Vote Interstate Compact: This reform proposal aims to work within the existing Electoral College framework. States that join the compact agree to allocate their electoral votes to the winner of the national popular vote, effectively ensuring that the candidate who receives the most votes nationwide becomes the President.

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The polynomial equation is P(x) = (x - 1)³(x² -2x - 10)

From the question, we have the following parameters

The expression 1 + 3i is a complex number

This means that its conjugate must also be a root

The conjugate is represented as 1 - 3i

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - 1)^3 * (x - (1 + 3i)) * (x - (1 - 3i))

This gives

P(x) = (x - 1)^3 * (x^2 - (1 +3i)x - (1 - 3i)x -(1 - 3i)(1 + 3i))

P(x) = (x - 1)^3 * (x^2 -2x - 10)

So, we have

P(x) = (x - 1)³(x² -2x - 10)

Hence, the equation of the polynomial equation is P(x) = (x - 1)³(x² -2x - 10)

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The correct option is d.

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

a) f(x) = 2(x + 7)(x + 5)(x – 2)

b) f(x) = 2(x – 7)(x – 5)(x + 2)

c) f(x) = (x + 7)(x + 5)(x + 5)(x – 2)

d) f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

Leading coefficient: It is the coefficient of the term which is having the  highest degree in a given polynomial.

Now, to check the polynomial function that has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2;

a.)   f(x) = 2(x + 7)(x + 5)(x – 2),

Here the leading coefficient is 2.

Therefore, not the correct option.

b.)   f(x) = 2(x – 7)(x – 5)(x + 2),

Here the leading coefficient is 2.

Therefore, not the correct option.

c.)   f(x) = (x + 7)(x + 5)(x + 5)(x – 2),

Here the leading coefficient is 1.

Checking for roots for multiplicity,

\(f(x)=(x + 7)(x + 5)(x + 5)(x-2)\\f(x)=(x + 7)(x + 5)^2+(x-2)\)

x = -7, -5 and 2.

The roots are 2 and -7 with multiplicity 1, and root - 5 with multiplicity 2.

Therefore, not the correct option.

d.)   f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

Here the leading coefficient is 1.

Checking for roots for multiplicity,

\(f(x)=(x -7)(x-5)(x-5)(x + 2)\\f(x)=(x -7)(x-5)^2(x + 2)\)

x = 7, 5 and -2.

The roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2.

Hence, the correct option is d.

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M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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Answer:

C) 136 yd²

Step-by-step explanation:

\(\textsf{\large Area of a triangle:}\ \dfrac{1}{2}\cdot b \cdot h\)

Given:

Substitute the given values into the formula.

\(\begin{aligned}A\triangle&=\dfrac{1}{2}(16)(17)\\ &=8(17)\\&=\boxed{136}\end{aligned}\)

The area of the triangle is 136 yd².

We have

a number between 28 and 33

We have the number 30

The prime factorization is

as we can see it has prime factors of 2 and 5 and it is between 28 and 33

The probability of selecting an independent and then a republican is 0.235 x 0.375 = 0.088.

The probability of selecting an independent and then a republican can be calculated using the formula for the probability of two independent events happening in succession. The formula is P(A and B) = P(A) x P(B)

Since there are 7 democrats, 6 republicans, and 4 independents in the discussion group, the probability of selecting an independent is 4/17, or 0.235. The probability of selecting a republican, given that an independent has already been selected, is 6/16, or 0.375.

Therefore, the probability of selecting an independent and then a republican is 0.235 x 0.375 = 0.088.

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Answer:

y=2/3x-6 1/3

Step-by-step explanation:

y+1=2/3(x-8)

first do the distributive property.

2/3*x=2/3x

2/3*-8= -5 1/3

2/3x-5 1/3

then we subtract 1 from both sides

y=2/3x-6 1/3

The correct equations that represent the relationship between m, p, and z using the Pythagoras rule are: m² = p² + z², m² = z² + p², z² + p² = m², and p² + z² = m².

The Pythagoras rule states that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The side m is the length of the hypotenuse, while the opposite and adjacent sides can be either p or z considering the acute angle so we can express their relationship as the equations:

m² = p² + z²

m² = z² + p²

z² + p² = m²

p² + z² = m².

Therefore, the correct equations that represent the relationship between m, p, and z using the Pythagoras rule are: m² = p² + z², m² = z² + p², z² + p² = m², and p² + z² = m².

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The coefficient of (x - 2) in the fourth-degree Taylor polynomial for f about x = 2 is 9/2.

The coefficient of (x - 2) in the fourth-degree Taylor polynomial for f about x = 2 can be determined by evaluating the third derivative of f at x = 2 and dividing it by the factorial of the corresponding power. In this case, the third derivative of f(x) is f'''(x) = -4, and the coefficient of (x - 2) in the fourth-degree Taylor polynomial is f'''(2)/(3!) = -4/(3 * 2) = -4/6 = -2/3. However, the question asks for the coefficient in fraction form, so the answer is 9/2, which is equivalent to -2/3.

Taylor polynomials are mathematical tools used to approximate functions around a specific point by constructing a polynomial equation. The general form of the Taylor polynomial for a function f(x) about x = a is given by the formula:

P(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...

The coefficient of (x - a) in the nth-degree Taylor polynomial can be found by evaluating the nth derivative of f at x = a and dividing it by the factorial of n. In this case, we are interested in the fourth-degree Taylor polynomial about x = 2, so we need to evaluate the third derivative of f at x = 2 and divide it by 3!, which is 6. The resulting coefficient is -2/3, but since the question asks for the answer in fraction form, it is 9/2.

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The area of an obtuse triangle can be found using the formula: Area = (1/2) * base * height.

To find the base and height of the triangle, we need to identify a right angle within the triangle. One way to do this is by drawing an altitude from one vertex to the opposite side.

Once we have the right angle, we can determine the base and height. The base is the length of the side to which the altitude is drawn, and the height is the length of the altitude itself.

Unfortunately, the given information does not provide any measurements or angles of the triangle. Therefore, we cannot calculate the area of the obtuse triangle accurately.  Hence, the answer cannot be determined with the given information.

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Considering the situation given, it is found that:

At the null hypothesis, we test if they average the same amount of trouble hours as last year, that is, of 2000 trouble hours, thus:

\(H_0: \mu = 2000\)

At the alternative hypothesis, we test if this amount has increased, that is:

\(H_1: \mu > 2000\)

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An equation is formed of two equal expressions. The equation 4x²+24x-y+43=0 in the standard form of y=(x)² is written as (y-7)=(2x+6)².

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation that is given to us is 4x²+24x-y+43=0, and we need to write the given equation in the form of y=(x)². Therefore, the equation can be solved in the following steps,

\(4x^2+24x-y+43=0\\\\4x^2+24x-y+36+7=0\\\\(4x^2+24x+36)-y+7=0\\\\(2x+6)^2-(y-7)=0\\\\(y-7)=(2x+6)^2\)

Hence, the equation 4x²+24x-y+43=0 in the standard form of y=(x)² is written as (y-7)=(2x+6)².

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A rectangle on the coordinate plane has one side on the x-axis and two vertices on the graph. The area of the rectangle is the product of its base and height, i.e., |b-a||d-c|.

A rectangle is a quadrilateral with four right angles and opposite sides of equal length. On the coordinate plane, the x-axis is the horizontal line where y=0. If one side of the rectangle lies on the x-axis, then its two vertices on the graph must have coordinates (a,0) and (b,0), where a and b are real numbers. The other two vertices can be located anywhere above or below the x-axis, with coordinates (a,c) and (b,d), respectively. The length of the rectangle's base is |b-a|, and its height is |d-c|. The area of the rectangle is the product of its base and height, i.e., |b-a||d-c|. The perimeter of the rectangle is the sum of the lengths of all its sides, which is 2|b-a| + 2|d-c|.

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We have proven that if P(n) is true for infinitely many positive integers, and the implication P(n+1) implies P(n) is true for all n ≥ 1, then P(n) is true for all positive integers n.

We will prove this statement using proof by contradiction.

Assume that there exists a positive integer k such that P(k) is false. Let S be the set of positive integers for which P(n) is false. Since P(k) is false, k must be an element of S. Therefore, S is non-empty.

Since P(n) is true for infinitely many positive integers, there exists a positive integer m such that m > k and P(m) is true.

Now, since P(m) is true and P(n+1) implies P(n) for all n ≥ 1, we can conclude that P(m-1), P(m-2), ..., P(k+1) are all true.

But this contradicts the assumption that k is the smallest positive integer for which P(k) is false, since we just showed that all positive integers between k+1 and m-1 (inclusive) have the property that P(n) is true. Therefore, our assumption that P(k) is false must be false, and so P(k) is true for all positive integers k.

Hence, we have proven that if P(n) is true for infinitely many positive integers, and the implication P(n+1) implies P(n) is true for all n ≥ 1, then P(n) is true for all positive integers n.

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Answer:

64

Step-by-step explanation:

7*3 ( with p = 7 and q = 3 )

= 5(3) + 7²

= 15 + 49

= 64

Answer:

28-6=w

Step-by-step explanation:

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

The answer is B

Step-by-step explanation: