How many unique permutations are in “HAPPINESS”

Answer:

ii) Reduce :

[tex]$\begin{aligned} 5 \ln x-2 \ln (x y) & =\ln x^5-\ln (x y)^2 \\ & =\ln \left(\frac{x^5}{(x y)^2}\right) \\ & =\ln \left(\frac{x^5}{x^2 y^2}\right) \\ & =\ln \left(\frac{x^3}{y^2}\right)\end{aligned}$[/tex]

iii ) Expand :

[tex]\begin{aligned}\log _3\left(\frac{x^5}{y}\right)^4 & =4 \log _3\left(\frac{x^5}{y}\right) \\& =4 \log _3 x^5-4 \log _3 y \\& =20 \log _3 x-4 \log _3 y\end{aligned}[/tex]

Answer:

[tex]\textsf{ii)} \quad \ln \left(\dfrac{x^3}{y^2}\right)[/tex]

[tex]\textsf{iii)} \quad 20 \log_3 x-4 \log_3y[/tex]

Step-by-step explanation:

Given expression:

[tex]5 \ln x-2 \ln (xy)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\implies \ln (x^5) - \ln ((xy)^2)[/tex]

[tex]\textsf{Apply the quotient law}: \quad \ln x - \ln y=\ln \left(\dfrac{x}{y}\right)[/tex]

[tex]\implies \ln \left(\dfrac{x^5}{(xy)^2}\right)[/tex]

This is where the error occurred in the original calculation as the log quotient law was applied incorrectly.

[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^{c}b^c\quad \textsf{to the denominator}:[/tex]

[tex]\implies \ln \left(\dfrac{x^5}{x^2y^2}\right)[/tex]

Simplify the fraction:

[tex]\implies \ln \left(\dfrac{x^3}{y^2}\right)[/tex]

Given expression:

[tex]\log_3\left(\dfrac{x^5}{y}\right)^4[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies 4\log_3\left(\dfrac{x^5}{y}\right)[/tex]

[tex]\textsf{Apply the log quotient law}: \quad n\log_a \left(\dfrac{x}{y}\right)=n\log_ax - n\log_ay[/tex]

[tex]\implies 4 \log_3 x^5-4 \log_3y[/tex]

This is where the error occurred in the original calculation as the coefficient 4 was not applied to the both logarithms when applying the log quotient law.

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies 5 \cdot 4 \log_3 x-4 \log_3y[/tex]

[tex]\implies 20 \log_3 x-4 \log_3y[/tex]

The required  inequality to represent the possible number of cakes sold ​is Cupcakes ≥ 144.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

Write an inequality to illustrate the potential amount of cakes sold if the business sold 144 cupcakes. ​

So,

Bakery can sold 144 cupcakes and more

Cupcakes ≥ 144

Thus, required inequality is Cupcakes ≥ 144.

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The required of the sidewalk to the nearest square foot is 13.14 ft².

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area.

We have,

Length = 5 ft, width = 2 ft, Radius of circle = 2 ft

Now,

Area of sidewalk = area of rectangle + area quadrant

Area of sidewalk = (5×2) + π(2)^2/4

Area of sidewalk = 10 + 3.14

Area of sidewalk = 13.14 ft²

Thus, required area of the sidewalk is 13.14 ft².

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The general solution of a linear second order homogeneous equation is represented as the combination of two particular solutions.

This is because the linear second order homogeneous equation is of the form ax2+bx+c=0 and has two distinct roots, i.e. x1 and x2. The general solution of the equation can be written as y=C1y1+C2y2, where C1 and C2 are constants and y1 and y2 are the two particular solutions. The particular solutions can be derived from the two distinct roots of the equation using the formula y1=e^(x1*t) and y2=e^(x2*t). The constants C1 and C2 can be found by solving the linear combination of the two particular solutions for the given initial conditions of the equation. This gives the general solution of the linear second order homogeneous equation as a combination of the two particular solutions.

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Answer: The area of the floor can be found by multiplying the width and the length.

Area of the floor = (6x - 9)(6x + 9) = 36x^2 - 63x - 81

The area of each tile can be found by evaluating the expression 24x^2 - 12x - 36.

Area of each tile = 24x^2 - 12x - 36

To find out how many tiles are needed to cover the floor we need to divide the area of the floor by the area of each tile.

Number of tiles needed = (36x^2 - 63x - 81) / (24x^2 - 12x - 36)

The division is simplified by canceling out common factors between the numerator and denominator, the number of tiles is a fraction that can't be simplified any further.

So the answer is (36x^2 - 63x - 81) / (24x^2 - 12x - 36) tiles are needed to cover the floor.

Step-by-step explanation:

The area under the density curve from 15 to 100 is 0.80.

With pdf f and cdf f, consider X to be a continuous random variable.

By definition, integrating the pdf yields the cdf: F(x)=x∫−∞f(t)dt.

By differentiating the cdf, one may find the pdf according to the Fundamental Theorem of Calculus: f(x) = ddx[F(x)]

An interval or group of intervals makes up the sample space of a continuous random variable, X.

1- 0.20 0.80

[tex]\int\limits^[/tex] f(x) dx from 0 to 100 = 1

[tex]\int\limits^[/tex]  f(x) dx from 0 to 15 + int 15 ^ 100 =1

[tex]\int\limits^[/tex]  d from 15 to 100 =1-0.20=0.80.

The area under the density curve from 15 to 100 is 0.80.

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Julio's down payment would be 20% of the total cost of the car. If he is financing $14,000 of the remaining cost, the total cost of the car would be $14,000 / (1 - 0.20) = $14,000 / 0.80 = $17,500. Therefore, Julio's down payment would be $17,500 * 0.20 = $3,500.

What is a percentage in plain English?

A percentage is a portion of a total stated as a number between 0 and 100 as opposed to being expressed as a fraction. The percentages of everything are 100%, nothing is 0%, 50% of something is 50%, and nothing is 0%. To calculate the percentage, divide the component by the total and multiply the result by 100.

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Using percentage, Julio's down payment would be  $3,500.

In contrast to being expressed as a fraction, a percentage is a portion of a total expressed as a number between 0 and 100. The percentages are as follows: 100% of everything, 0% of nothing, 50% of something, and 0% of nothing. Divide the component by the total, then multiply the result by 100 to get the percentage.

Julio's down payment would be 20% of the total cost of the car.

If he is financing $14,000 of the remaining cost,

the total cost of the car would be

$14,000 / (1 - 0.20)

= $14,000 / 0.80

= $17,500.

Therefore, Julio's down payment would be $17,500 * 0.20 = $3,500.

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The solution to the expression with decimals rounded to the nearest tenth is: -2

Examine the hundredth number to round the decimal number to the nearest tenth. If the number is more than 5, multiply it by one. If it is less than 5, leave the tenth place value alone and eliminate any numbers after the tenth. 4.624, for example, is 4.6 rounded to the closest tenth.

Thus, given the expression:
2.29 + 9.11 + 15.381 - 5.414 - 7.631.11 + 5.99 - 5.734 + 6.893 - 18.355 -4.411

We first round them up to the nearest tenths is:

2.1 + 9.1 + 15.4 - 5.4 - 7.6 + 6.0 - 5.7 + 6.9 - 18.4 - 4.4  = -2

Thus, it is correct to state that the version of the above-given expression resolved to the nearest tenths (2.1 + 9.1 + 15.4 - 5.4 - 7.6 + 6.0 - 5.7 + 6.9 - 18.4 - 4.4) = -2

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The value of x is 76°. The solution has been obtained using the properties of hexagon.

What is a hexagon?

A closed, two-dimensional, six-sided polygon in geometry is called a hexagon. It has six vertices, which together create six internal angles, and six line segments. The total of a hexagon's internal angles is 720°.

We know that sum of angles on a straight line is 180°.

So, on the first line with angle 60°, the other angle will be

180° - 60° = 120°

Similarly, on the second line with angle 64°, the other angle will be

180° - 64° = 116°

Similarly, on the third line with angle 36°, the other angle will be

180° - 36° = 144°

Similarly, on the fourth line with angle 48°, the other angle will be

180° - 48° = 132°

Similarly, on the fifth and sixth lines with angle x°, the other angles will be

180° - x° = (180-x)°

We know that sum of angles of interior angles of a hexagon is 720°

Therefore,

⇒ 120° + 116° + 144° + 132° + (180-x)° + (180-x)° = 720°

⇒ 512° + 180° - x° + 180° - x° = 720°

⇒ 872° - 2x° = 720°

⇒ 2x° = 152°

⇒ x = 76°

Hence, the value of x is 76°.

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The ending balance if the amount is compounded continusoly is $6,244.84

The interest earned is $4,244.84.

If an amount is compounded continuously, it means that both the amount invested and the interest earned increases in value infinitely over the investment period.

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

Interest = future value - amount invested

2000 x e^0.04 x 3 = $6,244.84

Interest = $6,244.84 - $2000 = $4,244.84

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Answer:

What is the question please respond so I may give a complete response

According to the information ∠1 and ∠2 are complementary to each other.

∠1 ⊥ ∠2
Since PR is parallel to VO and RO is parallel to PV, it follows that PR is congruent to RO. This means that ∠1 and ∠2 are supplementary angles and thus, complementary.
Since PR // VO and RO // PV, then by the Transitive Property of Congruence, VO // PV.

Since PR ≅ RO and VO // PV, then by the Corresponding Angles Postulate, ∠1 ≅ ∠2.

Since ∠1 and ∠2 are congruent, then by the definition of complementary angles, ∠1 and ∠2 are complementary.

Thus, ∠1 and ∠2 are complementary.

∴ ∠1 and ∠2 are complementary

Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

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The scale factor for the dilation in this problem is given as follows:

2.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

As the side lengths are changed, with a dilation the figure loses it's congruence relative to the original figure.

The equivalent side lengths in this problem are given as follows:

The dilated triangle is triangle DAB, hence the scale factor is obtained as follows:

k = 8/4 = 2.

(that is, the side lengths of triangle DEF were multiplied by 2 to generate triangle DAB).

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Answer:

height = 12

Step-by-step explanation:

The formula for the area of a triangle is: [tex]\frac{1}{2}(b*h)[/tex] = A

A = area of a triangle

b = base

h = height

The problem states that the area (A) of triangle is 48, and the base (b) is 8, so we can plug those values into the equation above:

48 = [tex]\frac{1}{2}(8*h)[/tex]

Let's solve for h now:

48 = [tex]\frac{1}{2}8h[/tex]

48 = 4h

h = 48/4

h = 12

Answer:

12 inches

Step-by-step explanation:

Formulae (Area of a triangle): 1/2 × Measure of Base × Measure of Height

Given Information:

Substitute the information into the formula to create an equation;

Solve the equation to find out the measure of the height;

Therefore, the measure of the height is 12 inches.

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Answer: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

its $89,372 i did the math took the test

The arrow diagram that represents a mapping include the following: arrow diagram C.

The domain of this arrow diagram is equal to {a, c, d}

The range of this arrow diagram is equal to {q, r, s}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.

In this scenario, we can reasonably infer and logically deduce that only the above mentioned relation (arrow diagram C) represents a function because each input variable (domain) has exactly an output variable (range) as illustrated in the diagram.

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Answer:

see below

Step-by-step explanation:

1 foot = 30 centimeters or 0.30 meters-

1 pound =450 grams or 0.45 kilograms-

1 fluid ounce = 29.5 milliliters-

The original matrix's rank > the augmented matrix's rank. So the option C "the solution set is empty" is correct.

The matrix is

[tex]\left [ \begin{matrix}1 & 7&3 & -4\\ 0& 1& -1 & 3\\ 0& 0 & 0& 2\\ 0&0 & 1&1 \end{matrix} \right ][/tex]

To determine the solution set we simplify the given matrix by performing the row operations.

[tex]R_{4}\leftrightarrow R_{3}[/tex]

[tex]\left[\left.\begin{matrix}1 & 7 &3 \\ 0& 1 & -1\\ 0& 0 & 1\\ 0&0 &0 \end{matrix}\right|\begin{matrix}-4\\ 3\\ 1\\ 2\end{matrix}\right][/tex]

The rank of main matrix = 3

The rank of augmented matrix = 4

The rank of main matrix < The rank of augmented matrix

So, there is no solution. The solution set is empty.

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The complete question is:

The augmented matrix of linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system:

[tex]\left [ \begin{matrix}1 & 7&3 & -4\\ 0& 1& -1 & 3\\ 0& 0 & 0& 2\\ 0&0 & 1&1 \end{matrix} \right ][/tex]

Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice.

A: The solution set has exactly one element

B. The solution set has infinitely many elements

C. The solution set is empty

The best interpretation for the given standard deviation as per given information is given by :

Option D. On an average, the number of breakdowns per day varies from the mean by about 0.28.

As given in the question,

Therefore, the best interpretation of standard deviation is :

Option D. On an average, the number of breakdowns per day varies from the mean by about 0.28.

The above question is incomplete , the complete question is:

The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

A. The number of breakdowns on a randomly selected day is expected to be 0.28.

B. The number of breakdowns on a randomly selected day will be 0.28 away from the mean.

C. The average number of breakdowns per day for a random sample of days is expected to be 0.28

D. On average, the number of breakdowns per day varies from the mean by about 0.28.

E. The number of breakdowns per day for a random sample of days is expected to be 0.28 away from the mean.

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Nine pencils at $0.05 each, 2. Five pencils at $0.10 each and three pencils at $0.05 each 3.Six pencils costing $0.05 apiece and three pencils costing $0.15 each. Pencils: four for $0.15 each, and five for $0.05 each.

This question uses the combination theory, which states that the total number of combinations of a set of items is equal to the number of variations in one item multiplied by the number of variations in the second item, and so on.

in this question

1. Nine pencils at $0.05 each: Kay can buy nine pencils for $0.45. Nine pencils times $0.05 each equal $0.45.

2. Five pencils at $0.10 each and three pencils at $0.05 each: Kay can buy five pencils for $0.50 and three pencils for $0.15.

Five pencils times $0.10 each equal $0.50 and three pencils times $0.05 each equal $0.15.

Adding the two totals together equals $0.45.

3. Three pencils at $0.15 each and six pencils at $0.05 each: Kay can buy three pencils for $0.45 and six pencils for $0.30.

Three pencils times $0.15 each equals $0.45 and six pencils times $0.05 each equal $0.30.

Adding the two totals together equals $0.45.

4. Four pencils at $0.15 each and five pencils at $0.05 each:

Kay can buy four pencils for $0.60 and five pencils for $0.25.

Therefore, Four pencils times $0.15 each equals $0.60 and five pencils times $0.05 each equal $0.25. Subtracting the two totals together equals $0.45.

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The inequality to determine the number of 100-kilogram crates that can be loaded into the shipping container is 27500 ≤ 5400 + 100x

A shipping container will be used to transport several 100-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 5400 kilograms have already been loaded into the container.

Therefore, the inequality that can be used to determine x, the number of 100-kg crates that can be loaded into the shipping container can be calculated as follows:

27500 ≤ 5400 + 100x

where

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Answer: The sum is -15

Step-by-step explanation:

The machine can make 20 soda bottles each minute.

In Mathematics and Geometry, the slope of any straight line simply refers to the rate of change and it can be calculated by using this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points located on the line:

Substituting the given points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (140 - 100)/(7 - 5)

Slope (m) = 40/2

Slope (m) = 20.

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The coordinate points on the first quadrant represent the possible dimensions of the rectangle with an area of 32 m².

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given are two figures as shown in the image attached.

{ 1 } -

The image in question {12} cannot be proved congruent by AAS congruence rule.

{ 2 } -

For the triangles shown in question {13}, we can prove the triangles congruent by AAS rule as -

90° = 90°    { Equal right angles }

Sides opposites to right angles are equal. So, the angles opposite to these angles {let x° and  y°} will be equal. We can write -

x° = y°

Two equal sides given

Hence, triangles are proved AAS congruent rule.

Therefore, the triangles along with their respective congruency proofs are given above.

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The equation in slope-intercept form for this line is y = -5/4x + 3.

What is the slope-intercept form of the line?

The slope-intercept form is a way of representing the equation of a straight line in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). The slope of a line represents the steepness of the line, and the y-intercept represents the point at which the line crosses the y-axis.

A line can be represented by two points (x1, y1) and (x2, y2) the slope can be calculated by the formula:

m = (y2 - y1) / (x2 - x1)

In this case, the line passes through the point (-8, -9) and has a slope of -5/4, we can use the point-slope form of the equation of a line to find the equation of this line:

y - y1 = m(x - x1)

y - (-9) = (-5/4)(x + 8)

y = (-5/4)x + (-9) + (2*9)

y = (-5/4)x + 3

Hence, the equation in slope-intercept form for this line is y = -5/4x + 3.

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If the ratio of profit shares is 3:7:9, then the total profit yield is 38000.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

The share of Juma's profit is = 3

The share of Ali's profit is = 7

The share of Hassan's profit is = 9

The ratios can be written as 3x : 7x : 9x

The amount of money Juma received is = 6000

The equation for Juma's profit is -

3x = 6000

x = 6000/3

x = 2000

So, the value for Ali's profit -

7x = 7 × 2000

= 14000

The value for Hassan's profit -

9x = 9 × 2000

= 18000

Now, the total profit is represented by the equation -

= 3x + 7x + 9x

= 6000 + 14000 + 18000

= 38000

Therefore, the total profit is 38000.

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Answer:1325

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

4(5x-3)-3(2x-5)=17

20x-12-6x+15=17

14x+3=17

     -3.  -3

14x=14

/14.  /14

x=1

For your data, the regression equation for Y is:

Y = 2.09697X - 0.55152

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given, a data set

x: -5, -3, 4, 1, -1, -2, 0, 2, 3, -4

y: -10, -8, 9, 1, -2, -6, -1, 3, 6, -8

Sum of X = -5

Sum of Y = -16

Mean X = -0.5

Mean Y = -1.6

Sum of squares (SSₓ) = 82.5

Sum of products (SP) = 173

Regression Equation = Y = bX + a

b = SP/SSₓ = 173/82.5 = 2.09697

a = Mₓ - bMₓ = -1.6 - (2.1*-0.5) = -0.55152

Y = 2.09697X - 0.55152

For x = 2.5 the value of y:

y = 2.09697* 2.5 - 0.55152

y = 4.69

Therefore, For your data, the regression equation for Y is:

Y = 2.09697X - 0.55152

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