DIRECTION: Determine the validity of the following arguments.

Answer:

19. x = 60

20. x= 27

Step-by-step explanation:

19. Given 2 triangles are congruent

so BQ/BC = BR/BD

30/84 = x/168

84x = 30(168)

84x = 5040

x = 5040/84 = 60

20. Given 2 triangles are congruent

QS/QP = ST/PR

18/x = 10/15

10x = 18(15)

10x = 270

x = 270/10 = 27

The value of the integral is π(540)^2.

We can change the order of integration as follows:

∫^(∞)(0)∫540∫9y6e−x2+zdxdydz = ∫^(540)(0)∫^∞_0∫^√(9y^6)_(−∞)e−x^2dzdxdy

The limits of z are from −∞ to ∞, but the integrand is an even function of z, so we can simplify the integral by taking the absolute value of the integrand and multiplying it by 2:

∫^(540)(0)∫^∞_0∫^√(9y^6)(−∞)e−x^2dzdxdy = 2∫^(540)_(0)∫^∞_0∫^√(9y^6)_0 e−x^2dzdxdy

We can now evaluate the integral with respect to z:

2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−√x^2+z)/2]|^√(9y^6)_0 dxdy

where erf is the error function.

Substituting the limits of integration and simplifying, we get:

2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−3y^3/√2x)/2]dxdy

Next, we can evaluate the integral with respect to x:

2∫^(540)_(0)[√π/2(x - √2/3y^3erf(−3y^3/√2x))]|^∞_0 dy

Since the limits of integration with respect to x are from 0 to ∞, the first term in the square brackets evaluates to ∞, and the second term evaluates to √π/2. Therefore, the integral reduces to:

2∫^(540)_(0)√π/2 dy = π(540)^2

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Answer:

Step-by-step explanation:

To determine which pairs satisfy the equation 2y - 8x = 6, we need to find values of x and y that make the equation true. One way to do this is to solve for y in terms of x:

2y - 8x = 6

2y = 8x + 6

y = 4x + 3

Now we can substitute different values of x into this equation and see what values of y we get. For example:

When x = 0, y = 3

When x = 1, y = 7

When x = -1, y = -1

When x = 2, y = 11/2

When x = -2, y = -5

So the pairs that satisfy the equation 2y - 8x = 6 are:

(0, 3), (1, 7), (-1, -1), (2, 11/2), (-2, -5)

In each of these pairs, when we substitute the values of x and y into the equation, we get a true statement

Reflection across x=3 is a transformation that involves reflecting a figure across a vertical line of symmetry at x=3.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.


This transformation produces a mirror image of the original figure. Reflection across x=3 can be represented in the form of a matrix equation,

A= [[-1, 0],
   [ 0, 1]]

This matrix equation demonstrates that the x coordinates of a point will be multiplied by -1, while the y coordinates will remain unchanged. This transformation is also known as a reflection over the y-axis.

Reflection across x=3 can be used to change the orientation of a figure in a 2-dimensional coordinate plane. For example, if a triangle is located at the position (2,4) and the coordinates need to be changed so the triangle is reflected across x=3, the coordinates would be transformed to (-2,4).

Reflection across x=3 can also be used to solve various types of mathematical problems. For example, if a problem asks for the coordinates of a point that is the reflection of a point across x=3, the coordinates of the reflected point can be calculated by multiplying the original x coordinate by -1 and leaving the y coordinate unchanged.

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The solution is, the required z-score is, 0.25.

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

here, we have,

Given that :

Mean score, μ = 69

Standard deviation, σ = 4

Score, x = 64

The standardized score, Zscore can be obtained using the formular :

Zscore = (x - μ) / σ

Zscore = (69 - 68) / 4

Zscore = 1 / 4

Zscore = 0.25

Hence, The solution is, the required z-score is, 0.25.

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The given expression is equivalent to [tex]x^{10}[/tex], not [tex]x^{6+3}[/tex] or [tex]x^9.[/tex]

What are the rules of exponents?

The rules of exponents are a set of mathematical rules that simplify expressions that involve powers or exponents. Some of the basic rules of exponents include:

The expression [tex]x^6 * x * x^3[/tex] can be simplified using the rules of exponents as follows:

[tex]x^6 * x * x^3 = x^{(6+1+3)} = x^{10}[/tex]

Therefore, the given expression is equivalent to [tex]x^{10}[/tex], not [tex]x^{6+3}[/tex] or [tex]x^9.[/tex]

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Answer:

Step-by-step explanation:

No.

Answer:

7.25

Step-by-step explanation:

Divide 8.99 by 1.24

The equation has no real solution.

Mathematical expression is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ y = 4 (x + 1)³ + 8

Now, All the zeroes are find by substitute y = 0,

⇒ y = 4 (x + 1)³ + 8

⇒ 0 = 4 (x + 1)³ + 8

⇒ 4 (x + 1)³ = - 8

⇒ (x + 1)³ = - 8

⇒ x + 1 = ∛- 8

⇒ x + 1 = ∛8i²

⇒ [tex]x + 1 = 2i^{2/3}[/tex]

⇒ [tex]x = 2i^{2/3} - 1[/tex]

Hence, It has no real solution.

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The proportion of people with IQs above 140 is 2.5% of a mean of 100 and standard deviation of 20.

Comparative magnitude or extent; ratio; the relationship between several entities or components in terms of relative size, number, or degree. the right or ideal relationship between components of a whole; symmetry or balance. If a change in one variable can be expected from a change in the other, two variables are said to be in proportion. For secondary school chemists, there are two separate sorts of proportional relationships: direct proportion and inverse proportion.

When we find the proportion , we obtain:

P(y > 140) = 1 - P(y< 140)

               = 1 - P[(x - α) / β < (140 - 100) / 20]  

               = 1 - P(z < 2)                                  

               = 1 - 0.9772

               = 0.0228

               = 2.5%.

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Answer:

Angle 1= 45°

Angle 2= 90°

Step-by-step explanation:

Angle is found when you divide 90 by 2

We do this because all edges of a square add up to 90 and this angle is split in half, which is why we divided by 2

The to find angle 2 you get 45 for the left side of the triangle, 45 on the right side add them, which will give you 90, then subtract from 180 because angles in triangle equals 180 when you do this you get 90.

Answer:

a+75+65= 180(sum of angle of triangle)

a+140=180

a=180-140

a=40

The domain where fx) is 1-to-1 is x ≥1 , and the inverse there is:

f⁻¹(x) =  √x + 1

Here we have the quadratic function:

f(x) = (x - 1)^2

If we look from the vertex to the right (or the left, is the same) we will have an one to one function.

Here the vertex is at x = 1

f(1) = (1 - 1)^2 = 0

Then for x ≥1 we have an one to one function.

Noe let's find the inverse, if the inverse is f⁻¹(x), then we must have that:

f( f⁻¹(x) ) = x

Solving that:

(f⁻¹(x)  - 1)^2 = x

(f⁻¹(x)  - 1) = √x    (here we only take the positive square root)

f⁻¹(x) =  √x + 1

That is the inverse.

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In order to run a successful charity event for 6 people, it is important to ensure that everyone has something to enjoy.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


One way to do this is to provide cupcakes to one out of every three people. This will ensure that some people get a special treat while the others still have a chance to get one if they come to the event again. It also allows for a sense of fairness and equality, as everyone has an equal chance of receiving a cupcake. Additionally, it helps to build a sense of community and fellowship among the participants, as they can share the cupcakes and enjoy the experience together. It is also a great way to raise awareness about the charity and its cause, as people can talk about it while enjoying the cupcakes. To make sure that the event runs smoothly, it is important to have plenty of cupcakes on hand and to make sure that everyone is aware of the rules for receiving one.

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The quadratic equation y = 4 · x² + 28 · x + 49 is an example of a perfect square trinomial.

There are two configurations for the dimensions of the rectangle:

Configuration 1: b = 6 · (x - 1 / 2), h = x + 4 / 3

Configuration 2: b = 6 · (x + 4 / 3), h = x - 1 / 2

In this problem we find the quadratic equation y = 4 · x² + 28 · x + 49 and we need to check if the expression represent a perfect square trinomial. A quadratic equation is a perfect square trinomial if and only if the following formula is fulfilled:

a · x² + b · x + c = r₁² · x² + 2 · r₁ · r₂ · x + r₂² = (r₁ · x + r₂)²

That is,

r₁² = a

r₁² = 4

r₁ = 2

r₂² = c

r₂² = 49

r₂ = 7

2 · r₁ · r₂ = b

2 · 2 · 7

28

The quadratic equation y = 4 · x² + 28 · x + 49 is a perfect square trinomial.

Finally, we determine the dimensions of a rectangle whose area is the quadratic equation A = 6 · x² + 5 · x - 4. The area formula for a rectangle is described by the following formula:

A = b · h

Where:

Then, the factored form of the quadratic equation is:

A = 6 · x² + 5 · x - 4

A = 6 · [x² + (5 / 6) · x - 2 / 3]

A = 6 · (x - 1 / 2) · (x + 4 / 3)

There are two possible configurations for the rectangle:

Configuration 1: b = 6 · (x - 1 / 2), h = x + 4 / 3

Configuration 2: b = 6 · (x + 4 / 3), h = x - 1 / 2

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The slope of this graph​ is equal to 0.375 or 3/8.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

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

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

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

Slope, m = (35 - 20)/(40 - 0)

Slope, m = 15/40

Slope, m = 0.375 or 3/8.

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Answer: i beleive it is the CEO

Step-by-step explanation:

Answer:

the correct answer is C, the general ledger.

Step-by-step explanation:

When adjusting entries in accounting, an accountant will compare their analysis of the trial balance with the company's general ledger accounts. The general ledger is the master set of accounts that contains all the transactions of the company, including adjusting entries. Adjusting entries are made at the end of an accounting period to update the accounts and ensure that the financial statements accurately reflect the company's financial position and results of operations. These entries may involve accruals of revenue or expenses, prepayments, depreciation, or other adjustments. After making these entries, the accountant will compare the updated balances in the general ledger to the trial balance to ensure that they are accurate and balanced. Therefore, the correct answer is C, the general ledger.

The probability of spinning a blue is is 1/4.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1. Probability is applied in many areas, including finance, statistics, weather forecasting, and gambling.


The probability of spinning a blued, then blue is 1/4. The numerator of this fraction is 1.

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The statement A and statement B are supported by the data in the table. The solution has been obtained by studying the bar graph.

What is a bar graph?

Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.

We are given a graph showing grasshopper numbers before and after blue jays preyed on them.

From the graph, we can observe that there is no change in the number of green grasshoppers. This means that blue jays did not prey them.

Also, there is a great fall in the brown grasshoppers which means that they are most visible to the blue jays.

Hence, the statement A and statement B are supported by the data in the table.

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The complete question has been attached below

Step-by-step explanation:

x - y = 16 ---eq(1)

x - y = 16 ---eq(2)

From eq(1)

x - y = 16

x = 16 + y ---eq(3)

Substituting the value of eq(3) into eq(2)

(16 + y) - y = 16

16 = 16

We can't get a proper value for this pair of linear Equations

But, Since both the equations are the same, the lines formed by them will be coincident and therefore they will have infinitely many solutions

The mean and the variance of the poisson distribution are;

Mean = 2.66

Variance = 1.277

The formula for the PMF of a Poisson distribution is;

p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......

Thus;

p(x = 0) =  [e^(-λ) * λ^(0)]/0!

e^(-λ) = 0.07

λ = - In 0.07

λ = 2.66

That is the mean

Variance is square root of standard deviation;

Variance = √√(2.66)

Variance = 1.277

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Answer:

2.65926003693 for mean and variance.

Step-by-step explanation:

First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.

On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Use the variables a and y to represent the number of student and adult tickets sold, respectively.

Then write the following system of inequalities -

a ≥ 10 (they must sell a minimum of 10 student tickets)

y ≥ 55 (they must sell at least 55 adult tickets)

7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)

The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.

To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.

Alternatively, solve the system of inequalities using algebra.

First, simplify the third inequality by subtracting 7a from both sides -

10y ≥ 690 - 7a

Then, divide both sides by 10 -

y ≥ (690 - 7a)/10

This inequality represents the revenue constraint in terms of the number of student tickets sold.

Now combine the revenue constraint with the other two constraints -

a ≥ 10

y ≥ 55

y ≥ (690 - 7a)/10

Use substitution to solve for a in terms of y -

y ≥ (690 - 7a)/10

10y ≥ 690 - 7a

7a ≥ 690 - 10y

a ≥ (690 - 10y)/7

To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -

(690 - 10y)/7 ≥ 10

y ≥ 55

These inequalities can be simplified -

690 - 10y ≥ 70

y ≥ 55

The first inequality can be solved for y -

-10y ≥ -620

y ≤ 62

Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -

55 ≤ y ≤ 62

Now use the expression for a in terms of y to find the corresponding values of a -

a = (690 - 10y)/7

For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -

a ≥ 10

y ≥ 55

7a + 10y ≥ 690

For example, when y = 55 -

a = (690 - 10(55))/7 = 20

7a + 10y = 7(20) + 10(55) = 690

Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.

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The piecewise function graphed is defined as follows:

A piecewise function is a function that has multiple definitions, depending on the input x of the function.

The function in this problem has definitions for two intervals, given as follows:

For x < -5, the function is decreasing with a slope of -2, as when x increases by 1, y decays by 2, hence:

y = -2x + b.

When x = -6, y = 0, hence the intercept b is given as follows:

0 = -2(-6) + b

b = -12.

Hence:

y = -2x - 12, x < -5.

For x > 3, the function is decreasing with a slope of -1, as when x increases by 1, y decays by 1, hence:

y = -x + b.

When x = 5, y = 0, hence the intercept b is given as follows:

0 = -5 + b

b = 5.

Hence:

y = -x + 5, x > 3.

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SOLUTION

TO DETERMINE

Decrease 72 in the ratio 4 : 3

EVALUATION

We have to Decrease 72 in the ratio 4 : 3

Let the numbers are 4x and 3x

So by the given condition

Hence the required number

= 3 × 18

= 54

FINAL ANSWER

Hence the required number = 54

A function that represents the height of Elmer's carriage is,

h(x) = 52cosx + 77.

The adjacent side to hypotenuse ratio is known as the cos function. It aids in determining the triangle's side lengths regardless of the provided angle. If the angle between the adjacent side and the hypotenuse of a right triangle is, we may write this using the cosine function. Adjacent Side/Hypotenuse = Cos.

Given:
Elmer is on a Ferris wheel which has a diameter of 104 ft and whose center is 129 ft off the ground.

That means the radius of the Ferris wheel is r = 104/2 = 52 feet.

The wheel is 129 - 52 = 77 feet off the ground.

Elmer's carriage makes an angle of x radians in a horizontal way.

So, the height of Elmer's carriage is,

= rcosx + a

Here, r = 52 and a = 77

So, we get,

h(x) = 52cosx + 77.

Therefore, the function is h(x) = 52cosx + 77.

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The dimensions of this rectangular swimming pool include the following:

Width = 10 meters.

Length = 21 meters.

Mathematically, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

From the information about the width, we have:

Width, W = L - 11

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

62 = 2(L + L - 11)

62 = 4L - 22

4L = 84

Length, L = 21 meters.

For the width, we have:

Width, W = L - 11

Width, W = 21 - 11

Width, W = 10 meters.

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Answer: i think for me its $10,300

Step-by-step explanation: Allowance account is deducted from Accounts Receivable to determine Net ... $300 credit balance + 10,000 additional credit = $10,300 credit balance.

Answer: D

please mark brainiest!!!!!111

Answer: i think its 20

Answer:

1 2/3 x 12 = 20

Step-by-step explanation:

1 2/3 x 12  = 5/3 x 12

5x12/ 3 x 1

60/3

60/3 / 3/3

= 20

Answer:

Second inequality is
12x + 16y ≥ 460

We also have implied inequalities x ≥ 0, y ≥ 0 meaning hours cannot be negative

Step-by-step explanation:

The other equality refers to the earnings

Let x be the hours worked in the first job
Earnings at $12 per hour = 12x

Let y be the hours worked in the second job
Earnings at $16 per hour = 16y

Total earnings = 12x + 16y
This must be at least $460
"at least" means ≥

So second inequality is
12x + 16y ≥ 460

The investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method.

The process through which an investment earns returns on both the principal and the accrued interest over time is known as compounding. To put it another way, it is the reinvestment of interest income into an investment that enables the investment to increase exponentially over time.

Compounding works on the basic premise that interest earned on an investment is added to the principal amount. The interest is then calculated using the new, higher principal amount during the subsequent interest period, yielding even more interest. When the money generated is reinvested and grows over time, this cycle keeps repeating, increasing the investment's value more swiftly.

The investment given has a principal of $1,000, an annual interest rate of 3%, and interest periods of 4 per year. The investment is held for 15 years. To compare this investment to one with the same principal and annual interest rate compounded annually, we need to calculate the future value of the investment using both methods and compare the results.

Using the given investment method, we can calculate the future value as follows:

FV = P(1 + r/n)^(nt)

FV = 1000(1 + 0.03/4)^(4*15)

FV = $1,489.36

Using annual compounding, we can calculate the future value as:

FV = P(1 + r)^t

FV = 1000(1 + 0.03)^15

FV = $1,520.10

So, the investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method. This difference occurs because compounding more frequently leads to more frequent accumulation of interest, resulting in a higher final amount.

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