If the denominator is a friendly number, you can Up or down, or use a

The equation of the line through the point(6,7) and (2,-1) is y = -2x + 3

The formula for the equation of a line is expressed as;

y = mx + c

Such that;

From the information given, the slope is expressed as;

Slope = y₂ -y₁/x₂ - x₁

Substitute the values

Slope = 8/-4 =-2

Then, substitute the values

-1 = -4 + c

collect like terms

c = 3

Hence, the equation is y = -2x + 3

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The value of 'B' in the table is 45.

Data refers to the elements that make up persons, things, events, and ideas.

It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics.

The presentation of data is the name given to such a configuration.

Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.

Given, A three-column table.

Part     A    C     D

Part    30   36   46        

Whole B    54   69

In D it is 23×2 and 23×3.

Similarly, in C it is 18×2 and 18×3.

Therefore, In A it is 15×2 and 15×3 = 45.

the value of B in the table is 45.

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Answer:

False

Step-by-step explanatio

its like saying

398

399

3100.

makes no sense

The correct statement regarding the exponential function in this problem is given as follows:

B. This table represents exponential growth because as the number gets bigger, so does the total number overall.

The situation is modeled with an increasing exponential function, which has the format presented as follows:

y = ab^x.

In which:

The rate of change for this problem is given as follows:

b = 5.

As the absolute value of the rate of change is greater than 1, the exponential function is a growth function.

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The [tex]& r_x(h)+r_y(h) \\[/tex] mean and autocovariance functions are free of t , the process [tex]$\left\{X_t+Y_t\right\}$[/tex] is stationary.

Solution: [tex]$\left\{x_t\right\} \&\left\{y_t\right\}$[/tex] are uncorrelated stationary process i.e.[tex]$x_\gamma \& I_s$[/tex] ax uncorrelated for every r and s process [tex]$\left\{x_t+y_t\right\}$[/tex] is stationary.

The sum of the autocovariance functions of {[tex]x_{t}[/tex]} and {[tex]y_{t}[/tex]}.

The autocovariance function (ACF) is defined as the sequence of covariances of a stationary process. That is suppose that {Xt} is a stationary process with mean zero, then {c(k) : k 2 Z} is the ACF of {Xt} where c(k) = E(X0Xk). Clearly different time series give rise to different features in the ACF.

⇒Var[tex]& \left(X_t+Y_t\right)={Var}\left(X_t\right)+{Var}\left(Y_t\right) \\[/tex]

⇒[tex]& E\left(X_t+Y_t\right)=\mu_x+\mu_y \\[/tex]

⇒[tex]& r_{x+y}(h)={cov}\left(X_{t+h}+Y_{t+h}, X_t+Y_t\right) \\[/tex]

[tex]& ={cov}\left(X_{t+h}, X_t\right)+{cov}\left(Y_{t+h}, Y_t\right)+0 \\[/tex]

[tex]& =r_x(h)+r_y(h) \\[/tex]

Since, the mean and autocovariance functions are free of t , the process [tex]$\left\{X_t+Y_t\right\}$[/tex] is stationary

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The sampling method being used is given as follows:

Systematic sampling.

Samples may be classified as:

Hence in this problem we have a systematic sample with k = 15.

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The solution to the system of inequalities is following as y ≤ -4 ;y ≤ - x + 4

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per option (A), we have the system of inequality as follows:

y ≤ -4

y ≤ - x + 4

The region is above the graph, hence our inequality should be y ≤ - x + 4

The inequality sign part comes from visible the graph, the line is drawn using a dashed line, hence the line is included in the region.

Thus, this graph corresponds to a system of inequalities which is the correct answer that would be option (A).

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Due to length restrictions, we kindly invite to check the explanation for further detail on how to complete a maze with trigonometric functions.

In this question we must go through a maze formed by 16 squares, fifteen of them with cases of right triangles, we must apply trigonometric functions to complete the maze. To complete this task, we need to use the following trigonometric function:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

Where:

Now we proceed to show how deal with the maze:

Step 1:

x = 19 · cos 28°

x = 16.78 (LEFT)

Step 2

x = 39 / tan 59°

x = 23.43 (LEFT)

Step 3:

x = 31 · sin 71°

x = 29.311 (RIGHT - DOWN)

Step 4:

x = 12 · tan 25°

x = 5.600 (RIGHT)

Step 5:

x = 27 / sin 48°

x = 36.332 (RIGHT)

Step 6:

x = 38 / cos 14°

x = 39.163 (DOWN - LEFT)

Step 7:

x = 16 · cos 54°

x = 9.405 (RIGHT)

Step 8:

x = 29 / tan 74°

x = 8.316 (DOWN)

Step 9:

x = 17 · sin 42°

x = 11.375 (LEFT)

Step 10:

x = 47 · tan 29°

x = 26.052 (LEFT)

Step 11:

x = 31 / sin 63°

x = 34.792 (LEFT)

Step 12:

x = 24 / cos 51°

x = 38.136 (UP)

Step 13:

x = 46 · tan 31°

x = 27.640 (RIGHT)

FINISH

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The lengths of the segments formed by two secants are proportional to the distances of the points where the secants intersect the circle from the center of the circle.

If we denote the lengths of the two segments as x and y, and the distance between the center of the circle and the point of intersection of the secants as d, then x/y = d1/d2, where d1 and d2 are the distances between the center and the points of intersection of the secant with the circle.

When two secants intersect a circle at two distinct points, the lengths of the segments formed by the two secants are proportional to the distances between the center of the circle and the points of intersection. This is because the two segments are radii that connect the center of the circle to the points of intersection of the secants with the circle.

The proportionality between the lengths of the segments and the distances from the center can be expressed mathematically as x/y = d1/d2, where x and y are the lengths of the two segments, d1 and d2 are the distances between the center and the points of intersection of the secants with the circle, and x/y represents the ratio of the lengths of the two segments.

So, as the distances from the center to the points of intersection increase, the lengths of the segments will also increase in the same ratio. And if the distances from the center decrease, the lengths of the segments will decrease in the same ratio.

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The respective units in the statements above are kg, L,cm

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given here: Different quantities

a) Boris saw an elephant and its mass is mentioned.

Now we know,The Metric System of Measurements uses the mass units: gram (g), kilogram (kg) and tonne (t).

Thus the mass of the elephant is 4000 kg/tonne(t)

b) Greg used some volume of liquid in the shower

Now the units of liquid primarily used daily life is liters

Thus Greg used about 130 L of water

c) "The spacebar on the keyboard " in this statement the emphasis is on length and we know the units of length are m, cm etc.

Thus the length of the spacebar on the keyboard is 11 cm long.

Hence, The respective units in the statements above are kg, L,cm

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Answer:

$168.75

Step-by-step explanation:

If you need this for 7 and a half hours, start off by multiplying 22.50 by 7.  

22.50 x 7 = 157.5

Now find half of 22.50 to account for the half.  

22.50/2 = 11.25

Finally, add 157.5 and 11.25, and that should be your answer.  :)

157.5 + 11.25 = $168.75

I hope this helped!! :)

The correct solution of the expression is, 31/40.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The expression is,

⇒ 2/5 + 3/8

Now, We can add the fraction as;

⇒ 2/5 + 3/8

⇒ (16 + 15) / 40

⇒ 31/40

Thus, The solution of fraction = 31/40

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Answer:

n =1/2

Step-by-step explanation:

24n + 60 = 72

24n = 72 - 60

24n = 12 /24

n = 1/2

Answer:

n=1/2

Step-by-step explanation:

24n+60=72

24n=72-60

24n=12

n=12/24

n=1/2

The number of wild mustangs in Utah and Nevada are 2745 and 18985

respectively.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

From the given information let the number of wild mustangs in Utah be 'x'

So, The number of wild mustangs in Nevada is 6x + 2515.

Therefore, x + 6x + 2515 = 21730.

7x = 21730 - 2515.

7x = 19215.

x = 19215/7.

x = 2745.

So, The number of wild mustangs in Utah is 2745 and hence the number of wild mustangs in Nevada is 6×2745 + 2515 = 18985.

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Answer:

33

Step-by-step explanation:

The highest number is 50 and the lowest number is 17.

50 - 17 = 33

[tex]\huge\begin{array}{ccc}y=\dfrac{4}{x}&\text{for}&x\neq0\end{array}[/tex]

We have:

[tex]xy=4[/tex]

We need:

[tex]y=?[/tex]

Let's transform the equation:

[tex]xy=4\\\\\dfrac{xy}{x}=\dfrac{4}{x}\qquad\text{for}\ x\neq0\\\\\boxed{y=\dfrac{4}{x}}[/tex]

The point $p$ has coordinates such that the ratio of the distances $ap$ to $pb$ is $1$ to $3$.

To find the coordinates of point $p$ along the directed line segment $ab$, we will use the ratio of $ap$ to $pb$ being $1$ to $3$. First, we need to find the length of $ap$ and $pb$. To do this, we will use the formula for the distance between two points: [tex]$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$[/tex]. We know the coordinates for points $a$ and $b$, so we can plug them into the formula to find the length of $ab$, which is $d_{ab}$. We can then use the ratio of $1$ to $3$ to find the lengths of $ap$ and $pb$. $d_{ap}=\frac{1}{4}d_{ab}$ and $d_{pb}=\frac{3}{4}d_{ab}$. We can then use the formula for the distance between two points again, this time with the coordinates of $a$ and $p$, to find the coordinates of $p$. Finally, we can plug the coordinates of $p$ back into the formula to check if the ratio of $ap$ to $pb$ is indeed $1$ to $3$.

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The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.

Since the angles of[tex]$\triangle A_0B_0C_0$[/tex]  are [tex]$59.999^\circ$, $60^\circ[/tex]  and [tex]$60.001^\circ$[/tex], the triangle is very close to being equilateral. Therefore, each time an altitude is drawn from one of the vertices, the triangle will become more acute, and it will take many iterations before an obtuse triangle is formed. The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex]  is obtuse is 15. To confirm this, we can use the Law of Cosines. For [tex]$\triangle A_15B_15C_15$[/tex] , we have [tex]$A_{15}B_{15} = 90 - 60.001 = 29.999$ and $B_{15}C_{15} = 90 - 59.999 = 30.001$[/tex]. Therefore,  [tex]$A_{15}C_{15}^2 = 29.999^2 + 30.001^2 - 2(29.999)(30.001)\cos \angle A_{15}B_{15}C_{15} = 899.998^2$[/tex] . Since [tex]$A_{15}C_{15}^2 > 899.997^2$, $\angle A_{15}B_{15}C_{15}$[/tex] is obtuse, and therefore the answer is (E) 15.

The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.

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Answer:

R10.00

Step-by-step explanation:

Purchase:

10 apples at R2.50 each = 10 × R2.50 = R25.00

He spent R25.00 on the 10 apples.

Sales:

25% discount on R4.00 is 0.75 × R4.00 = R3.00

5 apples at R4.00 = 5 × R4.00 = R20.00

5 apples at R3.00 = 5 × R3.00 = R15.00

Total sales = R20.00 + R15.00 = R35.00

Profit:

R35.00 - R25.00 = R10.00

The solution of the initial value problem is y = -3x/(3㏑x - 1)

An initial value problem is a differential equation in which the initial value of the function is given.

Since we have the initial value problem

y' = (xy + y²)/x² , y(1) = 3.

We see that it is a homogeneous differential equation.

A homogeneous differential equation is a differential equation in which the powers of x and y are the same.

So, we proceed to solve the equation as folows.

Let y = vx.

So,

So, substituting these two into the differential equation, we have that

y' = (xy + y²)/x²

dy/dx = (xy/x² + y²/x²

xdv/dx + v = y/x + (y/x)²

xdv/dx + v = v + v²

xdv/dx = v²

Now using the method of separation of variables, we have that

dv/v² = dx/x

Integrating both sides, we have that

∫dv/v² = ∫dx/x

-v⁻¹ = ㏑x + C

-1/v = ㏑x + C

Substituting v = y/x into the equation, we have that

- 1/y/x = ㏑x + C

-x/y = ㏑x + C

So, making y subject of the formula, we have that

y = -x/(㏑x + C)

Since y(1) = 3, we have that

3 = -1/(㏑1 + C)

3 = -1/(0 + C)

3 = -1/C

C = -1/3

So, y = -x/(㏑x + (-1/3))

y = -x/(㏑x - 1/3)

y = -x/(3㏑x - 1)/3

y = -3x/(3㏑x - 1)

So, the solution is y = -3x/(3㏑x - 1)

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The receiving and giving money, gifts, and other types to get a favor from the government or from an institution or from an organization is amounts to bribe which is not an ethical practice.

The magnitude of the corruption in the form of a bribe may vary from the place of practice that is in situations where it has taken place.

This practice of taking bribe is considered to be an immoral act and it is punishable under the Foreign Corrupt Practices Act (FCPA) which became law in 1977 in the USA.

The main aim of the Act is to fight bribery and corruption from foreign countries and the US government as used by this law to control the unethical practice.

Types of bribery:

Active bribery

Passive bribery

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Union of set A and set B' is A ∪ B' = {a, c, e, f, g}      

What is union of sets?

Union of two or more sets is the set containing all the elements of the given sets. Union of sets can be written using the symbol “⋃”

Given sets,

U = {a, b, c, d, e, f, g}

A = {a, c, e, g}

B = {a, b, c, d}

⇒ B' = {e, f, g}

A ∪ B' =  {a, c, e, g} ∪ {e, f, g}

A ∪ B' =  {a, c, e, f, g}          

Hence, A U B = {a, c, e, f, g} which union of both sets.

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Modal interval is discussed below.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given is the modal interval.

        MODE = [tex]$L + h\frac{(f_{m} -f_{1}) }{(f_{m} -f_{1} ) + (f_{m} - f_{2} )}[/tex]

Therefore, Modal interval is discussed above.

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The lateral surface area of a rectangular prism is 2(l + w)h sq units.

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).

The lateral surface area of a rectangular prism is given by

Where l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.

Without these values, it is not possible to determine the lateral surface area of the rectangular prism.

Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.

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Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.

One line of research Jackson could pursue to explore the scientific goal of control is control theory. Control theory is the study of how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances. Control theory uses mathematical models to describe the behavior of a system and the effects of control inputs on the system. For example, a simple linear control system can be modeled using the transfer function, which is a mathematical expression that describes how a system responds to an input signal. The transfer function can then be used to calculate the output of the system in response to different inputs. Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior.

Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.

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Complete question: Which of the following lines of research should Jackson pursue in order to explore the scientific goal of control?

Answer: Q is the answer.

Step-by-step explanation:

An inequality to represent the regular price of snacks, if i can buy using the coupon, x ≤ $13

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

There are two coupons available, $8 and a $5 off on buying snacks

Let's call the regular price of the snacks "x".

Since you have a $5 off coupon,

the price you would actually pay would be x - $5.

And since you only have $8, the price you pay for the snacks cannot be greater than $8:

x - $5 ≤ $8

Adding $5 to both sides:

x ≤ $13

So, the regular price of the snacks must be less than or equal to $13 if you want to use the coupon and still have enough money to pay for them.

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The statement can be proved by the property of similarity and adjacent angles of a line property.

An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle. In a triangle, it is that point where all the three altitudes of a triangle intersect.

Given here: A triangle ABC with an orthocenter O.

Now let BD and A-F be the altitudes that intersect on the sides of AC and BC

then we have in the triangles AOD and ACF we have

∠ADO=∠AFC=90 and ∠A is common and therefore ΔAOD≈ΔACF

thus ∠AOD=∠ACF=∠ACB

now ∠ACB and ∠AOB lie on a line BD thus we must have

∠ACB +∠AOB=180

Hence, The statement  ∠ACB +∠AOB=180 is proved.

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Answer:

Option A.

Step-by-step explanation: