Use the substitution method to solve the system of equations. Enter your
answer as an ordered pair.
3x - y = 6
x + 3y = 12

True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship.  If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.

In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.

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The dividend in the formula P3 = Dx/(R - g) is for period e. three.

In the given formula P3 = Dx/(R - g), the dividend, Dx, refers to the cash flow or payment made during a specific period. The subscript "3" in P3 indicates the period of time for which the dividend is associated.

In the given formula, P3 = Dx/(R - g), the subscript 3 represents the period of time for which we are calculating the dividend.

The dividend, Dx, represents the cashflow or payment made during a specific period. In this case, the dividend is associated with period 3.

Therefore, the dividend in the formula corresponds to period e. three.

The dividend in the formula P3 = Dx/(R - g) is for period e. three

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Answer:

In order to be called a 'rational' number, a number must be the quotient that results when one non-zero integer is divided by another. An irrational number can be written as a decimal, but not as a fraction. Your number is (3 sqrt(2)) / sqrt(2) = 3, and is a rational number indeed.

The equation is :

4x^2+ 17x+ 4

factorise it by:

= 4x^2 +x - 16x +4

= x(4x+1)-4( 4x-1)

=(x-4) (4x+1) (4x-1)

Hence x =4, -1/4,1/4 .

Hope this helps you.





Answer:

$14.80

Step-by-step explanation:

Original bike price: $185

Tax: 8% OR 0.08 as a DECIMAL

To find your answer, multiply the bike price by the DECIMAL (number) tax amount:

185 x 0.08

= 14.8

Therefore, Alex paid $14.80 in tax.

Answer: $14.80

Step-by-step explanation:

We know: The bike is $185, and the tax is 8% of the product.

So we multiply them together.

185 * 8 / 100 = 14.8

or

185 * 0.08 = 14.8

The tax will be $14.80.

The other way to solve this question is by cross multiply.

\(\ \frac{x}{185} = \frac{8}{100}\\)

But what you get would still be the same as just multiply it directly.

185*5/100 = 14.8

Not an efficient way of doing things :(

Answer:

x = 1.5

y = 8

3/4 = 1.2/2

3/4 = 6/8

Answer:

Approximately 1553.83

a) 280 points

b) 80 points

c) 240 points

d) 120 points

Yes, 9 is a positive number because 9 is a natural number and also we use 9 in our daily life counting problems also.

Let's first attempt to understand what numbers are.

A number is an arithmetic value that is computed and used to represent a quantity. Numbers are represented in writing by symbols like "3," which are numerical symbols. A number system is a methodical way of employing digits or other symbols to represent numbers. The numerical system is a useful set of numbers that reflects the mathematical and algebraic structure of the number. provides a typical illustration.

Positive numbers Any number that represents something other than zero is considered to be positive. When referring to the amount of money in your bank account, a positive figure would undoubtedly make you feel good as well.

So 9 is a positive number.

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Points $a$, $b$, $c$, and $d$ are the midpoints of the sides of the larger square. If the larger square has an area of 60, the smaller square's area is 15 square units.

A square's midpoints connect, making it possible to divide the square into four equal squares. Each of these four squares has a side length of half that of the larger square.

Consider the fact that the area of the larger square is 60, with sides of $s$ units. \($s^2=60$\\\). Now, the smaller square is created by connecting the midpoints of the larger square. Each side of the smaller square has a length of \($s/2$\) units.

Since the area of a square is \($s^2$\), the area of the smaller square is \($\left(\frac{s}{2}\right)^2$\). Simplifying gives \($\left(\frac{s}{2}\right)^2=\frac{s^2}{4}$\). So, the area of the smaller square is \($\frac{1}{4}$\) of the larger square's area.

We know that the area of the larger square is 60. Therefore, the area of the smaller square is \($\frac{1}{4}$\) (60) = 15 square units.

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The length of the loop for the given curve x=9t-3t³, y=9t² is 36√3

The distance measured from one end to the other of an object's longer or longest side. additionally: any measured distance. the state or trait of being long. the duration of something duration of a visit. The length of something is defined as its measurement or extent from end to end. In other terms, it is the biggest of two or the highest of three geometrical forms or objects' dimensions.

Given,

x=9t-3t³, y=9t²

The loop starts from x=0 and with x=0

Therefore, x=0

9t-3t³=0

3t(3-t²)=0

3-t²=0

t=±√3

dx/dt=9-9t²

dy/dt=18t

Hence length of a loop of a curve,

By using the integration,

=\(\int\limits^a_b\)√(dx/dt)²+(dy/dt)²

Here a=√3, b= -√3

=\(\int\limits^a_b\)√(9-9t²)²+(18t)²dt

=\(\int\limits^a_b\)√(1-t²)²+4t²dt

=\(\int\limits^a_b\)√1-t⁴-2t²+4t²dt

=\(\int\limits^a_b\)√1+t⁴+2t²

=\(\int\limits^a_b\)√(1+t²)dt

=9(t+t²/3)

=36√3

Therefore, the length of the loop is given by 36√3.

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The equation for the height of the rider on the ferris wheel as a function of time in seconds is h(t) = 90 * sin((π/30) * t).

To find an equation for the height of a rider on the ferris wheel as a function of time in seconds, we need to consider the circular motion of the wheel and the relationship between time and height.

Let's assume that at t = 0 seconds, the rider is at the ground level, which we can consider as the reference point for height.

The height of the rider on the ferris wheel can be determined by considering the circular path traced by the wheel. The height can be calculated as the vertical displacement from the reference point as the wheel rotates.

Given that the radius of the ferris wheel is 90 feet, we can use the equation of a circle to express the rider's height as a function of time. The equation for the height of the rider as a function of time (h(t)) can be written as:

h(t) = R * sin(θ)

Where:

h(t) represents the height of the rider at time t.

R is the radius of the ferris wheel.

θ is the angle (in radians) through which the wheel has rotated at time t.

To find the value of θ, we need to consider the rotation rate of the ferris wheel. We are given that the wheel completes two rotations every minute (60 seconds). Therefore, the angular velocity (ω) can be calculated as:

ω = (2π radians) / (60 seconds)

Now, we can express the angle θ as a function of time by multiplying the angular velocity by time:

θ = ω * t

Combining these equations, the height of the rider as a function of time can be written as:

h(t) = R * sin(ω * t)

Substituting the given values, we have:

h(t) = 90 * sin((2π/60) * t)

Simplifying further, the equation for the height of the rider as a function of time in seconds is:

h(t) = 90 * sin((π/30) * t)

Therefore, the equation for the height of the rider on the ferris wheel as a function of time in seconds is h(t) = 90 * sin((π/30) * t).

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Answer:

B: 3(x-6) = 3x-18

Step-by-step explanation:

The left and right sides of this equation are actually equal! We can see this by dividing the 3 on the left through the parentheses. This gives us \(3x-18\), which is equal to the right-hand side of the equation!

To solidify this, we add 18 to both sides, and subtract 3x from both sides, which gives us that 0=0, so there are infinitely many solutions for x(since no matter what x is, it will result in 0=0 which is always true).

I hope this helps!

Answer:

Step-by-step explanation:

Find the value of x if the perimeter is 20

20 = X + 4X - 6 + X + 8

20 + 6 - 8 = 6X

18 = 6X

x = 18 : 6

x = 3

-----------------

check

20 = 3 + 3 * 4 - 6 + 3 + 8

20 = 20

the answer is good

Answer:

Value of x is 3

Step-by-step explanation:

Given perimeter of figure = 20

x + (x+8) + (4x-6) = 20

x + x + 8 + 4x - 6 = 20

6x + 2 = 20

6x = 20 - 2

6x = 18

x = 18 / 6

x = 3

Accupunture is best these days for medication and health therapy.

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The average value of f(x,y,z) over the region W is (3/5) ((1/10) e^5 - 1/2).

The average value of a function over a region W can be computed using the following formula:
average value = (1/Volume of W) ∫∫∫_W f(x,y,z) dV

In this case, the function f(x,y,z) = e^5y and the region W is defined by the inequalities 0 ≤ y ≤ 1 – x^2, 0 ≤ z ≤ x. We can find the volume of W by integrating the function 1 over the region:

Volume of W = ∫∫∫_W 1 dV = ∫∫∫_W dz dy dx = ∫_0^1 ∫_0^(1-x^2) ∫_0^x 1 dz dy dx
= ∫_0^1 ∫_0^(1-x^2) x dy dx = ∫_0^1 x(1-x^2) dx = 1/3

Now we can compute the average value of f(x,y,z) over the region W by substituting the volume of W and the function f(x,y,z) into the formula:

average value = (1/(1/3)) ∫∫∫_W e^5y dV = 3 ∫_0^1 ∫_0^(1-x^2) ∫_0^x e^5y dz dy dx
= 3 ∫_0^1 ∫_0^(1-x^2) x e^5y dy dx = 3 ∫_0^1 (x/5) (e^5(1-x^2) - 1) dx
= (3/5) ∫_0^1 (x e^5(1-x^2) - x) dx = (3/5) ((1/10) e^5 - 1/2)

Therefore, the average value of f(x,y,z) over the region W is (3/5) ((1/10) e^5 - 1/2).

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The amount of land the railroad companies received for each mile of track they laid varied depending on the specific circumstances and agreements.

However, a common benchmark used during the construction of railroads in the United States was the granting of land through the Homestead Act of 1862. Under this act, railroad companies were granted approximately 6,400 acres (10 square miles) of land for every mile of track laid. This land was typically located alongside the tracks and served as an incentive for the companies to expand and develop the rail network across the country.

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Answer:

24 kilometers per hour

Step-by-step explanation:

15 kph x 8 h = 120 kilometers

120km/5 hours = 24 kph

Step-by-step explanation:

Hi, there!!!

According to the question,

1st case

At the speed of 15 km/ hr, it takes time 8 hrs to reach a point.

Then, we must find the distance first to calculate your speed in 2nd case,

So, let's find the distance first,

now,

distance (d) = s×t

or, d= 15km/ hr × 8hrs

Therefore, the distance is 120 km.

now,

In 2nd case,

As the question has asked to find speed on same point, it will have same distance covered.

time( t) = 5hrs.

distance (d)= 120km

now,

speed = distance/time taken

or, s= 120 km/5 hrs

or, s = 24km/ hr.

Therefore, your speed in 2nd case will be 24km/hr.

Hope it helps...

Answer: £67.875

Step-by-step explanation:

€90.50 x 3/4 = £67.875

The expression y = α · sin x + β · cos x is a solution of the ordinary differential equations if and only if (α, β) = (0, 0).

According to the statement, we must find in what conditions a given expression may be a solution of an ordinary differential equation. Then, first and second derivatives of the equation are:

y' = α · cos x - β · sin x                 (1)

y'' = - α · sin x - β · cos x              (2)

Then, we substitute on the ordinary differential equation:

(- α · sin x - β · cos x) + (α · cos x - β · sin x) = 0

And by algebraic handling we simplify the resulting expression:

- (α + β) · sin x + (α - β) · cos x = 0

Where each coefficient represents a constant of a linear combination:

α + β = 0

α - β = 0

Then, the solution of the system of linear equations is (α, β) = (0, 0). The expression y = α · sin x + β · cos x is a solution of the ordinary differential equations if and only if (α, β) = (0, 0).

The statement is incomplete and complete form cannot be found, then we decided to create a new statement:

Please prove that y = α · sin x + β · cos x is the solution of the differential equation d²y / dx² + dy /dx = 0 where the following condition is observed, if and only if α = β = 0.

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Answer:

KM=41.6

Step-by-step explanation:

\(\frac{HJ}{IJ} =\frac{KM}{ML} \\\frac{8}{6} =\frac{KM}{31.2} \\\)

Cross Multiply and Solve for KM.

\(6*KM=8*31.2\\KM=\frac{8*31.2}{6} \\KM=41.6\)

Answer: slope is 1

equation: 1x-2 or x-2

I hope this is good enough:

Answer:

5

Step-by-step explanation:

-4           -1           -5              

__    -   ___  =    ___   =    5

-2           1             -1

Answer:

29/80

Step-by-step explanation: It would be 29/80 because you cannot simplify that fraction. 29 is a prime number.

Answer:

table 1

Step-by-step explanation:

table one, because you have different value of x (inputs) with no repetition for the same value

Increasing the sample size has an effect on the standard error, but other factors determine whether the increased sample size will increase or decrease the standard error.


The standard error is a measure of the variability of the sample mean. When the sample size is increased, the standard error generally decreases because a larger sample size provides more precise estimates of the population mean. However, other factors such as the variability of the population and the sampling method used can also affect the standard error.

For example, if the population variability is high, increasing the sample size may not have a significant impact on reducing the standard error. On the other hand, if the population variability is low, increasing the sample size can lead to a substantial decrease in the standard error.

In summary, increasing the sample size generally decreases the standard error, but the magnitude of this effect depends on other factors such as population variability and sampling method.

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Two airplanes leaves an airport at the same time, one going northwest ( bearing 135 degree) at 407 mph and the other going east at 332 mph 1138 miles the planes after 2 hours (to the nearest miles). The correct option is D.

To find the distance between the two planes after 2 hours, we can use the concept of vector addition.

The northwest-bound plane is traveling at 407 mph at a bearing of 135 degrees. After 2 hours, it would have traveled a distance of 407 mph * 2 hours = 814 miles in the northwest direction.

The east-bound plane is traveling at 332 mph due east. After 2 hours, it would have traveled a distance of 332 mph * 2 hours = 664 miles due east.

To find the distance between the two planes, we can treat their paths as the adjacent sides of a right triangle. The distance between them would be the hypotenuse of this triangle.

Using the Pythagorean theorem, we can calculate the distance:

Distance = √(\(814^2 + 664^2\)) ≈ 1033.98 miles

Rounding this distance to the nearest mile, we get approximately 1034 miles.

Therefore, the correct option would be D. 1138 miles.

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Answer:

A

Step-by-step explanation:

The correct code to swap elements 0 and 1 in the given array {7, 8, 10, 11, 4, 3} would be: int save = array[0];array[0] = array[1];array[1] = save;

The code above uses a temporary variable "save" to store the value of the first element of the array, then assigns the value of the second element to the first element, and finally assigns the value of "save" (which holds the original value of the first element) to the second element.

The other lines of code following this swap code would perform additional operations on the array, but they do not correctly swap the first two elements of the array.

For example, the line array[0] = array[1]; in the given code only assigns the value of the second element to the first element, effectively overwriting the original value of the first element before it can be saved. Similarly, the line array[1] = array[0]; then assigns the overwritten value of the first element to the second element, resulting in no swap at all.

Therefore, the correct code to swap the first two elements of the array is the code I mentioned at the beginning of this answer.

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Which of the following swaps elements 0 and 1 in array?

The probability that X+Y=1 is 0.5.

To find the probability that X+Y=1, given that X is a Bernoulli random variable with P(X=1)=0.8 and Y is a Bernoulli random variable with P(Y=1)=0.5, follow these steps:

1. First, find the probabilities for the complementary events, i.e., P(X=0) and P(Y=0).
  P(X=0) = 1 - P(X=1) = 1 - 0.8 = 0.2
  P(Y=0) = 1 - P(Y=1) = 1 - 0.5 = 0.5

2. Now, consider the two possible cases where X+Y=1:
  a) X=1 and Y=0: P(X=1) * P(Y=0) = 0.8 * 0.5 = 0.4
  b) X=0 and Y=1: P(X=0) * P(Y=1) = 0.2 * 0.5 = 0.1

3. Finally, sum the probabilities of the two cases:
  P(X+Y=1) = P(X=1, Y=0) + P(X=0, Y=1) = 0.4 + 0.1 = 0.5

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The probability that X+Y=1 is 0.5.

To find the probability that X+Y=1, given that X is a Bernoulli random variable with P(X=1)=0.8 and Y is a Bernoulli random variable with P(Y=1)=0.5, follow these steps:

1. First, find the probabilities for the complementary events, i.e., P(X=0) and P(Y=0).
  P(X=0) = 1 - P(X=1) = 1 - 0.8 = 0.2
  P(Y=0) = 1 - P(Y=1) = 1 - 0.5 = 0.5

2. Now, consider the two possible cases where X+Y=1:
  a) X=1 and Y=0: P(X=1) * P(Y=0) = 0.8 * 0.5 = 0.4
  b) X=0 and Y=1: P(X=0) * P(Y=1) = 0.2 * 0.5 = 0.1

3. Finally, sum the probabilities of the two cases:
  P(X+Y=1) = P(X=1, Y=0) + P(X=0, Y=1) = 0.4 + 0.1 = 0.5

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