Which equation is equivalent to the given equation? x^2 - 10x = 14​

Given:

a.) The admission fee at a small fair is $2.50 for children and $4.00 for adults.

b.) On a certain day, 2400 people enter the fair and $7140 is collected.

Let,

x = total number of children

y = total number of adults

Let's generate two equations based on the given scenario:

EQUATION 1: Total number of children and adults entered the fair.

EQUATION 2: Total money collected from the admission.

We will be using the substitution method. We get,

Substitute to Equation 2:

Therefore, 1,640 children went to the fair.

For the adults,

x + y = 2400

1,640 + y = 2400

y = 2400 - 1,640

y = 760 adults

In summary: 1,640 children and 760 adults went to the fair.

Answer:

37.7

Step-by-step explanation:

C= 2×3.14×6

C= 37.7

Let me know if it's wrong!

Answer:

$3.6

Step-by-step explanation:

I looked it up, I don't know how to do that on my own

Answer: \(\frac{17}3}\) or 17:3

Step-by-step explanation:

Since Lydia got 17 out of 20 questions correct, that means she got 3 out of 20 incorrect. To get the ratio of correct (17) to incorrect (3) answers, we can simply divide the two numbers as follows:

\(\frac{17}3}\) or 17:3

Since this ratio is already in simplest terms, this is the final answer.

An answer option which distinguishes the element that needs to be adjusted on the chart in the following scenario is: C. x-axis value.

In an experiment, there are two (2) main types of variables and these include the following:

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it is represented by the x-axis value on a graph.

In this scenario, we can reasonably infer and logically deduce that the independent variable (x-axis value) represents the element that should be adjusted on Donna's demographic chart on population growth.

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Answer:

The answer is Choice A

Step-by-step explanation:

The graph of \(P'H'O'T'\) is A

9514 1404 393

Answer:

  a) x = {-1, 3, 4}

  b) (0.472, 13.128)

  c) (3.528, -1.128)

  d) x < 0.472 U x > 3.528

  e) 0.472 < x < 3.528

Step-by-step explanation:

This is a cubic (odd degree) function with a positive leading coefficient, so it will be increasing until the first turning point, and after the last turning point. It will be decreasing between the turning points.

a) A graph shows the zeros to be x = -1, x = 3, x = 4.

b) A graph shows the local maximum to be approximately (0.472, 13.128). The x-coordinate of this point is exactly 2-√(7/3).

c) The local minimum is about (3.528, -1.128). Its x-coordinate is exactly 2+√(7/3).

d) As stated above, the increasing intervals are (-∞, 0.428) ∪ (3.528, ∞).

e) The decreasing interval is (0.428, 3.528).

_____

Additional comments

The sum of odd-degree term coefficients is the same as the sum of coefficients of even-degree terms, so you know one of the roots is -1. Factoring that out gives the quadratic x^2 -7x +12 = (x -3)(x -4), so the other two roots are 3 and 4.

The derivative is 3x^2 -12x +5 = 3(x -2)^2 -7, so its roots (turning points of f(x)) are 2±√(7/3).

I find a graphing calculator can show me the roots and turning points easily.

The exact x-coordinate of the point  is frac{1163}{291}6

The curve is given by {x = t² + 1, y = t² - t}.

Let's find dy/dx in terms of t as follows:

frac{dy}{dx} = frac{dy/dt}{dx/dt} = frac{(2t - 1)}{(2t)} = 1 - frac{1}{2t}

Therefore, when dy/dx = 27, we have:

1 - frac{1}{2t} = 27

Rightarrow 2t - 1 = frac{2}{27}

Rightarrow t = frac{29}{54}

The x-coordinate is given by x = t² + 1, therefore, we have:

x = left(frac{29}{54}right)^2 + 1

= frac{1163}{2916}

Hence, the exact x-coordinate of the point on the curve where the tangent line has slope 27 is frac{1163}{291}6

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Answer:

The third option, (-30,10)

Step-by-step explanation:

A proportional relationship is when you multiply one number in the coordinate/pair to get the other number, and that number that you multiply with is consistent. For example, in (60,-20) you multiply the x coordinate 60 by -1/3 to get 20. Next, you have to check if the other answer choices follow the same pattern. For (-30,10), you multiply -30 by -1/3 and get 10! So it works.

lamo thought it said terrorists

Answer:

24.

Step-by-step explanation:

The pattern is clearly going up by twos.

So continuing the pattern,

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

1 2  3   4 5   6   7   8   9   10  11    12   13

Answer: b) (-1,-6)

use the slope equation y2-y1 divided by x2-x1

or just use a slope calculator like i did <3

anyways i hope this helps :)

Answer:

The ratio means that for every 9 boys there are 10 girls

Step-by-step explanation:

In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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The correct statement that describes Type I and Type II errors in hypothesis testing is:

b. Type I error occurs when the null hypothesis is rejected when it is actually true, while Type II error occurs when the null hypothesis is accepted when it is actually false.

In hypothesis testing, Type I error refers to rejecting the null hypothesis when it is actually true. This error represents a false positive result, indicating that a significant effect or relationship is detected when it does not exist in reality. Type II error, on the other hand, occurs when the null hypothesis is accepted (not rejected) when it is actually false. This error represents a false negative result, indicating a failure to detect a significant effect or relationship that does exist. The correct understanding and interpretation of Type I and Type II errors are crucial in hypothesis testing to ensure accurate conclusions.

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Option d is not correct as it uses "II" which is not a commonly used symbol to indicate less than and greater than.

The correct expression to indicate that x is greater than 10 and less than 20 is:

a. 10 < x < 20

This is read as "10 is less than x, and x is less than 20." The symbols "<" and ">" indicate "less than" and "greater than," respectively.

Option b is not correct as it uses parentheses instead of the less than/greater than symbols.

Option c is not correct as it uses "&" and "&&" which are not commonly used symbols to indicate less than and greater than.

Option d is not correct as it uses "II" which is not a commonly used symbol to indicate less than and greater than.

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Answer:

Step-by-step explanation:

A bitmap is a digital image format that is made up of a grid of square colored dots called pixels.

Each pixel in the bitmap contains information about its color and position, which allows the computer to display the image on a screen or print it on paper. Bitmaps are commonly used for photographs, illustrations, and other complex images that require a high degree of detail and color accuracy.

However, because bitmaps store information for each individual pixel, they can be memory-intensive and may result in large file sizes. Additionally, resizing a bitmap can lead to a loss of quality, as the computer must either interpolate or discard pixels to adjust the image size.

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The equilibrium interest rate is 10%, and the money supply should be set at $25 to increase the interest rate by 10 percentage points

The equilibrium interest rate and the corresponding money supply can be calculated based on the given money demand and money supply functions.

1. Equilibrium Interest Rate:

To find the equilibrium interest rate, we need to set the money demand equal to the money supply and solve for i.

Md = Ms

$Y(0.30 - i) = $50

Substituting the given value of $Y = $250, we have:

$250(0.30 - i) = $50

Simplifying the equation, we get:

75 - 250i = 50

-250i = 50 - 75

-250i = -25

i = -25 / -250

i = 0.1

The equilibrium interest rate is 0.1, or 10% (as a percentage).

2. Money Supply to Increase Interest Rate by 10 Percentage Points:

If the Federal Reserve wants to increase the interest rate by 10 percentage points above the equilibrium rate, we need to calculate the corresponding money supply.

New Interest Rate = Equilibrium Interest Rate + Increase in Interest Rate

New Interest Rate = 0.1 + 0.1 = 0.2

To find the new money supply, we set the new interest rate in the money demand equation and solve for Ms.

Md = Ms

$Y(0.30 - i) = Ms

$250(0.30 - 0.2) = Ms

$250(0.10) = Ms

Ms = $25

Therefore, the money supply should be set at $25 to achieve an interest rate increase of 10 percentage points above the equilibrium interest rate.

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Answer:  \(H = -16s(s-6)\)

Work Shown:

\(H = -16s^2+96s\\\\H = -16s*s+16s*6\\\\H = -16s(s-6)\\\\\)

The answer can be confirmed by using the distributive rule to multiply -16s by each term inside the parenthesis. You should get \(-16s^2+96s\) after distributing.

The break-even points for her graph are given approximately as follows:

C. 15 and 47.

The expenses and the revenue are defined as follows:

The break-even points are the points in which the expenses and the revenue are equal.

In the context of this problem, the functions are given as follows:

The break-even point is given by the intersection of the two curves, which happen around x = 15 and x = 47, hence option C is the correct option.

The problem is given by the image at the end of the answer.

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The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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15625=295.80x is the expression for the given condition.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

Let x be the number of month to payout.

15625=295.80x

x=52.82

The expression for given condition is 15625=295.80x.

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The minimum value for the heights is p1 = -4. To find the best straight line using the given points (0,0), (1,8), (3,8), and (4,20) and the given time points t = 0, 1, 3, and 4, we will use the least squares method.

We'll set up a system of linear equations, A^TAx = A^Tb, and solve for the unknowns.

First, let's define our matrix A, which will have the time points as the first column and 1s as the second column:

A = | 0 1 |
   | 1 1 |
   | 3 1 |
   | 4 1 |

The vector b represents the heights at each time point:

b = | 0  |
   | 8  |
   | 8  |
   | 20 |

Next, we will compute A^T (the transpose of A) and the product A^TA:

A^T = | 0 1 3 4 |
     | 1 1 1 1 |

A^TA = | 26  8 |
      | 8   4 |

Similarly, compute the product A^Tb:

A^Tb = | 104 |
      | 36  |

Now, solve the system A^TAx = A^Tb for the unknowns x:

x = (A^TA)^(-1) * A^Tb = | 2  |
                         | -4 |

So, the best straight line can be described as:

y = 2t - 4

Now we will find the four heights (pi) and four errors (ei):

For t = 0, p1 = 2(0) - 4 = -4, e1 = 0 - (-4) = 4
For t = 1, p2 = 2(1) - 4 = -2, e2 = 8 - (-2) = 10
For t = 3, p3 = 2(3) - 4 = 2,  e3 = 8 - 2 = 6
For t = 4, p4 = 2(4) - 4 = 4,  e4 = 20 - 4 = 16

The minimum value for the heights is p1 = -4.

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Answer:

2/15

Step-by-step explanation:

4/5-2/3

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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\(Perimeter = \\ 9v - 7 + v + 10 + 9v - 7 + v + 10 \\ = 9v - v + 9v + v - 7 + 10 - 7 + 10 \\ = 8v + 10v - 17 - 17 \\ = 18v - 34\)

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