In Exercises 1 and 2, segment AB is tangent to C. Find each value.
1. AB_ or_
2. m/ABC
In Exercises 3-5, find each value.
3. JF and GF are tangent to H. What is HJ? ​

Answer:

Step-by-step explanation:

Use this formula:

y - y1 = m ( x - x1 )

We are told m = -3 and given the point (12 , 5) ---- > so x1 = 12 and y1= 5

Put these values into the formula above and you get:

y - y1 = m ( x - x1 )

y - 5 = -3 ( x - 12 )

y - 5 = -3x + 36

y = -3x + 36 + 5

y = -3x + 41

Answer:

$1.75 per pint

Step-by-step explanation:

1 gallon has 8 pints

divide 13.99 by 8

Answer:

y = x³ - 12x² + 41x - 30

Answer:

Just 1 positive, odd factor

Step-by-step explanation:

48 has many factors. But not many odd factors. Only 3 is odd and bigger than 2 and less than 10.

So, just one odd, positive factor.

The error message "Difference order N must be a positive integer scalar" is indicating that there is an issue with the input argument for the diff function.

The diff function is used to calculate the difference between adjacent elements in a vector.
In the code you provided, the line that is causing the error is:
f_prime0 = diff(f,x0,xinc);
To fix this error, you need to ensure that the input arguments for the diff function are correct.

To fix this problem, you need to look at the code in the Newton_Raphson_tutorial function and possibly also the Tutorial_m function. You probably get an error when computing the derivative with the 'diff' function.

However, we can offer some general advice on how to fix this kind of error. The error message suggests that the variable N used to specify the difference order should be a positive integer scalar.

Make sure the variable N is defined correctly and has a positive integer value.

Make sure it is not assigned a non-integer or non-scalar value.

Make sure the arguments to the diff function are correct.

The diff function syntax may vary depending on the programming language or toolbox you are using.

Make sure the variable to differentiate ('f' in this case) is defined and suitable for differentiation.

Make sure that x0 and xinc are both positive integer scalars, and that f is a valid vector or matrix.
Additionally, it's important to check if there are any other errors or issues in the code that could be causing this error message to appear.

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Answer:

They are all positive because you must go right.

They are all negative because you must go down.

Step-by-step explanation:

Example. (1,-4)

You go over one.

Down 4

Answer: ok lol so what is you question

Step-by-step explanation:

The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

The value of cement mixer after t year is \(f(t) = 54,205(0. 87)^{t}\)

Given to us

The value of cement mixer when bought, \(P\)= $ 54,205

the value of cement mixer after 1 year, \(P_1\)=   $ 47,158. 35

the value of cement mixer after 2 year,\(P_2\)=  $ 41,027. 76

To find out depreciation we can use the formula for depreciation,

\(P_n= P(1-r)^n\\where,\\P_n= Value\ of\ asset\ after\ n\ year\\P= Value\ of\ asset\ when\ bought\\r= rate\ of\ depreciation\\n= number\ of\ years\)

By putting the value, in the formula we get,

\(P_1= P(1-r)^n\\\\47,158.35= 54,205\times (1-r)^1\\\\\dfrac{47,158.35}{54,205} = (1-r)\\\\0.87=1-r\\\\r=0.13\)

Therefore, putting the value of \(r\) and \(P\) in depreciation formula for \(t\) years we get,

\(P_n= P(1-r)^n\)

\(f(t) = 54,205(0. 87)^{t}\)

Hence, the value of cement mixer after t year is \(f(t) = 54,205(0. 87)^{t}\).

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Answer:

Mmm... a product would be like 10+4=14

Step-by-step explanation:

thats what you are looking for right

Answer:

y= 3x - 4

Step-by-step explanation:

hope this helps.

If Points A, B, C, D, and E are collinear and AC = 16. x is 3, AB is 10, BD is 14, CE is 17.

22. x

AC=AB+BC

Hence:

x+7+2x=16

3x=9

x=9/3

x=3

23. AB

AB=x+7

AB=3+7

AB=10

24. BD

BD=BC+CD

BD=2x+3x-1

BD=5x-1

BD=5(3)-1

BD=15-1

BD=14

25. CE

CE=CD+DE

CE=3x-1+2x+3

CE=5x+2

CE=5(3)+2

CE=15+2

CE=17

Therefore if Points A, B, C, D, and E are collinear and AC = 16. x is 3, AB is 10, BD is 14, CE is 17.

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A complete graph is one in which there is an edge connecting every vertex to every other vertex. In order to determine for what values of n a complete graph with n vertices has an Euler circuit and a Hamiltonian circuit, let's discuss the definitions and requirements of each type of circuit.

1. Euler Circuit: An Euler circuit is a path that traverses each edge of a graph exactly once and returns to its starting vertex. For a graph to have an Euler circuit, all vertices must have an even degree (number of edges connected to the vertex).

2. Hamiltonian Circuit: A Hamiltonian circuit is a path that visits every vertex in a graph exactly once and returns to its starting vertex. A complete graph always has a Hamiltonian circuit, regardless of the number of vertices.

Now, let's determine for what values of n a complete graph has an Euler circuit:

In a complete graph with n vertices, each vertex is connected to every other vertex, which means the degree of each vertex is (n-1). For a complete graph to have an Euler circuit, all vertices must have an even degree. This implies that (n-1) must be even, so n must be odd.

So, for a complete graph with n vertices to have an Euler circuit, n must be an odd number.

In summary:
- A complete graph with n vertices always has a Hamiltonian circuit.
- A complete graph with n vertices has an Euler circuit if n is an odd number.

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The ratio of protonated/deprotonated acetic acid at the given pH is:

Therefore, the ratio of protonated/deprotonated acetic acid at the given pH is:

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Answer:

x = -16 and x = 1

Step-by-step explanation:

"Finding the roots" means solving the equation. We'll set the equation equal to 0 (replace f(x) with zero) and factor.

0 = x^2 + 15x - 16

0 = (x + 16)(x - 1)

This is factored.

Using the Zero Product Property, we separate this into two small equations.

x+16 = 0 and x-1 = 0

Solve these one-step equations.

x = -16 and x = 1

These are the roots (and roots are solutions, are zeros, are x-intercepts) If the question ask for zeros, roots, solutions or x-intercepts, set it equal to 0, factor and solve.

As the upper bound of the 95% confidence interval for the difference of proportions Heavy - Regular is positive, there is not enough evidence to conclude that heavy-duty packaging reduces the proportion of damaged shipments.

The sample proportions are given as follows:

Then the difference of the proportions is given as follows:

0.01 - 0.0167 = -0.0067.

The standard error for each sample is given as follows:

Then the standard error for the distribution of differences is given as follows:

\(s = \sqrt{0.0037^2 + 0.0026^2}\)

s = 0.0045.

The critical value for a 95% confidence interval is given as follows:

z = 1.96.

Then the upper bound of the interval is given as follows:

-0.0067 + 1.96 x 0.0045 = 0.0021.

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Answer:

3.14

Step-by-step explanation:

The formula for the area of a circle is \(\pi r^2\), where r is the radius. In this circle, the area would therefore be \(3.14\cdot 2^2=12.56\). However, since this is only a quarter circle, you need to divide the area by 4, meaning that the area of this shape is 3.14 square units. Hope this helps!

Answer:

π

Step-by-step explanation:

calculate the the full circle: A = π*\(r^{2}\) = π*\(2^{2}\) = π*4 (the area of the full circle)

you've got 1/4 or the circle according to the picture, so divide the area of the full circle with 4:

(π*4)/4 = π

Answer:

c. P' (-4, -6)

Step-by-step explanation:

Since there's a dilation factor of 2, you would multiply x and y by 2.

Answer:

Below

Step-by-step explanation:

4 outlets/ 1.5 hr     *    7.5 hr = 20 outlets   ( see how 'hr' cancels out and you are left with 'outlets ?)

Answer: 20

Step-by-step explanation:

In 1.5 hours, the no. of electrical outlets rewired = 4

Then, in 1 hour the no. of electrical outlets rewired = 4/1.5

So, in 7.5 hours the no. of electrical outlets rewired =( 4/1.5 ) × 7.5 = 20.

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

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

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

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

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

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

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

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

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

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

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

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

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

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

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

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

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

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

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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Answer:

Slope = -4

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes, which means that multiplying their slopes result in a product of -1. Given the equation, x - 4y = - 12:

Transform the equation into its slope-intercept form, y = mx + b:

x - 4y  = - 12

x - x - 4y = - x - 12

-4y = -x - 12

Divide both sides by -4:

\(\frac{-4y}{-4} = \frac{-x - 12}{-4}\)

y =  ¼x + 3  ⇒ (This is the slope-intercept form of the given standard equation, x - 4y  = - 12).

Since the slope of the given equation is ¼, then it means that its negative reciprocal must be - 4:

(¼) (-4) = -1

Therefore, the slope of the line perpendicular to x - 4y = - 12 is - 4.

The required area of Fiona's circle is49π. Option D is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

The radius of Fiona's circle is half of the diameter, which is 14/2 = 7 meters.

The formula for the area of a circle is A = πr², where A is the area and r is the radius.

Substituting the value of the radius in the formula, we get:

A = π(7)² = 49π

So, the area of Fiona's circle is 154 square meters, if we use the value of π as 3.14.

Therefore, the answer is 49.

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The number of miles that Jamel drove the car on his vacation was 97 miles.

Let the number of miles that he traveled be represented by x.

Based in the information given, the equation to solve the question will be:

50 + (0.75 × x) = 122.75

50 + 0.75x = 122.75

Collect like terms

0.75x = 122.75 - 50

0.75x = 72.75

Divide both side by 0.75

0.75x/0.75 = 72.75/0.75

x = 97

Therefore, Jamel drove the car for 97 miles.

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The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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3m+6=24

3m=18

m=6

So mike traveled 6 miles by taxi.

We know that the taxi driver chargers $3 per mile, so we say M is the mile variable, and for every M there is $3. So 3m+6 (initial fee) is the first part of the formula.

We set 3m+6=24 (24 being the total amount the taxi driver is charging)

Answer:33

Step-by-step explanation:

The next term in the given sequence is 215.

The given sequence is -3, 2, 1, 0, 5, 22, 57, 116,...

This is a arithmetic sequence – a sequence in which each term after the first is obtained by adding a fixed number (which is called the common difference).

The common difference of this sequence is d = 5, since each term increases by 5 more than the preceding term.

Therefore, to find the next term, we add the common difference to the previous term, and get:

116 + 5 = 121

Therefore, the next term in the sequence is 215.

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Answer:

8.417

Step-by-step explanation:

The amount of 101 inches is equal to 8.4167 feet.

To convert inches to feet, we divide the number of inches by 12, since there are 12 inches in 1 foot.

As 1 foot= 12 inches

Therefore, to convert 101 inches to feet, we divide 101 by 12:

= 101 inches / 12 inches/foot

= 8.4167 feet

So, 101 inches is equal to 8.4167 feet.

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