For each pair of points, find the slope of the line that passes through the points.
(5, 4) and (0:1)
(3,7) and (-2,2)

Answer:

17a - 16

7b

Step-by-step explanation:

Given the following expressions

3a+4(5a - 4)=

Expand

3a + 4(5a)- 4(4)

= 3a + 20a - 16

= 17a - 16

For the expression

5b -2(5a -b) + 10a

Expand

5b - 2(5a)-2(-b) + 10a

5b - 10a  + 2b + 10a

= 5b + 2b -10a + 10a

= 7b + 0

= 7b

Answer:

Inverse of a 3 by 3 Matrix

MM-1 = M-1 M = I.

Step 1: The first step while finding the inverse matrix is to check whether the given matrix is invertible. ...

Step 2: Calculate the determinant of 2 × 2 minor matrices.

Step 3: Formulate the cofactor matrix.

Step-by-step explanation:

The inverse matrix formula, A-¹ = (1/|A|) Adj A, is used to determine the inverse of a 3×3 matrix.

The multiplicative identity is obtained by multiplying the provided matrix by the other matrix which serves as the inverse of a matrix. A matrix's inverse is A-1, since the I is the identity matrix, A A-1 = A-1 A = I.

The formula A-1 = (adj A)/(det A), where det A is in the denominator, is used to determine the inverse of a 3x3 matrix A. 

• adj A = The adjoint matrix of A

• det A = determinant of A

dAs a result, det A should not be 0 for A-1 to exist. i.e.,

• A-1 exists when det A ≠ 0 (i.e., when A is nonsingular)

• A-1 does not exist when det A = 0 (i.e., when A is singular).

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Step-by-step explanation:if you like it press thank you ❤❤❤

2x-3y=2 4x+7y= -9

2x=2+3y

2x=2+3y

2 2

x=2+3y 4(2+3y) + 7y= -9

2 2

8+12y + 7y= -9

2

8+12y+14y = -9

2

8+12y+14y= -18

26y= -26

26y = -26

26 26

y= -1

4x+7(-1)= -9

4x+(-7)= -9

4x-7= -9

4x = -2 now lets check,4(-1) + 7(-1)= -9 or 2(-1)-3(-1)=2

4 4 2 2

x=-1 -4 +(-7) = -9 -1-(-3)=2

2 2 -1+3=2

-2-7= -9 2=2

-9= -9

so the answer is x= -1 and y= -1

2

To determine the number of suppliers Witt Input Devices should use, we need to consider the probability of a "super-event" and the marginal cost of managing additional suppliers.

With a 3% probability of a total shutdown and an estimated cost of $400,000, along with a 5% "unique-event" risk per supplier, the company should aim to balance the costs and risks to make an informed decision on the number of suppliers.

Phillip Witt wants to create a portfolio of local suppliers for his keyboards. He faces the risk of "super-events" that could shut down all suppliers simultaneously for at least two weeks. The probability of such an event occurring is 3% per year, which would result in an estimated cost of $400,000 for the company.

Additionally, each individual supplier carries a "unique-event" risk of 5%. To mitigate the risks, Witt Input Devices needs to determine the optimal number of suppliers to use. However, it is stated that up to three nearly identical local suppliers are available.

To make a decision, the company needs to balance the costs and risks. Each additional supplier incurs a marginal cost of $15,000 per year. The company should evaluate the trade-off between the cost of managing additional suppliers and the risk reduction achieved by having multiple suppliers.

Considering these factors, Witt Input Devices should analyze the costs and benefits of each additional supplier and select the number of suppliers that provides an optimal balance between risk mitigation and cost management.

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Answer:

B. 59.66

Step-by-step explanation:

In order to solve this youd have to multiply 745.75 by 8% in order to find it

First you'd need to turn 8% into a decimal

8%/100 = 0.08

0.08 x 745.75 =59.66

So the sales tax rate for this price is 59.66

Therefore , the solution of the given problem of unitary method comes out to be correct response is (c) 750 mL.

Use the tried-and-true basic methodology, the actual variables, and any relevant information from the basic and specialist questions to complete the assignment. Customers may expression be given another chance to taste the products in response. We will lose out on significant advancements in our understanding of programmes if these adjustments don't occur.

Here,

We must compute the cost per millilitre for each bottle size in order to identify the optimal purchase. This can be accomplished by multiplying the cost of each bottle by its millilitre volume.

For a bottle of 275 mL:

=> price per milliliter = $2.10 / 275 mL = $0.0076/mL

For a bottle of 500 mL:

=> price per milliliter = $3.90 / 500 mL = $0.0078/mL

For a bottle of 750 mL:

=> price per milliliter = $5.10 / 750 mL = $0.0068/mL

A 1 L bottle would be:

=> price per milliliter = $6.90 / 1000 mL = $0.0069/mL

We can see from the calculations above that the 750 mL bottle is the greatest deal because it has the lowest price per millilitre.

The correct response is (c) 750 mL.

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The solutions are listed θ=π /3: This represents a line.

(b) x/y = y/3 = z/6: This represents a plane.
(c) y = z^2: This represents an elliptic paraboloid.
(d) 3x - 4y + 6 = 5: This represents a plane.
(e) z = 3: This represents a plane.
(f) r = 3: This represents a sphere.
(g) p = 4: This represents a sphere.
(h) r(t) =< 4 cost, 4 sint, t >: This represents a helix.
(i) r(t) =< 2t + 3, t - 4, 5 - t >: This represents a line.
(j) r(u, v) =< u cos v, usinv, u^2>: This represents a hyperbolic paraboloid.

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The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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Answer:

1/4 of ur pens

Step-by-step explanation:

The regular expression is ^(a(aa)*b)$.

To create a regular expression for the language L = {w = {a,b}* | w has an odd number of 'a's and ends with 'b'}, we can use the following expression:

^(b|(a(aa)*b))$

Breaking it down:

^ indicates the start of the string.

(b|(a(aa)*b)) matches either 'b' or a sequence of 'a's followed by an odd number of 'a's and 'b'.

(aa)* matches zero or more pairs of 'a's.

$ indicates the end of the string.

This regular expression ensures that the string starts with 'b' or a sequence of 'a's, followed by an odd number of 'a's, and ends with 'b'. Any additional characters or sequences in between are not allowed.

Please note that regular expressions can have different notations and conventions depending on the context or programming language you're using. The expression provided here follows a general pattern that should work in most cases.

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The equation of the line that bisects the given segment is y = -2x -3.

The given points coordinates;

A(-2, 4), B(-4, 2)

The mid-point of the given coordinate points;

\(Mid-point = \frac{x_1 + x_2 }{2} , \ \frac{y_1 + y_2}{2} \\\\Mid-point = \frac{-2 -4}{2} , \ \frac{4+2}{2} \\\\Mid-point = (-3, 3)\)

The slope of the given line is calculated as;

y = -2x + 5

slope = -2

The equation of the line that bisects the given coordinate points;

\(\frac{y-y_1}{x-x_1} = -2\\\\\frac{y-3}{x-(-3)} = -2\\\\\frac{y-3}{x+3} = -2\\\\y-3 = -2(x+3)\\\\y-3 = -2x -6\\\\y = -2x -3\)

Thus, the equation of the line that bisects the given segment is y = -2x -3.

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Answer:

(x, y) =(\(\frac{9}{2}\), -2)

um yuh?

Answer:

Step-by-step explanation:

A is the answer

Answer:

Option A. f(x) = 4(3)x

is the answer.

Step-by-step explanation:

b) \(\frac{5}{6} cos (\frac{2pi}{3} t)\) is the equation modeling the motion of the bobber at its high point at time t = 0.

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To measure the discrepancies using simulations from the posterior predictive distributions for each of the Poisson models in Exercise 2.13, follow these steps briefly explained below;

A more detailed explanation of the answer.

Step 1: Obtain the data and the four different Poisson models.
Get the counts of airline fatalities for each year from 1976-1985 and the four Poisson models that were fitted to the data in Exercise 2.13.

Step 2: Generate posterior predictive distributions.
For each of the four Poisson models, generate samples from the posterior predictive distribution. This is done by:
a) Sampling the model parameters from their posterior distributions.
b) Using the sampled parameters to generate data from the Poisson distribution for each year in the dataset.

Step 3: Calculate the discrepancies.
For each simulated dataset, calculate a discrepancy measure that compares the simulated data to the actual airline fatality data. A common discrepancy measure is the mean squared error (MSE), which is calculated as the mean of the squared differences between the observed and simulated data points.

Step 4: Display the results.
Create a table or graph to display the discrepancy measures for each of the four Poisson models. This will allow you to compare the models and determine which one best fits the data.

Remember that a lower discrepancy measure indicates a better fit to the data, so choose the model with the lowest discrepancy measure as the best-fitting model.

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Answer:

x=19.3333

Step-by-step explanation:

Cross multiply

6(x-3)=14*7

6x-18=98

6x=98+18

6x=116

x=19.3333

Answer:

1, 6, 15, 20, 15, 6, 1

Answer:

points

Step-by-step explanation:

A possible set of scores for the five students that meets the given criteria is {3, 4, 5, 6, 7}.

Based on the given information, we know that there are five students who took a quiz, and the lowest score was 3, the highest score was 7, and the median was 4. To create a possible set of scores that satisfies these conditions, we can arrange the scores in ascending order.

Since the median is 4, it must be the middle value. Therefore, we can assign the scores as follows:

{3, 4, ____, ____, 7}

The lowest score is 3 and the highest score is 7, so we can assign the remaining two scores between these values while maintaining the order. There are multiple possible combinations that fit this criteria, but one possible set of scores could be:

{3, 4, 5, 6, 7}

In this set, the lowest score is 3, the highest score is 7, and the median is 4, satisfying all the given conditions.

In summary, a possible set of scores for the five students that meets the given criteria is {3, 4, 5, 6, 7}.

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\(d = \frac{d(10 {}^{k + p} - 10 {}^{k}) }{(10 {}^{k + p} - 10 {}^{k})} \)

where

Step-by-step explanation:

Greetings !

use the above formula to change any decimal into fraction form

Thus, plug in the value and solve

Hope it helps !

Answer:

21

Step-by-step explanation:

because on a table, -21 and 21 are lined up together.

Answer:

x = 105

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, thus

sum = 180° × 5 = 900°

Sum the interior angles and equate to 900

x + 102 + 165 + 123 + x + 11 + 128 + 161 = 900, that is

2x + 690 = 900  ( subtract 690 from both sides )

2x = 210 ( divide both sides by 2 )

x = 105

Answer:

Step-by-step explanation:

Given that:

Number of books, b α number of children enrolled

b α C

b = kC

Number of books, b = 3 for each child, c = 1 enrolled

Total number of books in class room :

Total number of books = Number of books per child * Number of child)

Total number of books = 3 * Numbe of child

The answer is c i believe

In classification analysis, we are determining the probability of an observation belonging to a specific class.

Classification analysis is a machine learning technique used to predict the class or category to which an observation belongs. The goal is to assign a probability to each possible class, indicating the likelihood of the observation belonging to that class. This is typically done by training a classification model on a labeled dataset, where the classes are known for a set of observations. The model learns patterns and relationships from the training data and then uses that knowledge to predict the class of new, unseen observations. The predicted probabilities can be used to make informed decisions, such as determining the most likely class for a given observation or setting a threshold for making binary decisions.

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By mathematical induction we know that P(n) is true for all integers n > 4

We have proven that \(2^n > n^2\) for all integers n > 4.

=> Let P(n) be the proposition that \(2^n > n^2\), n > 4

Put n = 5

\(2^5 > 5^2\)

32 > 25

It is true for n = 5

=> For the inductive hypothesis we assume that P(k) holds for an arbitrary integer k > 4

Let P(k) be true where k is greater than 4

That is, we assume that

\(2^k > k^2\), k > 4

Under this assumption, it must be shown that, it is true for p(k+1).

\(= > 2^k^+^1=2.2^k\\\\=2^k+2^k > k^2+k^2\\\\=k^2+k.k > k^2+4k\\\\=(k+1)^2\\\\\)

This shows that P(k + 1)  is true under the assumption that P(k) is true.

This completes the inductive step.

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The area is then calculated as (1/2) * base * height, resulting in approximately 39.375 square feet.

To find the area of the actual banner, we need to scale up the dimensions from the drawing to real-world measurements. We are given that 1 inch on the drawing is equivalent to 1.5 feet on the actual banner.

The base of the triangle on the drawing is 5 inches, so the base of the actual triangle will be:

5 inches * 1.5 feet/inch = 7.5 feet

Similarly, the height of the actual triangle will be:

7 inches * 1.5 feet/inch = 10.5 feet

Now that we have the base and height of the actual triangle, we can calculate its area using the formula for the area of a triangle:

Area = (1/2) * base * height

Area = (1/2) * 7.5 feet * 10.5 feet

Area ≈ 39.375 square feet

Therefore, the area of the actual banner will be approximately 39.375 square feet.

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The number that could be expected to have cable television will be 138 people.

From the information, survey showed the 8 about of 20 home owners in a neighborhood had cable television

Therefore, when there were 320 homeowners in the neighborhood, the number that could be expected to have cable television will be:

= 8/20 ×320

= 8 × 16

= 128

The number of people will be 128.

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The height of squared pyramid is \(\frac{1}{3}h\) unit.

A cube is a solid three-dimensional object with six square faces or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

Volume of cube \(= (side)^3 \ unit^3\)

Given the height of cube is \(h\) unit.

Volume of cube is \(h^3 \ unit^3\)

Let the height of squared pyramid is \(x\) unit

Volume of squared pyramid is \(\frac{1}{3} h^{2} \times x \ unit^3\)

According to the question, we have

Volume of cube = \(6 \times\) volume of squared pyramid

\(\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h\)

Therefore, the height of squared pyramid is \(\frac{1}{3}h\) unit.

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