Find the first five terms of the sequence: an = 2an – 1 – an – 2; a1 = 4; a2 = 3.



A) {4, 3, 2, 2, 2}


B) {4, 3, 2, 1, 0}


C) {4, 3, 5, 1, 9}


D) {4, 3, 4, 5, 6}

Answer:

2n² + n - 15

Step-by-step explanation:

(n + 3) (2n - 5)

= 2n² - 5n + 6n - 15

= 2n² + n - 15

So, the answer is 2n² + n - 15

Answer:

Step-by-step explanation:

\((n + 3)(2n - 5)\\(n * 2n) + (n * -5) + (3 * 2n) + (3 * -5)\\(2n^2 ) + (-5n) + (6n) + (-15)\\2n^2 + n - 15\)

Answer:

7

Step-by-step explanation:

Answer:

You will have exact seven.

Answer:

I think it is associative! Not sure though bc of the q!

Step-by-step explanation:

c. 1,256 m³ is the approximate volume of the sphere.

The approximate volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere. In this case, the diameter of the sphere is given as 10m.

The radius of the sphere is half of the diameter, so the radius would be 10m/2 = 5m.

Plugging the radius value into the formula, we get V = (4/3)π(5m)^3. Simplifying further, we have V = (4/3)π(125m^3).

Calculating the value, V = (4/3)π(125m^3) ≈ 1,256 m³.

Therefore, the approximate volume of the sphere is approximately 1,256 m³.

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curl(f) = (∂f₂/∂x - ∂f₁/∂y) = (5 - (-5)) = 10

Using Green's theorem, we can compute the line integral of f along the boundary of the region r, which consists of two line segments: y = 0 from x = 0 to x = π, and y = sin(x) from x = π to x = 0 (going backwards along this segment). We can use the parametrization r(t) = <t, 0> for the first segment, and r(t) = <t, sin(t)> for the second segment, with 0 ≤ t ≤ π:

∫(C)f · dr = ∫∫(R)curl(f) dA = 10 × area(R)

The area of the region R is given by:

area(R) = ∫₀^π sin(x) dx = 2

Therefore, the line integral of f along the boundary of r is:

∫(C)f · dr = 10 × 2 = 20.

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The 5 Practices for Orchestrating Productive Mathematics Discussions is a framework for leading effective classroom discussions in mathematics. These practices were developed by Mary Kay Stein and her colleagues.

Anticipating: Teachers consider what students might do or say during the lesson and how they will respond.

Monitoring: Teachers keep track of student thinking and work during the lesson and use this information to guide instruction.

Selecting: Teachers choose which student ideas to highlight and pursue during the lesson.

Sequencing: Teachers plan and adjust the order in which student ideas are presented and discussed to maximize learning.

Connecting: Teachers help students connect and make sense of the mathematical ideas being discussed and link them to previous and future learning.

By using these practices, teachers can create a safe and supportive learning environment where students are encouraged to share their ideas and reasoning, and where meaningful mathematical discourse is promoted.

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Answer: AB +CD

Step-by-step explanation:

There is only 1 linearly independent subset consisting of 1 column for matrix A.

For k=2, 3, 4, and 5, there are no linearly independent subsets since the rank of matrix A is 1.

To find the number of linearly independent subsets consisting of k columns for each of the given matrices, follow these steps:

1. Determine the size and rank of the given matrix.

2. If k is greater than the rank of the matrix, there are no linearly independent subsets of k columns.

3. If k is equal to or less than the rank of the matrix, the number of linearly independent subsets of k columns is given

by the binomial coefficient: C(r, k), where r is the rank of the matrix, and k is the desired number of columns.

For example, let's find the number of linearly independent subsets consisting of k columns for the given matrix A:

Matrix A:
[ 1  2  3]
[ 2  4  6]
[ 3  6  9]

Determine the size and rank of the matrix.

The size of matrix A is 3x3. Its rank is 1, as all rows are linearly dependent.

Check if k is greater than the rank of the matrix.

For k=1, 2, ..., 5, only k=1 is less than or equal to the rank of matrix A (which is 1).

Calculate the number of linearly independent subsets of k columns.

For k=1, use the binomial coefficient formula: C(r, k) = C(1, 1) = 1.

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Answer:

2 more than 5 times a number

Step-by-step explanation:

This will produce a plot of the vector field for the function f(x,y) = x^4, y^4.

The vector field for f(x,y) = x^4, y^4 can be plotted by considering the gradient of the function, which gives us the direction and magnitude of the vector at each point (x,y).

The gradient of f(x,y) is given by:

grad(f) = (∂f/∂x)i + (∂f/∂y)j

= 4x^3 i + 4y^3 j

This tells us that at each point (x,y), the vector has a magnitude of sqrt((4x^3)^2 + (4y^3)^2) = 4sqrt(x^6 + y^6) and is pointing in the direction of (4x^3, 4y^3).

To plot the vector field, we can choose a set of points (x,y) on a grid and calculate the corresponding vectors. We can then draw an arrow at each point (x,y) with the length and direction given by the corresponding vector.

Alternatively, we can use software such as MATLAB or Python with a suitable library like matplotlib to plot the vector field. Here is an example code in Python:

import numpy as np

import matplotlib.pyplot as plt

# Define the vector field function

def f(x, y):

   return np.array([x**4, y**4])

# Define the grid of points to plot

x = np.linspace(-1, 1, 20)

y = np.linspace(-1, 1, 20)

X, Y = np.meshgrid(x, y)

# Evaluate the vector field at each point

U, V = f(X, Y)

# Plot the vector field

plt.quiver(X, Y, U, V)

# Add labels and show the plot

plt.xlabel('x')

plt.ylabel('y')

plt.title('Vector Field for f(x,y) = x^4, y^4')

plt.show()

This will produce a plot of the vector field for the function f(x,y) = x^4, y^4.

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Answer:

h(8) = - \(\frac{3}{7}\)

Step-by-step explanation:

Substitute x = 8 into h(x)

h(8) = \(\frac{8^2-11(8)+18}{8+6}\) = \(\frac{64-88+18}{14}\) = \(\frac{-6}{14}\) = - \(\frac{3}{7}\)

If the repayment on a loan was Php 23600, the principal amount is equal to Php 131,111.11.

Given the following data:

Conversion:

12 months = 1 year

18 months = 1.5 year

To calculate the principal amount if the interest rate is 12% a year:

Mathematically, simple interest is given by the formula:

\(S.I = \frac{PRT}{100}\)

Where:

Making P the subject of formula, we have:

\(P = \frac{100S.I}{RT}\)

Substituting the given parameters into the formula, we have;

\(P = \frac{100 \times 23600}{12 \times 1.5}\\\\P = \frac{2360000}{18}\)

Principal amount, P = Php 131,111.11

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The key underlying assumption of the single index model is that the return of a security can be explained by the return of a broad market index.

This assumption forms the basis of the single index model, also known as the market model or the capital asset pricing model (CAPM).

In this model, the return of a security is expressed as a function of the return of the market index. The single index model assumes that the relationship between the returns of a security and the market index is linear.

It suggests that the risk and return of a security can be explained by its exposure to systematic risk, which is represented by the market index.

The single index model assumes that the return of a security can be decomposed into two components: systematic risk and idiosyncratic risk.

Systematic risk refers to the risk that cannot be diversified away, as it affects the entire market. Idiosyncratic risk, on the other hand, is the risk that is specific to a particular security and can be diversified away by holding a well-diversified portfolio.

The single index model assumes that the systematic risk is the only risk that investors should be compensated for, as idiosyncratic risk can be eliminated through diversification.

It suggests that the expected return of a security is determined by its beta, which measures its sensitivity to the market index. A security with a higher beta is expected to have a higher return, as it is more sensitive to market movements.

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Answer:

B: The independent variable is d.

Step-by-step explanation:

I took the test on K12

The derivative of\(y = e^(6−6x)\) is found as \((dy)/(dx) = -6e^(6-6x).\)

In calculus, we often use the chain rule to differentiate complex functions. In this question, we use the chain rule of differentiation to find the derivative of \(y = e^(6−6x).\)

The chain rule states that if we have a function of the form f(g(x)), then the derivative of this function is given by

(df)/(dx) = (df)/(dg) * (dg)/(dx).

The given equation is  \(y = e^(6−6x).\)

Differentiate \(y = e^(6−6x).\)

We can differentiate y with respect to x using the chain rule of differentiation, which is given by

(dy)/(dx) = (dy)/(du) * (du)/(dx)

Where u = 6 - 6x and y = e^u

Hence, we can write

\((dy)/(dx) = e^u * (-6)\)

Now substituting u = 6 - 6x, we get

\((dy)/(dx) = e^(6-6x) * (-6)\)

Therefore, the derivative of\(y = e^(6−6x)\) is given by

\((dy)/(dx) = -6e^(6-6x).\)

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\(2 + \frac{19}{30} = \frac{60 + 19}{30} = \frac{79}{30} \)

\( \frac{79}{30} = 2 \frac{19}{30} \)

Answer:

79/30

Step-by-step explanation:

the whole number is 60/30. If we add that to the already existing 19/30 we get 79/30.

Answer:

B

Step-by-step explanation:

because b x b is equals to b raised to the power of 2

The expression that is equivalent to b x b will be b².

For this question to be solved, you simply have to multiply the values given. In this case, you're multiplying the same value twice and this will simply be raised to the power of 2.

Therefore, based on the question asked, b × b will be:

= b × b

= b²

Therefore, the value of b × b is b².

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Answer:

3/5

Step-by-step explanation:

SOHCAHTOA

Cos- adjacent/hypotenuse

adjacent side: 3

hypotenuse: 5

adj/hyp: 3/5

The probability of the spinner stopping on a blue section on the first spin and then a red section on the second spin is 3/49.

To find the probability of the spinner stopping on a blue section on the first spin and then a red section on the second spin, we need to multiply the probabilities of each event happening independently.

Step 1: Find the probability of landing on a blue section on the first spin.

There is 1 blue section out of 7 total sections, so the probability is 1/7.

Step 2: Find the probability of landing on a red section on the second spin.

There are 3 red sections out of 7 total sections, so the probability is 3/7.

Step 3: Multiply the probabilities from step 1 and step 2.

(1/7) * (3/7) = 3/49.

So, the probability of the spinner stopping on a blue section on the first spin and then a red section on the second spin is 3/49.

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Answer:

You need to add 12 pint of yellow.

Step-by-step explanation:

This is the method I used:

There is 4 pint of Yellow (Y) and 4 pint of Blue (B)

because they said is in equal amounts, so they are 50% each.

We need 80% Y and 20% B

so 4:20 = x=80   (4 pints is 20% as "how many pints" is 80%)

So x = 16

We already have 4 pint of Yellow, so we need more 12.

6.4 pint of yellow paint we need to add to the mixture.

"A percentage is a number or ratio that can be expressed as a fraction of 100."

"It is a statement which consists of equal symbol between two mathematical expressions."

For given example,

8 pint mixture of paint that is made up of equal amounts of yellow paint and blue paint.

Let we need 'x' amount of yellow paint.

To create a certain shade of green, you need a paint mixture that is 80% yellow.

So, we get an equation \(\frac{x}{8}\times 100 =80\)

We solve above equation.

\(\Rightarrow \frac{x}{8}\times 100 =80\\\\\Rightarrow \frac{x}{8} = \frac{80}{100}\\\\ \Rightarrow x = 0.8\times 8\\\\\Rightarrow x = 6.4~~pints\)

Therefore, 6.4 pint of yellow paint we need to add to the mixture.

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Statement Problem: The sum of two numbers is 7. Five times the larger number plus four times the smaller number is 48. Find the numbers.

Solution:

Let x be the larger number and y be the smaller number such that;

From equation 1, we have;

Substitute equation3 in equation2, we have;

Then, substitute the value of y in equation3;

Thus, the larger number is 20 and the smaller number is -13

To determine the optimal order quantity for Rocky Mountain Tire Center, you must consider ordering costs, storage costs, and the purchase price of the tires. The order quantity should minimize the total cost including both ordering cost and storage cost.

The EOQ formula is given by: EOQ = √((2DS) / H)

Where: D = Annual demand (7,000 go-cart tires)

S = Ordering cost per order ($40) H = Holding cost - percentage of the purchase price (40% of the purchase price)

we need to determine the purchase price per tire based on the quantity ordered.

EOQ = √((2 * 7,000 * 40) / (0.4 * 15))

=118 tires

they should order approximately 118 tires.

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Olivia might have used a combination of translation and rotation to move ABCDE onto A"B"C"D"E". This involves shifting the object's position and rotating it around a specific point.

One way Olivia might have transformed the shape ABCDE into A"B"C"D"E" is by combining two different transformations: translation and rotation. Translation is the process of moving an object from one position to another without changing its size, shape, or orientation. In this case, Olivia could have translated the shape horizontally or vertically until it aligned with A"B"C"D"E". Next, she would use rotation to spin the shape around a specific point, called the center of rotation, by a certain angle (e.g., 90, 180, or 270 degrees). By properly selecting the center of rotation and angle, Olivia can complete the transformation of ABCDE to A"B"C"D"E".

Calculation steps:
1. Identify the translation vector (horizontal and vertical distances) required to move ABCDE to A"B"C"D"E".
2. Translate the shape ABCDE by applying the translation vector.
3. Determine the center of rotation and the angle needed to align the translated shape with A"B"C"D"E".
4. Rotate the translated shape around the center of rotation by the determined angle.

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Answer:

ridiculous

Step-by-step explanation:

tssssk *extra characters*

Answer:

53912878951978360832q4918

Step-by-step explanation:

9257289357218q4918(5823829.943259)

=53912878951978360832q4918

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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Answer:

Step-by-step explanation:

.....-_-.....-__-....-___-_--____--_--_____--_--______________--_________________-u streched ma face dude.

Answer:

The answer is

\( - 6x + 17\)