use the inner product p, q = a0b0 a1b1 a2b2 to find p, q , p , q , and d(p, q) for the polynomials in p2. p(x) = 5 − x 3x2, q(x) = x − x2 (a) {p, q}
(b) ||p||
(c) ||q||
(d) d(p, q)

Answer:

A formula that uses one or more previous terms to find the next term is a recursive formula.

Step-by-step explanation:

A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s).

Let's begin by listing out the information given to us:

The slope is calculated using the formula:

We will proceed by substituting the values into the equation, we have:

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

plug in the solutions into both equations for all three and you'll get the answer they have to work for both for it to be a solution when u plug it in just solve normally

Answer: 16x+8

Step-by-step explanation:

you use the distributive property. 8 * 2x = 16x and 8 * 1 = 8

Answer:

what questions?

Step-by-step explanation:

This process may lead to a quadratic equation that needs to be solved, resulting in multiple x-values. These x-values will correspond to the points on the graph of y = f(x) where the tangent line passes through (1, -1).

To find the points on the graph of y = f(x) where the tangent line passes through the point (1, -1), we need to find the x-values that satisfy this condition.

First, we need to find the derivative of the function f(x). The derivative of f(x) = 3x^2 - 4x + 3 is f'(x) = 6x - 4.

Now, let's find the slope of the tangent line passing through the point (1, -1). We can use the point-slope form of a line, which is given by y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values (1, -1) into the equation, we get y - (-1) = (6x - 4)(x - 1). Simplifying this equation, we have y + 1 = 6x^2 - 10x - 4.

To find the x-values that satisfy this equation, we can substitute f(x) into y. So, y + 1 = 6(f(x)) - 10x - 4. Substituting f(x) = 3x^2 - 4x + 3, we have y + 1 = 6(3x^2 - 4x + 3) - 10x - 4.

Now, we can simplify the equation and solve for x to find the x-values for which the tangent line passes through (1, -1).

This process may lead to a quadratic equation that needs to be solved, resulting in multiple x-values. These x-values will correspond to the points on the graph of y = f(x) where the tangent line passes through (1, -1).

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Valve guides can be measured for roundness and diameter using a micrometer or a bore gauge. Both of these tools are commonly used in the automotive industry to measure the dimensions of engine parts such as valve guides.

A micrometer is a precision measuring tool that uses a calibrated screw to measure the diameter of an object with high accuracy. It can be used to measure the diameter of the valve guide at different points along its length to check for roundness. A bore gauge, also known as an inside micrometer, is a specialized tool used to measure the inside diameter of a cylinder, such as the bore of an engine block or the valve guide. It consists of a probe that is inserted into the cylinder and expands to take a measurement. A bore gauge is particularly useful for measuring the internal dimensions of complex shapes like valve guides, which can have irregular or non-circular profiles. Both micrometers and bore gauges come in various sizes and types, and the specific tool used will depend on the size and shape of the valve guide being measured.

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The zero of the function f(x) = x - 4 is 4

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 4

By definition, the zero of the function is the point where the fucnction has a value of 0

i.e. f(x) = 0

When the value f(x) = 0 is substituted in the above equation, we have the following equation

x - 4 = 0

Add 4 to both sides

So, we have

x - 4 + 4 = 0 + 4

Evaluate the sum

x = 4

Hence, the zero of the function is 4

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Answer:

25

Step-by-step explanation: this is because you have a negative

's' and 't' represent free parameters that can take on any real values.

In the given system of equations:

x1 - x2 + 4x3 = -4

6x1 - 5x2 + 7x3 = -5

3x1 - 39x3 = 45

To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:

Step 1: Write the augmented matrix for the system:

[1 -1 4 | -4]

[6 -5 7 | -5]

[3 0 -39 | 45]

Step 2: Perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 6R1

R3 = R3 - 3R1

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 3 -51 | 57]

Step 3: Perform additional row operations to further simplify the matrix:

R3 = R3 - 3R2

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 0 0 | 0]

Step 4: Write the system of equations corresponding to the row-echelon form:

x1 - x2 + 4x3 = -4

x2 - 17x3 = 19

0 = 0

Step 5: Express the variables in terms of a parameter:

x1 = s

x2 = 19 + 17s

x3 = t

where s and t are parameters.

Therefore, the solution to the system is:

[x1] = [s]

[x2] = [19 + 17s]

[x3] = [t]

In the provided solution format:

[x1] = [s] []

[x2] = [19 + 17s] + s []

[x3] = [t] [__]

Here, 's' and 't' represent free parameters that can take on any real values.

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The graph will be a parabola opening upwards, with x-intercepts at x = 9 and x = -2, and a y-intercept at (0, -18).

To graph the function f(x) = x² - 7x - 18, we can follow a step-by-step process:

To find the x-intercepts, we need to solve the equation f(x) = x² - 7x - 18 = 0. We can do this by factoring, completing the square, or by using the quadratic formula. In this case, let's use factoring:

x² - 7x - 18 = 0

To factor this quadratic equation, we need to find two numbers that multiply to give -18 and add up to -7. After some exploration, we find that -9 and 2 are the required numbers:

(x - 9)(x + 2) = 0

Setting each factor equal to zero, we get:

x - 9 = 0 --> x = 9

x + 2 = 0 --> x = -2

So the x-intercepts are x = 9 and x = -2.

The y-intercept is the point where the graph intersects the y-axis. To find it, we substitute x = 0 into the equation:

f(x) = (0)² - 7(0) - 18

f(x) = -18

Therefore, the y-intercept is (0, -18).

Now that we have the x-intercepts (9 and -2) and the y-intercept (0, -18), we can plot these points on the graph.

Let's start by marking the x and y axes. Choose a suitable scale for the x and y axes, ensuring that the points are within the visible range. For example, you can set the x-axis from -10 to 10, and the y-axis from -30 to 10.

Next, plot the points (9, 0) and (-2, 0) on the x-axis, representing the x-intercepts. These points indicate where the graph intersects the x-axis.

Then, plot the y-intercept (0, -18) on the y-axis. This point represents where the graph intersects the y-axis.

The completed graph should resemble a U-shape, with the vertex  located in the middle. You can also choose additional points to plot on the graph to help visualize the shape and characteristics of the parabola.

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Complete Question:

Plot the graph for the function  f(x) = x² - 7x - 18

The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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Answer:

9√6

Step-by-step explanation:

3√2 × 3√3

3√2×3 ×3

3√6×3

9√6

Juana would have to pay approximately $29.40 in interest for the $10,686.00 loan over a 20-day period, assuming an annual interest rate of 5.79%.

The interest Juana would have to pay in 20 days can be calculated using the formula:

Interest = Principal × Interest Rate × Time

In this case, the principal amount is $10,686.00 and the interest rate is 5.79% per annum. To calculate the interest for 20 days, we need to convert the time to a fraction of a year. Since there are 365 days in a year, the time in years would be 20/365.

Using the formula and substituting the values:

Interest = $10,686.00 × 0.0579 × (20/365)

Calculating this expression, we find that the interest amount Juana would have to pay in 20 days is approximately $29.40.

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Answer:

21 windows

Step-by-step explanation:

colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answer: Let the number of window Colleen father would paint be x while that of her mother be y. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father x = 2y

Let the number of windows each painted by Colleen and her 2 brothers be z since they would paint the same number of windows. The total number of windows to be painted = 2y + y + z + z + z = 3y + 3z = 3(y + z).

Then number of windows needed to be painted by Colleen and her mother is given as z + y. Since Colleen painted 7 windows as her share and her mother share i.e. y + z = 7

Therefore the total number of windows = 3(y + z) = 3(7) = 21 windows

Mila will receive 68 EUROS of money after the exchange of 80 US dollar.

USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.

Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.

According to the given data in the question,

1 USD =0.85 EURO

80 USD = 0.85*80 EURO

80 USD= 68 EURO

Hence 80USD will be converted to 68 EUROS

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Answer:

5x-15+90+2x=7x+75

Step-by-step explanation:

you just want to add together the like terms which gives you 7x+75 like terms are just numbers that are similar such as 5x and 2x, or -15 and 90.

Answer:

According to the above statement,

\((10 + 11) + (10 \times 11) + (10 - 11) \\ 21 + 110 - 1 = \boxed{120}\)

Answer:

\(8v^{3} +27=(2v)^{3} +3^{3}=(2v+3)(4v^{2} -6v+9)\\\)

Step-by-step explanation:

from  formula a³ – b³ = (a – b) (a² + ab + b² )

Answer:

C, D, E, F

Step-by-step explanation:

Remember y=mxb?

m is slope and b is y-intercept

so y=2/7x-9

Remember that slope is RISE/RUN so for every 2 squares that you go up, you go 7 squares to the right.

Also remember that since your graph is going thru your Cartiesian Plane in quadrent 4, your y value in your ordered pairs will most probably be a negative.

Please see the image to help you viualize this.

Answer:

x = 2.5y - 1

Step-by-step explanation:

Subtract 2 from both sides

then you get 2x = 5y - 2

then divide everything by 2 for the answer

x = 2.5y -1

Answer:

y = -2x.

Step-by-step explanation:

2y = x - 3

y = 1/2x - 3/2

- so, the slope of this line is 1/2

and the slope of a line perpendicular to it is - 1/ 1/2

= -2.

Using the point slope form of a line the equation of the required line is

y - y1 = m(x - x1)

m = -2, x1 = -1 and y1 = 2.

So,

y - 2 = -2(x - (-1))

y - 2 = -2x - 2

y = -2x - 2 + 2

y = -2x.

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 sample space can be represented as: {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT} where each element represents a sequence of four coin flips, with H representing heads and T representing tails.

In probability theory, the sample space is the set of all possible outcomes of a random experiment or event. It is the set of all possible results that can occur when an experiment is performed. The sample space is an important concept in probability theory because it defines the set of possible events that can occur, and allows us to calculate the probabilities of different events. The probability of an event is defined as the number of outcomes that satisfy the event divided by the total number of possible outcomes in the sample space.

Here,

The sample space of flipping a fair coin 4 times, where H represents the heads side of the coin and T represents the tails side of the coin, consists of all possible outcomes of the 4 flips. Each flip has two possible outcomes, so the total number of possible outcomes is 2 x 2 x 2 x 2 = 16.

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Complete question:

What is the sample space of flipping a fair coin 4 times where h represents the heads side of the coin and t represents the tails side of the coin?

Answer:

x<-3

Step-by-step explanation:

Answer:

C: 2

Step-by-step explanation:

count up 2 from the point (0,3) and over 1 to get to the point (1,5) to get 2/1 or 2. This method is the rise/run method. You rise up 2 units and over 1 unit from each point.

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 5) ← 2 points on the line

m = \(\frac{5-3}{1-0}\) = \(\frac{2}{1}\) = 2

(a) To determine if the market is complete, we need to check if the rank of matrix A is equal to the number of basis assets. The rank of A is 2, but there are 3 basis assets. Therefore, the market in this model is incomplete.

(b) The return on the riskless asset can be calculated by finding the dot product of the price vector S and the riskless asset payoff vector. The riskless asset has a payoff vector of (1, 1, 2), so the return is given by:

Return = S · (1, 1, 2) = 1 (1) + 1 (1) + 2 (2) = 1 + 1 + 4 = 6

Therefore, the return on the riskless asset is 6.

(c) To find the state prices consistent with A and S, we need to solve the equation A' * p = S, where p is the vector of state prices. The transpose of matrix A, denoted as A', is:

A' =

[1, 0, 2; 0, 1, 2; 0, 2, 2]

Solving the equation A' * p = S, we get:

[1, 0, 2; 0, 1, 2; 0, 2, 2] * p = [1, 1, 2]

By solving this system of linear equations, we can find the state prices p. If there are no solutions to the system, then there are no consistent state prices, indicating the presence of arbitrage opportunities.

(d) If there are arbitrage opportunities, the type of arbitrage can be determined based on the sign of the state prices. If all state prices are non-negative, then there is no arbitrage. However, if any of the state prices are negative, it indicates the presence of arbitrage.

To find the arbitrage portfolio, we need to identify a portfolio of assets that has a non-negative initial value and positive future values in all states. The specific arbitrage portfolio would depend on the values of the state prices and the prices of the basis assets.

If there are no arbitrage opportunities (i.e., all state prices are non-negative), we can find the risk-neutral probabilities by normalizing the state prices. The risk-neutral probabilities represent the likelihood of each state occurring in a risk-neutral world.

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To solve the system of equations y = -2x + 8 and y = x + 5 by graphing, we need to plot the graphs of both equations on the same coordinate plane and identify their point of intersection.

To graph the equations y = -2x + 8 and y = x + 5, we can plot points on a coordinate plane to represent the solutions for each equation. For the first equation, y = -2x + 8, we can choose different values of x and calculate the corresponding values of y. For example, when x = 0, y = 8, and when x = 4, y = 0. Plotting these points and drawing a straight line passing through them gives us the graph of y = -2x + 8.

For the second equation, y = x + 5, we can follow the same process. When x = 0, y = 5, and when x = -5, y = 0. Plotting these points and drawing a straight line through them gives us the graph of y = x + 5. Now, we can observe the graph and identify the point where the two lines intersect. This point represents the solution to the system of equations. By selecting the point of intersection on the graph, we can determine the values of x and y that satisfy both equations.

In this case, the point of intersection appears to be (3, 8). Therefore, the solution to the system of equations y = -2x + 8 and y = x + 5 is x = 3 and y = 8. This means that the two equations intersect at the point (3, 8), and these values satisfy both equations simultaneously.

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The graph has y-intercept (0,5) and increases with a constant ratio of 3.

A function in mathematics is a connection between a set of inputs (sometimes referred to as the domain) and a set of outputs (also referred to as the range). Each input value is given a different output value.

The y-intercept lies at (0, 5) because the value of the function at x=0 is 530 = 5. The 'constant ratio' is 3, meaning that any increment of 1 in x causes the function value to grow by a factor of 3. (That serves as the exponential term's foundation.)

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Missing parts;

Which of the following statements is true for a function with equation f(x) = 5(3)*?

The graph has y-intercept (0,5) and increases with a constant ratio of 3.

The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.

The graph has y-intercept (0, 3) and increases with a constant ratio of 5.

The graph has y-intercept (0,5) and decreases with a constant ratio of 3.