The number of coffee shops in a certain country can be modeled by the quadratic function ​f(x)105x²+680x+4296, where​ f(x) is the number of coffee shops and x is the number of years after 2000. Complete parts a and b.
a. Find the number of coffee shops in 2006.
b. If the trend described by the model​ continues, predict the year after 2000 in which the number of coffee shops will be 21;500.

Answer:

9 is a rational number.

Step-by-step explanation:

Answer:

irrational

Step-by-step explanation:

How the number 9 is irrational is that irrational numbers are numbers that are not expressed as fractions or decimals. So some examples of irrational numbers is 1,2,6,22,12,9

can I get brainlest?

Jody will be forced to repay a total of $2,377.69 when the loan matures.

Ordinary interest, commonly referred to as simple interest, is computed by dividing the annual marginal rate by the 365 days that make up a year. It does not take compounding into account.

The number of days can be calculated as follows:

19(Sep), 31(Oct), 30(Nov), and 31(Dec) add up to 111 days in year 1.

Second-year days: 26 (Jan)

137 days in total

Rate = 0.09 Principal = $2,300

time = 137 ÷ 365

Interest = 2300 × 0.09 × (137 ÷ 365) = $77.69

Amount due at maturity is $2,300 plus $77.69, for a total of $2,377.69.

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Step-by-step explanation:

5(-25) + 9(-25) +75 +(-25)

28,175

Answer:

90 degrees

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

First you have to identify the black line at the bottom so it means it's 180 degrees. No notice the red box it means it's 90 degrees. We can conclude from this that the other side of the red box should also equal 90 degrees. So to find x you have to set up this equation: 6x+4+32=90. Then you solve for x which ends up being 9.

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Answer:

The x would be 9

Step-by-step explanation:

9 times 6 equals 54 plus 4 equals 58

the square is 90 degrees and 90 plus 58 plus 32 equals 180 degrees which is the right amount of a flat line

Answer:

in total 21 miles

Step-by-step explanation:

Answer:E

Step-by-step explanation:

just took the test

The atmosphere is divided into five different layers, based on temperature.

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The teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

In order to help the students understand that the triangle is equivalent to half a square, the teacher can adopt different methods, including the following:

1. Drawing diagrams of the triangle and the square to show the comparison. The teacher can draw diagrams of a triangle and a square on the board and label the different parts.

They can then show the students that a triangle can be created by halving the square diagonally. This way, the students will be able to visualize the comparison and understand it better.

2. Demonstrating the concept practically. The teacher can also demonstrate the concept by using physical objects such as paper or cardboard.

They can show the students how to create a triangle by folding a square diagonally and cutting it along the fold. This way, the students will be able to see the practical application of the concept.

3. Using real-world examples. The teacher can also use real-world examples to help the students understand the concept better.

For example, they can show the students pictures of tents or rooftops that are shaped like triangles and explain how they are related to squares.

4. Conducting group discussions. The teacher can conduct group discussions where the students can share their understanding of the concept and ask questions.

This way, the students will be able to learn from each other and clarify any doubts they may have.

Overall, the teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

The key is to use different approaches that cater to different learning styles and to encourage the students to participate actively in the learning process.

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The unit step response of the system, obtained through the Laplace transform, is s(t) = 0.2u(t) + 2.68\(e^{(-t)}\)cos(t + 50.4°).

To find the unit step response of the system modeled by the transfer function H(s) = (s + 1)/(s² + 2s + 5), we need to perform the inverse Laplace transform of H(s).

First, let's express H(s) in the partial fraction form:

H(s) = A/(s - α) + (Bs + C)/(s² + 2s + 5)

To find the values of A, B, and C, we can equate the numerators:

s + 1 = A(s² + 2s + 5) + (Bs + C)(s - α)

Expanding and equating the coefficients of like powers of s, we get:

s + 1 = (A + B)s² + (2A + C - αB)s + (5A - αC)

Comparing the coefficients, we have the following equations:

A + B = 0 (coefficients of s²)

2A + C - αB = 1 (coefficients of s)

5A - αC = 1 (constant term)

Solving these equations, we find the values:

A = 1/5

B = -1/5

C = 6/5

α = -1

Now, we can rewrite H(s) as:

H(s) = 1/5/(s + 1) - 1/5s + 6/5/(s² + 2s + 5)

Taking the inverse Laplace transform of each term, we get:

h(t) = (1/5)\(e^{(-t)}\) - (1/5) + (6/5)\(e^{(-t/2)\)cos((√(19)/2)t - atan(1/√(19)))

The unit step response is obtained by multiplying h(t) by the unit step function u(t):

s(t) = u(t) × [(1/5)\(e^{(-t)}\) - (1/5) + (6/5)\(e^{(-t/2)\)cos((√(19)/2)t - atan(1/√(19)))]

After simplifying the expression, we find that the unit step response of the system is:

s(t) = 0.2u(t) + 2.68\(e^{(-t)}\)cos(t + 50.4°)

Therefore, the correct answer is option B: s(t) = 0.2u(t) + 2.68\(e^{(-t)}\)cos(t + 50.4°).

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Find the unit step response of the system modeled by the following transfer function H(s) =(s+1)/s²+2s+5

A. s(t) = 0.2u(t) +0.446e^{-t} cos(2t - 116.5°)

B. s(t) = 0.2u(t) +2.68e^{-t} cos(t + 50.4°)

C. s(t) = u(t) - 2.3e^{-t} cos(2t -85.3°)

D. none of these

Answer:

F=ma

F=1250*40

F=50000N

The diameter of the circle is √74. Answer: C.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.

To find the diameter of the circle, we need to find the distance between points A and B, which will give us the length of the diameter.

Using the distance formula, we have:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) = (-3, 6) and (x2, y2) = (-8, -1).

Plugging in the values, we get:

d = √[(-8 - (-3))² + (-1 - 6)²]

= √[(-5)² + (-7)²]

= √[25 + 49]

= √74

Therefore, the diameter of the circle is √74. Answer: C.

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Answer:

x=75

Step-by-step explanation:

180-165=15

15+90=105

180-105=75

Answer: true

Step-by-step explanation:

Answer: True, these both exist.

The grams of antimony present in the alloy is 80 grams

To find the grams of antimony present in the alloy we have use the formula:

\(Weight = (\frac{Mass\: Compound}{Mass \:alloy}) \times100\)

Here Weight = 16

Mass alloy = 500

Mass Compound = ?

\(16 = \frac{Mass compound}{5}\)

Mass compound = 16 * 5 = 80 grams

The grams of antimony present in the alloy is 80 grams

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An independent basic service set (IBSS) does not consist of any access points.

In an IBSS, devices such as laptops or smartphones connect with each other on a peer-to-peer basis, forming a temporary network. This type of network can be useful in situations where there is no existing infrastructure or when devices need to communicate with each other directly.

Since an IBSS does not involve any access points, it is not limited by the number of access points. Instead, the number of devices that can be part of an IBSS depends on the capabilities of the devices themselves and the network protocols being used.

To summarize, an IBSS does not consist of any access points. Instead, it is a network configuration where wireless devices communicate directly with each other. The number of devices that can be part of an IBSS depends on the capabilities of the devices and the network protocols being used.

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Answer:

37,640

Step-by-step explanation:

MATHSSSS

Answer:

37,640

Step-by-step explanation:

its so simple good luck

Answer:

53.89%

Step-by-step explanation:

total no. obtainable = 80 + 100 = 180

total scores acquired = 22 + 75 = 97

percentage = (total acquired/total possible) × 100

= (97/180) × 100

= 53.89 %

Let be x the amount the owner withdrew. Then, we can write and solve the following equation:

Answer

The owner withdraws $2,000.

Answer:

Answer:

Here is a answer to the question

Answer:

145°

Step-by-step explanation:

because opposite angles r equal

To use a triple integral to find the volume of the solid bounded by the surfaces z and z over the rectangle.

1. Determine the limits of integration for the rectangular region: Let's say the rectangular region is given by x ranges from a to b, y ranges from c to d, and z ranges from f(x, y) to g(x, y).

2. Set up the triple integral: The triple integral will have the form:
  ∫∫∫(dV) = ∫[a, b] ∫[c, d] ∫[f(x, y), g(x, y)] (dz dy dx)

3. Evaluate the innermost integral: Compute the integral with respect to z, keeping x and y constant.
  ∫[f(x, y), g(x, y)] (dz) = g(x, y) - f(x, y)

4. Substitute the result into the original triple integral: Now we have:
  ∫∫∫(dV) = ∫[a, b] ∫[c, d] (g(x, y) - f(x, y)) (dy dx)

5. Evaluate the remaining integrals: Compute the double integral by first integrating with respect to y, then with respect to x.

6. The result of the final integration will be the volume of the solid bounded by the surfaces z and z over the rectangle.

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a) y=-2780.85+1.447x

b) There are 142.09 voters estimated in the year 2012

Regression analysis is a group of statistical techniques used in statistical modelling to identify relationships between a dependent variable and one or more independent variables. The dependent variable is frequently referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon (often referred to as "predictors," "covariates," "explanatory variables," or "features"). The line (or more complex linear combination) that most closely matches the data in terms of a specified mathematical criterion is found in linear regression, the most common type of regression analysis. For instance, the line (or hyperplane) that minimises the sum of squared differences between the real data and that line is determined when using the ordinary least squares approach (or hyperplane).

x = 11940 / 6 = 1990y = 593.8/6 = 98.9667

let the regression equation be y = a + bx

b = \(\frac{ ∑xy - nxy }{∑x^{2} -nx^{2} }\) = \(\frac{1182067 - 6 * 1990 * 98.9667}{23760880 - 6 * 1990^{2} }\) = 1.447

a = y - bx = 98.667  -  1.447 x 1990 = -2780.85

The regression equation is

x = 2020 in regression equation

substituting x=2020 in the regression equation

y = 142.09

There are 142.09 voters estimated in the year 2012

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Answer:

The expected mass of the sample in the year 2009 is approximately 60 miligrams.

Step-by-step explanation:

The mass of radioactive isotopes decays exponentially in time, the equation that represents this phenomenon is presented below:

\(m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }\) (1)

Where:

\(m(t)\) - Current mass of the radioactive isotope, in miligrams.

\(m_{o}\) - Initial mass of the radioactive isotope, in miligrams.

\(t\) - Time, in years.

\(\tau\) - Time constant, in years.

First, we must find the time constant associated to the decay of the radioactive isotope by clearing the respective term in (1):

\(-\frac{t}{\tau} = \ln \frac{m(t)}{m_{o}}\)

\(\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }\)

If we know that \(t = 5\,y\), \(m(t) = 190\,mg\) and \(m_{o} = 800\,mg\), then the time constant is:

\(\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }\)

\(\tau = -\frac{5\,y}{\ln \frac{190\,mg}{800\,mg} }\)

\(\tau \approx 3.478\,y\)

Now, we calculate the mass of the radioactive isotope in 2009 (\(t = 9\,y\)). If we know that \(t = 9\,y\), \(\tau \approx 3.478\,y\) and \(m_{o} = 800\,mg\), then the mass of the radioactive isotope is:

\(m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }\)

\(m(9\,y) = (800\,mg)\cdot e^{-\frac{9\,y}{3.478\,y} }\)

\(m(9\,y) \approx 60.155\,mg\)

The expected mass of the sample in the year 2009 is approximately 60 miligrams.

Answer:

y = 2(x + 4)² - 6

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define function

y = 2x² + 16x + 26

Step 2: Find vertex form

\(The given equation is h(t)= −2.5t² + 94t + 15 where h is the height of the ball in meters tt seconds after it has been thrown.\)

To find the maximum height of the ball, we need to find the vertex of the parabolic equation. We know that the x-coordinate of the vertex is given by\(:\[\frac{-b}{2a}\]Where, a = -2.5, b = 94h(t) = −2.5t² + 94t + 15 => h(t) = -2.5(t - 18.8)² + 351.5\)

Thus, the maximum height reached by the ball is 351.5 m and the time at which it happens is 18.8 seconds after the ball has been thrown.

An alternate way to solve this is to differentiate the equation and equate it to zero to find the maximum. But we are not given the differential equation, and that's why we are going with the vertex method.

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We have the following information; a ball is thrown into the air and its position is given by h(t) = −2.5t² + 94t + 15

where h is the height of the ball in meters tt seconds after it has been thrown.

To find the maximum height reached by the ball and the time at which that happens

we need to complete the square as follows;

h(t) = −2.5t² + 94t + 15

=> h(t) = -2.5(t² - 37.6t - 6)

The square of half of the coefficient of t is added and subtracted from the expression inside the bracket above.

The value subtracted is compensated by multiplying by 2.5 to ensure the overall value of h(t) is not altered.

h(t) = -2.5(t² - 37.6t + (37.6/2)² - (37.6/2)² - 6)

=> h(t) = -2.5(t - 18.8)² + 482.7

When t = 18.8,

h(t) is maximum and given by;

h(18.8) = -2.5(18.8 - 18.8)² + 482.7

=> h(18.8) = 482.7

The maximum height reached by the ball is 482.7m and the time at which that happens is 18.8s.

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