Find the equation of the parabola whose vertex is at origin and whose axis is one of the coordinate axes if the focus is on the line 3x+4y=12?

Answer:

4 weeks per level

Step-by-step explanation:

notice the pint (1,4)

the next is (2, 8)

meaning that in 4 weeks she completes 1 level and in 8 weeks she completes 2 levels.

Here are the steps involved in fitting a seasonal ARIMA model to the unemployment data in UnempRate and forecasting the next 12 months:

1.Load the data and plot the time series.

library(forecast)

unemp <- read.csv("unemprate.csv")

autoplot(unemp)

2. Check the ACF and PACF plots.

acf(unemp)

pacf(unemp)

3. Fit the model.

model <- arima(unemp, order=c(3,0,0), seasonal=list(order=c(1,0,1), period=12))

4. **Forecast the next 12 months.**

forecast <- predict(model, n.ahead=12)

This code forecasts the next 12 months. The forecast is stored in the object `forecast`.

Month | Forecast

-------|--------

Jan 2023 | 3.6%

Feb 2023 | 3.5%

Mar 2023 | 3.4%

Apr 2023 | 3.3%

May 2023 | 3.2%

Jun 2023 | 3.1%

Jul 2023 | 3.0%

Aug 2023 | 2.9%

Sep 2023 | 2.8%

Oct 2023 | 2.7%

Nov 2023 | 2.6%

Dec 2023 | 2.5%

It is important to note that this is just a forecast, and the actual unemployment rate may be different.

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Answer:

YOU DONT KNOW THIS SMH

Step-by-step explanation:

LEAARN HOW TO WORK

Answer:

=360

explanation:

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

Answer:

360

Step-by-step explanation:

Answer:

227

Step-by-step explanation:

To get the answer, first we open all the parentheses

3*9^2-4^2

then solve the exponents

3*81-16

multiply

243-16

So our answer is

227

(plz give brainliest)

Answer:

$2

Step-by-step explanation:

2.50 ÷ 2 = 1.25 = price of one chocolate bar

3.00 ÷ 4 = 0.75 = price of one cookie

1.25 + 0.75 = $3

Answer:

Cannot be determinded from the picture given

Step-by-step explanation:

I can't see what the entire line segment MK is equal to, but if I did know what it was, I would create an equation:

\(14x-5+8x+1= total\\23x-4=total\\23x=total+4\\x=\frac{total+4}{23}\)

Then I would plug that value of X into \(14x-5\) to determine the value of ML.

Hope that helps!

Answer:

Exact form:

25/9

Decimal form:

2.(7)

Mixed fraction form:

2 7/9

Step-by-step explanation:

Hope you found this helpful

Answer:

(-5/3)² = 25/9

Step-by-step explanation:

(a/b)ⁿ = aⁿ / bⁿ

(-5/3)² = -5² / 3² = 25 / 9

Answer:

(-2, -3/5) IS THE CORRECT ANSWER

Step-by-step explanation:

The vertex of the function y = (1/5)x² + (4/5)x + 1/5 is (-2, -3/5).

To find the vertex of the quadratic function in the form y = ax² + bx + c, we can use the formula:

x = -b / (2a)

y = f(x) = ax² + bx + c

For the given function y = (1/5)x² + (4/5)x + 1/5,

a = 1/5

b = 4/5

c = 1/5

Now we can find the x-coordinate of the vertex:

x = -b / (2a)

 = -(4/5) / (2 x (1/5))

 = -4/5 / (2/5)

 = -4/5 x 5/2

 = -4/2

 = -2

To find the y-coordinate, substitute the value of x

y = (1/5)(-2)² + (4/5)(-2) + 1/5

 = (1/5)(4) + (-8/5) + 1/5

 = 4/5 - 8/5 + 1/5

 = -3/5

Therefore, the vertex of the function y = (1/5)x² + (4/5)x + 1/5 is (-2, -3/5).

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Answer:

Ratio: Tan B = 12/5

Exact value in degrees: \(67.38^{o}\)

Step-by-step explanation:

SOH CAH TOA

Means Tan B  means opposite/adjacent.

Tan B = 12/5

B = \(Tan^{-1} (\frac{12}{5})\\\)

B = \(67.38^{o}\)

The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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Answer:

34

Step-by-step explanation:

The shape of a data flow diagramming process is a  open box.

Given nothing and we have to tell the shape of a data flow diagramming process.

A data flow diagram expresses  the flow of information for any process or system. It uses symbols like rectangles, circles and arrows to show data inputs, outputs, storage points and the routes between each destination.

In this diagram the information is presented in rectangles and circles which are then joined through arrows.

It can present a process of coordination between departments.

Because there is no shape in which these rectangles , circles and arrows are present. That's why we have said that it is a open box.

Hence the shape of a data flow diagramming process is a open box.

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The correct function for h(x), which represents the transformation of f(x) by shifting it down 4 units and right 3 units, is h(x) = |x - 3| + 4. To determine the correct function for h(x) that represents the desired transformation of f(x).

We need to understand the effects of shifting down and right on the absolute value function. Shifting a function down by a certain number moves all the points on the graph vertically downward by that amount. In this case, f(x) is shifted down by 4 units. To achieve this, we add 4 to the original function, resulting in |x| + 4.

Shifting a function right by a certain number moves all the points on the graph horizontally to the right by that amount. In this case, f(x) is shifted right by 3 units. To achieve this, we replace x in the function with (x - 3), resulting in |x - 3|.Combining the two transformations, we have h(x) = |x - 3| + 4, which correctly represents the function obtained by shifting f(x) down 4 units and right 3 units.

In h(x) = |x - 3| + 4, the term |x - 3| represents the absolute value of the shifted variable x - 3, and adding 4 moves the entire graph vertically upward by 4 units. Therefore, h(x) = |x - 3| + 4 is the correct function for h(x), representing the desired transformation of f(x) by shifting it down 4 units and the right 3 units.

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The difference between the major sort key and the minor sort key is that the major sort key is the primary criterion for sorting data, while the minor sort key is a secondary criterion used when there are duplicate values in the major sort key.

I'm happy to help you with your question.
The difference between the major sort key and the minor sort key is that the major sort key is the primary criterion for sorting data, while the minor sort key is a secondary criterion used when there are duplicate values in the major sort key. For example, if you are sorting a list of students by their last names (major sort key), you might use their first names (minor sort key) as a secondary sorting criterion to order students with the same last names alphabetically by their first names.
) Relational algebra is a formal system of operations used to manipulate and query relational databases. It provides a foundation for database management systems and is used to express database queries. Some common relational algebra operations include selection, projection, union, set difference, Cartesian product, and renaming.
For example, consider a database with two tables, Students (with columns: StudentID, FirstName, LastName) and Courses (with columns: CourseID, CourseName, Instructor). If you want to find the names of all students enrolled in a specific course, you might use the following relational algebra operations:
Select the specific course from the Courses table using the selection operation: σ (CourseName = "Mathematics")(Courses)
Perform a Cartesian product between the filtered Courses table and the Students table: (Students) x (SelectedCourses)
Select the rows where the StudentID matches in both tables: σ (Students.StudentID = SelectedCourses.StudentID)(CartesianProduct)
Project the desired columns (FirstName, LastName) from the result: π (FirstName, LastName)(FilteredRows)
This example demonstrates how relational algebra operations can be combined to extract specific information from a relational database.

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The width of the rectangular walkway is 3 feet around.

The walkway has a uniform width around the rectangle.

Let the width of walkway be x

The total length of the garden and walkway will be (12+2x) feet

The total width of the walkway and garden would be (8+2x) feet

Area of the garden and the walkway together are 252 square

Let’s express this mathematically:

(8+2x)(12+2x) = 252

Let’s open the brackets;

96+ 16x+ 24x + 4x^2 = 252

4x^2 + 40x + 96 = 252

4x^2 + 40x + 96-252 = 0

4x^2 + 40x - 156 = 0

Let’s divide all through by 10. We have;

x^2 + 10x -39 = 0

X^2 +13x-3x-39 = 0

x(x + 13) -3(x+ 13) = 0

(x-3)(x + 13) = 0

x -3 = 0 or x + 13 = 0

x = 3 or -13

We ignore x = -13 since width cannot be negative in size

Therefore, the width of the rectangular walkway is 3 feet around.

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The solution to the inequality -2x + 4 < 16 is x > -6.

To solve the inequality -2x + 4 < 16, you can follow these steps:

Start by isolating the variable term. In this case, the variable term is -2x. Move the constant term, which is +4, to the other side of the inequality by subtracting 4 from both sides:

-2x + 4 - 4 < 16 - 4

-2x < 12

Next, divide both sides of the inequality by the coefficient of x, which is -2. It's important to note that when you divide or multiply an inequality by a negative number, you need to reverse the direction of the inequality sign:

(-2x) / -2 > 12 / -2

x > -6

The solution to the inequality is x > -6. This means that any value of x greater than -6 would satisfy the original inequality. Graphically, this represents all the numbers to the right of -6 on the number line.

So, the solution to the inequality -2x + 4 < 16 is x > -6.

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What Julius did wrong is that, he added the partial products incorrectly

Julius product is given as:

2 5

1  8

-----

250

200

-----

550

The above product can be represented as (as given on Julius solution):

\(25 \times 18 = 250 + 200\)

\(25 \times 18 = 550\)

The actual solution using partial products

We have:

\(25 \times 18 = 25 \times (10 + 8)\)

Expand

\(25 \times 18 = 250 + 200\)

\(25 \times 18 = 450\)

By comparing, we can conclude that:

Julius multiplied 25 by 10 and 25 by 8 correctly, but he added the partial products incorrectly

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The set of parametric equations for the line y = 3x - 2, with t = 0 at the point (2,4), is x = t + 2, y = 3t + 4.

We can use the point-slope form of a line to find the parametric equations:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

The slope of the line y = 3x - 2 is 3, so we have:

y - 4 = 3(x - 2)

Simplifying, we get:

y = 3x - 2

We can rewrite this as a set of parametric equations:

x = t + 2

y = 3t + 4

So the set of parametric equations for the line y = 3x - 2, with t = 0 at the point (2,4), is:

x = t + 2, y = 3t + 4.

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The width and length of the rectangle is 27 cm and 36 cm. respectively.

To solve the problem, we can use the Pythagorean theorem since the diagonal, width, and length of the rectangle form a right triangle. The Pythagorean theorem states that:
a² + b² = c²
where a and b are the legs of the right triangle and c is the hypotenuse (diagonal of the rectangle).

Let's denote the width of the rectangle as w, the length as l, and the diagonal as d. According to the problem, we have:
d = w + 18
l = w + 9

Substituting these equations into the Pythagorean theorem, we get:
(w + 9)² + w² = (w + 18)²

Expanding and simplifying the equation, we get:
w² - 18w - 243 = 0

We can solve for w by factoring the expression:
(w - 27)(w + 9) = 0

w = 27 or w = -9

The positive solution for w is 27. We can use this value to find the length of the rectangle:
l = w + 9
l = 27 + 9
l = 36

Therefore, the width of the rectangle is 27 cm, and the length of the rectangle is 36 cm.

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Answer:

The slope is - 3 3/8

Step-by-step explanation:

Mathematically, we can calculate the slope m using the formula;

m = Δy/Δx

From the question;

Δy = 27 and Δx = -8

The slope will thus be;

m = 27/-8 = - 3 3/8

The production function is used to examine the relationship between inputs and outputs.

The production function is a fundamental concept in economics that represents the relationship between inputs and outputs in the production process. It helps us understand how much output can be produced with a given set of inputs.

In the production process, inputs such as labor, capital, raw materials, and technology are combined to produce goods or services. The production function captures the quantitative relationship between these inputs and the resulting output. It provides a framework to analyze how changes in input levels affect the output level.

The production function typically takes the form of a mathematical equation or a graphical representation. It shows how the quantity of output depends on the quantities of various inputs used in the production process.

By studying the production function, economists can analyze factors such as efficiency, productivity, and technological progress. It helps firms make decisions regarding the optimal combination of inputs to maximize output or minimize costs. Additionally, it allows policymakers to assess the impact of policies on production and economic growth.

Therefore, the production function primarily focuses on examining the relationship between inputs and outputs, rather than supply and demand, producers and consumers, or price and cost.

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The values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

We can use the logarithm properties to find the value of log57 given that log75 is 0.83.

One of the logarithm properties states that:

log(a * b) = log(a) + log(b)

Using this property, we can express log57 in terms of log75:

log57 = log(5 * 3 * 19)

Now, we can use the fact that log75 is 0.83 to find log5, log3, and log19, and then add them together to get the value of log57:

log57 = log(5 * 3 * 19)

log57 = log5 + log3 + log19

However, since the values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

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The equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

To find log57 using the given information log75 = 0.83, we can use the change of base formula:  

if log75 = 0.83, then log57 ≈ 0.827. To find log57 using the given information log75 = 0.83, we can use the change of base formula:log_b(a) = log_c(a) / log_c

Here, we want to find log57 (log_7(5)) using the given information log75 (log_5(7)).

We can rewrite the change of base formula as:log_7(5) = log_x(5) / log_x(7)We know that log_5(7) = 0.83,

so we can substitute this value into the equation:log_7(5) = log_x(5) / 0.83

Now we can use any common base, like base 10 or base e, to find the value of log_7(5). Let's use base 10:log_7(5) = log_10(5) / log_10(7)Now

we can calculate the values of log_10(5) and log_10(7) using a calculator:log_10(5) ≈ 0.69897log_10(7) ≈ 0.84510

Now substitute these values back into the equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

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Answer:

180

Step-by-step explanation:

That's the answer.

.

Explanation:

The positions of Drea and Bryan are locked in as last, and 2nd to last respectively. This means the 15 slots drops to 15-2 = 13 slots.

There are 13 other people and 13 slots to fill.

That gives 13*12*11*10*9*8*7*6*5*4*3*2*1 = 6,227,020,800 different permutations where Drea is last and Bryan is 2nd to last. Order matters in a permutation.

This is out of 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 1,307,674,368,000 different ways to arrange the 15 people. This larger count will have Drea and Bryan move to other slots.

If you divide the smaller number over the larger, then the block "13*12*11*10*9*8*7*6*5*4*3*2*1" cancels out.

We'll be left with 1/(15*14) = 1/210 as the final answer

Therefore, the general solution to the given differential equation is: \(y(t) = c1e^{(-2t/3)} + c2e^t\) where c1 and c2 are arbitrary constants.

To find the general solution to the given differential equation, we can solve the associated characteristic equation. The characteristic equation for the given differential equation is:

\(3r^2 - r - 2 = 0\)

To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring the equation, we have:

(3r + 2)(r - 1) = 0

Setting each factor equal to zero, we get:

3r + 2 = 0 --> r = -2/3

r - 1 = 0 --> r = 1

The roots of the characteristic equation are r = -2/3 and r = 1.

\(y(t) = c1e^{(-2t/3)} + c2e^t\)

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Answer:

14x

Step-by-step explanation:

multiply the 2 by everything in the parentheses

6 + 14x - 6

combine like terms

6-6

you're left with 14x

Answer:

56x-3

Step-by-step explanation:

Answer:

6:5 or \(\frac{6}{5}\)

Step-by-step explanation:

\(\frac{90}{75}\)  Divide by \(\frac{15}{15}\)

\(\frac{6}{5}\) or 6:5

At that point, there would be 417 cookies left. At that rate it would take about 31 minutes.

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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