Tiana was designing a fish tank that could hold 5,364 ml of water. She's already filled the tank a quarter of the way. How many more liters of water does Tiana need to fill up the tank completely?​

The center of the hyperbola is (2, -6), and its vertices are (2, -4) and (2, -8).

Mathematically, the standard form of the equation of a hyperbola is represented by this mathematical expression:

(y - k)²/a² - (x - h)²/b² = 1          .......equation 1.

Where:

From the information provided above, we have the following equation of a hyperbola:

-4x² + y² + 16x + 12y + 16 = 0      .......equation 2.

Next, we would rewrite the given equation of a hyperbola in standard form as follows:

-4x² + 16x + y² + 12y = -16

-4(x - 4x) + y² + 12y = -16

Also, , we add (half the coefficient of the x-term and y-term)² to both sides of the equation as follows:

-4(x - 4x + 4) + (y² + 12y + 36) = -16 -4(4) + 36

-4(x - 2)² + (y + 6)² = 4

Dividing both sides of the equation, we have:

-(x - 2)² + ((y + 6)/2)² = 1

((y + 6)/2)² - (x - 2)² = 1      .....equation 3.

Comparing equation 1 and equation 3, we have:

Center (x, y) = (2, -6)

Vertices (h, k ± a) = (2, -6 + 2) and (2, -6 - 2)

Vertices (h, k ± a) = (2, -4) and (2, -8).

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Answer:

y=4x-9

Step-by-step explanation:

-9=y intercept

up 4 over 1

4/1=4

slope =4

I'll do problems 2 through 6 to get you started.

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Problem 1

You have the correct answer. You add the take home pay of his first job (504.64) to the amount he earns on his second job (40) to get 541.64 as his net monthly income.

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Problem 2

Add up any dollar amount that's leaving his pocket. Only focus on expenses that occur monthly. So we will ignore the one time payment of getting that theme park ticket, and we'll also ignore any gifts he buys.

In the second paragraph of the info you're given, all of the expenses we need are here. He has car insurance (110), gas and maintenance (65), and a cell plan (30). In total, his monthly expenses are 110+65+30 = 205 dollars per month.

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Problem 3

Subtract the net monthly income (problem 1) and the expenses (problem 2) to get the amount of discretionary spending he has

541.64 - 205 = 336.64

This value is a positive number, so that means he has money to do whatever he wants with it such as buying that park ticket or buying those gifts.

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Problem 4

His short-term goals are to buy the Six Flags ticket, and buy gifts for his friends and family. He also wants to buy an e-reader for himself.

These are all short-term goals as they are in a relatively short time window of less than a year.

Add up those values to get

135+200+80 = 415

So his short-term goals will cost a total of $415

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Problem 5

His long-term goals are saving up for college to pay for tuition and books. As the instructions say, long-term goals are ones that you need more than a year in advance to plan for. This is because the expense is much greater compared to those various short-term goal items.

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Problem 6

Subtract 135 from the net monthly income you calculated in problem 1

541.64 - 135 = 406.64

Answer:

\(y = \frac{3}{2}x - 5\)

Step-by-step explanation:

General format for the slope-intercept form of an equation:

\(y = mx + c\)

where:

m = slope

c = y-intercept

\((x_{1} , y_{1})\) = \((2, -2)\)

\((x_{2} ,y_{2})\) = \((4, 1)\)

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

   = \(\frac{1- (-2)}{4-2}\)

   =\(\frac{1+2}{2}\)

m = \(\frac{3}{2}\)

Substituting this value of m into our equation:

\(y = \frac{3}{2}x + c\)

Substituting the coordinates of any of the two points into the above equation to solve for c:

1 = \(\frac{3}{2}\)(4) + c

1 = \(\frac{12}{2}\) + c

1 = 6 + c

Isolate c and make it the subject of the equation:

c = \(1 -6\)

c  = \(-5\)

∴The slope-intercept form of the equation after substituting the calculated values of m and c:

\(y = \frac{3}{2}x + (-5)\)

\(y = \frac{3}{2}x - 5\)

Answer:

poopooooo1p1p1p1pp11p1p1

AAS conguerence rule states that if two congruent triangles have any two pairs of corresponding angles that are equal and one pair of corresponding sides that are equal.

Triangles that are congruent have the same area since all of their matching angles and side lengths are the same.

You are aware that a triangle's three angles add up to 180 degrees. As a result, the third pair of angles is also equal if the first two pairs are (180° - sum of equal angles). Hence, if any two pairs of angles and one pair of corresponding sides are equal, two triangles are said to be congruent. It could be referred to as the AAS Congruence Rule.

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Accoding to the information, the equation would be: Weight = 48.411 + 70.870 * Fuel Capacity and the predicted weight of a small motorcycle would be 618.66 pounds.

To find the equation for a linear regression model, we need to find the slope and y-intercept of the line that best fits the data. According to the above, we can infer that the equation is:

On the othe hand, to evaluate how well the linear regression equation fits the model, we have to look at how closely the trendline (represented by the equation) matches the pattern of the data points. So, we can see that the trendline appears to capture the overall trend in the data fairly well, with a positive slope that reflects the general pattern of increasing weight with increasing fuel capacity.

To use the linear regression model to predict the weight of a small motorcycle with a fuel capacity of 6 gallons, we can simply plug in the value of 6 for Fuel Capacity in the equation:

According to this prediction, a small motorcycle with a fuel capacity of 6 gallons would have an estimated weight of approximately 498.84 pounds.

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By using trigonometry,

we have shown that tan(15°) = 2 - √3.

One of the most significant areas of mathematics, trigonometry has a wide range of applications. T

he study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."

Hence, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.

Angles in trigonometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently employed in computations.

We can use the half-angle formula for tangent to show that:

tan(15°) = tan(30°/2) = (1 - cos(30°)) / sin(30°)

We know that cos(30°) = √3/2 and sin(30°) = 1/2, so we can substitute those values in:

tan(15°) = (1 - √3/2) / 1/2

Simplifying the denominator and multiplying by the reciprocal:

tan(15°) = 2(1 - √3/2)

Simplifying the expression:

tan(15°) = 2 - √3

Therefore, we have shown that tan(15°) = 2 - √3.

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The margin of error for a 95% confidence interval is 0.93.

mean (μ) = 23.4, standard deviation (σ) = 7.6, sample (n) = 254, confidence = 95% = 0.95

α = 1 - C = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

The z score of α/2 is equal to the z score of 0.475 (0.5 - 0.025) which is equal to 1.96.

The margin of error (E) is given by:

\(E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.96*\frac{7.6}{\sqrt{254} } \\\\E=0.93\)

The margin of error for a 95% confidence interval is 0.93.

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An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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If Secant Line RQ and tangent line QX, angle XRQ is labeled 56 degrees, then the measure of angle RXQ is 34 degrees.

Since the line QX is tangent to the circle R, we know that angle QXR is a right angle. We also know that angle XRQ is labeled as 56 degrees. Therefore, we can find angle RXQ using the fact that the sum of the angles in a triangle is 180 degrees.

We have:

m∠RXQ + m∠QXR + m∠XRQ = 180 degrees

Since m∠QXR is a right angle (90 degrees), we can substitute:

m∠RXQ + 90 degrees + 56 degrees = 180 degrees

Simplifying:

m∠RXQ = 34 degrees

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The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

To solve the given system of differential equations, we can use the substitution method to obtain first-order linear differential equations and solve them for x and y. Alternatively, we can apply the operator method to rewrite the system as a second-order linear differential equation.

To solve the given system of differential equations using three different methods - substitution method, operator method, and eigen-analysis method - we start by representing the system in matrix form: Let X = [x y]' and X' = [x' y']'. The given system can be written as: X' = A * X + B, where A is the coefficient matrix and B is the vector of constants.

Substitution Method:

In this method, we substitute the expressions for x' and y' from the given system into the equations and solve for x and y. By substituting the given expressions, we obtain two first-order linear differential equations. We can then solve these equations using standard methods such as separation of variables or integrating factors to find the solutions for x and y.

Operator Method:

The operator method involves defining operators D = d/dt and E = d/de, where t is the independent variable and e is the exponential function. We can rewrite the given system as a single second-order linear differential equation in terms of these operators. By manipulating the equations using operator algebra, we can find the characteristic equation and the solutions for x and y.

Eigen-analysis Method:

The eigen-analysis method involves finding the eigenvalues and eigenvectors of the coefficient matrix A. By calculating the eigenvalues, we can determine the type of critical points in the system. The eigenvectors corresponding to the eigenvalues provide the basis for the solutions. Using the eigenvalues and eigenvectors, we can construct the general solution for the system. Lastly, the eigen-analysis method helps us determine the critical points and construct the general solution using eigenvalues and eigenvectors.

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To be able to understand this question, we need to understand what each of the terms we are using mean.

Rotation is simply turning the figure using a specific point. For example , a case of doing a 360 turn around of a vehicle.

Dilation is simply increasing the dimension of the said object. In simpler terms, we are magnifying the dimensions

Reflection simply works with a mirror. When we get a mirror image, then we are reflecting

and Lastly translation. We are simply moving the given object in its entirety(no sides get left out) a particular distance without a change in size or dimension of the object.

Now let us take on the individual options

1. This is a reflection

We can see that the shape of the Deer appears to be in front of an object (mirror) which has helped to change the way it looked

2. This is a Dilation

We can see that the dimenion of the object was increased. In simpler terms, we can see that it was zoomed

3. This is a Rotation

The Bicycle in this case simply moved from a specific position to another at a certain angle (like moving around a ring road junction)

4. This is Translation

The Panda was simply moved in its entirety from one point to the other.

Summarily, we have the following for each of the images;

1. Reflection

2. Dilation

3. Rotation

4. Translation

Answer: 2x-3=10

(x=the number)

Answer:

Step-by-step explanation:

You want to know the number of adult ticket sold if there were 61 fewer student tickets sold and the total number sold was 689.

Let a = the number of adult tickets sold. Then a-61 is the number of student tickets sold, and the total is ...

  a + (a -61) = 689

Simplifying, we get

  2a -61 = 689

  2a = 750 . . . . . . add 61

  a = 375 . . . . . . . divide by 2

The number of adult tickets sold was 375.

__

Additional comment

The number of student tickets is 375-61 = 314.

Answer:

-63

Step-by-step explanation:

-63 plus 52 is-11. have a good day

Answer:

Step-by-step explanation:52+x=-11

X=-63

Answer:

6

Step-by-step explanation:

220-100=120, 120/20=6

Pan tool do the data analyst use to select the area on the map representing Finland.    

What is data analyst?

A data analyst is working with the world happiness data in table. To use Pan tool to select the area on the map representing Finland.

A data professional examines data to uncover critical insights about a company's consumers and how the data may be utilized to address problems. They also share this information with corporate executives and other stakeholders.

Pan allows us to shift the map to focus on it or present the areas in the way we wish. Simply pick the Pan Option and move the map around to suit your needs. Alternatively, you may move the map by holding down the Shift key.

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Answer:

She would be at an elevation of 1314 meters.

Step-by-step explanation:

1245 - 475 + 544

Answer:

20m

11m

20m2

5m

11m

8x8

11x2

All the events in the sample space that are not part of the specified event are called Complement of Event.

Complement of event:

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

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We are given the production function of the economy to be Y=F(K,L)=1.0K^3/2L^1/2. It is also given that people generally save 32.3% of their income and that 14.2% of the capital stock depreciates per year. And we are also given that the economy has 38 units of capital per worker.

The steady state value of output can be defined as the value of output when the capital stock, labor and production become constant. Therefore, Y/L = f(K/L)

= K^3/2 / L^1/2Y/L

= K^3/2 / (K/L)^1/2Y/L

= K^3/2 / (K/L)^1/2

= K^3/2 L^1/2 / K

= K^1/2 L^1/2where Y/L is output per worker. Therefore, we can substitute the values given to us and solve for Y/L.K/L = 38, S

= 0.323, and δ

= 0.142K/L

= S/δK/L

= 0.323/0.142K/L

= 2.28Therefore, K

= (2.28)LTherefore, the economy's steady-state value of output is 1.512. Hence, 1.512.

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The base of an exponent is a number that is increased to a definite power. So, the base of an exponent defines the number that is multiplied by itself.

The exponent means how many times the base number is multiplied.

The power can be expressed as the number obtained by increasing the base number to the exponent.

So, in the power \(a^{n}\), the letter “a” is the base. The letter n is the exponent.

It says, a is multiplied by itself n number of times.

Example - (-5) ² = (-5) × (-5) = 25

Example: (-5)³ = (-5) × (-5)× (-5) = -125

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Answer:

B

Step-by-step explanation:

To find which ordered pairs are solutions to the inequalities we can simply plug in the x and y values of the ordered pairs into the inequalities and if the equation is true for both inequalities then the ordered pair is a solution to the inequalities.

For (0,0)

x = 0

y = 0

y > x + 5

Substitute 0 for y and x

0 > 0 + 5

Simplify right side

0 > 5

The inequality is not true as 5 is greater than 0, not less than. So immediately we can eliminate answer choice A.

For (5,1).

x = 5

y = 1

y > x + 5

Substitute 5 for x and 1 for y

1 > 5 + 5

Simplify right side

1 > 10

Again, the equation is not true as 1 is not greater than 10. This means that c cannot be the answer

For (3,7)

x = 3

y = 7

y > x + 5

Substitute 3 for x and y for 7

7 > 3 + 5

Simplify right side

7 > 8

7 is not greater than 8 meaning that (3,7) cannot be a solution to the inequalities

None of the ordered pairs created true equations hence the answer is B

The sample space in this problem is the total number of married couples who were studied for their personality type preferences.

The sample space is the set of all possible outcomes or events in a particular study or experiment. In this case, the sample space refers to the total number of married couples who were included in the study on personality type preferences. It is the entire population of interest for this problem, and it includes all the couples who were surveyed and their respective scores on the personality type preferences.

The data provided in the question is a representation of the sample space, and it shows the number of married couples with different levels of similarity in their personality type preferences.
The sample space in this problem, which refers to the total number of possible outcomes, can be found by summing the number of married couples with each level of similar preferences.

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You solve the first two the same way