Consider the ellipse with equation (x-7)^2/(7)^2 + (y+1)^2/(2)^2 =1. The semimajor axis has length The semiminor axis has length (enter the coordinates of each vertex, The vertices are located at separated by commas) The focal length is (enter the coordinates of each focus, separated by The foci are located at commas)

Start this problem off writing down the slope formula.

m = y2 - y1/x2 - x1

We take our second y minus our first y which in this case is 2 - -3

over our second x minus our first x which in this case is 6 - -2.

So 2 - -3 over 6 - -2 simplifies to 5/8.

So the slope of this line is 5/8.

The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Answer:

for 7 fabric (square meters), he can make 2 cloaks. for 4 cloaks, he needs 14 fabric (square meters).

Answer:

y=-5cos(pi/8(x+2))-21

Step-by-step explanation:

y=acos(b(x-c))+d

Let's find the max and then the min first. We are aiming to find the amplitude, a, which is the half the distance from the max to the min.

Max is y=-16

Min is y=-26

a=(-16--26)/2=-8--13=5

a could also tell us if y=cos(x) has been reflected about the x-axis if it is -5, which it looks like it has considering cos(0)=1 not -1.

I'm looking at the point (-2,-26) which is the lowest point of our curve and comparing it to our high point of (0,1) on y=cos(x).

So far we have, y=-5cos(b(x-c))+d.

Let's look at d, vertical shift. The average of our max and min is (-26+-16)/2=-13-8=-21.

So our vertical shift is d=-21.

So now equation is y=-5cos(b(x-c))+-21.

Now since we are using (-2,-26) as our (0,1) point on y=cos(x) then c=-2.

So now equation is y=-5cos(b(x--2))+-21

Now we are going to plug in a point haven't mentioned to find b. So looking at graph I will use (6,-16).

-16=-5cos(b(6--2))+-21

Add 21 on both sides:

5=-5cos(b(6--2))

Divide both sides by -5:

-1=cos(b(6--2))

Simplify inside:

-1=cos(b8)

Multiplication is commutative:

-1=cos(8b)

8b=pi * cos(pi)=-1

b=pi/8

The equation is

y=-5cos(pi/8(x--2))+-21

Simplify:

y=-5cos(pi/8(x+2))-21

The Cost of the juice per gallon is the $9.

According to the statement, We have to find that the cost of the juice.

So, For this purpose, we know that the

A cost function may be a mathematical formula wont to used to chart how production expenses will change at different output levels.

From the given information:

The price of eight 4.23 ounce juice boxes is $2.39. we should always know that: 1 Gallon = 128 Ounces and 1 juice boxes = 4.23 ounce

So, juice boxes per gallon = 128/4.23 = 30.26

But the worth of 8 juice boxes is $2.39

The value of 1 gallon = (30.26/8) * 2.39 = 9.04

Then,

the price per gallon of the juice = $9

So, The Cost of the juice per gallon is the $9.

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Answer:

Step-by-step explanation:

-11

The total distance Fiona covers in 2 laps is 439.6 meters.

To calculate the total distance Fiona covers in two laps, we first need to find the distance of one lap and then multiply it by 2.

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is a constant equal to approximately 3.14, and r is the radius of the circle.

Given that the course is 70 meters, we know that the diameter of the circle is also 70 meters.

We can find the radius by dividing the diameter by 2:radius (r) = diameter (d) / 2r = 70 m / 2r = 35 m

Now we can use the formula for the circumference of a circle to find the distance of one lap:

C = 2πrC = 2 × 3.14 × 35C ≈ 219.8 m

Therefore, the total distance Fiona covers in 2 laps is 2 × 219.8 = 439.6 meters or approximately 440 meters.

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When 80 inches is converted to feet it will be 6.66667 feet.

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Answer:

They can finish the race in 15 x 14 x 13 x 12 x 11 = 360360 order.

Step-by-step explanation:

There are 15 bicyclists in the race. The first position would come from the first bicyclist to the 15th. Meaning the first position can be occupied by 15 individuals. The second position can only be occupied by 14 individuals since one person is already first. Same way the third, fourth and fifth positions can be occupied by 13, 12 and 11 individuals respectively.

Therefore, they can finish the race in

15 x 14 x 13 x 12 x 11 = 360360 order.

The geometric power series for the function f(x) = 1 / (9 + x), centered at 0, using long division is (9 - x) / ((9 + x) * (9 - x)).

To find a geometric power series for the function f(x) = 1 / (9 + x) using long division, we can start by expanding the function into a fraction:

f(x) = 1 / (9 + x)

To begin the long division process, we divide 1 by 9 + x:

1 ÷ (9 + x)

To simplify the division, we can multiply the numerator and denominator by the conjugate of the denominator:

1 * (9 - x) / ((9 + x) * (9 - x))

Simplifying further:

(9 - x) / (81 - x^2)

Now, we have expressed the function f(x) as a fraction with a simplified denominator. To find the geometric power series, we can rewrite the denominator using the concept of a geometric series:

(9 - x) / (81 - x^2) = (9 - x) / (9^2 - x^2)

We can see that the denominator is now in the form a^2 - b^2, which can be factored as (a + b)(a - b). In this case, a = 9 and b = x:

(9 - x) / (9^2 - x^2) = (9 - x) / ((9 + x)(9 - x))

Now, we can express the function f(x) as a geometric power series:

f(x) = (9 - x) / ((9 + x)(9 - x))

f(x) = 1 / (9 + x) = (9 - x) / ((9 + x)(9 - x))

f(x) = (9 - x) / (9^2 - x^2) = (9 - x) / ((9 + x)(9 - x))

f(x) = (9 - x) / ((9 + x) * (9 - x))

f(x) = 1 / (9 + x) = (9 - x) / ((9 + x) * (9 - x))

The geometric power series for the function f(x) centered at 0 is given by (9 - x) / ((9 + x) * (9 - x)).

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Answer:

6.4 x 10 to the power of 3

Step-by-step explanation:

always have 1 number after the decimal point and then times by ten to the power of 3.

Answer:

64x10²

Just move it to the left 2 times.

Answer:

  8

Step-by-step explanation:

Put the numbers where the variables are and do the arithmetic.

  13 -0.75w +8x

  = 13 -0.75(12) +8(1/2) . . . . . substitute for w and x

  = 13 -9 +4

  = 4 +4

  = 8

A "required parameter" requires an assigned value for the argument used to call the method, while "optional parameters" do not need to be included in the method call and have a default value assigned to them.

The type of parameter that requires that the argument used to call the method must have an assigned value is a "required parameter".

Required parameters are parameters that must be included in the method call, and the argument passed for the required parameter must have a value assigned to it. If a required parameter is not included in the method call, or if the argument passed for the required parameter does not have a value assigned to it, an error will be thrown.

In contrast, there are also optional parameters, which are parameters that do not need to be included in the method call. If an optional parameter is not included in the method call, the method will use a default value assigned to the parameter.

In many programming languages, the syntax for specifying required and optional parameters in a method or function call is specified using different symbols, such as parentheses or square brackets.

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Answer:

8 x 8 x 8 = 512

Step-by-step explanation:

Hope this helps! Have a great day :)

Answer:

512

Step-by-step explanation:

LxWxH

8x8x8=512

The nth term of the sequence can be expressed as: \(1 / (n^2)\)

The given sequence is: 1, 2, 1/3, 1/7, 1/25, 1/121, ...

To find an expression for the nth term of this sequence, we can observe that each term is the reciprocal of a specific pattern of numbers: 1, 2, 3, 4, 5, 6, ...

Notice that the numerator of each term follows a pattern of increasing consecutive positive integers: 1, 2, 3, 4, 5, 6, ...

The denominator of each term follows a pattern of perfect squares: \(1^2, 2^2, 3^2, 4^2, 5^2, 6^2, ...\)

Therefore, the nth term of the sequence can be expressed as:

\(1 / (n^2)\)

So, the expression for the nth term of the sequence is \(1 / (n^2)\). This formula will work for n = 1, 2, 3, and so on.

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Answer:

The first one

Step-by-step explanation:

Answer:

Division and subtraction/B

have a good day/night :)

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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Answer:

-4/5

Step-by-step explanation:

To find the slope of a line with two points, we do y2-y1/x2-x1.

y2 is 2. y1 is 6.

2-6 = -4

x2 is 8. x1 is 3

8-3 = 5

-4/5 is the answer meaning it is the slope.

Answer:

Slope of this line = -4/5.

Step-by-step explanation:

The formula is

Slope = (y2-y1)/(x2-x1)  where (x1, y1) and (x2, y2)  are  the 2 points.

So here we have:

(6-2)/(3-8)

= -4/5.

The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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If twice Brittany's age is less than the age of Abraham Lincoln when he died, then the answers are;

2b < 56

n = b - 2

b = n + 2

b < 28

n = b - 2 < 26

Yes, Brittany could be 27 years old and Nate 26

Let Brittany's age = b

Twice Brittany's age = 2 × b = 2b

Lincoln's age = 56

Inequality to represent Brittany's age: 2b < 56

b < 56/2 = 28

Nate's age = n

in terms of Brittany's age: n = b - 2

Isolating b: b = n + 2

Substituting b: b < 28

Solving for b: b < 28 and n = b - 2 < 26

Could Brittany be 27 years old and Nate 26? Yes, Brittany could be 27 years old and Nate 26 as both are within the range defined by the inequality (b < 28 and n < 26).

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The complete question is:

Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death. Write an inequality to represent Brittany’s age, b. Brittany’s brother, Nate, is two years younger than Brittany. Write an equation for Nate’s age, n, in terms of Brittany’s age, b. Rewrite the expression from Part B to get the variable b alone on one side of the equation. (This is also called isolating b.) Substitute the value of b from Part C into the inequality you found in Part A. Solve the inequalities from parts A and D for the variables b and n, respectively. Could Brittany be 27 years old and Nate 26? Why or why not?

Answer:

Jake is incorrect with his methodology for solving these problems

Step-by-step explanation:

Jake is incorrect with his methodology for solving these problems. This is because dividing a number by 10 requires moving the decimal point one digit to the left. When dividing 630 by 10, removing the zero works because by moving the decimal one digit to the left we would simply drop the zero and the decimal would not be needed leaving the answer as 63. However, this does not work on numbers that already have a decimal such as 35.270. This number divided by 10 would be 3.527 but simply removing the 0 like Jake states would give us the incorrect answer of 35.27

Answer:

Step-by-step explanation:

The surface area of the given prism is 386 square inches.

To find the surface area of a prism, we need to find the area of all its faces and add them up.

The given prism has a rectangular base with dimensions of 7 inches by 15 inches, and a height of 4 inches.

The two rectangular faces (front and back) have dimensions of 7 inches by 4 inches,

so each has an area of 7 x 4 = 28 square inches.

The two rectangular faces (sides) have dimensions of 15 inches by 4 inches,

so each has an area of 15 x 4 = 60 square inches.

The top and bottom faces are both rectangles with dimensions of 7 inches by 15 inches,

so each has an area of 7 x 15 = 105 square inches.

Therefore, the total surface area of the prism is:

2(28 sq in) + 2(60 sq in) + 2(105 sq in) = 56 sq in + 120 sq in + 210 sq in

                                                               = 386 sq in.

So, the surface area of the given prism is 386 square inches.

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The transformation that translates the point (4, 5) to the point (12, 13) is:

\(T_{(8,8)}\)

Here we will have a translation:

\(T_{(a, b)}\)

Such that when applied to a point (x, y) we get:

\(T_{(a, b)}(x, y) = (x + a, y + b)\)

Now, let's apply that translation to (4, 5) such that we get (12, 13).

\(T_{(a, b)}(4, 5) = (4 + a, 5 + b) = (12, 13)\)

Then we must have:

4 + a = 12

5 + b = 13

Solving for a and b we get:

a = 12 - 4 = 8

b = 13 - 5 = 8

Then the translation is:

\(T_{(8,8)}\)

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Answer:

4.5 centimeters

Step-by-step explanation:

For the triangle with area 144 square cm:

144 = (1/2)(6)x

144 = 3x, so x = 48 cm

So for the triangle with area 81 square cm:

(1/2)(x)(8x) = 81

4x^2 = 81

x^2 = 81/4 so x = 9/2 = 4.5 cm and

8x = 36 cm

Answer:

4.5

Step-by-step explanation:

The function to model the water used by the car wash on a shorter day is (C) \(4x^{3} +7x^{2} -14x-6\).

To find the function to model the water used by the car wash on a shorter day:

Given that the amount of water used on normal days is given by the equation:

The amount of decrease in water used is modeled by the equation:

To get the function \(C(x)\) that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).

Therefore, the function to model the water used by the car wash on a shorter day is (C) \(4x^{3} +7x^{2} -14x-6\).

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The correct question is shown below:

The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day.

(A) c(x) = 5x3 7x2 − 14x − 6

(B) c(x) = 4x3 7x2 − 14x 6

(C) c(x) = 4x3 7x2 − 14x − 6

(D) c(x) = 5x3 7x2 − 14x 6

Answer:

see below

Step-by-step explanation:

The amount she withdrew is 45*4 =180

405 - 4*45=

405 -180 =225

There is 225 in the account

Answer: a) $225

Step-by-step explanation:

405 - 45 (4) = x

405 - 180 = x

225 = x

Part A: A dot plot would best represent the data shown because a dot plot shows each data point as a dot along a number line, making it easy to see the frequency of each individual score.

Part B: we follow the steps described below to plot a dot plot:

What is a dot pot?

A dot chart or dot plot is  described as a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles.

The stacked dots in the plotted graph reflect the frequency of each score, and the dots themselves represent the individual scores.

The figure reveals that 4 and 3 were the most frequent scores, respectively, and that a score of 12 was an exception.

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