and a friend buy two fruit smoothies and leave a tip. You split the

the value of x? 20

total and your half comes to $3.60. What percent tip (in decimal form)

did you and your friend leave if the fruit smoothies cost $3 each?​

The value of given equation i.e. \(m^{3} -\frac{1}{m^{3} }\) is \(\frac{63}{8}\)

Given a equation i.e.\(\frac{m-1}{m}\)=3 and asked  to calculate the value of the equation  \(m^{3} -\frac{1}{m^{3} }\)

To calculate the value of   \(m^{3} -\frac{1}{m^{3} }\) , Need to use various operations like subtraction and division)

Given .\(\frac{m-1}{m}\)=3

⇒m-1=3m ( cross multiplies 3 and m)

⇒2m=-1( subtraction is used)

⇒m=-\(\frac{1}{2}\)( division is used)

Thefore the value of m in the given equation i.e.\(\frac{m-1}{m}\)=3 is -\(\frac{1}{2}\)

⇒ \(m^{3} -\frac{1}{m^{3} }\)

Here the value of m =-\(\frac{1}{2}\)

Substituting the value of m in the given equation

⇒\((\frac{-1}{2} )^{3}\)-\((-2)^{3}\)

⇒\(\frac{-1}{8}\)+8(addition is used)

⇒\(\frac{64-1}{8}\)

⇒\(\frac{63}{8}\)

Therefore, the value of the given equation i.e.  \(m^{3} -\frac{1}{m^{3} }\) is \(\frac{63}{8}\)

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Nastya's annual payments on the loan will be approximately $7,350.68 (rounded to the nearest cent).

To find Jean's equity as a percent of the house value, we need to calculate the equity and divide it by the house value, then multiply by 100 to get the percentage.

Jean's equity is the difference between the house value and the mortgage amount. So, the equity is $792078.31 - $600,000 = $192,078.31.

To calculate the percentage, we divide the equity by the house value and multiply by 100: ($192,078.31 / $792078.31) * 100 = 24.26%.

Therefore, Jean's equity as a percent of the house value is 24.26%.

Now, let's move on to Nastya's question.

To calculate Nastya's annual payments on a fully amortizing loan, we need to use the formula for calculating the monthly payment:

P = r * PV / (1 - (1 + r)^(-n))

Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the loan
n = Total number of payments

Given:
PV = $622,422
Annual interest rate = 5.2%
n = 10 years

First, we need to convert the annual interest rate to a monthly interest rate: 5.2% / 12 = 0.43333%.

Next, we substitute the values into the formula and solve for P:

P = (0.0043333 * 622422) / (1 - (1 + 0.0043333)^(-10))

Using a calculator, we get P ≈ $7,350.68.

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Answer:

(8,0)

Step-by-step explanation

Answer: no no yes

Step-by-step explanation:

Using arithmetic operation Jude's typing rate is 182 characters per minute, which is option C.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the typing rate in characters per minute, we need use arithmetic operation of division.

Divide the number of characters by the number of minutes -

Typing rate = Number of characters / Number of minutes

In this case, Jude types 1,274 characters in 7 minutes, so her typing rate is -

Typing rate = 1274 / 7 = 182

Therefore, the typing rate is 182 characters/minute.

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(a) Quadrant 1 corner points: (4, 4) and (0, 4). (b) Area(S_3) = 128 square units. (c) Area(S_1) = 128 square units.

(a) The corner points in Quadrant 1, where x≥0 and y≥0, can be found by setting x or y to zero in the given inequalities. For x = 0, we have 30y ≤ 64, which gives y ≤ 64/30. For y = 0, we have 30x ≤ 64, which gives x ≤ 64/30. Therefore, the corner points in Quadrant 1 are (0, 64/30) and (64/30, 0).

(b) To find the area of S_3, we integrate the inequality 30y ≤ 64 - x^2 over the region in Quadrant 3, where x ≤ 0 and y ≤ 0. Integrating with respect to y, we get the bounds 0 ≤ y ≤ sqrt((64 - x^2)/30) and integrating with respect to x, we get the bounds -4 ≤ x ≤ 0. Evaluating the integral, we find the area of S_3 to be 128 square units.

(c) Similarly, to find the area of S_1, we integrate the inequality 30x ≤ 64 - y^2 over the region in Quadrant 1, where x ≥ 0 and y ≥ 0. Integrating with respect to x, we get the bounds 0 ≤ x ≤ sqrt((64 - y^2)/30) and integrating with respect to y, we get the bounds 0 ≤ y ≤ 4. Evaluating the integral, we find the area of S_1 to be 128 square units.

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Answer:

x = 7.3

Step-by-step explanation:

area = base × height / 2

21.9 = 6 × x / 2

43.8 = 6x

x = 7.3

Answer:

7.3

Step-by-step explanation:

The formula to find the area of a triangle is (1/2)(a)h = A.

Replace the variable h (height) with x.

Isolate the x variable (height) in order to find the height value.

(1/2)(6)x = 21.9

3x = 21.9

x = 21.9/3

x = 7.3

The standard deviation of quiz scores is 0.

To find the standard deviation:

Therefore, the standard deviation of quiz scores is 0.

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Answer:

The 8 oz has lower unit rate, it's lower by .2.

Step-by-step explanation:

8 oz divided by $6 = $1.333 for 1 oz  ---- (round to 1.3)

6 oz divided by $4 = $1.5 for 1 oz

The answer is <1,-1,1>.The given surface is In(xyz) + x² + y² + z² = 3.The gradient of the function f(x,y,z) = In(xyz) + x² + y² + z² = 3 is given by:grad f(x,y,z) = At the point P = (1,-1,-1), we have grad f(P) = <-1,-3,-2>.

Hence the equation of the tangent plane to the given surface at P is given by:-1(x - 1) - 3(y + 1) - 2(z + 1) = 0Simplifying we get x - 3y - 2z = -4Taking dot product of this normal vector <1,-3,-2> with each of the given vectors we get the following results:<1,1,0>.<1,-3,-2> = -5 ≠ 0<1,1,-1>.<1,-3,-2> = 0  [Answer]<-1,1,1>.<1,-3,-2> = 0<1,0,-1>.<1,-3,-2> = -5 ≠ 0<1,-1,1>.<1,-3,-2> = 0

Therefore the vector 0 <1,1,-1> is orthogonal to the tangent plane of the given surface at the point (1,-1,-1).Hence the correct option is 0 <1,1,-1>.

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Answer:

h + 10 = 24

Step-by-step explanation:

h = 24 - 10

h = 14

Answer:

h+10=24

Step-by-step explanation:

h+10=24

collect like trems

h= 24-10

subtract the numbers to find h

h=14

The factored form of 2x^3 + 11x + 15 is:

(2x + 1)(x^2 + 5) + 15

To factor 2x^3 + 11x + 15, we need to find two binomials that multiply to give us the expression.

One way to approach this is to use a method called grouping. We can first group the first two terms and the last two terms:

2x^3 + 11x + 15 = (2x^3 + 10x) + (x + 15)

Notice that we factored out a common factor of 2x from the first two terms, and a common factor of 1 from the last two terms.

Next, we can factor each group separately:

2x^3 + 10x = 2x(x^2 + 5)

x + 15 = 1(x + 15)

Putting these factors together, we get:

2x^3 + 11x + 15 = 2x(x^2 + 5) + 1(x + 15)

Therefore, the factored form of 2x^3 + 11x + 15 is:

(2x + 1)(x^2 + 5) + 15

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Answer:

You can find slope of line using the slope formula. The slope formula is Y2-Y1/X2-X1. Substitute in the points and solve.

6-2/6-5

4/1

4

The slope of the line is 4.

Hope this helps! :)

A. State-space model of the nonlinear system dynamics, and it is valid only in the vicinity of the equilibrium points.

The state-space model of the nonlinear system dynamics is given by the following equations:

where

B. Equilibrium points

The equilibrium points of the system are given by the solutions to the system of equations x = 0. These equations are:

```

Assuming that x1c = R, which is the nominal point for r in orbit, we can solve for the equilibrium points as follows:

C. Linearized state-space representation of the system

The linearized state-space representation of the system is given by the following equations: x = Ax + Bu

where

This is a simplified version of the nonlinear system dynamics, and it is valid only in the vicinity of the equilibrium points.

The state-space model of a dynamical system is a mathematical representation of the system that uses state variables to describe the system's behavior.

The state variables are a set of variables that completely describe the system's state at a given time. The state-space model is typically used to analyze the stability and controllability of dynamical systems.

In the case of the satellite orbit-plane motion system, the state variables are r, θ, r, and θ˙. The state-space model of the system describes how these state variables evolve over time.

The equations of the state-space model can be used to analyze the stability of the system's equilibrium points. They can also be used to design controllers for the system.

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Answer:

dividing 10 by 1.2

Step-by-step explanation:

Answer: This question cannot be answered.

Explanation:

If you add three odd numbers, the sum must also be an odd number. To get an even number, you have to add an even number of odd numbers, e.g. 2 or 4. Adding 3 odd numbers to get 30 is therefore not possible. So the question cannot be answered.

Answer:

7

Step-by-step explanation:

part B is the correct answer

Answer:

B) 7

Step-by-step explanation:

f(x)=2(3)+1

2(3)=6

6+1=7

\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

Among the given relations {(1,4),(2,5), (3,6), (4,7)} represents a function.

Given three options as under:

1)  {(1,4), (2,5), (3,6), (4,7)}

2)  {(1,4), (2,4), (3,5), (6,10)}

3) {(-3,9), (-2,4), (0,0), (1,1), (-3,8)}

We are required to choose the relation which represents a function.

Function is basically from a set X to a set Y assigns to each element of X exactly one element of Y.

Among the given options the relation which is a function is

{(1,4),(2,5), (3,6), (4,7)} because the other options have two values for one value of x or one value is giving two values of y which is opposite to the characteristics of a relation to be a function.

Hence among the given relations {(1,4),(2,5), (3,6), (4,7)} represents a function.

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The length of the line segment AC is 25.5 cm.

A line segment in geometry is a section of a line that has two clearly defined ends as its boundaries. It may be compared to a straight line that has two points where it begins and ends. Letters or points on the line, such as A and B, are frequently used to represent the two ends of a line segment. In contrast to a line, which extends forever in both directions, a line segment has a limited length. A ruler or other measuring device can be used to determine the length of a line segment.

To find the length of segment AC, we can use the fact that the sum of the lengths of two segments on a line is equal to the length of the entire line. That is:

AB + BC = AC

Substituting the given values, we get:

12 cm + 13.5 cm = AC

Simplifying:

AC = 25.5 cm

Therefore, the length of segment AC is 25.5 cm.

There is only one possible answer for the length of segment AC since it is uniquely determined by the lengths of segments AB and BC.

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The random variable X represents the number of days Ellen practices music in a selected week.

Probability distribution table for X:

X (Number of Days) | P(X)

0 | 0.03

1 | 0.04

2 | 0.08

3 | 0.85

In the table, P(X) represents the probability of Ellen practicing music for a certain number of days in a selected week. For example, P(X = 0) is 0.03, indicating the probability of Ellen not practicing music for any of the three days in a week is 0.03.

The other characteristic required for a probability distribution function to be discrete is that each individual probability must be between 0 and 1 (inclusive). In other words, the probabilities cannot be negative or greater than 1. This ensures that the probabilities represent valid chances of occurrence within the given context.

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To clean the office building's 200-gallon aquarium It will take Candice 20 minutes to drain the entire 200-gallon aquarium.

To clean the office building's 200-gallon aquarium, Candice needs to remove the fish and drain the water. The water drains at a constant rate of 10 gallons per minute.
So, the time it takes to drain the entire 200-gallon aquarium can be calculated by dividing the total volume of water by the drain rate.
200 gallons / 10 gallons per minute = 20 minutes
Therefore, it will take Candice 20 minutes to drain the entire 200-gallon aquarium.

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The equivalent of the equation ¼(8x +56) = 20 are 2x = 6 and 56+8x = 80

Two equations are said to be equivalent when they have the same solution set. For example, x + 2 = 6 and 2x = 8 are equivalent equations.

This is because x +2 = 6 can also be simplified by collecting like terms,

x+2 = 6

x = 6 - 2 = 4

Also 2x = 8

x = 8/2 = 4

This means that x+2 = 6 and 2x = 8 have thesame solution , therefore they are equivalent.

Similarly,

¼(8x +56) = 20 can be simplified by opening the bracket.

= 2x + 14 = 20

2x = 20-14

2x = 6

Also, using 4 to multiply both sides,

¼(8x +56) = 20

8x +56 = 80

therefore the equivalent equation is 2x = 6 and 56+8x = 80

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The rate at which body cover distance is given by speed.

The formual for the speed is,

For the given question, distance is d=34 miles and time is t=4/5 hours.

Substitute the value in the formula to obtain the speed of Camden.

So the speed at which camden cover distance is 85/2 miles per hour.

None of the provided equations help determine the lowest cost for producing the cone-shaped paper cup.

To determine the lowest cost of producing the cone-shaped paper cup, we need to minimize the cost function based on the given conditions.

Let's analyze the provided options:

a) 4(0.257r^2 + 0.257r - 2√90000) = 0

This equation seems incorrect as it involves taking the square root of 90000, which is unrelated to the given problem.

b) 22.4(300d c) 0.254(ar/r^2 dr = 0 ar^2 d

These options are unrelated to finding the lowest cost for producing the cone-shaped paper cup.

d) 0.254(nr^2 + rer, dr r^2 + 300/5) = 0 ar^2

This equation also seems unrelated to the problem at hand.

None of the provided equations help determine the lowest cost for producing the cone-shaped paper cup. It appears that none of the given options are correct or relevant to the problem.

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From the options given, it seems that option c) 0.254(ar/r^2 dr = 0 ar^2 d) is the most likely to represent the equation that will help determine the lowest cost.

To determine the lowest cost of producing the cone-shaped paper cup, we need to find the equation that represents the cost as a function of the cup's dimensions.
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height.
In this case, we are given that the cone-shaped cup holds 100 cm^3 of liquid. So we can write the equation as 100 = (1/3)πr^2h.
We are also given that the slant height, s, is defined as s = 12 + h.
To find the cost, we need to consider the surface area of the cone. The lateral surface area of a cone can be calculated using the formula A = πrs, where A is the surface area, r is the radius, and s is the slant height.
Since the base of the cup is open and not included in the cost calculation, we can ignore the area of the base.
The cost of the material used to produce the cups is given as 0.25 cents per cm^2.
To find the lowest cost, we need to minimize the surface area equation. We can do this by substituting the value of s from the given definition (s = 12 + h) into the equation for surface area (A = πrs).
Now, let's look at the options provided:
a) 4 (0.257r^2 + 0.257r, 1 - 2 90000 -) = 0
b) 22,4 300 d c) 0.254(ar/r^2 dr = 0 ar^2 d d) 0.254_(nr^2 + rer, dr r^2 + 300 5) = 0 ar^2
From the options given, it seems that option c) 0.254(ar/r^2 dr = 0 ar^2 d) is the most likely to represent the equation that will help determine the lowest cost. However, it is important to note that without knowing the full equation and the proper notation, it is difficult to determine the exact equation.

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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:

Step-by-step explanation:The tangent of an angle is the trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle. Example: In the triangle shown, tan(A)=68 or 34 and tan(B)=86 or 43 .

Given two sides

if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)

if leg b is unknown, then. b = √(c² - a²)

for hypotenuse c missing, the formula is. c = √(a² + b²)

Answer:

it’s 3/4

Step-by-step explanation:

it’s right for khan (trigonometric ratios in right triangles)