Lily mixed a batch of punch for the class party. Her recipe called for 2 1/2 cups of orange juice, 1 1/2 cups lemonade, and 3 quarts of ginger ale. How many 1-cup servings does the recipe make?

Since the polynomial given has both positive and negative terms, the shaded region representing the area of the polynomial should have both positive and negative areas.

This means that the area under the curve should cross the x-axis at least once. Looking at the options, only option C has a shaded region that crosses the x-axis, which means that the area represented by the shaded region includes both positive and negative areas. Therefore, option C is the correct figure with a shaded region that has an area equal to the given polynomial.

The shaded region in the graph represents the area between the curve of the function and the x-axis, and the height of the shaded region is given by the value of the function at each point along the x-axis. When the function has both positive and negative values, it means that the area above the x-axis cancels out some of the area below the x-axis, resulting in a net area that may be positive, negative, or zero.

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Answer:

640 cm²

Step-by-step explanation:

The ratio of the area of 2 similar polygons = the ratio of the square of their corresponding lengths

Thus:

Area of Trapezoid ABCD to Area of Trapezoid EFGH = AB² to EF²

Area of Trapezoid ABCD = ? = x

Area of Trapezoid EFGH = 40 cm²

AB = 20 cm

EF = 5 cm

Substitute

x:40 = 20²:5²

x/40 = 400/25

x/40 = 16

Cross multiply

x = 16*40

x = 640

Area of trapezoid ABCD = 640 cm²

The distance Brett covered was 12 km, but his displacement was 8.6 km.

Displacement is a vector quantity that is measured as a change in an object's position, so the length of the position from the object's initial point to the object's end point.

Distance is a scalar quantity which is defined as the length of the entire path traveled by an object.

Given:

Distance = S₁ + S₂

Distance = 7 + 5

Distance = 12 km

The distance Brett has covered is 12 km.

Starting position = A

Final position = C

Displacement = AC

The displacement in this case is calculated by the Pythagorean theorem.

AC² = AB² + BC²

Displacement² = S₁² + S₂²

Displacement² = 7² + 5²

Displacement² = 49 + 25

Displacement² = 74

Displacement = \(\sqrt{74}\)

Displacement = 8.6 km

The displacement that Brett has covered is 8.6 km.

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Answer:

g=-12

Step-by-step explanation:

3+g=-9

-3     -3

g=-12

Answer:

Alrighty so number one is 5 z (x + 2y), and number two is 13x + 19y - 34z

1. Component form of a force vector: An engineer analyzes forces on a car's suspension system during turns. Breaking down the force vector into components ensures stability and safety.

2. Overlaying a polar coordinate system: Air traffic controllers use polar coordinates to guide aircraft during landings, accurately representing positions relative to a control tower for efficient airspace management and safety.

Let us discuss in a detailed way:

1. To find the component form of a force vector, let's consider the following real-world situation:

Imagine you are an engineer designing a suspension system for a new car model. One of the crucial design factors is ensuring the system can handle forces acting on the wheels during turns. To analyze these forces, you need to break down the resultant force acting on the wheels into its component form.

By breaking down the force vector into its components, you can determine the specific forces acting in the horizontal and vertical directions. This information is vital for calculating the stresses and strains on various suspension components, such as springs and shock absorbers, and ensuring they can handle the load.

Analyzing the component form of the force vector allows you to understand the individual forces acting on the suspension system. It helps you determine the necessary design parameters and select appropriate materials to ensure the system's stability, performance, and safety.

2. Now, let's consider a real-world situation where overlaying a polar coordinate system is useful:

Imagine you are an air traffic controller responsible for guiding aircraft during landing procedures. To efficiently direct the planes, you need to determine the positions of the aircraft relative to a specific reference point, such as the control tower.

In this situation, overlaying a polar coordinate system allows you to represent the positions of the aircraft accurately. By choosing the control tower as the pole and extending the polar axis outward, you can use polar coordinates to specify the distance and direction of each aircraft from the control tower.

This polar coordinate system enables you to quickly identify the location of each aircraft, calculate the distances between them, and provide precise instructions for landing sequences. By using polar coordinates, you can effectively manage the airspace, ensure the safety of incoming aircraft, and prevent any potential collisions.

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Answer:

56.54866776

Step-by-step explanation:

To find the circumference multiply the diameter of the circle with π (pi) or multiply the radius 2x with pi (π=3.14).

So18x π= 56.54866776

Hope this helps ^-^

(If u like it mark brainliest, plz)

Step-by-step explanation:

i answered this one already as well.

Answer:

-6

Step-by-step explanation:

- 28 – 6b= 8

step 1 add 28 to each side

-28 + 28 cancels out

28 + 8 = 36

we now have -6b = 36

step 2 divide each side by -6

-6b / -6 = b

36 / -6 = -6

we're left with b = -6

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(b=-6\)  

»»————-　★　————-««  

Here’s why:  

We will have to preform inverse operations to solve for 'b'.

\(\boxed{\text{Solving the equation for 'b':}}\\\\-28-6b=8\\\\--------\\\rightarrow-28+28-6b=8+28\\\\\rightarrow-6b=36\\\\\rightarrow\frac{-6b=36}{-6}\\\\\rightarrow \boxed{\text{b=-6}}\\\\\text{The value of 'b' is \boxed{-6}.}\)

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

you didn't give me access so I can't edit or solve the problem  and if this is extra credit to bring your grade up, shouldn't you be doing it?

The answer of the given question based on the the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20, the correct answer is (1) 142 , (1) or more.

An equation is  mathematical statement that shows  equality of two expressions, typically separated by  equal sign. Equations are used to express relationships between variables and to solve problems in various fields of mathematics, science, and engineering. In essence, an equation is representation of  real-world scenario or problem in mathematical terms.

The variables in equation can take on different values, and  equation remains true regardless of the values chosen for  variables. Solving  equation means finding  values of the variables that make  equation true.

Equations can be linear, quadratic, polynomial, exponential, logarithmic, or trigonometric, among other types. They are fundamental tool in mathematics and have numerous applications in fields like physics, engineering, economics, and finance.

There are 155 students or more students that use this lunch line.

The correct answer is 1. or more.

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Answer:

order pair (2,1) is the solution to the inequality.

As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).

In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.

The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.

The third set of data is 24, 25, 25, 25, 26, 26.

The median is the middle value, which is also (25+25)/2 = 25.

The mode is the value that appears most frequently, which is 25.

Therefore, the mode and median are the same, fulfilling Marjane's requirement.

Therefore, the correct option is (c).

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The angles (x + 7)° and (3x - 21)° are vertical angles and the value of x is equal to 14.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

so we shall solve for x and y as follows:

3x - 21 = x + 7

3x - x = 21 + 7 {collect like terms}

2x = 28

2x/2 = 28/2 {divide through by 2}

x = 14

Therefore, the value of x is equal to 14 for the vertical angles (x + 7)° and (3x - 21)°.

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Answer:the answer is D. I, II, and III

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The interval of convergence for the given power series is (2, 8).

To find the interval of convergence for the given power series. We have the power series:

∑(n=2 to ∞) ((x-5)ⁿ)/(3ⁿ)

To find the interval of convergence, we'll use the Ratio Test. For the Ratio Test, we need to compute the limit:

L = lim (n → ∞) |(a_(n+1)/a_n)|

For our series, a_n = ((x-5)ⁿ)/(3ⁿ). Therefore, a_(n+1) = ((x-5)(n+1))/(3(n+1)). Now, let's compute the ratio:

|(a_(n+1)/a_n)| = |(((x-5)(n+1))/(3(n+1))) / (((x-5)ⁿ)/(3ⁿ))|

Simplify the expression:

|(a_(n+1)/a_n)| = |(x-5)/3|

The series converges if L < 1. So we have:

|(x-5)/3| < 1

Now, we'll solve for x to find the interval of convergence:

-1 < (x-5)/3 < 1

Multiply each term by 3:

-3 < x-5 < 3

Add 5 to each term:

2 < x < 8

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Answer:

wait what was the question i might be able to help if i know what it is

Answer:

Step-by-step explanation:

12x - 4 = 5x + 24

First subtract 5x from both sides

That's

12x - 5x - 4 = 5x - 5x + 24

7x - 4 = 24

Add 4 to both sides

That's

7x - 4 + 4 = 24 + 4

7x = 28

Divide both sides by 7

We have the final answer as

Hope this helps you

Answer:4

Step-by-step explanation:First, add 4 to both sides of the equation. Then subtract 5x from both sides. Finally, divide both sides by 7.

Answer:

\(y = \sqrt{ 900 - x\²\)

Step-by-step explanation:

In the complete question, the area of  the roller coaster is:

\(x\² + y^2 = 900\)

Required

Solve for y

We have:

\(x\² + y^2 = 900\)

Subtract \(x\²\) from both sides

\(y^2 = 900 - x\²\)

Take positive roots of both sides

\(y = \sqrt{ 900 - x\²\)

Answer:

BC = 17.1

m<B = 6.7 deg

m<C = 83.3 deg

Step-by-step explanation:

Find BC

a^2 + b^2 = c^2

AC^2 + AB^2 = BC^2

2^2 + 17^2 = BC^2

4 + 289 = BC^2

BC^2 = 293

BC = sqrt(293)

BC = 17.1

Find <B

tan B = opp/adj

tan B = 2/17

B = tan^-1 2/17

B = 6.7 deg

Find <C

m<A + m<B + m<C = 180

90 + 6.7 + m<C = 180

m<C = 180 - 90 - 6.7

m<C = 83.3

The question presents the velocity and acceleration vectors of an object at a certain instant. The choices given include options related to the object's motion, such as speeding up, slowing down, moving in a straight line, or following a curved path.

To analyze the motion of the object based on the given velocity and acceleration vectors, we need to consider the relationship between these vectors. If the velocity and acceleration vectors have the same direction, the object is either speeding up or moving in a straight line. If they have opposite directions, the object is either slowing down or following a curved path.

Looking at the given vectors, the velocity vector v has a magnitude of 3.0 m/s and points in the y-direction (ʀ^). The acceleration vector a has a magnitude of 0.5 m/s² and points in the x-direction (ɨ^), with a component in the negative y-direction (-0.2 m/s²). Since the velocity and acceleration vectors have different directions (ʀ^ and ɨ^), the object is slowing down and following a curved path.

Therefore, the correct answer is (C) slowing down and following a curved path.

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Answer:the best predicted value of ý when the twin born first has an IQ of 109 is 107.50

Step-by-step explanation:

Given the regression equation:

ŷ = -2.59 + 1.01x

We need to predict the value of ý when x (IQ score of the twin born first) is 109.

So we substitute x = 109 into the regression equation:

ŷ = -2.59 + 1.01(109)

ŷ = -2.59 + 110.09

ŷ = 107.50

Therefore, the best predicted value of ý when the twin born first has an IQ of 109 is 107.50.

Answer: 2.5

Step-by-step explanation:

I believe 2.5 because If we take y/x we have 4,10 so I divide.

Answer:

1000xm

Step-by-step explanation:

1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️

It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.

Given:

Distance traveled by light = 10,000 km

Time taken by light = 3.0 x 10² seconds

To convert km to meters, we know that 1 km = 1 x 10³ m, so:

10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m

Now, we can find the time taken to travel one meter by dividing the total time by the total distance:

Time taken to travel one meter = Total time / Total distance

Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)

To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:

Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)

Now, we get the final answer:

Time taken to travel one meter = 3.0 x 10⁻⁵ seconds

So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

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The factorization of 18y - 21 = 3(6y - 7)

Factorization is the simplification of an expression by grouping similar term together into smaller terms.

Since we have the expression 18y - 21, and we desire to factorize it, we proceeds as folows.

Since we have 18y - 21. we write each term out as a product of their common factors.

So,

18y - 21 = 3 × 6 × y - 3 × 7

Factorizing out the common factor 3, we have that

18y - 21 = 3 × 6 × y - 3 × 7

18y - 21 = 3(6 × y - 7)

= 3(6y - 7)

So, we have the expression as 3(6y - 7)

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The system of equations has a unique solution when the determinant of the coefficient matrix is non-zero.

In this case, the coefficient matrix is:

|  0  1  2k |

|  1  2   6  |

|  k  0   2  |

The determinant of this matrix is given by:

D = 0(2(2) - 0(6)) - 1(1(2) - 6(k)) + 2k(1(0) - 2(2))

 = -12k + 12k

 = 0

When the determinant is zero, the system may have infinitely many solutions or no solution. Therefore, we need to investigate further to determine the values of k for which the system has a unique solution.

(b) To determine the values of k for which the system has no solution, we can check if the rank of the coefficient matrix is less than the rank of the augmented matrix. If the ranks are equal, the system has a unique solution. If the ranks differ, the system has no solution.

By performing row reduction on the augmented matrix, we find that the ranks of both the coefficient matrix and the augmented matrix are equal to 2. Therefore, for any value of k, the system has a unique solution.

In summary, for all values of the constant k, the given system of equations has a unique solution and does not have any solution.

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The probability that Delta Airlines will receive no complaints on a given day is approximately 0.082 or 8.2%.

If the average number of complaints per day is 2.5, we can model the number of complaints as a Poisson distribution with a rate parameter of λ = 2.5.

The Poisson distribution gives the probability of observing k events in a given time interval, given the average rate of occurrence of those events. The probability of observing k events is given by the formula:

P(k events) = \((e^(-λ) * λ^k) / k!\)

where e is the mathematical constant approximately equal to 2.71828.

To find the probability that Delta Airlines will receive no complaints on a given day, we set k = 0 in the formula:

P(0 events) = \((e^(-2.5) * 2.5^0) / 0!\)

P(0 events) = \((e^(-2.5)) / 1\)

P(0 events) = 0.082

So the probability that Delta Airlines will receive no complaints on a given day is approximately 0.082 or 8.2%.

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The probability that Delta Airlines will receive no complaints on a given day is approximately____________

APR, or effective annual rate, can also be called an effective annual rate or EAR when "r" is the annual interest rate and "n" is the number of compounding periods to be completed each year. :D

Answer:

The correct answer is "\(64*x^2 - 16\)".

Step-by-step explanation:

The product \((8*x - 4)*(8*x + 4)\) is a notable product, which happens when we have the product of the sum of two values with the subtraction of these same two values. In cases like this the answer will always be the first term squared minus the second term squared, therefore we have:

\((8*x - 4)*(8*x + 4) = 64*x^2 - 16\)

The correct answer is "\(64*x^2 - 16\)".

Answer:

64x^2 -16

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