2. Apply the brute-force method to find the minimum cost Hamilton Circuit for the given graph. Start
with vertex A.
Circuit
AC,AD, AB
BA, BD, BC
I
B
8
D
Weight
26
20
20
C

Answer:

B

Step-by-step explanation:

[tex]x^{2} +7x+49[/tex] is a prime equation.

Rounding to the nearest 50 dollars, we get:

value = $12,550.

The annual rate of change refers to the percentage change in a quantity over a period of one year. It is commonly used to express the growth or decline of economic indicators, such as GDP, inflation, or employment, as well as the performance of financial assets, such as stocks or bonds. To calculate the annual rate of change, you need to take the difference between the initial and final values of the quantity, divide it by the initial value, and multiply the result by 100 to express it as a percentage. For example, if a company's revenue was $1 million in 2021 and $1.2 million in 2022, the annual rate of change in revenue would be (1.2-1)/1 * 100 = 20%.

A) The car depreciated from $44,000 in 1992 to $15,000 in 2006, a period of 14 years.

The annual rate of change can be found using the formula:

[tex]r = (V2/V1)^{(1/n)} - 1[/tex]

where V1 is the initial value, V2 is the final value, and n is the number of years.

Substituting the given values, we get:

[tex]r = ($15,000/$44,000)^{(1/14)} - 1[/tex]

[tex]r = 0.0576[/tex]

So, the annual rate of change (or depreciation) is 0.0576.

B) To express this rate as a percentage, we can multiply it by 100 and add a percent sign:

[tex]r = 0.0576 x 100%[/tex]

[tex]r = 5.76%[/tex]

So, the car depreciated at an annual rate of 5.76%.

C) If we assume that the car value continues to drop by the same percentage, we can use the formula for exponential decay:

[tex]V = V0*(1-r)^t[/tex]

where V0 is the initial value, r is the rate of change, and t is the time elapsed.

Substituting the given values, we get:

[tex]V = $15,000*(1-0.0576)^3[/tex]

[tex]V = $12,527.31[/tex]

Rounding to the nearest 50 dollars, we get:

[tex]value=12,550[/tex]

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The equation that can be solved to predict the number of times Harris will spin a sum less than 10 is B) 12/500 = x/15

Harris should expect to spin a sum of 10 or greater 240 times.

It should be noted that to predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of experiments (500).

The possible sums that can be obtained are: 5, 6, 7, 8, 9, 10, 11, and 12. The probability of getting a sum less than 10 is the sum of the probabilities of getting each of these outcomes, which is:

P(sum less than 10) = P(1 and 4, 1 and 5, 2 and 4, 2 and 5, 3 and 4, 3 and 5)

= 6/15 * 2/5

= 4/25

Multiplying this probability by the total number of experiments (500), we get:

Number of times Harris will spin a sum less than 10 = (4/25) * 500 = 80

Therefore, the correct equation to predict the number of times Harris will spin a sum less than 10 is: 12/500 = x/15

Part B: Based on the information, the possible outcomes that give a sum of 10 or greater are: 10, 11, and 12. The probability of getting a sum of 10 or greater is the sum of the probabilities of getting each of these outcomes, which is:

P(sum of 10 or greater) = P(1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, 6 and 4, 7 and 3, 8 and 2, 9 and 1, 8 and 3, 7 and 4, 6 and 5)

= 12/15 * 3/5

= 36/75

= 12/25

Multiplying this probability by the total number of experiments (500), we get:

Number of times Harris should expect to spin a sum of 10 or greater = (12/25) * 500 = 240

Therefore, Harris should expect to spin a sum of 10 or greater 240 times.

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The expressions whose solutions are represented by the graph are:

A. 5 - X > 4

D. 6x - 7 > 5

The mathematical expressions, whose solutions are represented by the graph are those that fall within the shaded region of the graph. For instance, in the mathematical expression, 5 - x > 4, the shaded region points to 4 and values greater than it.

So, this expression satisfies the condition and can be described as a solution represented by the graph.

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Answer: h = 7

Step-by-step explanation:

63 = 1/2 * 18 * h

63 = 9 * h

63 = 9h

*Divide 9 on both sides.

7 = h

If x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.  the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.

To find the inverse function of f(x) = 5x - 3, we need to follow these steps:

Step 1: Replace f(x) with y:

y = 5x - 3

Step 2: Solve for x in terms of y:

y = 5x - 3

y + 3 = 5x

x = (y + 3)/5

Step 3: Replace x with f^(-1)(x) and y with x:

f^(-1)(x) = (x + 3)/5

Step 4: Check if the inverse function is valid by verifying if f(f^(-1)(x)) = x and f^(-1)(f(x)) = x:

f(f^(-1)(x)) = f((x+3)/5) = 5((x+3)/5) - 3 = x + 2

f^(-1)(f(x)) = f^(-1)(5x - 3) = (5x - 3 + 3)/5 = x/5

Since f(f^(-1)(x)) = x + 2 and f^(-1)(f(x)) = x/5, the inverse function is valid.

Therefore, the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.

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The complete question is:

if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.

What are the step to find the inverse to this function?

Answer:

Step-by-step explanation:

1) -2

2) 0

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Lyla pays  $ 24.14 in total.

What is the total amount?

To add two or more numbers and determine the final total, use the sum. A series of any form of numbers, known as addends or summands, is added; the outcome is their sum or total.

Here, we have

Given: Lyla goes out to dinner with her friends where the subtotal is $23.89. A 7% tax and 18% tip are added to the subtotal.

we have to find out how much did she pay in total.

= $23.89 + 7% + 18%

= $23.89 + 7/100 + 18/100

= $23.89 + 0.07 + 0.18

= $ 24.14

Hence, Lyla pays  $ 24.14 in total.

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Hence, they are different because they drawn from the different scales values.

Data in math is a collection of facts and figures that can be in any form—numerical or non-numerical.

Numerical data is the one you can calculate, and it is always collected in number form, such as scores of students in class, wages of workers in an organization or height of players on a football team, etc.

As per the given graphs they are different because they drawn with the help of different scales.

Hence, they are different because they drawn from the different scales values.

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the measurement of the fourth angle of the quadrilateral is 95 degrees.

To find the measurement of the fourth angle of a quadrilateral when the measures of three angles are given, we can use the fact that the sum of the measures of the angles in a quadrilateral is 360 degrees.

Let's denote the measure of the fourth angle as x. Then we can write an equation:

80 + 120 + 65 + x = 360

Simplifying this equation, we get:

x = 360 - 80 - 120 - 65 = 95

Therefore, the measurement of the fourth angle of the quadrilateral is 95 degrees.

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Answer:

150.00

Step-by-step explanation:

a = 1/2bh

a = 1/2(2)(10)

a = 10 [tex]m^{2}[/tex]

10x15 = 150

Helping in the name of Jesus.

Answer:

-349

Step-by-step explanation:

1)[-6-22]+[-321]

2)(-28)-321

3)-349

The calculated value of the derivative f'(x) at x = -2/3 if f(x) = 5x√(x + 1) is f'(-2/3) = 0

Given the function

f(x) = 5x√(x + 1)

Factor out 5

So, we have

f(x) = 5[x√(x + 1)]

The derivative is then calculated using the following chain rule

f'(x) = 5[du/dx * dy/du]

When differentiated, we have

f'(x) = 5[√(x + 1) + x/2[√(x + 1)]]

This gives

f'(x) = 5[3x + 2/2[√(x + 1)]]

So, we have

f'(x) = [15x + 10]/[2√(x + 1)]

Substitute -2/3 for x

f'(-2/3) = [15(-2/3) + 10]/[2√((-2/3) + 1)]

Evaluate

f'(-2/3) = [0]/[2√1/3]

Evaluate the quotient

f'(-2/3) = 0

Hence, the value of the derivative is 0

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Answer: Slope-intercept form : y-y₁=m(x-x₁)

Passes through (-12, 7)

Slope = -5/3

m = slope

Simply plug everything in :)

y - y₁ = m(x - x₁)

y - 7 = -5/3(x + 12)

Simplify.

y - 7 = -5/3x - 20

Add 7 to both sides.

y = -5/3x = -13

~Hope I helped~

Step-by-step explanation:

Answer: r=89.1

Step-by-step explanation: It has been given that,

PQ=PR

So, it is an isosceles triangle, hence ∠Q=∠R. let it be x

Now, we know that the sum of the angles of a triangle = is 180

∘

.

So,

∠P+∠Q+∠R=180

38.2+52.7+x=180

90.9+x=180

taking 90.9 in RHS it becomes -, so

x=180-90.9

x=89.1

Answer:

So the composite function that gives the area of a circle in terms of time is:

A(r(t)) = π(0.25+2t+4t²)

The coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.

A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.

When a point is reflected over the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.

Therefore, to find the coordinates of point B' after reflecting point B over the x-axis, we simply need to change the sign of the y-coordinate of point B.

Starting with point B at (8, -3), reflecting over the x-axis changes the sign of the y-coordinate, so the new point B' is at:

B' = (8, 3)

Therefore, the coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.

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The revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016. 2. The revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.

A factor is a number that represents how two quantities are related to one another. It is frequently used to indicate how much one amount exceeds or falls short of another. For instance, if a business's revenue. On the other hand, a percentage is a technique to represent a portion or ratio of something as a fraction of 100. For instance, if a company made money.

The given revenue for the two years is $138200 and $164900.

The factor of the two revenue is:

factor = 164900 / 138200 = 1.193

Hence, the revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016.

percentage = (164900 / 138200) * 100% = 119.3%

Therefore, the revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.

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1. Data is approx bell-shaped and symmetric

2. Median is between 150 to 175

A histogram is a graphical representation of a frequency distribution of a set of continuous data. It is used to display the shape of the data and to show how frequently certain values occur within a given range or interval.

In a histogram, the x-axis represents the range or interval of the data, and the y-axis represents the frequency of occurrence of values within each interval.

The data is divided into a set of bins or intervals, and the height of each bar on the histogram represents the number of data points that fall within that particular bin. The bars of the histogram are typically drawn adjacent to each other, with no gaps between them, to emphasize the continuity of the data.

Therefore, from the histogram used to represent the given data, it can be seen that the data is symmetric and also the median has the values between 150 to 175

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Answer:

Here are the angles in each quadrant with a common reference angle of 165°:

First quadrant: angle is 15° (subtract 165° from 180°)

Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)

Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)

Fourth quadrant: angle is 195° (subtract 165° from 360°)

Answer:

Step-by-step explanation:

To make x the subject of y = ax^2 + b, we can use the following steps:

1.Subtract b from both sides to isolate the term with x^2:

y - b = ax^2

2.Divide both sides by a to isolate x^2:

(y - b) / a = x^2

3.Take the square root of both sides to solve for x:

x = ± sqrt((y - b) / a))

Therefore, the expression for x as a subject of y = ax^2 + b is:

x = ± sqrt((y - b) / a))

The cost of the fence for a rectangular field of 1,500 square yards will be 150k√50 dollars.

Let the length of the rectangular field be L and the width be W. Since the area of the field is 1,500 square yards, we have:

L × W = 1,500

P = 2L + W

C = kP + (1/2)k(L/2)

C = (2k)L + (k/2)W

W = 1500/L

Substituting this into the expression for C, we get:

C = (2k)L + (k/2)(1500/L)

dC/dL = 2k - (k/2)(1500/[tex]L^2[/tex]) = 0

Solving for L, we get:

L = 30√50 yards

Substituting this back into the equation for W, we get:

W = 50/√50 yards

Therefore, the dimensions of the rectangular field that minimize the cost of the fence are L = 30√50 yards and W = 50/√50 yards.

P = 2L + W = 60√50 + 50/√50 yards

C = (2k)L + (k/2)(1500/L) = 90k√50 dollars

k/2 = k/2

Substituting this into the expression for C, we get:

C = 150k√50 dollars

Therefore, to minimize the cost of the fence, the rancher should build a rectangular field with dimensions of L = 30√50 yards and W = 50/√50 yards, and the total cost of the fence will be 150k√50 dollars.

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We can long divide (24x^3 - 2x^2 - 8x + 30) by (x - 2) as follows:

            24x^2  +  46x  +  86

         _______________________

x - 2   |   24x^3  -  2x^2  - 8x  + 30

        -(24x^3  - 48x^2)

        _______________

                 46x^2 - 8x

                 46x^2 - 92x

                 ___________

                           84x + 30

                           84x - 168

                           ________

                               198

Therefore, (24x^3 - 2x^2 - 8x + 30) ÷ (x - 2) = 24x^2 + 46x + 86 with a remainder of 198/(x - 2).

Answer:

the quotient is 24x² + 46x + 86 and the remainder is 198. Thus, we can write:

(24x³ - 2x² - 8x + 30) ÷ (x - 2) = 24x² + 46x + 86 + 198/(x - 2)

Step-by-step explanation:

We can perform polynomial long division to divide (24x³ - 2x² - 8x + 30) by (x - 2).

24x² + 46x + 86

----------------------

x - 2 | 24x³ - 2x² - 8x + 30

- (24x³ - 48x²)

------------------

46x² - 8x

- (46x² - 92x)

--------------

84x + 30

- (84x - 168)

--------------

198

Therefore, the quotient is 24x² + 46x + 86 and the remainder is 198. Thus, we can write:

(24x³ - 2x² - 8x + 30) ÷ (x - 2) = 24x² + 46x + 86 + 198/(x - 2)

Answer:

1) 2160000000

2) 3.24 * 10^14

Step-by-step explanation:

30*8000(5-)1800

240000 * 5 * 1800

1200000 * 1800

2160000000

1500(800-)15000*18000

1200000 * 15000 * 18000

18000000000 * 18000

3.24 * 10^14

About the equation [tex]7 * 3 = 21[/tex], the generalization we can make is that dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction.

We use generalizations to describe the pattern they see in the relationship of a specific group of numbers. It's a pattern that holds true every time.

In mathematics, generalization can be defined as a statement that is true for an entire class of objects, the process by which we obtain a general statement, or the method by which knowledge is transferred from one setting to another.

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Answer:

Step-by-step explanation:

Let's call the weight of Karen's package "w" in pounds.

For the first courier, the cost is given by:

Cost = 20 + 2w

For the second courier, the cost is given by:

Cost = 12 + 3w

We know that these costs are equivalent, so we can set them equal to each other:

20 + 2w = 12 + 3w

Simplifying this equation, we get:

8 = w

So the weight of Karen's package is 8 pounds.

To find the cost, we can plug this weight into either of the equations above:

For the first courier:

Cost = 20 + 2(8) = 36

For the second courier:

Cost = 12 + 3(8) = 36

So it will cost Karen $36 to deliver her package, and the weight of the package is 8 pounds.

After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.

CB = 8 cm * tan(25°)

≈ 3.45 cm

To find the segment CB, we need to use the tangent of the angle α (25°). We also need to know the length of the segment AB, which is 8 cm. To solve for CB, we use the equation CB = 8 cm * tan(25°). After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.

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In light of this, the cylinder's total surface area falls between approximately 1017.9 cm²and 1357.2 cm².

A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h." The entire surface area of the cylinder is calculated as follows:

Total Surface Area of Cylinder = 2r (h + r) square units.

The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. It is seen as a prism since its base is a circular. It is frequently used as a container and can either be solid or hollow 13.

The following formula can be used to get a cylinder's total surface area:

A = 2πr² + 2πrh

where r is the cylinder's base's radius, h is the cylinder's height, and is a mathematical constant roughly equal to 3.14159.

Yet, we can locate a variety of potential surface areas using the provided information. With the assumption that the radius is equal to the feedback's half (9 cm), we can

after which, we can determine the surface area as follows:

A = 2π(9)² + 2π(9)(18) (18)

A=  2π(81) + 2π(2916)

A ≈ 1017.9 cm²

The surface area can be calculated as follows if we assume that the radius is equal to two-thirds of the feedback (i.e., r = 12 cm):

A = 2π(12)² + 2π(12)(18) (18)

A ≈ 1357.2 cm²

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The ball will reach its maximum height after 3.5 seconds.

What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and then moves along a curved path under the influence of gravity.

In projectile motion, the object follows a parabolic trajectory, which is a curve described by a quadratic function. The path of the object depends on the initial velocity, angle of projection, and acceleration due to gravity.

The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately.

The height function of the ball thrown The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately. is given by h(t) = 112t - 16t^2, where t is the time in seconds and h(t) is the height of the ball at time t.

To find the maximum height, we need to find the vertex of the parabolic function h(t). The vertex of a parabola given by the equation y = ax^2 + bx + c is located at x = -b/2a.

In the case of our height function h(t) = -16t^2 + 112t, the coefficient of the squared term is -16, and the coefficient of the linear term is 112. Therefore, the time at which the ball reaches its maximum height is given by:

t = -b/2a = -112/(2*(-16)) = 3.5

So, the ball will reach its maximum height after 3.5 seconds.

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