Which of the following is true with respect to the Chi-Square Test of Independence? (1/2 pt.) a. The test requires interval/ratio data. b. The test is appropriate for categorical data. C. The test requires an equal number of cases in the marginal totals. d. The number of cases in each category of the contingency table must be equal.

Answer:

Step-by-step explanation

b/sin(102°) =27/sin(28°)
⇔b ≈56,2548

Using sine rule of triangles, the length of the hypotenuse is 56.3 rounded to the nearest tenth

Sine rule of triangles is related using the formula :

Inputting values into the relation

b/sin(102) = 27/sin(28)

cross multiply

b * sin(28) = 27 * sin(102)

divide both sides by sin(28)

b = 26.40998/sin(28)

b = 56.254

Therefore, the length of b in the figure given is 56.3

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The value of the equivalent fraction is 5/1000 and 0.005. Options C and E

A fraction that, while having a different numerator and denominator, reflects the same value or amount as another fraction is said to be equal. The same proportion or part of a whole is represented by equivalent fractions, which have distinct numbers.

You can multiply or divide a fraction's numerator and denominator by the same non-zero value to produce an analogous fraction.

We have;

1/2%

This is the same as;

1/2/100/1

1/2 * 1/100

= 1/200 or 0.005 or 5/1000

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Missing parts;

Choose each number that show 1/2 % as an equivalent fraction, decimal, or percent. Select all that apply. A) 0.05 B) 2% C) 5/1000 D) 5/100 E) 0.005

Answer:

Step-by-step explanation:

The value of a of the given cube root expression is: a = 1

The cube root of a number is defined as that number which when  multiplied 3 times gives us the original number. Whenever a number (x) is multiplied three times, then we can say that the resultant number is known as the cube of that number.

We are given the expression as:

∛(81x¹⁵y⁹)

Now, expressing this individually gives us the expression:

[tex]81^{\frac{1}{3} } * x^{\frac{15}{3}} * y^{\frac{9}{3}}[/tex]

= 3¹x⁵y³

Thus, a = 1

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The Taylor polynomial t2(x) for the function f(x) = ln(1+x) based at b=0 is t2(x) = x - ([tex]x^{2}[/tex])/2.

The Taylor polynomial provides an approximation of a function around a given point using its derivatives. The polynomial is constructed by evaluating the function and its derivatives at the chosen point.

To find the Taylor polynomial t2(x) for f(x) = ln(1+x) based at b=0, we need to calculate the function's derivatives up to the second order.

First, let's find the first derivative of f(x):

f'(x) = d/dx ln(1+x) = 1 / (1+x)

Next, let's find the second derivative of f(x):

f''(x) = d/dx (1 / (1+x)) = -1 / [tex](1+x)^{2}[/tex]

Now, we can evaluate the derivatives at b=0:

f(0) = ln(1+0) = 0

f'(0) = 1 / (1+0) = 1

f''(0) = -1 / 1 = -1

Using these values, we can construct the Taylor polynomial t2(x) as follows:

t2(x) = f(0) + f'(0)(x-0) + f''(0)[tex](x-0)^{2}[/tex] / 2

= 0 + 1(x-0) - 1(x-0)^2 / 2

= x - ([tex]x^{2}[/tex]) / 2

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Are you kidding me , you can't solve such easy answers

just subtract 1 by 2

0 = y - 6

y = 6

x = 4

like I literally did without using single sheet of papz

After 11 seconds the hovercraft will land on ground

Given a function that shows the height of a hovercraft,

h(x) = -(x-11)(x+3)

Where,

x = number of seconds.

When the hovercraft land on the ground,

(x-11)(x+3)

By zero product property,

x - 11 = 0 or x + 3 = 0

⇒ x = 11 or x = -3 ( not possible ),

Hence, after 11 seconds the hovercraft will land on ground.

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A hovercraft takes off from a platform. Its height (in meters), xxx seconds after takeoff, is modeled by h(x)=-(x-11)(x+3)h(x)=−(x−11)(x+3)h, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 11, right parenthesis, left parenthesis, x, plus, 3, right parenthesis How many seconds after takeoff will the hovercraft land on the ground?

Answer:

therefore, it would take 93 days to build a similar house with 4 workers.

Step-by-step explanation:

so we well do 12 x 31 = d2 x 4

372 = 4d2

d2 = 93

Answer:

the width of the crate is 19 inches.

Step-by-step explanation:

we know the length is 30 inches and the height is 22 inches. We also know the total volume of the crate is 12,540 cubic inches. So we can plug these values into the formula and solve for the width:

12,540 = 30 x width x 22

Dividing both sides by 30x 22 we get:

width = 12,540 / 30 x 22 = 19 inches

therefore the width is 19 inches.

The Lotka-Volterra predator-prey model is a widely-used mathematical model to describe the dynamics of two interacting populations in an ecosystem, namely rabbits and foxes.

The model is represented by two coupled ordinary differential equations, where the first equation describes the change in the population of rabbits over time, while the second equation describes the change in the population of foxes over time.
The first term in the model, aR, represents the natural growth rate of the rabbit population, where a is a positive parameter and R is the number of rabbits. This term implies that the population of rabbits increases over time in the absence of any other factors affecting their growth. The second term in the model, bRF, represents the predation of rabbits by foxes, where b is a positive parameter and F is the number of foxes. This term implies that the population of rabbits decreases over time due to predation by foxes.
The third term in the model, -cF, represents the natural mortality rate of the fox population, where c is a positive parameter and F is the number of foxes. This term implies that the population of foxes decreases over time in the absence of any other factors affecting their growth. The fourth term in the model, dRF, represents the growth of the fox population due to predation on rabbits, where d is a positive parameter and R is the number of rabbits. This term implies that the population of foxes increases over time due to predation on rabbits.
However, there are some unrealistic assumptions in the model. For instance, the model assumes that the rabbit population has an unlimited food supply and is not affected by any other factors such as disease or habitat destruction. Similarly, the model assumes that the fox population feeds only on rabbits and is not affected by any other factors such as competition for resources or predation by other animals. Therefore, while the Lotka-Volterra predator-prey model provides a useful framework for understanding the dynamics of predator-prey interactions, it should be used with caution when making predictions about real-world ecosystems.

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Step-by-step explanation:

Triangle side length rule states the sum of any two sides must be greater than the third side

soooo    

7+9 > x           x < 16

9+x > 7         all x

7 + x > 9     x > 2           so      2 < x < 16  

Answer:

No solution

Step-by-step explanation:

3(x-2) + 4 = 3x + 6

3x - 6 + 4 = 3x + 6

3x - 2 = 3x + 6

-2 = 6

This is not true; -2 is not equal to 6. So, the answer is No solution.

if the radius is doubled how would it affect the original volume of a cylinder is the volume is quadrupled

The formula for calculating the volume of a cylinder is expressed as;

V = πr²h

Such that;

Substitute the values, we have;

Volume = 3.14 × 4.5² × 15

Find the square and multiply the values, we get;

Volume = 953. 8 in³

If the radius is doubled, we get;

Volume = 3.14 × 9² × 15

Multiply the values, we have;

Volume = 3815. 1 in³

The volume is quadrupled

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There were approximately 7250 visitors to the historic site in 2013.

To find the number of visitors in 2013, we need to work backward using the given information about the percentage changes.

Let's assume the number of visitors in 2013 as 'x'.

In 2014, the number of visitors increased by 22% compared to the previous year. This means the number of visitors in 2014 is 100% + 22% = 122% of the number of visitors in 2013.

So, the number of visitors in 2014 is 1.22x.

In 2015, the number of visitors decreased by 20% compared to the previous year. This means the number of visitors in 2015 is 100% - 20% = 80% of the number of visitors in 2014.

So, the number of visitors in 2015 is 0.8(1.22x) = 0.976x.

Given that there were 7076 visitors in 2015, we can set up the following equation:

0.976x = 7076

To solve for x, we divide both sides of the equation by 0.976:

x = 7076 / 0.976

x ≈ 7250

Therefore, there were approximately 7250 visitors to the historic site in 2013.

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The symmetric difference, denoted by the symbol ⊕, between two sets A and B is defined as the set of elements that are in either A or B, but not in both.

a) If a is a subset of u, then a⊕a will contain all elements that are in a and not in a, which is an empty set (∅). Therefore, a⊕a=∅.
b) The symmetric difference between a and an empty set (∅) is simply a, because there are no elements in ∅ that are not in a. Thus, a⊕∅=a.
c) The symmetric difference between a and the universal set u will contain all elements that are in either a or u, but not in both. Since a is already a subset of u, a⊕u will simply be all elements in u that are not in a, which is just a. Therefore, a⊕u=a.
d) The symmetric difference between a and itself (a⊕a) will contain all elements that are in either a or a, but not in both. This is equivalent to the set of elements that are not in a, which is the complement of a in u. Therefore, a⊕a is equal to u-a, or simply the universal set u. Hence, a⊕a=u.
In conclusion, if a is a subset of a universal set u, then a) a⊕a=∅, b) a⊕∅=a, c) a⊕u=a, and d) a⊕a=u.

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The volume of the triangular prism-shaped planter is calculated as: 20 cubic feet.

To find the volume of the planter, we can use the formula for the volume of a right triangular prism, which is given by:

Volume = (1/2) * base * height * length

In this case, the base of the planter is the area of the right triangle formed by the legs, and the length is the height of the planter.

Given that the legs of the triangle measure ten feet, we can calculate the area of the triangle:

Area = (1/2) * base * height

= (1/2) * 10 * 2

= 10 ft²

Now, we can find the volume of the planter:

Volume = (1/2) * 10 * 2

= 10  * 2

= 20 ft³

Therefore, the volume of the planter is 20 cubic feet.

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The net area of a region equals the area of the region when there are no holes or gaps within the region, and the net area includes both the interior and exterior of the boundaries.

The net area of a region refers to the total area enclosed by its boundaries, including both the interior and exterior regions. It represents the complete surface area of the region, regardless of whether it contains any voids or holes.

In cases where there are no voids or gaps within the region, the net area will be equal to the area of the region. This occurs when the boundaries of the region completely enclose a continuous and solid area, without any missing or excluded parts.

In conclusion, the net area of a region equals the area of the region when there are no holes or gaps within the region, and the net area includes both the interior and exterior of the boundaries.

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The value of the constant C is 1 and the exponent r is 3/2. The largest interval that guarantees the existence of a unique solution is  (-∞, ∞).

To find the value of the constant C and the exponent r for the solution y = Ctr, we can substitute this solution into the initial value problem and solve for C and r.

We have 2ty' = 6y, which can be written as y' = 3y/(2t).

Now, differentiate y = Ctr with respect to t:

y' = C × r × [tex]t^{(r-1)}[/tex]

Substituting this into the equation, we get:

C × r × [tex]t^{(r-1)}[/tex] = 3C × [tex]t^{(r-1)}[/tex]/(2t)

Simplifying, we have:

C × r = 3C/2

Dividing both sides by C, we get:

r = 3/2

Substituting this value of r back into the equation, we have:

3/2 × C = 3C/2

Simplifying, we find:

C = 1

Therefore, the value of the constant C is 1 and the exponent r is 3/2.

The existence and uniqueness theorem for first-order linear differential equations guarantees the existence of a unique solution in an interval of the form a < t < b, where a and b are real numbers.

To determine the largest such interval, we need to consider the behavior of the coefficient 2t in the differential equation.

Since 2t is defined for all real numbers, the largest interval of existence is determined by the behavior of 2t as t approaches any boundary points a or b.

In this case, since the differential equation does not involve any singularities or points of discontinuity, we can consider the whole real line as the interval of existence, (-∞, ∞).

In part a, we found that the solution to the initial value problem is y = Ctr, where C = 1 and r = 3/2.

The actual interval of existence for the solution depends on the initial condition y(1) = -2.

Substituting t = 1 into the solution, we have:

y(1) = [tex]1^{(3/2)}[/tex] = 1

Since the given initial condition is y(1) = -2, we can see that the solution y = Ctr does not satisfy this initial condition.

Therefore, there is no actual interval of existence for the solution in this case.

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The function that suits the graph attached is written below

y = 1.2 (x - 1)² (x - 5)²

The graph plotted has a two zeros at and multiplicity of 2. The zero occurs at points

1 and 5

With this information, we write the polynomial as follows

y = a (x - 1)² (x - 5)²

We solve for "a" using another point on the graph such as the y intercept which is (0, 30)

Solving for a

y = a (x - 1)² (x - 5)²

30 = a (0 - 1)² (0 - 5)²

30 = a (-1)² (-5)²

30 = 25a

isolating a by dividing through by 25

a = 30/25

a = 6/5 = 1.2

the equation is written by substituting for a

y = 1.2 (x - 1)² (x - 5)²

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Therefore, the slope of the tangent line to the polar curve at the point specified by θ = π/4 is -24.

To find the slope of the tangent line to a polar curve at a specific point specified by the value of theta, we can differentiate the polar equation with respect to theta and then substitute the given value of theta into the resulting expression.

Given polar curve: r = 12 cos(2theta), theta = π/4

First, let's differentiate the polar equation with respect to theta:

dr/dθ = -24 sin(2θ)

Substituting θ = π/4 into the derivative:

dr/dθ = -24 sin(2(π/4)) = -24 sin(π/2) = -24

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The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting[tex]y = x^2[/tex]and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression [tex]2\pi x(5x - x^2)dx[/tex] from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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The table represents a function because each input has exactly one output.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Here the set A represents the x values which are the input values or the domain and the set B represents the y values which are output values or the range.

The x values are :

-2, -1, 0, 1, 2

Corresponding y values are :

7, 4, 3, 4, 7

If each of the x value only maps to 1 y value, then the table represents a function.

Here each of the x value only maps to one y value. No x value has more than one y value.

So this is a function.

Hence the correct option is C.

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True. The cost feasibility of a systems development project is indeed dependent on the project's scope.

The cost feasibility of a systems development project refers to the evaluation of whether the project can be completed within the allocated budget. One of the key factors influencing cost feasibility is the scope of the project. The scope defines the boundaries and objectives of the project, including the features, functionalities, and deliverables that are expected to be developed.

When the scope of a project is well-defined and limited, it tends to be more cost-feasible. A smaller scope usually requires fewer resources, less development time, and ultimately, lower costs. On the other hand, projects with a broader or more complex scope often involve a larger number of requirements, greater integration challenges, and increased development efforts, which can drive up the costs.

Therefore, the scope of a systems development project plays a crucial role in determining its cost feasibility. Project managers and stakeholders need to carefully analyze and define the project's scope to ensure that it aligns with the available resources and budget, thereby increasing the chances of successful and cost-effective project completion.

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Answer: √5

Have a great day

Step-by-step explanation:

The calculated volume of the cube is 10714.1 cubic inches

From the question, we have the following parameters that can be used in our computation:

[tex]A = V^{2/3}[/tex]

Where

A = Surface area

V = Volume

From the question, we have

Surface area of 486

This means that

A = 486

So, we have

[tex]V^{2/3} = 486[/tex]

Take the 3/2nd root of both sides

So, we have

V = 10714.1

Hence, the volume of the cube is 10714.1 cubic inches

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The intervals on which f is increasing or decreasing are

To find the intervals on which the function f(x) = 4x^3 - 9x^2 - 30x^4 is increasing or decreasing, we need to examine its first derivative.

Taking the derivative of f(x) with respect to x, we get:

f'(x) = 12x^2 - 18x - 120x^3

To determine the intervals of increase and decrease, we need to find the critical points where f'(x) = 0 and identify the intervals between these points.

Setting f'(x) = 0 and solving for x, we have:

12x^2 - 18x - 120x^3 = 0

Factoring out 6x, we get:

6x(2x - 3 - 20x^2) = 0

From this equation, we find two critical points:

x = 0

2x - 3 - 20x^2 = 0 (This equation does not have real solutions)

Now we can test the intervals between these critical points and determine the intervals of increase and decrease.

For x < 0, we choose a test point, let's say x = -1, and evaluate f'(-1):

f'(-1) = 12(-1)^2 - 18(-1) - 120(-1)^3 = 12 + 18 + 120 = 150

Since f'(-1) > 0, the function is increasing for x < 0.

For 0 < x < 1, we choose a test point, let's say x = 0.5, and evaluate f'(0.5):

f'(0.5) = 12(0.5)^2 - 18(0.5) - 120(0.5)^3 = 3 - 9 - 15 = -21

Since f'(0.5) < 0, the function is decreasing for 0 < x < 1.

For x > 1, we choose a test point, let's say x = 2, and evaluate f'(2):

f'(2) = 12(2)^2 - 18(2) - 120(2)^3 = 48 - 36 - 960 = -948

Since f'(2) < 0, the function is decreasing for x > 1.

Therefore, we can summarize the intervals of increase and decrease as follows:

Increasing: (-∞, 0)

Decreasing: (0, 1), (1, ∞)

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The only true statement is

To begin converting the equation to standard form, abate 36 from both sides.

To dissect the given circle equation x² + 2 + 4x - 64 - 36 = 0, let's go through the handed statements one by one

1. To begin converting the equation to standard form, abate 36 from both sides.

This statement is true.

By abating 36 from both sides, the equation becomes x² + 2x + 4x -100 = 0.

2. To complete the forecourt for the × terms, add 4 to both sides.

This statement isn't true.

Adding 4 to both sides would not complete the forecourt for the x terms. In this equation, we do not need to complete the square since the x terms are formerly in standard form.

3. The center of the circle is at(- 2, 3).

This statement isn't true.

The equation x² + 2x + 4x -100 = 0 isn't in the form( x- h)² + ( y- k)² = r², which represents the equation of a circle centered at the point( h, k). thus, we can not determine the center of the circle from this equation.

4. The center of the circle is at( 4,-6).

This statement isn't true. As explained in statement 3, we can not determine the center of the circle from the given equation.

5. The compass of the circle is 6 units.

This statement isn't true. The compass of the circle can not be determined from the given equation.

6. The compass of the circle is 49 units.

This statement isn't true. The compass of the circle can not be determined from the given equation.

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The polar equation that expresses r in terms of θ is:
r = -6 * sin(θ)

To convert the rectangular equation x^2 + (y + 3)^2 = 9 to a polar equation that expresses r in terms of θ, we can use the following conversion formulas:
x = r * cos(θ)
y = r * sin(θ)
Substitute the x and y expressions into the given rectangular equation:
(r * cos(θ))^2 + (r * sin(θ) + 3)^2 = 9
Now, simplify the equation by expanding and combining like terms:
r^2 * cos^2(θ) + r^2 * sin^2(θ) + 6 * r * sin(θ) + 9 = 9
Notice that r^2 * cos^2(θ) + r^2 * sin^2(θ) = r^2 * (cos^2(θ) + sin^2(θ)). Since cos^2(θ) + sin^2(θ) = 1, the equation becomes:
r^2 + 6 * r * sin(θ) = 0
Now, we can factor out r from the equation:
r * (r + 6 * sin(θ)) = 0
So, there are two possible cases:
1) r = 0
2) r + 6 * sin(θ) = 0
For the second case, we can express r in terms of θ:
r = -6 * sin(θ)
Thus, the polar equation that expresses r in terms of θ is:
r = -6 * sin(θ)

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Answer:

32pi meter square

Step-by-step explanation:

1.calculater the area of the smaller circle

area=pi radius square,radius is 7meter, area =49pi meter square

2.calculate the area of larfer circle

radius ÷radius of smalle4 circle +radius of larger circle

area =81pi meter square