Please explain to me 1) the similarities/differences in the two lines, 2) how are the two graphs related to one another, and 3) how do the equations show this relationship for the following:

Answer:

Step-by-step explanation:

Given is a table showing the surface area y in square inches, of a shrinking puddle in x hours

x y

2 25

5 15

8 9

11 2

r -0.993835256

Hence correlation coefficient is option B) -0.99

Part b:

Time Sur area

x y

2 25

5 15

8 9

11 2

r -0.993835256

slope -0.395083406

Intercept 11.53731343

slope =-0.395

Between 5 and 8, slope = [tex]\frac{change in y}{change in x} \\=\frac{9-15}{8-5} \\=-2[/tex]

Slope represents the change of y with respect to 1 unit change in x.

Part c:

Yes correlation strong and negative.

To find common factors between numbers, list all factors of each number and identify numbers that are in both lists. When multiplying fractions, multiply numerators and denominators then simplify by common factors. Multiplying both sides by the same factor can help in solving equations with fractions.

To find common factors between two or more numbers, you first list out all the factors of each number. Factors are numbers that divide into the original number without leaving a remainder. For instance, if we are looking for common factors of 8 and 12, we list their factors as follows: the factors of 8 are 1, 2, 4, and 8, and the factors of 12 are 1, 2, 3, 4, 6, and 12. After listing out the factors, you look for numbers that appear in both lists. In this example, the common factors of 8 and 12 are 1, 2, and 4.

Another approach mentioned involves multiplying both sides by the same factor to make both sides integers when working with equations. This can be useful when seeking to simplify fractions or solve equations with fractional components.

It is also important to recognize that while multiplying fractions, we multiply the numerators together and the denominators together. Simplifying the result by common factors as needed helps in reducing fractions to their simplest form. For example, if we multiply ½ by ¾, we get a result of ¼ (numerator 1x3=3, denominator 2x4=8) which we can simplify to ¾ by dividing both numerator and denominator by the common factor 3.

Answer:

A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is called chord of the circle.

Step-by-step explanation:

Consider the provided information.

It is given that the line segment goes from one side of the circle to the other side of the circle and doesn’t go through the center.

Diameter: A line segment goes from one side to another side of a circle passes through the center is called the diameter of the circle.

Chord:  A line segment goes from one side to another side of a circle but do not passes through the center is called the chord of the circle.

For better understanding refer the attached figure:

Hence, A line segment that goes from one side of the circle to the other side of the circle and doesn’t go through the center is called chord of the circle.

5(3x-7) = 20

15x-35 = 20

15x = 55

x = 3.666666

 so 6(3.666666) -8 = 13.99999 round to 14

The change to be recieved is equal to $8.45

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: The price per steak is given as $3.85 per pound.

Thus 3 pound of steak will cost 3×3.85=$11.55

Therefore the change to be recieved is =20-11.55

                                                                  =$8.45

Hence, The change to be recieved is equal to $8.45

Learn more about the unitary method here:

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To find the flux of a vector field through a closed boundary using the divergence theorem, calculate the divergence of the vector field and evaluate the triple integral of the divergence over the solid bounded by the boundary. In this case, the flux is 3 times the volume of the solid.

The student is asking how to use the divergence theorem to find the flux of a vector field through a closed boundary. In this case, the vector field is defined as f(x, y, z) = ⟨x, y, 4z⟩ and the closed boundary is a solid bounded by the paraboloid z = x^2 + y^2 and the plane z = 9.

To use the divergence theorem, we need to calculate the divergence of the vector field, which is the sum of the partial derivatives of f with respect to each variable. In this case, the divergence is 3.

Then, we can use the divergence theorem to find the flux through the closed boundary by evaluating the triple integral of the divergence over the solid bounded by the paraboloid and the plane. In this case, the flux is 3 times the volume of the solid.

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The flux of [tex]\(\vec{F}\)[/tex] through S is 24π.

To apply the divergence theorem, we first compute the divergence of [tex]\(\vec{F}\)[/tex]:

[tex]\nabla \cdot \vec{F} = \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial y} (y) + \frac{\partial}{\partial z} (4z) = 1 + 1 + 4 = 6.[/tex]

The divergence theorem states that the flux of a vector field through a closed surface is equal to the triple integral of its divergence over the region enclosed by the surface.

Thus, we have:

[tex]\iint_S \vec{F} \cdot d\vec{A} = \iiint_W (\nabla \cdot \vec{F}) \, dV = \iiint_W 6 \, dV[/tex]

The region W is bounded below by the paraboloid [tex]\(z = x^2 + y^2\)[/tex], and above by the plane z = 4.

Converting to cylindrical coordinates, we have:

[tex]\iiint_W 6 \, dV = \int_0^{2\pi} \int_0^2 \int_{r^2}^4 6 \cdot r \, dz \, dr \, d\theta = 24\pi.[/tex]

Answer:

Z and B are independent events because P(Z∣B) = P(Z).

Step-by-step explanation:

Z and B are independent events

When Z  and B  are independent events then

P(Z and B) = P(Z) * P(B)

P(Z∣B)= [tex]\frac{P(Z and B)}{P(B)}[/tex]

P(Z∣B)= [tex]\frac{P(Z)*P(B)}{P(B)}[/tex]

We cancel out P(B) on both sides

P(Z|B) = P(Z)

replace x with 75

 20x-50 becomes

20(75)-50

20*75 = 1500-50 = 1450

 the profit was $1450

Answer:

B

Step-by-step explanation:

multiply 5 13/16 by 76

5 13/16 * 76 = 441 3/4 revolutions

Final answer:

To find the x-intercepts of the parabola with vertex (5,-12) and y intercept (0,63), substitute the vertex values into the equation of the parabola and find the value of the constant. Then, substitute the value of the constant back into the equation and solve for x to find the x-intercepts. The x-intercepts of the parabola are x = 3 and x = 7.

Explanation:

To find the x-intercepts of the parabola with vertex (5,-12) and y-intercept (0,63), we need to find the values of x when y is equal to zero. Since the vertex of the parabola is (5,-12), the equation of the parabola can be written as[tex]y = a(x-5)^2 - 12.[/tex] To find the value of a, we can use the y-intercept (0,63) by substituting the values of x and y into the equation.

[tex]63 = a(0-5)^2 - 12[/tex]

63 = 25a - 12

25a = 75

a = 3

Now that we have the value of a, we can substitute it back into the equation and solve for the x-intercepts:

[tex]0 = 3(x-5)^2 - 12[/tex]

[tex]3(x-5)^2 = 12[/tex]

[tex](x-5)^2 = 4[/tex]

x-5 = ±2

x = 5 ± 2

Therefore, the x-intercepts of the parabola are x = 3 and x = 7.

Answer:

.

Step-by-step explanation:

.

Final answer:

To find the interval of increase for the function F(x) = 9*sin(x) + cot(x), we need to find where the derivative is positive. The interval of increase for the function is (0, π/2) and (π, 3π/2).

Explanation:

In order to find the interval of increase for the function F(x) = 9*sin(x) + cot(x), we need to find where the derivative is positive. Let's first find the derivative of F(x). The derivative of sin(x) is cos(x) and the derivative of cot(x) is -csc^2(x).

So, the derivative of F(x) is 9*cos(x) - csc^2(x). Now, to find where the derivative is positive, we need to find the intervals where 9*cos(x) - csc^2(x) > 0. We can solve this inequality by analyzing the sign changes of the derivative function.

By analyzing the sign changes of 9*cos(x) - csc^2(x), we find that the derivative is positive when x is in the intervals (0, π/2) and (π, 3π/2). Therefore, the interval of increase for the function F(x) = 9*sin(x) + cot(x) is (0, π/2) and (π, 3π/2).