Part A: Using computer software, a correlation coefficient of r = 0. 01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)

Answer:

1914

Step-by-step explanation:

interest for one year = 33

interest of 8 years = 264

1650+264 will be in the account in 8 years.

The equation of the curve is: y = \(2x^(^3^/^2^) - 11\)

To find the curve in the xy-plane that passes through the point (4, 5) and has a slope of 3√(x) at each point, we can integrate the given slope function to obtain the equation of the curve.

The slope function is given as: dy/dx = 3√(x)

Integrating both sides with respect to x:

∫ dy = ∫ 3√(x) dx

Integrating the left side with respect to y gives us y:

y = ∫ 3√(x) dx

To integrate 3√(x), we can rewrite it as 3\(x^(^1^/^2^)\):

y = 3 ∫ \(x^(^1^/^2^)\)dx

Integrating \(x^(^1^/^2^)\) gives us (2/3)\(x^(^3^/^2^)\):

y = 3 * (2/3)\(x^(^3^/^2^)\) + C

Simplifying:

y = 2\(x^(^3^/^2^)\) + C

Now, we can use the given point (4, 5) to determine the value of the constant C:

Therefore, the equation of the curve that passes through the point (4, 5) and has a slope of 3√(x) at each point is:

y = \(2x^(^3^/^2^) - 11\)

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Answer:

The quotient of: \(\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}\) is: \(\mathbf{3.3\times 10^{-4}}\)

Step-by-step explanation:

We need to find quotient of: \(\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}\)

We know that \(10^0=1\)

Now solving:

\(\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}\\=\frac{2.64\cdot 10^{-3}}{8.0}\\=\frac{0.00264}{8}\\=0.00033\)

Writing it in scientific notation

\(0.00033\\=3.3\times10^{-4}\)

So, the quotient of: \(\frac{2.64\cdot 10^{-3}}{8.0\cdot 10^0}\) is: \(\mathbf{3.3\times 10^{-4}}\)

To prove that it is possible to choose 11 dalmatians whose total number of spots is divisible by 11, we will use the given hint and associate each dalmatian with its number of spots mod 11.

There are 11 possible remainders when the number of spots is divided by 11: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

Case 1: There is at least one dalmatian in each of the 11 categories (i.e., one dalmatian with 0 spots mod 11, one with 1 spot mod 11, and so on).

In this case, we can simply choose one dalmatian from each category and their total number of spots will be divisible by 11. This is because the sum of the remainders when you divide each number by 11 will also be divisible by 11 (i.e., 0+1+2+3+4+5+6+7+8+9+10 = 55, which is divisible by 11).

Case 2: There is at least one category with no dalmatians.

In this case, we can choose any 11 dalmatians and associate them with their number of spots mod 11. This will give us 11 remainders. If there is at least one category with no dalmatians, then there must be at least one category with two or more dalmatians. We can choose one dalmatian from each of the other categories and add them to the group of 11. The sum of their remainders will be divisible by 11, and the sum of their total number of spots will be divisible by 11 as well.

Therefore, we have shown that it is always possible to choose 11 dalmatians whose total number of spots is divisible by 11.

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Answer:

x = 19

Step-by-step explanation:

x-42+x-32+180-x+17 = 180

3x +123 = 180

3x = 57

x=19

x = 91.

Putting 91 into the two equations inside the triangle makes the angles 59 and 49, and makes the outside angle 108. Those two angles must add and equal the outside angle, and they do, meaning x = 91.

We have found and simplified the expression for f(a+h) and f(a), and then found the expression for f(a+h) - f(a). [For more detail scroll down]

To find f(a+h), we simply replace x in the function f(x) with a+h. This gives us:
f(a+h) = 4 - 2(a+h) + 6(a+h)²
To simplify this, we need to expand the squared term:
f(a+h) = 4 - 2a - 2h + 6(a² + 2ah + h²)
Simplifying further:
f(a+h) = 4 + 6a² + 12ah + 6h² - 2a - 2h
Now, to find f(a) we simply replace x in the function f(x) with a. This gives us:
f(a) = 4 - 2a + 6a²
To find f(a+h) - f(a), we simply subtract f(a) from f(a+h):
f(a+h) - f(a) = (4 + 6a² + 12ah + 6h² - 2a - 2h) - (4 - 2a + 6a²)
Simplifying further:
f(a+h) - f(a) = 12ah + 6h² - 2h
Therefore, the simplified expression for f(a+h) - f(a) is:
f(a+h) - f(a) = 2h(6a + 3h - 1)
In conclusion, we have found and simplified the expression for f(a+h) and f(a), and then found the expression for f(a+h) - f(a).

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Answer:

-1.33333333333

Step-by-step explanation:

Answer:

-1 1/3

Step-by-step explanation:

Answer:

√{2545×2545}=√2545²=±2545

Answer:

The area of the sector is approximately 3.1 square meters.

Step-by-step explanation:

The area of a circular sector is given by the formula A = (θ/2)R^2, where θ is the central angle in radians and R is the radius of the sector.

Plugging in the given values, we get:

A = (π/8)(4)^2/2

A ≈ 3.1 m^2

Therefore, the area of the sector is approximately 3.1 square meters.

Step-by-step explanation:

4+5 (2x-3)-6x

9 (2x-3)-6x

18x-27-6x

12x-27

Answer:

\( \sf \: 4x - 11 \)

Step-by-step explanation:

Given expression,

→ 4 + 5(2x - 3) - 6x

Let's simplify the expression,

→ 4 + 5(2x - 3) - 6x

→ 4 + 10x - 15 - 6x

→ (10x - 6x) + (4 - 15)

→ (4x) + (-11)

→ 4x - 11

Hence, the answer is 4x - 11.

Answer:

✓ 42.25-39.85=2.437+1 1/4= 38.2539.25-38.25=1Eric came closer.\\

Step-by-step explanation:

:]

Answer:

eric came closer

Step-by-step explanation:

Answer:\(-\frac{3}{10}\)

Step-by-step explanation:

Fractal design is a concept that originates from the field of mathematics and is characterized by the repetition of patterns at different scales. It is based on fractals, which are complex geometric shapes or patterns that exhibit self-similarity.

Fractals possess intricate detail and structure, with similar patterns repeating at infinitely smaller scales. Fractals are created through iterative processes or recursive equations. They are often generated using computer algorithms such as the Mandelbrot set or Julia set, which allow for the visualization and exploration of these fascinating structures.

Fractals have a deep connection to various mathematical concepts, including chaos theory, non-Euclidean geometry, and dynamical systems.

Incorporating fractal design in technology offers numerous applications. Fractals can be used in computer graphics, digital art, and visual effects to create realistic landscapes, textures, and intricate patterns. They have found applications in image compression algorithms, data analysis, and signal processing.

Fractals also inspire the development of efficient algorithms and data structures for computer graphics and simulations.

In summary, fractal design harnesses the mathematical principles of self-similarity and iteration to create intricate and visually captivating patterns. It finds applications in various technological domains, contributing to computer graphics, data analysis, and algorithm development.

The study and utilization of fractals continue to inspire advancements in both mathematics and technology.

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Answer:

26.3 feet

Step-by-step explanation:

We have to first find the length of the side of each tile.

The area of each tile is 19.2 \(ft^2\).

The area of a square is:

A = \(L^2\)

where L = length of side

Therefore:

\(19.2 = L^2\\\\L = \sqrt{19.2} = 4.38 feet\)

6 tiles will be lined end to end to construct the walkway, hence, the length of the walkway is:

6 * 4.38 ≅ 26.3 feet

The parametric equations \(x = 6 cos θ\)and\(y = 3 sin θ\) trace out the ellipse \(2x^2 + y^2 = 36\).

To find the parametric equation for the curve \(2x^2 + y^2 = 36\)., we can use the following steps:

1. Choose a parameter, say t.
2. Express x and y in terms of t using symbolic notation and fractions where needed.
3. Substitute the expressions for x and y into the equation \(2x^2 + y^2 = 36\) to verify that the curve is traced out by the parametric equations.

One possible choice for the parameter is t = θ, where θ is the angle measured from the positive x-axis to the point (x, y) on the curve. Using this approach, we can write:
\(x = 6 cos θ\\y = 3 sin θ\)

To verify that these equations trace out the curve \(2x^2 + y^2 = 36\)., we substitute the expressions for x and y into the equation:
\(2(6 cos θ)^2 + (3 sin θ)^2 = 36\)

Simplifying this expression using trigonometric identities, we get:
\(72 cos^2 θ + 9 sin^2 θ = 36\)

Dividing both sides by 9 and using the identity \(cos^2 θ + sin^2 θ = 1\), we obtain:
\(8 cos^2 θ + sin^2 θ = 4\)

Multiplying both sides by 8 and using the identity \(cos 2θ = 2 cos^2 θ - 1\)and\(sin 2θ = 2 sin θ cos θ\), we get:
\(cos 2θ = -3/4\\sin 2θ = ±\sqrt{7}/4\)

These equations represent a curve that has two branches, one in the first and fourth quadrants and the other in the second and third quadrants. Therefore, the parametric equations\(x = 6 cos θ\) and \(y = 3 sin θ\) trace out the ellipse\(2x^2 + y^2 = 36\).

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Answer:

Arun father age will be 3X+5 and his age will be X+5

Answer:

an increase of 12%

Step-by-step explanation:

68 divided by 77 is 0.88 approximately

100-88 is 12

Tip:

do this for increase and decrease in percentage question

divide small number by big number, and subtract the quotient from 100

Answer:

13%

Step-by-step explanation:

Percent increase is solved as such:

Percent Increase =  %∧ = \((\frac{New~Amount~-~Original~Amount}{Original~Amount}) ~*~10\)

%∧ = \((\frac{77~-~68}{68}) ~*~100 = (\frac{9}{68}) ~*~100 = 0.13 * 100 = 13\%\)

Remember you want to know what percentage the difference is compared to how much your original amount is.

Hope this helps :)

Answer:

-2x(x^2+2x+3)

Step-by-step explanation:

-2x^3-4x^2-6x

You can only factor out the 2x the other part is not factorable.

Answer:

5

Step-by-step explanation:

180-108=72 interior + exterior angle add to 180

360/72=5

Answer:

Number of polygon sides = 360 / (180 - ONE INTERIOR ANGLE)

Number of polygon sides = 360 / (180 -108)

Number of polygon sides = 360 / 72

Number of polygon sides = 5

Source: http://www.1728.org/polygon.htm

Step-by-step explanation:

The required pair of length and width is given as 2 x 6 square feet and 6 x 2 square feet respectively.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,
According to the question,
Perimeter = 16
2L + 2W = 16
L = 8 - W - - - - - (1)

Area  = 12
L × W = 12
(8 - W)W= 12
W² - 8W + 12 = 0
(W - 6)(W - 2) = 0
W = 6 and W = 2
Put this W in equation 1
L = 2 and L = 6

Thus, the required pair of length and width is given as 2 x 6 square feet and 6 x 2 square feet respectively.

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Answer:

4

Step-by-step explanation:

3/.75=4

Answer:

4

Step-by-step explanation:

48/16 equals to 3. 18/24 equals to 3/4 or 0.75. 3 divided by 0.75 equals to 4

Answer:

\(y=-2(sin(2x))-7\)

Step-by-step explanation:

1. Approach

Given information:

What conclusions can be made about this function:

Therefore, one has the following information figured out:

\(y=-n(sin(ax))+b\)

Now one has to find the following information:

2. Midline

The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:

y = -7

2. Amplitude

The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.

point of minimum: \((\frac{\pi}{4},9)\)

midline: \(y=-7\)

Amplitude: 9 - |-7| = 9 - 7 = 2

3. Period

The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).

point of minimum: \((\frac{\pi}{4},9)\)

midline intersection: \((0, -7)\)

Period: \(4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi\)

However, in order to input this into the function in place of the variable (a), one has to divide this number by (\(2\pi\)).

\(a=\frac{2\pi}{\pi}=2\)

4. Assemble the function

One now has the following solutions to the variables:

\(n =-16\\a=2\\b=-7\\\)

Substitute these values into the function:

\(y=-2(sin(2x))-7\)

Answer:

All of the views will be rectangles. The front view will be a rectangle 8 squares wide and 5 squares tall. The side view will be a rectangle 4 squares wide and 5 squares tall. The top view will be a rectangle 8 squares wide and 4 squares tall.

Step-by-step explanation:

The proportional relationship between the price and quantity of ears of corn can be represented using a table or a graph, showing how the price and quantity vary in a consistent manner.

One way to represent the proportional relationship between the price and quantity of ears of corn is by using a table:

Price (in dollars) Quantity (in ears of corn)

             2             5

             4             10

This table shows the corresponding values of the price and quantity.

As we can observe, when the price is $2, the quantity is 5 ears of corn, and when the price is $4, the quantity is 10 ears of corn.

The relationship is proportional because as the price doubles, the quantity also doubles.

Another representation of this proportional relationship is through a graph.

We can plot the points (2, 5) and (4, 10) on a coordinate plane, where the x-axis represents the price and the y-axis represents the quantity.

By connecting these two points with a straight line, we can visualize the proportional relationship.

The line will pass through the origin (0, 0) since zero price corresponds to zero quantity.

The slope of the line will indicate the rate of change between price and quantity.

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Answer:

46

Step-by-step explanation:

length x width x height

7 x 5 x 3

Answer: surface area = 142

Volume = 105

* make sure to add labels (units^2, etc.)

Step-by-step explanation:

Area = length x height

Volume = length x width x height

Answer:

5.94 and -9.94

Explanation:

Use complete the square to answer the question and then type the last line into a calculator to get 5.94 and -9.94

Answer:

infinite

Step-by-step explanation:

the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite

                            -hope this helps-

Answer:

43/10 pounds = 4 3/10 pounds

Step-by-step explanation:

for this you want to subtract 6 7/10 minus 2 2/5. You first have to get a common denominator and find the numerator then subtract.

Answer:

8 pieces of string

Step-by-step explanation:

Given that :

Total yards of string = 4

Length in yd of each string = 1/2 yards

Number of pieces of string Ms. Cole has :

Total. Yards / length in yard of each string

4 / (1/2)

4 * (2 /1)

= 8/1

= 8 pieces of string.