When creating lines of best fit, do you believe that estimation by inspection of the equation is best or do you think it should be determined exactly? In what situations would it be best to use one over the other?




Your response should be 3-5 sentences long and show that you’ve thought about the topic/question at hand

Hey there! :)

Answer:

(x + 27)(x + 1)

Step-by-step explanation:

Given:

a² + 28a + 27

Find numbers that add up to 28 and multiply to 27:

We can find that the numbers 27 and 1 add up to 28 and multiply to form 27. Therefore, the equation in factored form is:

(x + 27)(x + 1)

Answer:

Solution,

\( {a}^{2} + 28a + 27 \\ = {a}^{2} + (27 + 1)a + 27 \\ = {a}^{2} + 27a + a + 27 \\ = a(a + 27) + 1(a + 27) \\ = (a + 27)(a + 1)\)

Hope this helps..

Good luck on your assignment..

Answer:

15

Step-by-step explanation:

(x+3)(x+5)=0

x^2+8x+15=0

For a two-tailed hypothesis test about μ, we can use any of the following approaches except comparing the level of significance; to the confidence coefficient

To determine if the sample mean is substantially more than or significantly less than the population mean, a two-tailed hypothesis test is used. The area under both tails or sides of a normal distribution is what gives the two-tailed test its name.

Any of the following methods, with the exception of comparing the level of significance to the confidence coefficient, can be used for a two-tailed hypothesis test regarding. To create a confidence interval estimate for the population mean, approach (d) compares the level of significance which is a to the confidence coefficient which is 1- a. This method is employed to estimate the population parameter rather than test a hypothesis.

Complete Question:

For a two-tailed hypothesis test about μ, we can use any of the following approaches EXCEPT compare the _____ to the _____.

a.confidence interval estimate of μ; hypothesized value of μ

b.p-value; value of α

c.value of the test statistic; critical value

d.level of significance; confidence coefficient

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Answer:

V = π r^2 h = π · 10^2 · 15 ≈ 4712.38898

As a result, the solid's volume in the first octant, which is restricted by the paraboloid z = 4 + 2 x + 2 y, is 9.

We must determine the limits of integration for x, y, and z in order to determine the volume of the solid in the first octant bounded by the paraboloid z = 4 + 2x + 2y + 2 and the plane z = 10.

At z = 10, where the paraboloid and plane overlap, we put the two equations equal and find z:

4 + 2x^2 + 2y^2 = 10

2x^2 + 2y^2 = 6

x^2 + y^2 = 3

This is the equation for a circle in the xy plane with a radius of 3, centred at the origin. We just need to take into account the area of the circle where x and y are both positive as we are only interested in the first octant.

Integrating over the circle in the xy-plane, we may determine the limits of integration for x and y:

∫∫[x^2 + y^2 ≤ 3] dx dy

Switching to polar coordinates, we have:

∫[0,π/2]∫[0,√3] r dr dθ

Integrating with respect to r first gives:

∫[0,π/2] [(1/2)(√3)^2] dθ

= (3/2)π

So the volume of the solid is:

V = ∫∫[4 + 2x^2 + 2y^2 ≤ 10] dV

= (3/2)π(10-4)

= 9π

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Answer: -8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Reverse the steps and reverse the operations (divide to multiply, add to subtract)

Multiply 6 by 2 to get 12 and subtract 4 to get 8

Answer:

Subtract 10

Step-by-step explanation:

The first option, "take the ones digit", is obviously incorrect because the ones digit of 9 is not -1. The second one is incorrect because you are dividing by 2 and then adding 5. Dividing odd numbers by 2 will give you a decimal and a decimal plus an integer (the integer is 5 in this case) will still be a decimal (provided that the decimal is not an integer as well). However, both of the outputs are integers, so we know that the second one is wrong. The third one is wrong as well because 9 / 3 = 3, not -1. The last one is correct because 15 - 10 = 5 and 9 - 10 = -1.

Answer:

Step-by-step explanation:

Step one:

given data

Maya

P=$1650

r=5%= 0.05

t= 4 years

The simple interest expression is

A=P(1+rt)

A=1650(1+0.08*4)

A=1650(1+0.32)

A=1650(1.32)

A=1650*1.32

A=$2178

James

P=$1600

r=8%= 0.08

t=4years

The compound interest expression is

A=P(1+r)^t

A=1600(1+0.08)^4

A=1600(1.08)^4

A=1600*1.360

A=$2176

After 4 years Mayas' balance is $2178

After 4 years James' balance is $2176

the difference is =2178-2176=$2

Answer:

It's -11/5

Step-by-step explanation:

-11/5 x 3 = -33/5

-33/5 = -6 3/5

To find the perimeter of triangle formed by the tangents to the circles, find radii of circles and side lengths of triangle. The perimeter of triangle formed by the tangents to the circles is 12 times the radius of each circle.

Let's denote the radius of each circle as r. Since the circles are externally tangent to each other, the distance between their centers is equal to the sum of their radii, which is 2r.

When a triangle is formed by connecting the points of tangency on each circle, it creates three isosceles triangles. Each of these isosceles triangles has two congruent sides, which are the radii of the circles.By drawing the triangle, we can observe that the base of each isosceles triangle is equal to 2r, which corresponds to the diameter of one of the circles. The height of each isosceles triangle is equal to r, which is the radius of the circle.

Therefore, each side of the triangle formed by the tangents has a length of 4r.Since the triangle has three equal sides, its perimeter is given by 3 times the length of one side, which is 3 * 4r = 12r.The perimeter of the triangle formed by the tangents to the circles is 12 times the radius of each circle.

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The patient underwent a three-stage surgical procedure to remove squamous cell carcinoma on the tip of their nose.

Based on the given information, the patient underwent a three-stage surgical procedure for the removal of squamous cell carcinoma on the tip of the nose. The tumor was initially removed (first stage) and divided into seven blocks for examination. However, positive margins were observed. Consequently, a second stage was performed, and the tumor was divided into five blocks, again revealing positive margins. Finally, a third stage was carried out, and the specimen was divided into three blocks, which were found to be clear of skin cancer.

The multiple stages of the surgical procedure indicate the physician's effort to ensure the complete removal of squamous cell carcinoma by progressively resecting the affected tissue until clear margins were achieved. This stepwise approach is common in cases where the tumor extends beyond the initial resection boundaries to ensure complete eradication of the cancer cells.

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Answer:

5/9

Step-by-step explanation:

brainliest when possible.

\(-(5\cdot(-4))=-(-20)=20\)

Distributive property works only for addition.

\(a(b+c)=ab+ac\) but \(a(bc)=abc\), not \(ab+ac\) or something like that.

Answer:

\(-(-5\times(-4))=-(-20)=20\)

Step-by-step explanation:

Notice that the product within the brackets is:

\(5\times(-4)=-20\)

Then, by first evaluating the product within the brackets, we get the following:

\(-(5\times(-4))=-(-20)\)

Finally, note that the negative of negative twenty is twenty as follows:

\(-(-20)=20\)

*Note on your mistake:

You cannot distribute the negative sign to each component of a product.

This can only happen if the expression within the bracket is a sum, for instance:

\(-(5+(-4))=-5+4\)

Answer: hb=8.4cm

Step-by-step explanation:

Using the formula

A=hbb

2

Solving forhb

hb=2A

b=2·67.2

16=8.4cm

Answer:

\(y=-x+11\)

Step-by-step explanation:

We know that the new equation must be parallel to \(y=-x-5\).

Therefore, since they are parallel, the slope of the new equation must be the same as the old.

The slope of the original equation is -1.

Therefore, the slope of our new equation is also -1.

We also know that it has a y-intercept at (0, 11).

And as determined earlier, it has a slope of -1.

So, we can use the slope-intercept form:

\(y=mx+b\)

Where m is the slope and b is the y-intercept.

We will substitute -1 for m and 11 for b. Thus, our equation is:

\(y=-x+11\)

Answer:

106

Explain how you found your answer:

Step-by-step explanation:

|-13| = 13

13 = 13 Option A is true

-|13| = 13

-13 = 13

-13 ≠ 13 Option B isn't true

|13| = -13

13 = -13

13 ≠ -13 Option C isn't true

-|-13| = 13

-13 = 13

-13 ≠ 13 Option D isn't true

Answer:

\(\frac{3}{5}\)

Step-by-step explanation:

Hey there,

\(\frac{7}{10} -\frac{1}{10}\)

\(\frac{7-1}{10}\)

\(\frac{6}{10}\)

To make the fraction in the simplest form divide both sides by 2

\(\frac{3}{5}\)

Hope this helps you.

Let me if you have any other questions :-)

The area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

\(x^2 + y^2 = r^2\) about the line y = r, we can use the method of cylindrical shells.

The circle \(x^2 + y^2 = r^2\) is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle \(x^2 + y^2 = r^2:\\y^2 = r^2 - x^2\)

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

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The change in the approximation to f(0.3) is:

Δf(0.3) = 21.775 - 14.775 = 7.0The approximation should be changed by 7.0 units.

To approximate the value of f(0.3) using Newton's divided difference formula, we need to construct a divided difference table. Given the following data:

Ii     | x    | 0.6  | 0.0  | 0.2  | 0.4  

-------|------|------|------|------|------

fx    | 15.0 | 21.0 | 30.0 |

We can construct the divided difference table as follows:

x      | fx       | 1st Diff.  | 2nd Diff. | 3rd Diff.

-------|----------|------------|-----------|-----------

0.6    | 15.0     |            |           |

0.0    | 21.0     | -6.0       |           |

0.2    | 30.0     | 9.0        | 5.0       |

0.4    |           | 15.0       | 7.5       |

      |          |            | 22.5      |

      |          |            |           | 15.0

Using this table, we can apply Newton's divided difference formula to approximate f(0.3):

f(0.3) ≈ fx0 + (x - x0) * Diff1,0 + (x - x0)(x - x1) * Diff2,0,1

Substituting the values from the divided difference table:

f(0.3) ≈ 15.0 + (0.3 - 0.6) * (-6.0) + (0.3 - 0.6)(0.3 - 0.0) * 22.5

Simplifying the equation:

f(0.3) ≈ 15.0 + (-0.3) * (-6.0) + (-0.3)(0.3) * 22.5

f(0.3) ≈ 15.0 + 1.8 + (-0.09) * 22.5

f(0.3) ≈ 15.0 + 1.8 - 2.025

f(0.3) ≈ 14.775

Now, to determine the change in the approximation due to the adjustments in f(0.4) and f(0.6), we need to recalculate the approximation considering the new values.

Suppose f(0.4) was understated by 10, which means the corrected value is 15 + 10 = 25.

And suppose f(0.6) was overstated by 5, which means the corrected value is 30 - 5 = 25.

We update the divided difference table with the corrected values:

x      | fx       | 1st Diff.  | 2nd Diff. | 3rd Diff.

-------|----------|------------|-----------|-----------

0.6    | 25.0     |            |           |

0.0    | 21.0     | 4.0        |           |

0.2    | 30.0     | 9.0        | 2.5       |

0.4    |           | 15.0       | 3.75      |

      |          |            | 22.5      |

      |          |            |           | 15.0

Using the updated table, we can now calculate the new approximation for f(0.3):

f(0.3) ≈ 25.0 + (0.3 - 0.6) * 4.0 + (

0.3 - 0.6)(0.3 - 0.0) * 22.5

Simplifying the equation:

f(0.3) ≈ 25.0 + (-0.3) * 4.0 + (-0.3)(0.3) * 22.5

f(0.3) ≈ 25.0 - 1.2 + (-0.09) * 22.5

f(0.3) ≈ 25.0 - 1.2 - 2.025

f(0.3) ≈ 21.775

Therefore, the change in the approximation to f(0.3) is:

Δf(0.3) = 21.775 - 14.775 = 7.0

The approximation should be changed by 7.0 units.

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Answer:

  -1056.87

Step-by-step explanation:

You want to know the number that represents the change in a bank balance from +$708.88 to -$347.99.

The change in a value is found by subtracting the beginning value from the ending value:

  -$347.99 -708.88 = -$1056.87

The number -1056.87 can be used to describe the change in the account balance.

Answer:

b=− 3/4 =−1.333

b= 2/3=1.500

explanation

middle term, which is   -1 .  

     -72    +    1    =    -71

     -36    +    2    =    -34

     -24    +    3    =    -21

     -18    +    4    =    -14

     -12    +    6    =    -6

     -9    +    8    =    -1    That's it

Two real solutions:

b =(1+√289)/12=(1+17)/12= 1.500

or:

b =(1-√289)/12=(1-17)/12= -1.333

Answer:

52

Step-by-step explanation:

196-144=52

Answer:

-812

Step-by-step explanation:

(1×106)-(9×102)

106-918

-812

Answer:

A B and C

Step-by-step explanation:

it's a simple question

Here, we want to simplify the given expression

We shall use the order of simplification for this

The order is PEDMAS

We shall start with the terms in parentheses before we move to the exponents

We have;

Next is the exponent

The next thing to do is to divide

The next thing to do is to multiply

We then proceed to subtract;