Identify the coefficients.
4x - 7 + 2x

The satellite is approximately 9,200 miles from the Earth's surface.

To find the approximate distance the satellite is from the Earth's surface, we can subtract the Earth's radius from the distance between the satellite and the horizon. The distance from the satellite to the horizon is the sum of the Earth's radius and the distance from the satellite to the Earth's surface.

Given that the satellite is 13,200 miles from the horizon and the Earth's radius is about 4,000 miles, we subtract the Earth's radius from the distance to the horizon:

13,200 miles - 4,000 miles = 9,200 miles.

Therefore, the approximate distance of the satellite from the Earth's surface is around 9,200 miles.

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Answer:

There are 7 handshakes.

Step-by-step explanation:

The profesor is shaking hands with 7 people, so there are 7 handshakes between them.

The number of handshakes that take place are  \(^nC_{k}\)= \(\frac{n!}{k!(n-k)!}$\)  i.e 28

In mathematics, permutation relates to the act of arranging all the members of a set into some sequence or order. The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. The formula for permutation is nPr = (n!) / (n-r)! and combination formula is  nCr = n!/[r! (n-r)!]

Given here Prof. Anne Bishon has a meeting with 7 other academics, they all shake hands before sitting down thus

\(^8C_{2}\)   = \(\frac{8!}{2!(8-2)!}$\)

\(^8C_{2}\) = 28

Hence, The number of handshakes that takes place is equal to 28

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Answer:

-3p

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

5p - 4p = 1p - 4p = -3p

The amount that Stephen owed after 2 weeks is $100.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, Stephan borrowed $125 to buy an electric scooter and the function f(x) = 125 - 12.5x

can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.

The amount after 2 weeks will be:

f(x) = 125 - 12.5x

= 125 - 12.5(2)

= 125 - 25

= $100

The amount is $100.

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Complete question

Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x

can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan. What is the amount owed after 2 weeks?

Answer:

x is 4.

Step-by-step explanation:

8 times 8 is 64

64 minus 4 is 60

60 divided by 15 is 4

Answer:

10 1/24

Step-by-step explanation:

We will need to add the wood Jermaine has and how much he needs together. Because the fractions denominators are not equal, we will multiply them.

(3/8) × 3 = 9/24

(2/3) × 8 = 16/24

Now we can add these together.

4 9/24 + 5 16/24 = 10 1/24

The answer is simplified already.

Whole part = 10 feet

Fractional part = 1/24 of a foot (aka half an inch)

===================================================

Explanation:

For now, let's focus on the fractions.

The new equivalent fractions formed both involve the same denominator 24, allowing us to add those fractions.

3/8 + 2/3 = 9/24 + 16/24 = (9+16)/24 = 25/24

We can then rewrite that improper fraction into a mixed number like this

25/24 = (24+1)/24

25/24 = 24/24 + 1/24

25/24 = 1 + 1/24

25/24 = 1 & 1/24

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

To recap so far, adding the fractions only gets us the mixed number 1 & 1/24

We get 1 full foot, plus an additional 1/24 of a foot

That "1 full foot" portion carries over to the whole parts 4 and 5 being added to get us 4+5+1 = 10

The whole parts add to 10 and we have the fractional part 1/24 tag along to end up with the final answer of 10 & 1/24 feet

Jermaine will need 10 full feet, plus an additional 1/24 of a foot, of lumber.

1/24 of a foot = (1/24)*12 = 12/24 = 0.5 inches

Answer:

they probably do it just to get more answer points or whatever the brianily thing is called

Step-by-step explanation:

Answer:

a 64/3

Step-by-step explanation:

4^3 * 1/3 = 64/3

Answer:

234 mm²

Step-by-step explanation:

area of each side = L x W

(15 x 3 x 2) + (15 x 4 x 2) +(3 x 4 x 2) = 234 mm²

The angle that is an alternate interior angle to ∠3 will be 60°.

From the complete information, it should be noted that the value of angle 3 is 120°.

It should be noted that the angle on straight line is 180°.

Therefore, the angle that is an alternate interior angle to ∠3 will be:

= 180° - 120°

= 60°

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Which angle is an alternate interior angle to ∠3?

60

120

10

30

The answer is: a. Yes, the forecast fails the bias test.

To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.

If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.

In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.

Therefore, the answer is:

a. Yes, the forecast fails the bias test.

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Step-by-step explanation:

(a)4/5×5=4-1/8=3.875or (32 if a is division)

(b)1 1/3=4/3×9=12 12×1/6=2

(c)7/8×8=7÷2/5=0.7 or 2.8

(d)16×6/4=24×10=240

Answer:

The answer is D.72°

Step-by-step explanation:

hope this helps.

The point (7, -π/2) in polar coordinates corresponds to the rectangular coordinates (0, -7), representing a point on the negative y-axis.

In polar coordinates, a point is represented by its distance from the origin (r) and its angle from the positive x-axis (θ). For the given point (7, -π/2), the distance from the origin is 7 units (r = 7), and the angle is -π/2 radians.

To convert this point to rectangular coordinates, we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

Applying these formulas to the given values, we get:

x = 7 * cos(-π/2)

y = 7 * sin(-π/2)

The cosine of -π/2 is 0, and the sine of -π/2 is -1, so we can substitute these values into the formulas:

x = 7 * 0 = 0

y = 7 * (-1) = -7

Therefore, the rectangular coordinates for the point (7, -π/2) are (0, -7). This represents a point on the negative y-axis, where the x-coordinate is 0 and the y-coordinate is -7.

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Answer:

that is reading my friend

Step-by-step explanation:

Answer:

Sidney  is shallow but busy. One common boating hazard in this city are the rocks, stingrays, and sharks. Rounf trip fair: $2000 hotel cost: 250 for 1 night and and or 2500 for 10 nights. total travel expense: $4500.

Step-by-step explanation:

Sidney is shallow but busy. One common boating hazard in this city are the rocks, stingrays, and sharks. Rounf trip fair: $2000 hotel cost: 250 for 1 night and and or 2500 for 10 nights. total travel expense: $4500. 

(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The Fourier transform pair for a function f(x) is defined as follows:

F(k) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

f(x) = (1/2π) ∫[-∞,∞] F(k) \(e^{2\pi iyx}\) dk

Now let's prove the given properties:

(i) If f is an even function, then f(y) = 2∫[0,∞] f(x) cos(2πxy) dx.

To prove this, we start with the Fourier transform pair and substitute y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is even, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[-∞,0] f(x) \(e^{2\pi iyx}\) dx

Since f(x) is even, f(x) = f(-x), and by substituting -x for x in the second integral, we get:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[0,∞] f(-x) \(e^{2\pi iyx}\)dx

Using the property that cos(x) = (\(e^{ ix}\) + \(e^{- ix}\))/2, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dx

Now, using the definition of the inverse Fourier transform, we can write f(y) as follows:

f(y) = (1/2π) ∫[-∞,∞] F(y) \(e^{2\pi iyx}\) dy

Substituting F(y) with the expression derived above:

f(y) = (1/2π) ∫[-∞,∞] ∫[0,∞] f(x) \(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\)/2 dx dy

Interchanging the order of integration and evaluating the integral with respect to y, we get:

f(y) = (1/2π) ∫[0,∞] f(x) ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy dx

Since ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy = 2πδ(x), where δ(x) is the Dirac delta function, we have:

f(y) = (1/2) ∫[0,∞] f(x) 2πδ(x) dx

f(y) = 2 ∫[0,∞] f(x) δ(x) dx

f(y) = 2f(0) (since the Dirac delta function evaluates to 1 at x=0)

Therefore, f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx, which proves property (i).

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The proof for this property follows a similar approach as the one for even functions.

Starting with the Fourier transform pair and substituting y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is odd, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx - ∫[-∞,0] f(x) \(e^{-2\pi iyx}\) dx

Using the property that sin(x) = (\(e^{ ix}\) - \(e^{-ix}\))/2i, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) - \(e^{2\pi iyx}\)/2i dx

Now, following the same steps as in the proof for even functions, we can show that

f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx

This completes the proof of property (ii).

In summary:

(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

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Answer:

0.40390 km

Step-by-step explanation:

1 cm = 1 / 100000 km

40390 cm

= 40390 / 100000

= 0.40390 km

The interval that contains the root of f(x) = 2x − x3 + 0.5 is [-2, -1].

To find which interval contains the root of the equation f(x) = 2x − x3 + 0.5, we can use the intermediate value theorem. This theorem states that if a function is continuous on a closed interval [a, b], and takes on values f(a) and f(b) at the endpoints, then for any value y between f(a) and f(b), there exists a value c in [a, b] such that f(c) = y.

In this case, we can evaluate f(x) at the endpoints of the intervals [-2, -1], [-1, 0], [0, 1], and [1, 2], as follows

For [-2, -1]: f(-2) = -11.5 and f(-1) = 1.5
For [-1, 0]: f(-1) = 1.5 and f(0) = 0.5
For [0, 1]: f(0) = 0.5 and f(1) = 1.5
For [1, 2]: f(1) = 1.5 and f(2) = -11.5

From this, we can see that the function changes sign from negative to positive in the interval [-2, -1], which means there must be a root in this interval. We can also see that the function is positive throughout the interval [1, 2], so there cannot be a root in this interval. The intervals [-1, 0] and [0, 1] do not change sign, so we cannot conclude whether or not there is a root in these intervals.

Therefore, the interval that contains the root of f(x) = 2x − x3 + 0.5 is [-2, -1].

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A free-body diagram is a visual representation of the forces acting on an object. For this beam, we have a pin at point A and a rocker at point B.

To draw the free-body diagram, we need to identify all the forces acting on the beam. We can start by drawing a rectangle to represent the beam and placing a dot at points A and B.

At point A, there will be a force acting in the vertical direction due to the weight of the beam. We can draw this vector pointing downwards from point A. At point B, there will also be a force acting in the vertical direction due to the weight of the beam, so we can draw another vector pointing downwards from point B.

Additionally, there will be horizontal forces acting on the beam at point A and point B. These forces are due to the fact that the beam is supported by a pin and a rocker. At point A, there will be a horizontal force acting towards the left, and at point B, there will be a horizontal force acting towards the right. We can draw these vectors starting from point A and point B respectively.

Overall, the free-body diagram for the beam will show four forces acting on it: two forces in the vertical direction and two forces in the horizontal direction. By representing these forces visually, we can better understand how they interact with the beam and how the beam is supported.

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Answer:

x=7

Step-by-step explanation:

↝ Quadratic Function has the domain of all real numbers. (Even not given the specific domain.)

↝ The equation \(y=-3(x-5)+8\) is a parabola with (5,8) as a vertex. We call the equation \(y=a(x-h)^2+k\) as vertex equation.

The domain of -3(x-5)+8 is all set of real numbers.

↝ Interval Notation ↝

Since the domain of the equation is set of all real numbers.

Therefore, the domain is x ∈ R or (-∞,∞) or -∞<x<∞

There of them work. Recall that the domain of quadratic function is all set of real numbers.

The directional derivative of \(\(f(x, y, z) = 4x^2y + xz^2 + 0y^3z\)\)) in the direction of the origin is approximately -44.041. The closest value to the directional derivative is 44.041000852586912

To find the directional derivative of the function\(\(f(x, y, z) = 4x^2y + xz^2 + 0y^3z\)\) at the point \(\((2, -6, 1)\)\)in the direction of the origin, we need to compute the dot product of the gradient of the function at that point and the unit vector in the direction of the origin.

First, let's find the gradient of \(\(f(x, y, z)\):\)

\(\(\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)\)\)

Taking partial derivatives:

\(\(\frac{\partial f}{\partial x} = 8xy\)\\\(\frac{\partial f}{\partial y} = 4x^2 + 0\)\\\(\frac{\partial f}{\partial z} = xz^2\)\)

Evaluating the partial derivatives at the point (2, -6, 1):

\(\(\frac{\partial f}{\partial x}(2, -6, 1) = 8(2)(-6) = -96\)\\\(\frac{\partial f}{\partial y}(2, -6, 1) = 4(2)^2 + 0 = 16\)\\\(\frac{\partial f}{\partial z}(2, -6, 1) = 2(1)^2 = 2\)\)

So the gradient of f(x, y, z) at (2, -6, 1) is \(\(\nabla f(2, -6, 1) = (-96, 16, 2)\).\)

Next, we need to find the unit vector in the direction of the origin, which is the normalized vector \(\(\mathbf{u}\):\)

\(\(\mathbf{u} = \frac{\mathbf{v}}{\|\mathbf{v}\|}\)\)

Where  \(\(\mathbf{v}\)\) is the vector pointing from the origin to the point (2, -6, 1):

\(\(\mathbf{v} = (2, -6, 1)\)\)

Finding the magnitude of  \(\(\mathbf{v}\)\):

\(\(\|\mathbf{v}\| = \sqrt{2^2 + (-6)^2 + 1^2} = \sqrt{41}\)\)

Normalizing \(\(\mathbf{v}\)\):

\(\(\mathbf{u} = \frac{1}{\sqrt{41}}(2, -6, 1)\)\)

Finally, computing the directional derivative by taking the dot product of the gradient and the unit vector:

Directional derivative \(= \(\nabla f(2, -6, 1) \cdot \mathbf{u}\) = \((-96, 16, 2) \cdot \frac{1}{\sqrt{41}}(2, -6, 1)\) = \(-96 \cdot \frac{2}{\sqrt{41}} + 16 \cdot \frac{-6}{\sqrt{41}} + 2 \cdot \frac{1}{\sqrt{41}}\) = \(\frac{-192}{\sqrt{41}} + \frac{-96}{\sqrt{41}} + \frac{2}{\sqrt{41}}\) = \(\frac{-192 - 96 + 2}{\sqrt{41}}\) = \(\frac{-286}{\sqrt{41}}\)\)                      

Approximatingthe numerical value of the directional derivative, we get:

Directional derivative ≈ -44.041

Among the given options, the closest value to the directional derivative is 44.041000852586912, which corresponds to the second option.

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Let's write the ration as a fraction:

1 cm to 1.5 cm

Ratio : 1/1.5 but we need to write it without decimals,

1/1.5 = 2/3 (multiplying by 2 numerator and denominator)

K, the correct answer is 2/3

To estimate the integral √(ln(2)) ln(x) dx within an accuracy of 0.01 using upper and lower sums for a uniform partition of the interval [1, e], we need to divide the interval into at least n subintervals. The answer is obtained by finding the minimum value of n that satisfies the given accuracy condition.

We start by determining the interval [1, e], where e is approximately 2.718. The function ln(x)^2 is increasing, meaning that its values increase as x increases. To estimate the integral, we use upper and lower sums with a uniform partition. In this case, the width of each subinterval is (e - 1)/n, where n is the number of subintervals.

To find the minimum value of n that ensures the accuracy condition S - S < 0.01, we need to evaluate the difference between the upper sum (S) and the lower sum (S) for the given partition. The upper sum is the sum of the maximum values of the function within each subinterval, while the lower sum is the sum of the minimum values.

Since ln(x)^2 is increasing, the maximum value of ln(x)^2 within each subinterval occurs at the right endpoint. Therefore, the upper sum can be calculated as the sum of ln(e)^2, ln(e - (e - 1)/n)^2, ln(e - 2(e - 1)/n)^2, and so on, up to ln(e - (n - 1)(e - 1)/n)^2.

Similarly, the minimum value of ln(x)^2 within each subinterval occurs at the left endpoint. Therefore, the lower sum can be calculated as the sum of ln(1)^2, ln(1 + (e - 1)/n)^2, ln(1 + 2(e - 1)/n)^2, and so on, up to ln(1 + (n - 1)(e - 1)/n)^2.

We need to find the minimum value of n such that the difference between the upper sum and the lower sum is less than 0.01. This can be done by iteratively increasing the value of n until the condition is satisfied. Once the minimum value of n is determined, we have the required number of subintervals for the given accuracy.

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In the above problem, note that the percent powdered sugar in mixture B was approximately 25.81%. See table attached.

The last column shows the amount of powdered sugar in each mixture, which we can calculate using the percent powdered sugar and the pounds of mixture.

To find the percent powdered sugar in mixture B, we can use the fact that the total amount of powdered sugar in the final mixture is the sum of the amounts of powdered sugar in each of the original mixtures. So we have:

1 + 0.11x = 3.84

Solving for x, we get:

0.11x = 2.84

x = 25.81

Therefore, the percent powdered sugar in mixture B was approximately 25.81%.

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Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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The margin of error for a 95% confidence interval estimate is 0.01.

a. Point estimateThe point estimate of the population mean can be calculated using the following formula:Point Estimate = Sample Meanx = 3.01Therefore, the point estimate of the population mean is 3.01.

b. Margin of ErrorThe margin of error (ME) for a 95% confidence interval estimate can be calculated using the following formula:ME = t* * (s/√n)where t* is the critical value of t for a 95% confidence level with 35 degrees of freedom (n - 1), s is the standard deviation of the sample, and n is the sample size.t* can be obtained using the t-distribution table or a calculator. For a 95% confidence level with 35 degrees of freedom, t* is approximately equal to 2.030.ME = 2.030 * (0.03/√36)ME = 0.0129 or 0.01 (rounded to two decimal places)Therefore, the margin of error for a 95% confidence interval estimate is 0.01.

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