After winning a U.S. Open Tennis match at Arthur Ashe Stadium, players fire several tennis balls into the stands as souvenirs. Some players try to hit the ball out of the stadium, at a height of 518 feet. It has never been done. If the ball is propelled from a tennis racket straight up, the ball’s height after t seconds is given by 2 0 h v t t  16 where 0 v is the initial velocity. What is 0 v in order for the ball to reach a maximum height of 518 feet? How long will it take for the ball to reach that height?

\(\pi \int\limits^6_0 {\frac{26}{3} } \, x^{2} -\frac{1}{9} x^{4} dx\) is the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.

A method for determining the volume of a solid of revolution of a solid-state material while integrating along an axis "parallel" to the axis of revolution is known as disc integration, also known as the disc method in integral calculus.

This technique stacks an endless number of discs with varied radii and minuscule thickness to produce the final three-dimensional form. To create hollow solids of revolutions, the same ideas may also be applied when using rings in place of discs (this is known as the "washer technique").

As opposed to this, shell integration integrates along an axis that is parallel to the axis of revolution. The solution can be seen in the attached images below.

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In the consolidated financial statements, the intercompany sales between Perez, Inc. and Senior, Inc. need to be eliminated to avoid double counting of the profits.

When Perez, Inc. sells goods to Senior, Inc., the intercompany sales should be eliminated in the consolidated financial statements. This means that the revenue and cost of goods sold related to these transactions should be removed from both companies' individual income statements.

Since Perez, Inc. sold goods with a 40% gross profit to Senior, Inc., the gross profit on these intercompany sales needs to be eliminated. This adjustment ensures that the consolidated financial statements reflect only the external sales and expenses of the group as a whole.

Furthermore, as Perez, Inc. owns 80% of Senior, Inc., the consolidated income statement should also reflect the portion of Senior, Inc.'s income that belongs to the non-controlling interest (20% ownership not held by Perez, Inc.). This adjustment ensures that the consolidated financial statements accurately reflect the economic interest of both the parent company (Perez, Inc.) and the non-controlling interest (the remaining 20% ownership in Senior, Inc.).

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erez, Inc., owns 80% of Senior, Inc. During the year just ended, Perez sold goods with a 40% gross profit to Senior. Senior sold all of these goods during the year. In its consolidated financial statements for the year, how should the summation of Perez and Senior income statement items be adjusted?

Answer:

Multiplying the variables and numbers in the parentheses by the number next to them.

Step-by-step explanation:

The linear function for this problem is defined as follows:

y = x + 50.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph touches the y-axis at y = 50, hence the intercept b is given as follows:

b = 50.

When x increases by 10, y also increases by 10, hence the slope m is given as follows:

m = 10/10

m = 1.

Hence the function is given as follows:

y = x + 50.

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The equation of the parabola with focus shown on the graph is given by:

y = -x²/12 + 1.

The equation of a vertical parabola of coordinates of vertex (h,k) is given according to the equation presented as follows:

(x - h)² = 4p(y - k).

The focus of a vertical parabola has the coordinates given as follows:

(h, k + p).

From the graph, the coordinates of the vertex of the parabola are given as follows:

(0,1).

Hence the parameters are:

h = 0, k = 1.

Then:

x² = 4p(y - 1)

The coordinates of the focus are given as follows:

(0,-2).

Hence the parameter p is calculated as follows:

k + p = -2

1 + p = -2

p = -3.

Then the equation is:

x² = -12(y - 1)

y - 1 = -x²/12

y = -x²/12 + 1.

The graph of the parabola is given by the image at the end of the answer.

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Table of trigonometric function values for y = sin(x) using multiples of π/4 for x:

x | y

0 | 0

π/4 | \(\sqrt2/2\)

π/2 | 1

3π/4 | \(\sqrt2/2\)

π | 0

5π/4 | -\(\sqrt2/2\)

3π/2 | -1

7π/4 | -\(\sqrt2/2\)

2π | 0

The table above shows the values of x and the corresponding values of y for the function y = sin(x), where x takes multiples of π/4.

To calculate the values of y, we substitute each value of x into the equation \(y = sin(x)\) and evaluate it. The sine function represents the ratio of the length of the side opposite the angle to the hypotenuse in a right triangle.

For x = 0, sin(0) = 0.

At x = π/4, sin(π/4) = \(\sqrt2/2\).

For x = π/2, sin(π/2) = 1.

As x progresses through 3π/4 and π, the values of y repeat but with opposite signs.

At x = 5π/4, sin(5π/4) = -\(\sqrt2/2\). , and

at x = 3π/2, sin(3π/2) = -1.

Finally, at x = 7π/4 and 2π, the values of y repeat the same as at x = π/4 and 0, respectively.

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The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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There are 15 ways for Minnie to select the 4 subjects and decide the order of doing homework. Minnie has 6 subjects to finish homework for including calculus and statistics.

Out of these 6 subjects, she wants to finish homework for 4 subjects.

Since she wants to finish statistics before calculus, there are only 2 ways to select the subjects to do first i.e. either statistics or calculus.

Statistics must be one of the subjects selected to finish homework for today and hence there are only 5 subjects left to choose from for the other 3 subjects.

So, Minnie has to select 3 subjects from a total of 5 subjects which can be done in 5C3 ways.

5C3 = 10

There are 10 ways for Minnie to choose the remaining 3 subjects.

Now, since Minnie wants to finish statistics before calculus, there is only one possible way to arrange these two subjects in the order she wants.

Hence, there are only 2 possible ways to arrange these two subjects for doing homework.

To arrange the remaining 2 subjects,

Minnie has 2 options.

Hence, there are 2 ways to arrange the last 2 subjects.

So, total number of ways to select the 4 subjects and then decide the order of doing homework is:

10 × 2 × 2 = 40.

Therefore, there are 15 ways for Minnie to select the 4 subjects and decide the order of doing homework.

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Given non-homogeneous linear equation is x^2(d^2y/dx^2) + 3x(dy/dx) + y = exThe main answer to the given problem is that we can obtain a particular solution to this non-homogeneous linear equation only by the method of variation of parameters.

Methods to solve a non-homogeneous linear equation.There are two methods to solve a non-homogeneous linear equation, which are:Method of Undetermined Coefficients Method of Variation of Parameters.The Method of Undetermined Coefficients can be used only in certain conditions, which are:When the function f(x) in the equation is of a special form like sin(x), cos(x), e^x, e^(kx), and so on.The differential equation should have a constant coefficient.The forcing function in the equation should not be a polynomial or any other type that is a solution of a homogeneous equation.The method of Variation of Parameters is a powerful technique used to solve non-homogeneous linear equations with variable coefficients. The method can be used in any situation where the Method of Undetermined Coefficients fails. A particular solution can always be obtained by the method of Variation of Parameters.:Therefore, we can obtain a particular solution to this non-homogeneous linear equation only by the method of variation of parameters. It can not be obtained by the Method of Undetermined Coefficients since the function e^x is not of a special form.

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Answer:

6/8, 9/12

Step-by-step explanation:

Answer: 6:8 9:12

It is 3/4 and when you simplify both of them they equal 3/4

6/8 = 3/4

9/12 = 3/4

Step-by-step explanation:

Answer:

all of them are right answers

\(x = \frac{24}{23 \\ } \)

or

\(x = 1.04\)

or

\(x = 1 \frac{1}{23} \)

The circle with radius=7.95 is larger when a 100-unit long line is split in half.

A circle is a shape produced by all points in a plane that are a certain distance from the center. It is the curve drawn by a point traveling in a plane so that its distance from a specified point remains constant. The radius is the distance between any two points on a circle and the center. Typically, the radius must be positive. A degenerate instance is a circle with radius r=0. Except when otherwise noted, this article is about circles in Euclidean geometry, specifically the Euclidean plane.

A circle, in instance, is a fundamental closed curve that divides the plane into two regions: interior and exterior.

The perimeter of larger circle is 50 units

Therefore, 2πr=50

Radius=7.95

The perimeter of smaller circle is 25 units

Therefore, 2πr=35

Radius=3.97

The circle with radius=7.95 is larger.

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Answer:

\( 9.72 \times {10}^{2} \)

Step-by-step explanation:

\(54 \times 18 = 972 \\ \\ 972 \: in \: standard \: form \: is \: written \: as \\ 9.72 \times {10}^{2} \)

9.72×10

Step-by-step explanation:

To construct a confidence interval to estimate the true average tip with 90% confidence, we can use the following formula:
Confidence Interval = mean ± (critical value * standard deviation / sqrt(sample size))

In this case, the sample mean is 11.6% and the standard deviation is 2.5%. The critical value for a 90% confidence level is 1.645 (obtained from the z-table).

Plugging in the values, we have:

Confidence Interval = 11.6 ± (1.645 * 2.5 / sqrt(sample size))

Since the sample size is not mentioned in the question, we cannot calculate the exact confidence interval. However, you can use the formula provided above and substitute the actual sample size to obtain the interval. Remember to round the endpoints to two decimal places, if necessary.

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The 4 angles inside EVERY 4-sided figure ALWAYS add up to 360 degrees.

Now you have been found !

Answer:

Since we are attempting to sell a store owner a new product.

The plan of a free trial option will be used to use the product for six months. Additionally, we will display a graph to them demonstrating how using this product will increase sales.

Moreover, the testimonials from other store owners who spoke well of the product.

They are all the most successful presentation techniques

Step-by-step explanation:

Answer: All of the above is the correct answer

Step-by-step explanation: Confirmed correct on test

The variance of the length of the critical path is 5.76.

Option A is the correct answer.

We have,

To calculate the variance of the length of the critical path in the Critical Path Method (CPM) with three-time estimates (PERT), we can use the formula:

Variance = (Standard Deviation)²

Given that the standard deviation is 2.4, we can substitute it into the formula:

Variance = (2.4)² = 5.76

Therefore,

The variance of the length of the critical path is 5.76.

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The volume of the cylinder is approximately 960 cubic centimeters.

To find the volume of the cylinder, we need to use the formula V = πr^2h, where r is the radius of the cylinder, h is its height, and π is the mathematical constant approximately equal to 3.14.

Given that the diameter of the cylinder is 8 cm, we can find the radius by dividing the diameter by 2:

radius (r) = diameter / 2

r = 8 cm / 2

r = 4 cm

We are also given that the height of the cylinder is 20 cm.

Substituting the values for r and h into the formula, we get:

V = πr^2h

V = π(4 cm)^2(20 cm)

V = π(16 cm^2)(20 cm)

V = 320π cm^3

Using the value of π as 3, we can approximate the volume as:

V ≈ 320(3)

V ≈ 960 cm^3

When the value of π is rounded to 3 and the radius is 4 cm and the height is 20 cm.

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a) The average selling price in Bloomington is $301,596.27.

b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.

c) There are 98 houses made primarily of brick and 102 not.

d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.

e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

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Answer:

Total surface = 102.4 cm^2 (second answer in the list of options)

Step-by-step explanation:

Notice that we need to add the surface of 4 rectangles, two have smaller sizes than the other two. A pair of rectangles are 7.2 cm x 4 cm = 28.8 cm^2, while the other pair has 7.2 cm x 2 cm = 14.4 cm^2

There are also two equal bases each one of size 4 cm x 2 cm = 8 cm^2

Now we add two of each of the individual surfaces discussed above to complete the total surface area:

2 * 28.8 + 2 * 14.4 + 2 * 8 =  102.4 cm^2

which agrees with the second answer option provided.

The statements is true of the function f(x)= x^2 + 6x^3 - 4 + 2x^5 is C.the graph has exactly one x-intercept

It is shown that the function has one intercept in the x direction by plotting the graph of the polynomial

The graph showed one x intercept is at the coordinate (0.778, 0)

x intercept refers to the value of x when y is zero

The graph is plotted and attached

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The value of Average slope is -509.6.

We can calculate the slope of a function by finding its derivative. Therefore, we can find the derivative of f(x) first:f'(x) = -24x³ - 2x² - 3

We can then calculate the slope of the function at x=2 and x=4:

f'(2) = -24(2)³ - 2(2)² - 3

= -197f'(4)

= -24(4)³ - 2(4)² - 3

= -822

Now, we can find the average slope of the function on the interval [2,4] by using the formula:Average slope = (f'(4) - f'(2))/(4-2)= (-822 - (-197))/(4-2)= -625/2= -312.5

However, we need to be careful as we have been using approximation in the above calculation.

Therefore, we need to evaluate the definite integral of f'(x) from 2 to 4:∫(2,4) f'(x)dx= [-6x⁴/2 - 2x³/3 - 3x²/2] from 2 to 4= (-6(4)⁴/2 - 2(4)³/3 - 3(4)²/2) - (-6(2)⁴/2 - 2(2)³/3 - 3(2)²/2)= -509.6

Therefore, the average slope of the function on the interval [2,4] is -509.6.

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As the volume of the sphere is decreasing at a constant rate of 3 cm³/s, the radius of the sphere is 0.98 cm

The volume of the sphere is given by:

V = 4/3. πr³

Where:

r = radius.

Take the derivative with respect to t

dV/dt = 4. πr² dr/dt

Data from the problem:

dV/dt = 3 cm³/s

dr/dt = 0.25 cm/s

Plug these parameters into the equation:

3 = 4. πr² (0.25)

πr² = 3

r² = 3/π

r = sqrt (3/π) = 0.98 cm

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To determine the number of tons of metal per year needed for Machine A to be favored over Machine B, we compare their costs. Machine A costs $323,000 with an annual operating cost of $2.40/ton, while Machine B costs $178,000 with an annual operating cost of $8.00/ton. The machines have useful lives of 10 years and 6 years, respectively, and the minimum attractive rate of return (MARR) is 18% per year.

By calculating the equivalent annual costs (EAC) for each machine using the given formula and comparing them, we can determine the point at which Machine A becomes more favorable. However, specific values for the discounting factors and the tons per year needed are missing, making it impossible to provide an exact answer.

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The value of x is 4.47 units

In the given figure, there are two right angle triangle, to find the value of x we have to solve each triangle using the Pythagorean theorem.

Consider the bottom triangle

Base of the triangle = 6 units

The hypotenuse of the triangle = 9 units

Apply the Pythagorean theorem

The third side of the triangle = \(\sqrt{9^2-6^2}\)

= \(\sqrt{81-36}\)

= \(\sqrt{45}\) units

Similarly consider the top triangle

The base of the triangle = 5 units

The hypotenuse of the triangle = \(\sqrt{45}\) units

The third side of the triangle = \(\sqrt{\sqrt{45}^2- 5^2}\)

= \(\sqrt{45-25}\)

= \(\sqrt{20}\)

= 4.47 units

Hence, the value of x is 4.47 units

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Using the segment addition postulate, the value of p = 5, and YZ = 9 units.

Since point Y lies between points X and Z, the three points are collinear, therefore, based on the segment addition postulate, XY + YZ = XZ.

Given the following:

XY = 3p

YZ = 2p - 1

XZ = 6p - 6

Substitute

3p + 2p - 1 = 6p - 6

Add like terms

5p - 1 = 6p - 6

5p - 6p = 1 - 6

-p = -5

p = 5

YZ = 2p - 1

Plug in the value of x

YZ = 2(5) - 1

YZ = 9 units.

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For the shown figure:

Given:

We will prove:

The proof will be as follows:

Statement Reason

1. PQ ≅ RS Given

2. QR ≅ SP Given

3. PR ≅ RP Reflexive property

4. ΔPQR ≅ RSP Congruent by SSS postuelate

Answer: 47.5

Step-by-step explanation:

\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Indices and BODMASS rule,

according to the BODMASS rule, we must always give high priority to the, parentheses "()" ,hence we will solve the bracket index powers first,

this we get as

\( ({x}^{3} . {x}^{ - 6}) ^{2} = > ( {x}^{3 - 6} )^{2} = = > ( {x}^{ - 3})^{2} \)

hence, the above option is 2.) is correct.