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Pr. #10) Using triple integrals, find the volume of the solid contained in the first octant, bounded above and below by the cone 32 = }(x+y), and to the side by the sphere ? + y2 + 2 = a > 0.

Using the remainder theorem, the remainder of the divisions of p(x) = 4x³ + 6x² - 8x - 2 by the polynomials are given as follows:

Suppose that we have a polynomial p(x), that is divided by a linear term x - a, the remainder is given by the numeric value of p(x) at x = a, that is, p(a).

For this problem, the polynomial is given as follows:

p(x) = 4x³ + 6x² - 8x - 2.

Then the remainder for each division is given as follows:

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Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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Answer:

216\(\pi\)

Step-by-step explanation:

Given the figure.

And the perimeter in the ratio 4: 2: 1.

Perimeter of smallest circle = \(8\pi\)

To find:

Area of shaded region.

Solution:

To find the area, we need to have radius first.

And radius can be calculated by the given perimeter.

Formula for Perimeter is given as:

Perimeter = \(2\pi r\)

\(8\pi = 2\pi r\\\Rightarrow r = 4\ cm\)

Radius of smallest circle = 4 cm

Ratio of perimeter is equal to the ratio of the radii.

Radius of 2nd smallest circle by the given ratio = 8 cm

Radius of largest circle = 16 cm

Area of a circle is given the formula:

\(A = \pi r^2\)

Area of the smallest circle = \(\pi 4^2 = 16\pi\ cm^2\)

Area of the 2nd smallest circle = \(\pi 8^2 = 64\pi\ cm^2\)

Area of the largest circle = \(\pi 16^2 = 256\pi\ cm^2\)

Area of the shaded region = Area of largest circle + 2 \(\times\) Area of 2nd smallest circle + 3 \(\times\) Area of smallest circle - 2 \(\times\) Area of smallest circle - 3 \(\times\) Area of 2nd smallest circle

Area of the shaded region = Area of largest circle - Area of 2nd smallest circle + Area of smallest circle = \(256\pi - 64\pi +16\pi = 216\pi\)

The domain is the collection of possible inputs (values of x) for which a function is defined, according to mathematical terminology. The domain of a function is usually determined by analyzing its graph, which represents all feasible inputs to the function.

The domain of a graphed function is given in the question; it is the range of values for x that are represented on the horizontal axis of the graph. The domain can also be written as an interval of the form [a, b], where a and b are the leftmost and rightmost values of x that appear on the graph respectively.

When looking at the graph, we can see that the leftmost value is -6, and the rightmost value is 9. As a result, the domain of the function is given by the inequality -6 ≤ x ≤ 9, which is option A: -6≤x≤9. This is because any value of x that lies between -6 and 9 (inclusive) is shown on the graph, and any other value of x is not displayed on the graph.

The domain is one of the most important elements of any function, as it determines the set of all possible input values that a function can accept. Knowing the domain of a function is critical in determining if a function is defined for a given input value, among other things.

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The number of ways the ribbons can be awarded in a race with "x" runners is x * (x-1).

The number of ways the ribbons can be awarded depends on the total number of runners participating in the 100-meter dash.

If there are "x" runners participating, the winner can be any one of the x runners, and the second-place runner can be any one of the remaining (x-1) runners.

Therefore, the number of ways the ribbons can be awarded is equal to the number of possible choices for the winner multiplied by the number of possible choices for the second-place runner.

Mathematically, this can be expressed as:

Number of Ways = x * (x-1)

For example, if there are 5 runners in the race, there are 5 ways to choose the winner. After selecting the winner, there are 4 remaining runners from which we can choose the second-place runner. So, in this case, the number of ways the ribbons can be awarded is:

Number of Ways = 5 * 4 = 20

In general, the number of ways the ribbons can be awarded in a race with "x" runners is x * (x-1).

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It is given that the height of the wall is H.

Number of brick layers is n.

The height of the wall is proportional to the number of brick layers.

The walls height in inches is given by the formula:

h=3n

We can see from the above formula that the height of the wall increases by Three inches for every additional layers of bricks.

so we conclude the height of each brick layer is 3.

When n= 12,

h= 3n = 3 * 12 = 36 inches

so the bricks wall is 36 inches high with 12 layers. The result corresponds to point A (12,36) . As shown in the plot.

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_______ The given question is incomplete, the complete question is here:

A brick wall is being built with layers of bricks one on top of another. The height of the wall H is proportional to the number of brick layers n. The walls height in inches is given by the formula h=3n

The slope (m) of the line y = x + 3 is 1, while the y-intercept of the line is 3.

If an equation of a line is expressed in slope-intercept form as y = mx + b, we can easily determine its slope and the y-intercept which are:

m is the slope

b is the y-intercept.

Given the equation y = x + 3, therefore:

the coefficient of x is the slope (m), which is 1.

the y-intercept (b) of the line is 3.

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Answer:

1b 2a 3c

Step-by-step explanation:

Its hegarty right?

Answer:

(x,y)-->(x+8,y-3)

Step-by-step explanation:

just took the test

Answer:

(x, y) → (x + 8, y – 3)

Step-by-step explanation:

I completed the assignment on edge and got 100%

The length and width will be 18 feet and 10 feet respectively.

From the information, Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 26 ft long and she wants to leave a uniform strip of floor around the rug and can afford to buy 180 square feet of carpeting.

The dimensions are 28 by 16 feet

The dimensions of the rug will be:

= (26 - 2x)(18 - 2x)

Maximum area = 180 feet²

(26 - 2x)(18 - 2x) = 180

468 - 88x + 4x² = 180

4x² - 88x + 288 = 0

x² - 22x + 72 = 0

x = 4 and 18

The width will be:

= 18 - 2x

= 18 - 2(4)

= 10

The length will be:

= 26 - 8

= 18 feet

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A minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

Therefore, a minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

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The answer is 85, with no real component (a = 0) and an imaginary component (b = 0).

Given that, w=a+bi=√z where a and b are real number.

√(-13+84i)

First, expand the expression into its absolute value form:

√(-13 + 84i) = √((-13)² + (84)²)

Then, using the formula for the absolute value of a complex number, simplifying:

√((-13)² + (84)²) = √(-13² + 84i×84i)

= √(169 + 7056)

= √7225 = 85

Therefore, the answer is 85, with no real component (a = 0) and an imaginary component (b = 0).

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The appropriate hypothesis test for this scenario is a Goodness of Fit test.

A Goodness of Fit test is used to determine whether an observed frequency distribution fits a theoretical distribution or expected frequency distribution. In this case, we have a theoretical distribution of the US resident population by region in 2000, and we want to determine whether the observed frequency distribution from the sample fits this distribution.

The null hypothesis for this test is that the observed frequency distribution from the sample is not significantly different from the theoretical frequency distribution of the US resident population by region in 2000. The alternative hypothesis is that the observed frequency distribution is significantly different from the theoretical frequency distribution.

We can use a chi-squared test for goodness of fit to test this hypothesis.

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Answer:

The price of a child ticket in dollars $8.00

Step-by-step explanation:

Answer:

is there like a picture to go with it that will help solve it???

Step-by-step explanation:

d = 100miles

t = 45 × 60 = 2700sec

dis = speed × time

relationship btw speed and time when d distance is 100miles is

100 = speed × 2700sec

speed = 100 = 0.037m/s

2700

True. If p(x) is the Taylor series for f centered at 0, then p(x-1) is not the Taylor series for f centered at 1. Instead, to obtain the Taylor series for f centered at 1, you would need to compute a new series with the center shifted to 1.

True. Shifting the center of a Taylor series by adding or subtracting a constant simply results in a new Taylor series centered at the shifted point. In this case, we are shifting the center from 0 to 1 by replacing x with (x-1) in the Taylor series for f, resulting in p(x-1).
In mathematics, the Taylor series or Taylor expansion of a function is an infinite number of points defined by the function at one point. For most ordinary functions, the partial function and its Taylor series are equal at point. The first n + 1 terms of the Taylor series form an n-order polynomial called the nth-order Taylor polynomial function. Taylor polynomials are generally approximate for functions that get better as n increases. Taylor's theorem provides a quantitative estimate of the resulting error using this approach. If the series of Taylor functions converge, the sum is the limit of an infinite number of Taylor polynomials.

A function can diverge from the equation of the Taylor series even if the Taylor series converges. A function is the definition of a point x if it is equal to the sum of the Taylor series over an open interval (or opening in the complex plane) containing x. This means that transactions are resolved anywhere on the clock (or disk).

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

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond\)

         Write an equation for the line that passes through (0, 1) and has a slope of 2 (in point-slope form).

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond\)

Point-slope form:-

      \(\sf{y-y_1=m(x-x_1)}\)

Substitute 1 for y₁, 2 for m, and 0 for x₁:-

\(\sf{y-1=2(x-0)}\)

So we conclude that Option B is correct.

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

Given data:

The standard expression for the proportionality is,

It means the graph must pass through the origin.

5)

Thus, the amount of money raised by Phil's is proportionally related.

6)

The unit rate change is the slope of the line which is,

Thus, the unit rate change is $7.5/mile.

Step-by-step explanation:

Given

(2+3) (4-1)

= 5 * 3

= 15

Hope it will help :)

Answer:

15

Step-by-step explanation:

(2+3) (4-1)

(5) (3)

15

According to the question c is a circle centered at the​ origin, oriented​ counterclockwise, that encloses disk r in the plane The two-dimensional curl of the vector field \(\(f = 2x, 2y\) is \(0\)\).

To calculate the curl of a vector field, we use the formula \(\(\text{curl}(f) = \frac{\partial f_y}{\partial x} - \frac{\partial f_x}{\partial y}\)\).

For the given vector field \(\(f = 2x, 2y\)\), the partial derivatives are

\(\(\frac{\partial f_y}{\partial x} = 0\) and \(\frac{\partial f_x}{\partial y} = 0\)\).

Substituting these values into the curl formula, we have \(\(\text{curl}(f) = 0 - 0 = 0\)\).

Therefore, the two-dimensional curl of the vector field \(\(f = 2x, 2y\) is \(0\)\).

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Answer:

Step-by-step explanation:

Answer:

1.6 pizzas

Step-by-step explanation:

Answer:

option 3-- 16 pizzas

Step-by-step explanation:

divide 48 by 3 = 16

Answer:

16 pizzas will feed 48 people

Step-by-step explanation:

If 1 pizza feeds 3 people it will take 16 pizzas to feed 48.

48/3=16

Answer:

6t = 9

Step-by-step explanation:

The two pieces of tape are the same length and one tape represents 9 while the other represents 6 pieces of t. Thus, the equation should be:

6t has the same length as 9.

6t = 9

Answer:

Cubed

Explanation:

Given the function:

The highest power of the function = 3

Therefore, it is a cubic/cubed function.

Note:

• If the highest power is 1, it is a linear function.

• If the highest power is 2, it is a square/quadratic function.

If the Rockwell hardness of pins of a certain type has a mean value of 50 and a standard deviation of 1.4, then we can use these values to make predictions about the hardness of individual pins.

For example, we might expect that approximately 68% of pins will have a hardness value between 48.6 and 51.4 (i.e., within one standard deviation of the mean), and approximately 95% of pins will have a hardness value between 47.2 and 52.8 (i.e., within two standard deviations of the mean). Additionally, we can use the mean and standard deviation values to calculate the probability of obtaining a particular hardness value or range of values, using tools like the normal distribution or z-scores. Overall, knowing the mean and standard deviation of the Rockwell hardness of pins of a certain type provides valuable information for understanding the variability and distribution of this important characteristic.

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The surface area of a similar box given the ratio of volume to surface area of first box is 67.5 square inches

Box A:

Box B:

Volume : surface area

64 : 160 = 27 : x

64/160 = 27/x

64 × x = 160 × 27

64x = 4,320

x = 67.5 square inches

Therefore, the surface area of a similar box given the ratio of volume to surface area of first box is 67.5 square inches

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