Find the volume of the solid generated by revolving about the y-axis the region under the curve y = 5e^-2x in the first quadrant. if the answer does not exist, enter dne. otherwise, round to four decimal places.

From given volume, length of each section is 18 inches.

In mathematics, ‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Let's call the length, width, and height of each section l, w, and h, respectively.

Since both sections are the same size, we can set up the following equation for their combined volume:

2(lwh) = 2640

Simplifying this equation, we get:

lwh = 1320

Now we need to find the length of each section, which is represented by the variable l. We can solve for l by dividing both sides of the equation by wh:

l = 1320/wh

We don't have enough information to determine w and h individually, but we do know that the two sections are identical, which means they have the same proportions. This means that w and h must be equal.

Let's call this common value x. Then we can rewrite the equation for l as:

[tex]l = 1320/x^2[/tex]

We can simplify this equation by multiplying both sides by [tex]x^2[/tex]:

[tex]lx^2 = 1320[/tex]

Now we can solve for x:

[tex]x^2 = 1320/l\\\\x = \sqrt{(1320/l)}[/tex]

Since w = h = x, the length of each section is:

[tex]l = 2x = 2 \sqrt{(1320/l)}[/tex]

We can simplify this expression by multiplying both sides by l:

[tex]l^2 = 4*1320/l \\l^3 = 5280\\l = 18[/tex]

Therefore, the length of each section is 18 inches.

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When a voltage is applied across a copper wire or conductor, the electric field generated by the voltage pushes the free electrons in the copper atoms, causing them to move in the direction of the electric field.

This creates an electric current that flows through the wire or conductor.

Copper is a popular material used for transmitting electrical currents because of its excellent properties.

How copper transmits electrical currents:
Conductivity:

Copper has high electrical conductivity, which means it allows the flow of electrons with minimal resistance.

This property enables it to transmit electrical currents efficiently.
Ductility:

Copper is a ductile material, making it easy to form into thin wires without breaking.

This property allows for the creation of long and flexible copper cables that can be installed in various environments for transmitting electrical currents.
Low electrical resistance:

The low resistance of copper minimizes energy loss in the form of heat when transmitting electrical currents.

This helps to maintain the efficiency and performance of electrical systems.
Availability:

Copper is a relatively abundant material, making it an accessible and cost-effective choice for transmitting electrical currents in various applications.
Durability:

Copper is resistant to corrosion and wear, which means it can maintain its performance over time.

This makes it a reliable material for transmitting electrical currents in both short-term and long-term installations.
In summary, copper transmits electrical currents effectively due to its high conductivity, ductility, low electrical resistance, availability, and durability.

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An estimate for the mean daily energy output is 5 kw/h.

The mean is the average value of a data set.

The mean is computed as the quotient of the total value divided by the number of data items.

Energy Output    Frequency    Cumulative      Cumulative

      (kw/h)                                   Frequency    Energy Output

          1                          1                    1                         1

         2                          1                    2                       3

         3                          1                    3                       6

         4                          4                   7                     22

         5                          4                 11                      42

         6                          3                 14                     60

         7                          2                 16                     74

         8                          2                18                      90

Mean Daily Energy Output = 5 (90 ÷ 18)

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The value of secant theta is 29/20

First, it is important to note the different trigonometric identities and their ratios, we have;

sin θ= opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

From the information given, we have that;

tan θ = 21/20

Adjacent = 20

Opposite = 21

Using the Pythagorean theorem, we have;

x² = 21² + 20²

find the squares

x² = 441 + 400

add the values

x² = 841

Find the square root

x = 29

Then, sec θ = 29/20

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Answer:

Non-statistical I think

Step-by-step explanation:

As the degrees of freedom increase, the Student's t distribution becomes more like the standard normal (z) distribution. Correct option is C.

The Student's t distribution is a probability distribution that is used to estimate the mean of a population when the sample size is small or when the population standard deviation is unknown. It is similar to the standard normal distribution, but it has heavier tails and more spread out.

As the degrees of freedom increase, the t-distribution approaches the normal distribution because the shape of the t-distribution becomes more and more similar to the normal distribution.

This is due to the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches the normal distribution.

When the degrees of freedom is large, the t-distribution becomes less variable, and the tails become less heavy, approaching the normal distribution. Therefore, the standard normal (z) distribution is the limiting distribution of the Student's t distribution as the degrees of freedom increase.

Therefore, Correct option is C.

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complete question is:

As the degrees of freedom increase, what distribution does the student's t distribution become more like?

a) uniform

b) chi-square

c) standard normal (z)

d) binomial

Answer:

A

Step-by-step explanation:

given the x- intercepts x = a and x = b then the corresponding factors are

(x - a) and (x - b)

the equation of the quadratic is then the product of the factors , that is

y = a(x - a)(x - b) ← a is a multiplier

here the x- intercepts are x = 4 and x = 8 , then factors are

(x - 4) and (x - 8 ) , so

y = a(x - 4)(x - 8)

to find a substitute any other point on the graph into the equation

given vertex = (6, - 4 ) , then

- 4 = a(6 - 4)(6 - 8)

- 4 = a(2)(- 2) = - 4a ( divide both sides by - 4 )

1 = a , then

y = (x - 4)(x - 8) ← expand using FOIL

y = x² - 12x + 32

Answer:

104

Step-by-step explanation:

You add 65+ 39 and that gives you 104

Step-by-step explanation:

let's see.

first, let's deal with the asymptotes.

the vertical asymptote at x = -2.

it means that for x getting close to that value y is getting enormously larger and larger, so that for x = -2 we would get what we call y = infinity. we could even accept +infinity or -infinity. in both cases we get the same asymptote

I personally think using both +infinity and -infinity is easier to define. because coming from the left (negative direction) and from the right (positive direction) we can use the same expression and don't need to worry about the sign.

so, I go for something like

y = 1/(x + 2)

or even better considering we need a horizontal asymptote too :

y = x/(x + 2)

this will divide by 0 for x = -2 creating the asymptote.

now for the horizontal asymptote of y = 3.

it means that for x getting close to infinity (+infinity and/or -infinity) y has to get closer and closer to this finite value (3).

we achieve this by dividing a dimension of x by the same dimension of x.

so, for large values of x any additive parts of the terms become irrelevant for the limit.

as we had above

y = x/(x + 2)

the limit for x going to +infinity AND to -infinity would be

x/x = 1.

but we need the limit of 3.

so, all we need to do is to multiply the expression by 3 :

y = 3x/(x + 2)

now the limit for x going to +/- infinity is

3x/x = 3

and now for the y-intersect at (0, -4) :

we need to do something, so that y = -4 for x = 0.

let's look at what we have so far :

y = 3x/(x + 2)

-4 = 3×0/(0 + 2) = 0/2 = 0

clearly, that is wrong and therefore still not covered.

imagine, we keep the denominator of the fraction unchanged.

what do we need to do on the numerator side to create -4 as result ?

in other words, we need to find an n so that

-4 = (3x + n)/(x + 2)

for x = 0

-4 = n/2

n = -8

and we get as final result

y = (3x - 8)/(x + 2)

that includes the point (0, -4), and has the asymptotes at x = -2 and y = 3.

Answer:

21 - 8 = x

21 - 8 = 13

Step-by-step explanation:

because you send a total of 21, and you send 8, just do 21 - 8 and thats how many text messages she sends

(a) margin of error; sample statistic.

The center of the confidence interval is determined by the sample statistic, and the width of the confidence interval is determined by the margin of error.

Therefore, the correct option is (a) margin of error; sample statistic.

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Use circumcenter to draw a circle through three non-collinear points.

a) Draw diameter, construct equilateral triangle with one vertex at center and other two on circle.

b) Draw diameter, construct regular hexagon with one vertex at center and other vertices on circle.

Step 1: To construct a circle through three points not on a line, we can use the circumcenter of a triangle. We first construct the perpendicular bisectors of any two sides of the triangle. The point where these two lines intersect is the circumcenter of the triangle. We can then draw a circle with this point as the center, which passes through all three vertices of the triangle.

Step 2:

a) To construct an equilateral triangle inscribed in a circle, we can draw a diameter of the circle and then construct an equilateral triangle with one of the endpoints at the center of the circle and the other two endpoints on the circle itself.

b) To construct a regular hexagon inscribed in a circle, we can draw a diameter of the circle and then construct a regular hexagon with one of the vertices at the center of the circle and the other vertices on the circle itself.

c) To construct a square inscribed in a circle, we can draw a diameter of the circle and then construct a square with one of the vertices at the center of the circle and the other vertices on the circle itself.

Step 3:

a) To construct a tangent to a circle through a point on the circle, we can draw a radius of the circle to the point of tangency, and then construct the perpendicular bisector of this radius. The line where the perpendicular bisector intersects the circle is the tangent line.

b) To construct a tangent to a circle through a point outside the circle, we can draw a line from the point to the center of the circle, and then construct the perpendicular to this line at the point of tangency. The line where the perpendicular intersects the circle is the tangent line.

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Answer:

35

Step-by-step explanation:

Answer: B: (7, -4)

Step-by-step explanation:

To solve for x and y, we can use either substitution or elimination method. Here, we'll use the elimination method to solve for x and y:

2x - 4y = 36 (Equation 1)

4x + 3y = -5 (Equation 2)

To eliminate y, we can multiply Equation 1 by 3 and Equation 2 by 2, and then add the two resulting equations:

6(2x - 4y) = 6(36) (Multiplying Equation 1 by 3)

2(4x + 3y) = 2(-5) (Multiplying Equation 2 by 2)

Simplifying, we get:

12x - 24y = 216

8x + 6y = -10

Adding the two equations, we get:

20x = 206

Dividing both sides by 20, we get:

x = 10.3

Now, substituting x = 10.3 into Equation 1 or Equation 2, we can solve for y. Let's use Equation 1:

2x - 4y = 36

2(10.3) - 4y = 36

20.6 - 4y = 36

-4y = 15.4

y = -3.85

Therefore, the solution to the system of equations is (x,y) = (10.3,-3.85).

Rounded to the nearest integer, the solution is approximately (x,y) = (10,-4).

So, the answer is option B: (7, -4).

Answer:

D. (4, 7)

Step-by-step explanation:

2x - 4y = 36

4x + 3y = -5

2(4) - 4(-7) = 36

4(4) + 3(-7) = -5

Answer:

144 sq. units

Step-by-step explanation:

Area of Square =[tex][side] ^{2}[/tex]

Answer:

  7467 ft 1 in = 89605 inches on a side

Step-by-step explanation:

You want the dimensions of a square with an area of 2 square miles, to the nearest inch.

The area of a square is given by ...

  A = s² . . . . . . where s is the side length

For an area of 2 mi², the side length is ...

  2 mi² = s²

  √(2 mi²) = s = √2 mi

You want the distance to the nearest inch, so we need to convert this to inches.

  √2 mi = (√2 mi) × (5280 ft/mi) × (12 in/ft) ≈ 89604.57 in

Rounded to the nearest inch, this is

  89605 inches

In feet and inches, this is

  89605/12 ft = 7467 1/12 ft = 7467 ft 1 in.

There are 26.24 cubic feet of sand in the rectangular container based on volume.

We must determine the volume of sand in the rectangular container in order to determine how much is there.

Let's start by determining the container's volume:

Container volume equals length, width, and height

Container volume: 6.5 feet by 3.2 feet by two feet

Container volume is 41.6 cubic feet.

The amount of sand in the container's volume must then be determined. We can determine the volume of sand by using the following formula because it fills the container to a depth of 1.3 feet:

Sand volume is determined by its length, width, and depth.

Sand volume = 6.5 feet by 3.2 feet by 1.3 feet

Sand volume = 26.24 cubic feet

As a result, the container contains 26.24 cubic feet of sand.

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The book that weighs 3/4 pounds is greater than 1/2 pounds.

To compare the weights of the two books with 1/2 pound, we need to convert 1/2 pound into a fraction with a common denominator as the given weights. The common denominator of 8 and 4 is 8. So, we can convert 1/2 pound to 4/8 pound.

Now we can compare the weights of the two books with 4/8 pounds. The weight of the first book is 3/8 pounds, which is less than 4/8 pounds. The weight of the second book is 3/4 pounds, which is greater than 4/8 pounds.

Therefore, the book that weighs 3/4 pounds is greater than 1/2 pound.

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Vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2, vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3, vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.

What is axis of symmetry?

In mathematics, the axis of symmetry is a line that divides a given shape into two symmetrical parts, such that each part is a mirror image of the other.

We can use the standard form of a quadratic function, which is given by:

[tex]F(x) = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola and the axis of symmetry is the line x = h.

For [tex]h(x) = (x + 2)^2[/tex], we have:

h = -2 (since x + 2 = 0 when x = -2)

k = 0 (since the square of any real number is non-negative)

Therefore, the vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2.

For [tex]g(x) = (x - 3)^2[/tex], we have:

h = 3

k = 0

Therefore, the vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3.

For [tex]j(x) = (x - 3)^2 + 2[/tex], we have:

h = 3

k = 2

Therefore, the vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.

To find the y-intercept of each function, we can simply plug in x = 0:

For h(x):

[tex]h(0) = (0 + 2)^2 = 4[/tex]

Therefore, the y-intercept of h(x) is 4.

For g(x):

[tex]g(0) = (0 - 3)^2 = 9[/tex]

Therefore, the y-intercept of g(x) is 9.

For j(x):

[tex]j(0) = (0 - 3)^2 + 2 = 11[/tex]

Therefore, the y-intercept of j(x) is 11.

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Answer:

309

Step-by-step explanation:

Turn - and - into +:

-212 + 384 + 137

Then add:

172 + 137

= 309

Answer:

We can use the distributive property of multiplication to expand the given expression as follows:

(x - 8) (x - 3) (x + 9) = (x - 8) (x^2 + 6x - 27) [Using (a - b)(a + b) = a^2 - b^2]

= x(x^2 + 6x - 27) - 8(x^2 + 6x - 27) [Using distributive property]

= x^3 + 6x^2 - 27x - 8x^2 - 48x + 216 [Using distributive property]

= x^3 - 2x^2 - 75x + 216

Therefore, the answer is (B) x^2-2x-59

Hope This Helps!

Answer:

older than those found in shallower layers of sediment. This is because sedimentary rock layers form over time, with the oldest layers at the bottom and the newest layers at the top. As sedimentary rocks form, they often trap the remains of plants and animals, which then become fossils. The deeper layers have been buried for a longer period of time, so they contain older fossils. This principle is known as the law of superposition and is an important tool for dating fossils and determining the relative ages of different rock layers.

The distribution will exhibit symmetry. The solution has been obtained by using the histogram.

What is a histogram?

A graph known as a histogram uses rectangles to show the frequency of numerical values. The vertical axis of a rectangle's height (which represents the distribution frequency of a variable) (the amount, or how often that variable appears).

The given histogram's form demonstrates that the distribution's shape exhibits symmetry (i.e. the shorter bars are to the left and to the right while the longer bars are in the middle).

Sales of vehicles under $5,000 and those between $45,000 and $50,000, with expected sales of 200 vehicles each, will be added, resulting in bars at both ends of the histogram that are the same size as the shortest bar.

Due to the distribution's continued symmetry, this won't change the histogram's initial shape of the distribution.

Hence, the first option is the correct answer.

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The complete question and the figure is attached below.

Question: A salesman sells cars with prices ranging from $5,000 to $45,000. the histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.

How would the shape of the distribution change if the salesman decides to also deal in cars priced under $5,000 and in cars priced from $45,000 to $50,000 and projects sales of 200 cars in each category?

a. the distribution will exhibit symmetry.

b. the distribution will exhibit a positive skew.

c. the distribution will exhibit a negative skew.

d. the distribution will uniform throughout.

150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.

The apex of the angle is the intersection of two rays that together form the geometric shape known as an angle. The component rays that make up the angle are known as the sides or arms of something like the angle.

Angles are expressed as degrees in radians, with 360 degrees or 2 radians equaling a full revolution around a point. The rotational difference between two angles' two sides determines the angle's size. Depending on their measure, angles can be categorised into various categories, including: An acute angle is one that is smaller than 90 degrees. A right angle is one that is precisely 90 degrees. The angles of a right triangle are parallel to one another.

given

We must first determine the measure of angle C because arc DAB is twice as large as angle C.

As inscribed angles of the circle, angles B and C have measurements that are equal to half those of their intercepted arcs.

m(arc BC) equals 2mB

m(arc AD) equals 2mC

Finding m(arc DAB), the product of arcs AD and AB, is what we're after.

m(arc DAB) equals m(arc AD) plus m. (arc AB)

We obtain the following by substituting the equations for the arc measures in terms of angles:

m(arc DAB)=2mC+2mB

We can use the formula we discovered for mB + mC, which equals 75 degrees, instead.

150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.

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Using quantitative techniques in the context of The New York Times has both advantages and disadvantages.

The advantages  are:

accuracy:

Quantitative techniques can provide more precise and accurate data, which can lead to more accurate reporting and analysis of news articles.

Data-Driven Insights:

Quantitative techniques help identify trends and patterns in data and help journalists make informed decisions about what to report on.

Objectivity:

Quantitative techniques help reduce bias and subjectivity in reporting by relying on data rather than personal opinions or interpretations.

The disadvantages include:

Lack of context:

Quantitative methods can oversimplify complex issues, resulting in misleading or inaccurate reporting.

Data limit:

Quantitative methods are data-dependent and results may not be reliable if data are incomplete or inaccurate.

Overall, it is very useful for the journalists in the New York Times to use  quantitative techniques

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Answer:

(-1, 2)

Step-by-step explanation:

1.) The way to use elimination is to add or subtract both of the equations together to eliminate a variable. If we add the two equations together, the -6x and 6x cancel out. Since we added the equations together, -12y and 10y would add up to -2y, and -18 and 14 would add up to -4

2.) Now, we have the equation -2y = -4. By dividing by -2 on both sides, we get y=2.

3.) Next, we need to substitute y back in to get the x value. If you use the first equation, we get -6x - 12 * 2 = -18.

4.) By simplifying, you get that -6x - 24 = -18. If you add 24 on both sides, you get -6x = 6, and by dividing by -6 on both sides, you get x = -1.

5.) Finally, you have to put the answer in form of a point. -1 would be the x-coordinate and 2 would be the y-coordinate. Therefore, the point is (-1, 2)

Answer:

To solve this problem, we can use the equations of motion for a vertically launched object. First, we need to find the initial velocity of the snowball when it is kicked off the ground. We know that its speed is 24 feet per second, but we also need to take into account the angle at which it is kicked. Let's assume that Max kicks the snowball at a 45-degree angle. Using trigonometry, we can find that the horizontal velocity of the snowball is also 24 feet per second, and the vertical velocity is 24 feet per second times the sine of 45 degrees, which is approximately 16.97 feet per second. Now we can use the following equation to find the time it takes for the snowball to hit the ground: h = vi*t + 0.5*a*t^2 where h is the maximum height, vi

Answer:

[tex] \sqrt{(22 - 4.25)^{2} +(6.25 - 6.25) ^{2} } \\ [/tex]

[tex] \sqrt{(15.75)^{2} } [/tex]

=15.75 units