A company is replacing cables with fiber optic lines in rectangular casing bcde. if segment de = 2.5 cm and segment be = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? round your answer to the nearest hundredth.

The maximum and minimum values of f(x,y,z) = 2xyz are [tex]\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }[/tex]

The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Differentiate the given function.

f(x,y,z)=2xyz

Computation:

Differentiating the given equation up to second order

[tex]\begin{gathered}f_x=2yz\Rightarrow 2yz=0 either y=0 or z=0\\f_y=0\Rightarrow 2xz=0 either x=0 or z=0\\f_z=0\Rightarrow 2xy=0 either x=0 or y=0\end{gathered}[/tex]

So, the critical point is (0,0,0)

Now, using the Lagrange's on the boundary,

[tex]\begin{gathered}g(x,y,z)=x^2+y^2+z^2-1=0\\g_x=2x\\g_y=2y\\g_z=2z\end{gathered}[/tex]

[tex]So, \bigtriangledown f=\lambda \bigtriangledown g\left < 5yz,5xz,5xy \right > =\lambda \left < 2x,2y,2z )[/tex]

By solving we get,

[tex]x^2=y^2=z^2[/tex] then,

[tex]\begin{gathered}x^2+y^2+z^2=1\\3z^2=1\\z=\pm \frac{1}{\sqrt{3} } \\y=\pm \frac{1}{\sqrt{3} } \\\\x=\pm \frac{1}{\sqrt{3} } \\\end{gathered} x 2+y 2+z 2=13z 2=1z=± 31[/tex]

[tex]So, the critical points are (0,0,0),(\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } ,\frac{1}{\sqrt{3} } )and (\frac{-1}{\sqrt{3} }, \frac{-1}{\sqrt{3} },\frac{-1}{\sqrt{3} })[/tex]

So, by substituting the critical points we get,

[tex]\begin{gathered}f(0,0,0)=0\\f(\frac{1}{\sqrt{3} }, \frac{1}{\sqrt{3} },\frac{1}{\sqrt{3} })=2(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })(\frac{1}{\sqrt{3} })\\=\frac{2}{3\sqrt{3} } \\f(-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} },-\frac{1}{\sqrt{3} })=2(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })(-\frac{1}{\sqrt{3} })\\=-\frac{2}{3\sqrt{3} }\end{gathered}[/tex]

Hence the maximum and minimum values of f(x,y,z) are [tex]\frac{2}{\sqrt{3} } and \frac{-2}{\sqrt{3} }[/tex]

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A dot plot displays the individual data values and a histogram displays data ranges along the x-axis and uses rectangular bars to show the frequencies of values that fall into each range.

It should be noted that dot plots, histograms, and box plots are all common graphical ways to represent data sets.

The dot plot represents data by placing a dot for each data point. Also, the histogram groups the data into ranges and then plots the frequency that data occurs in each range.

The similarities is that the dot plot and the histogram can more easily tell us the mode of our data set. A dot plot gives you a visual idea of your data, but histogram gives you additional information.

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Answer:

  (b)  x = 10.5

Step-by-step explanation:

The angle bisector divides the triangle line segments proportionally.

The proportion between corresponding line segments can be written several ways. One of them is ...

  long side/long side = short side/short side

  x/19.3 = 3.9/7.2

Multiplying by 19.3, we get ...

  x = 19.3×3.9/7.2 ≈ 10.5 . . . units

__

Additional comment

You can eliminate the incorrect answer choices simply by looking at the possible side lengths of x.

  19.3 -(3.9+7.2) < x < 19.3 +(3.9+7.2) . . . . . from triangle inequality

  8.2 < x < 30.4 . . . . . . . simplify

There is only one answer choice in this range: the correct one.

Answer:

  A)  (-3, -2)

  B)  (-7, 3) and (-3, -2)

  C)  (4.074, 1.032)

Step-by-step explanation:

An ordered pair is a solution to an equation if it satisfies the equation — makes it true. The given points are solutions to the functions whose graphs pass through those points.

The function p(x) is defined to pass through points (4, 1) and (-3, -2).

The function f(x) is defined to pass through points (-7, 3) and (-3, -2).

These function definitions have point (-3, -2) in common.

(-3, -2) is the solution to the equation p(x) = f(x).

The function f(x) is defined to pass through points (-7, 3) and (-3, -2).

Two solutions to f(x) are (-7, 3) and (-3, -2).

We could identify other solutions, (1, -7) for example, but there is no need since the problem statement already gives us two solutions.

The solution to the equation p(x) = g(x) can be read from the graph as approximately (4.074, 1.032). This is close to the point (4, 1) that is used to define p(x). With some refinement (iteration), we can show the irrational solution is closer to ...

  (4.07369423957, 1.03158324553)

Answer:

A)  (-3, -2)

B)  (1, -7) and (5, -12)

C)  (4, 1) to the nearest whole number

Step-by-step explanation:

Function g(x):

[tex]g(x)=2(0.85)^x[/tex]

Function f(x) (straight line):

Given ordered pairs:

Calculate the slope of the straight line:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-3-(-7)}=-\dfrac{5}{4}[/tex]

Using the Point-slope form of linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=-\dfrac{5}{4}(x-(-7))[/tex]

[tex]\implies y=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]

[tex]\implies f(x)=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]

Function p(x) (straight line):

Given ordered pairs:

Calculate the slope of the straight line:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-1}{-3-4}=\dfrac{3}{7}[/tex]

Using the Point-slope form of linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=\dfrac{3}{7}(x-4)[/tex]

[tex]\implies y=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]

[tex]\implies p(x)=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]

We have been given two ordered pairs for function f(x) and function p(x).

One of those ordered pairs is the same for both functions.  

The solution to a pair of equations is their point(s) of intersection.  

Therefore, as both functions pass through (-3, -2), this is their point of intersection and therefore the solution.

The solutions for f(x) are any points on the line of the function f(x).  

To find any two points, substitute values of x into the found equation for f(x):

[tex]\implies f(1)=-\dfrac{5}{4}(1)-\dfrac{23}{4}=-7[/tex]

[tex]\implies f(5)=-\dfrac{5}{4}(5)-\dfrac{23}{4}=-12[/tex]

Therefore, two solutions are (1, -7) and (5, -12).

Part C

The solution to p(x) = g(x) is where the two graphs intersect.  From inspection of the graphs, p(x) intersects g(x) at approximately (4, 1).  

Therefore, the approximate solution to p(x) = g(x) is (4, 1).

To prove this, substitute x = 4 into the equations for p(x) and g(x):

[tex]\implies p(4)=\dfrac{3}{7}(4)-\dfrac{5}{7}=1[/tex]

[tex]\implies g(4)=2(0.85)^4=1.0440125=1.0\:(\sf nearest\:tenth)[/tex]

The actual solution to p(x) = g(x) is (4.074, 1.032) to three decimal places, which can be found by equating the functions and solving for x using a numerical method such as iteration.

Answer:

Step-by-step explanation:

(4+8/2)*5-1

8*5-1

39 is your answer

Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:

(8.34%, 17.66%).

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the estimate and the sample size are given, respectively, by:

[tex]\pi = 0.13, n = 200[/tex]

Hence the bounds of the interval are:

As a percentage, the interval is:

(8.34%, 17.66%).

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Answer:

x = 7

Step-by-step explanation:

Distribute -

12x − 66 + 15 = 3x + 12

Combine Numbers and Variables -

12x - 51 = 3x +12

Get x on one side (isolate x) -

9x - 51 = 12

9x = 63

Divide 9 -

x =7

The height of the pyramid is 14.4 cm.

volume of a pyramid = 1 / 3 Bh

where

Therefore,

volume of the cube = L³

where

Hence,

volume of the cube = 10³

volume of the cube = 1000 cm³

The volume of the pyramid is the same with the  volume of the cube.

Hence,

1000 = 1 / 3 Bh

The height of the pyramid is the same as the square base.

Therefore,

1000 = 1 / 3 (h²)h

1000 = 1  / 3 h³

cross multiply

3000 = h³

h = ∛3000

h = 14.4224957031

Hence, the height of the pyramid is 14.4 cm.

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Answer:

f-1(x) = +- sqrt(x + 6)

Step-by-step explanation:

f(x) = x^2 - 6

y = x^2 - 6

x = y^2 - 6

x + 6 = y^2

y = +- sqrt(x + 6)

f-1(x) = +- sqrt(x + 6)

Hi :)

Let's find the inverse of the function

Remember, inverse functions do the opposite things in the opposite order.

To find the inverse,

Replace f(x) with y. (one step)

Then

[tex]\boldsymbol{y=x^2+6}[/tex]

Swap x's and y's (one step)

Then

[tex]\boldsymbol{x=y^2+6}[/tex]

Solve for y (several steps)

[tex]\boldsymbol{x-6=y^2}[/tex] > square root both sides

[tex]\boldsymbol{\sqrt{x-6}=y}[/tex] > swap y and √x-6

[tex]\boldsymbol{y=\sqrt{x-6}}[/tex]

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

When both sides of the equal sign are equal, there are infinite solutions.

When you are able to isolate the variable, there is only one solution.

When the equation states an untrue expression, there is no solution.

1=3 is an untrue fact. Therefore, there would be no solutions to the system.

There is no solution

Answer:

x =  45 degrees.

Step-by-step explanation:

The arc of 90 degrees  an angle of 1/2 its value on  the circumference.

1/2 * 90

= 45 degrees.

the vertex of the function g(x) = f(x 2) .

If a quadratic equation is expressed as the following

                          [tex]y=a(x-h)^{2}+k[/tex]

It is then said to be in vertex form. Because the vertex point (peak point) occurs on the graph of this equation, it is so named (h,k)

The parabola that the quadratic equation depicts has this point (h,k) as its vertex.

We first remove the x squared coefficient, and then inside the bracket, we strive to create a condition that resembles a perfect square.

So, this is what we have:

                         [tex]$f(x)=x^{2}+6 x+3$\\$g(x)=f(x-2)$[/tex]

Thus, we obtain:

                        [tex]\begin{aligned}&g(x)=f(x-2) \\&g(x)=(x-2)^{2}+6(x-2)+3 \\&g(x)=x^{2}-4 x+4+6 x-12+3 \\&g(x)=x^{2}+2 x-5\end{aligned}[/tex]

Vertex form transformation of g(x):

                             [tex]\begin{aligned}&g(x)=x^{2}+2 x-5 \\&g(x)=x^{2}+2 x+1-1-5 \\&g(x)=(x+1)^{2}-9 \\&g(x)=(x-(-1))^{2}-6 \\&g(x)=(x-(-1))^{2}+(-6)\end{aligned}[/tex]

By comparing this[tex]a(x-h)^{2}+k[/tex] to, we obtain the coordinates of the vertex of the graph of g(x) as (h,k) = (-1,-6), as shown below.

As a result, the vertex of the function g(x) = f(x 2) .

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Answer:

D

Step-by-step explanation:

circles are parallel to the base and therefore only pass through 1 nappe

if the plane weren't parallel, we would make an ellipse

The sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340

Series are defined as the sum of sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:

S = n/2[2a+(n-1)d]

where;

n is the number of terms

d is the common difference

a is the first term

Given the following parameters from the question

a -2

d = 35

n = 12

Substitute

S = 12/2[2(2)+(12-1)(35)]

S = 6(4+11(35))

S = 6(5+385)
S = 6(390)

S = 2340

Hence the sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340

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The five-number summary and the interquartile range for the data set are given as follows:

In this problem, we have that:

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Answer:

D. Midpoint...

Step-by-step explanation:

I hope it helps You:)

Answer:

15^6

Step-by-step explanation:

According to BODMAS

where;

B - Bracket ()

O - Off (*)

D - Division (/)

M - Multiplication (*)

A - Addition (-)

S - Subtraction (+)

Bracket should be solved first

therefore;

(3*5)^6

15^6 = 11390625

Which can be approximately in standard form written as 1.1*10^7

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

The experimental probability of selecting an orange marble is 0.33.

The experimental probability of landing on a number less than 2 is 12 over 60.

The experimental probability of landing on heads is 49%.

The theoretical probability of a fair coin landing on heads is 0.5.

It should be noted that a coin has a head and tail. Therefore, the probability of getting either will be:

= 1/2 = 0.5

Therefore, Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The statement that compares the theoretical and experimental probability of landing on orange is that the theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

The experimental probability will be:

= 4/(6+3+7+4)

= 4/20 = 1/5

Based on the given frequency, the experimental probability of selecting an orange marble will be:

= 5/(4+6+5)

= 5/15

= 0.33

The experimental probability of landing on a number less than 2 is 12 over 60.

The experimental probability of landing on heads will be:

= 98/(98 + 102)

= 98/200

= 49%

The theoretical probability of a fair coin landing on heads will be:

= 1/2 = 0.5

Flip a coin 14 times and record the frequency of each outcome gives:

Head, Tail, Head, Head, Head, Tail, Tail, Head, Tail, Tail, Tail, Tail, Head, Head. The theoretical and experimental probability are 0.5.

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the gardener would need (1 + 1/6) liters of water to water the whole garden.

Here we know that the gardener needs 1/3 of a liter of water to water 2/7 of a garden.

Then we have the relation:

1/3 L = 2/7 of a garden.

Now, we want to get a "1 garden" in the right side of the equation, then we can multiply both sides by (7/2), so we get:

(7/2)*(1/3) L = (7/2)*(2/7) of a garden

(7/6)L = 1 garden.

(1 + 1/6) L = 1 garden

This means that the gardener would need (1 + 1/6) liters of water to water the whole garden.

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The correct order is 3,1,4,2.

Marshaling of assets:

Therefore, the correct order is 3,1,4,2.

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The correct question is given below:
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is:

(1) $20,000 loan from a partner.

(2) $30,000 of profits from the last year of operations.

(3) $3,000 payable to a supplier.

(4) $100,000 in capital balances of the partners.

Answer:  18 cows

Step-by-step explanation: C = how many cows can graze on 720 acres of land. 40(C) = 720. 720/40 = 18 C = 18.

Answer:

40x = 720

x = 18

Step-by-step explanation:

x = number of cows

Answer:

The all common Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

Answer:

180.

Step-by-step explanation:

100 contains 2  zero digits.

101 - 109 have 9 numbers,  110 to 200 have 11 numbers

so for 101 to 200 its 20 numbers

Its also 20 for 201 to 300  and for all sets of 100 up to 900.

- that is 7 * 20 = 140 numbers

Finally from 901 to 999 we have 18.

Total = 20 + 140 + 18

= 2 + 20 + 140 + 18

= 180.

By the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.

Herein we have a quadratic equation of the form a · m² + b · m + c = 0, whose solution set can be determined by the quadratic formula:

x = - [b / (2 · a)] ± [1 / (2 · a)] · √(b² - 4 · a · c)      (1)

If we know that a = - 1, b = 12 and c = 0, then the solution set of the quadratic equation is:

x = - [12 / [2 · (- 1)]] ± [1 / [2 · (- 1)]] · √[12² - 4 · (- 1) · 0]

x = - 6 ± (1 / 2) · 12

x = - 6 ± 6

Then, by the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.

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Answer:

t = G/(a + h)

t(a + h) = G

a + h = G/t

a = (G/t) - h

t = (G/a) + h

t - h = G/a

a(t - h) = G

a = G/(t - h)

Area of the shaded region is 1397.46 square feet.

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.

We are to find the area of the shaded region. For that, we will divide the figure into smaller shapes, find their areas separately and then add them up.

From the given figure, we can see that there are two semi circles or say one whole circle if we combine them at the ends while 2 rectangles at the top and bottom.

Radius of circle = [tex]\frac{20+7+7}{2}[/tex] = 17

Area of circle = [tex]\pi r^{2}[/tex]

                      = [tex]\pi( 17)^{2}[/tex]

                      = 907.92 square ft.

Area of rectangles =2×(l×b)

                              = 2×20×35

                              = 490 square ft

Then,

Area of the shaded region = 907.92 +490

                                            = 1397.46 square ft

Hence,Area of the shaded region is 1397.46 square ft.

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

Work Shown:

|3x-12| ≥ 6

3x-12 ≥ 6 or 3x-12 ≤ -6  ..... see note below

3x ≥ 6+12 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ 6

x ≥ 18/3 or x ≤ 6/3

x ≥ 6 or x ≤ 2

x ≤ 2 or x ≥ 6

----

Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.

Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5

Answer:

The answer is

→ 91.5 feet

Step-by-step explanation:

Given:

183 feet

What were supposed to find:

The radius of the SkyWheel

183 / 2 = 91.5

How to find the radius:

To find the radius, you must divide 183 with 2, giving 91.5

Hence, the answer you are looking for is 91.5

It takes the time for the wave to travel 6.0 m in the x-direction of 8s.

A wave's wavelength is measured in meters since it is the separation between its two peaks (or troughs). Since waves can be any size or shape, the prefix for meters can vary significantly, from km for radio waves to micrometers for visible light (although it is sometimes stated in nanometers) to picometers for gamma rays..

the wavelength is 1.5 m.

λ/2 = 1 s

1.5/2 =1 s

0.75 m in 1 s is travelled  by the wave.

To travel 6m , the time required is

= 6/0.75

=8s

Thus,

it takes the time for the wave to travel 6.0 m in the x-direction is 8s.

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Answer:

A plastic board