I roll two dice and observe two numbers X and Y . If Z = X − Y , find the range and PMF of Z.

Answer:

2.52 m

Step-by-step explanation:

let the height be h m.

let the shorter ladder be x m away from the base of wall.

(x+1.96)²+h²=5.6²

x²+h²=4.2²

subtract

(x+1.96)²-x²=5.6²-4.2²

(x+1.96+x)(x+1.96-x)=31.36-17.64

(2x+1.96)(1.96)=13.72

2x+1.96=13.72/1.96=7

2x=7-1.96=5.04

x=5.04/2=2.52

Answer:

Step-by-step explanation:

C = 2 π r

A = π r²

~~~~~~~~~~~

(1). C = 8 π

Let the length of the arc ADB is "x"

x = ( 8π ÷ 360° ) × 340°

x = [tex]\frac{68}{9} \pi[/tex]

(2). A = 16 π

The area of shaded region is

( 16 π ÷ 360° ) × 340° = [tex]\frac{136}{9} \pi[/tex]

[tex]\bold{Answer} \downarrow[/tex]

[tex]Length\ of\ Arc\ ADB = \large\boxed{\frac{68\pi}{9} }[/tex]

[tex]Area\ of\ shaded\ region= \large\boxed{\frac{136\pi}{9} }[/tex]

Formulas needed:

[tex]Arc\ length=\boxed{2\pi r(\frac{\theta}{360} )}[/tex]

[tex]Area \ of\ a\ sector=\boxed{(\frac{n}{360})\times\pi \times r^2}[/tex]

[tex]Area\ of\ Circle=\boxed {\pi\times r^2}[/tex]

Step-by-step explanation:

First, let's find the arc length:

[tex]Arc\ length=2\pi r(\frac{\theta}{360})[/tex]

[tex]=2\pi (4)(\frac{340}{360})[/tex]

[tex]=2\pi (4)(\frac{17}{18})[/tex]

[tex]=2\pi(\frac{68}{18})[/tex]

[tex]=\frac{136\pi }{18}[/tex]

[tex]\longrightarrow \large\boxed{\frac{68\pi}{9} }[/tex]

Next, let's find the area of the sliver of the circle we just found the arc length of.

[tex]Area \ of\ a\ sector=(\frac{n}{360})\times\pi \times r^2[/tex]

[tex]=(\frac{20}{360} )\times \pi \times 4^2[/tex]

[tex]=(\frac{1}{18})\times \pi \times 16[/tex]

[tex]=\frac{16\pi}{18}[/tex]

[tex]\longrightarrow \frac{8 \pi}{9}[/tex]

Finally, find the area of the entire circle and subtract the sliver area by that.

[tex]Area\ of\ Circle= {\pi\times r^2[/tex]

[tex]=\pi \times 4^2[/tex]

[tex]\longrightarrow16\pi[/tex]

Subtracting the area by the sliver.

[tex]Area\ of\ entire\ circle \ -\ Area\ of\ sliver\ of\ circle[/tex]

[tex]=16\pi -\frac{8\pi}{9}[/tex]

[tex]=\frac{144\pi}{9} -\frac{8\pi }{9}[/tex]

[tex]\longrightarrow \large\boxed{\frac{136\pi}{9} }[/tex]

Answer:

The answer is G.

f-5 drop the class while s class is 3(f-5)

therefore, s=3(f-5)

From the constraint, we have

[tex]x+y+z=9 \implies z = 9-x-y[/tex]

so that [tex]s[/tex] depends only on [tex]x,y[/tex].

[tex]s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy[/tex]

Find the critical points of [tex]g[/tex].

[tex]\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9[/tex]

[tex]\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0[/tex]

Using the given constraint again, we have the condition

[tex]x+y+z = 2x+y \implies x=z[/tex]

so that

[tex]x = 9 - x - y \implies y = 9 - 2x[/tex]

and [tex]s[/tex] depends only on [tex]x[/tex].

[tex]s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2[/tex]

Find the critical points of [tex]h[/tex].

[tex]\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3[/tex]

It follows that [tex]y = 9-2\cdot3 = 3[/tex] and [tex]z=3[/tex], so the only critical point of [tex]s[/tex] is at (3, 3, 3).

Differentiate [tex]h[/tex] again and check the sign of the second derivative at the critical point.

[tex]\dfrac{d^2h}{dx^2} = -6 < 0[/tex]

for all [tex]x[/tex], which indicates a maximum.

We find that

[tex]\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)[/tex]

The second derivative at the critical point exists

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex] for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

[tex]$&\frac{\partial g}{\partial x}[/tex] = 9 - 2x - y = 0

[tex]$&\frac{\partial g}{\partial y}[/tex] = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

[tex]$\frac{d h}{d x}=18-6 x=0[/tex]

⇒ x = 3

It pursues that y = 9 - 2 [tex]*[/tex] 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex]

for all x, which suggests a maximum.

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Answer:

x = 5

Step-by-step explanation:

There's a Secant Theorem that someone else figured out (waaaay back in history) we just need to memorize it. So a secant is a line that touches the circle in two places. Your picture has two secants that both go thru the same point that's outside the circle. The secants each have a bit that's inside the circle and a bit that's outside the circle. And we could add together the inside and outside bits and get a total for the whole thing.

The secant theorem says that the outside piece × the whole thing on one secant = the outside piece × the whole thing on the other secant.

For the secant on top the "outside" bit is 9 and the whole thing is (2x+1+9). We'll times these together.

For the bottom secant the outside piece is 10 and the whole thing is (x+3+10). We'll multiply these together.

9(2x+1+9)=10(x+3+10)

simplify.

9(2x+10) = 10(x+13)

distribute.

18x + 90 = 101x + 130

combine like terms.

8x + 90 = 130

subtract 90

8x = 40

divide by 8

x = 5

see image.

Answer:

a)

Step-by-step explanation:

Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=9\\ h=7 \end{cases}\implies \begin{array}{llll} A=\cfrac{7(5+9)}{2}\implies A=\cfrac{7(14)}{2} \\\\\\ A=49 \end{array}[/tex]

Answer:

80 cups

Step-by-step explanation:

Answer:

6a³b²

Step-by-step explanation:

3 × 2 = 6

a²× a¹ = a³

b × b = b²

Answer:

y= -3x+4

Step-by-step explanation:

y=mx+c

m= y2-y1 ÷ x2-x1

m= -3

y=-3x+c

7=-3(-1)+c

c=4

y=-3+4

Answer:

135

Step-by-step explanation:

You can add the number which are in negative o

as well

The number is in descending order by 4.

Then add the first and last number i.e.

433+107===> 540

divide 540 by 4

540/4

= 135

Answer: 50 and 59

I divided 2950 by 25 because I knew it would somehow factor into that since it ends in 50. Then, I got 25 and 118. From there, I just divided 118 by 2 since I knew that it would end in a 9 and I multiplied 25 by 2. Not sure if this is really helpful, but you also try using a GCF calculator and look up all the factors of that number next time!

The equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

In step 4 of the proof, we have the following equation

m<w + m<x = m<y + m<z

In step 5, we have

m<x = m<y

When m<x = m<y is substituted to the equation in step 4, we have:

m<w + m<x = m<x + m<z

Hence, the equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

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Answer:

[tex]P(x) -0.1(x+1)(x-3)^2[/tex]

Step-by-step explanation:

So you can express a polynomial in factored form, where each factor of the polynomial is being multiplied by each other to get the original polynomial as such: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex] notice the a in front? Sometimes the value is 1, sometimes it's not, and I'm assuming it's not 1, since the y-intercept is given.

Anyways, when we express a polynomial in factored form: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex], it's pretty easy to see that -a, -b, and -c are roots, since if we plug in -a, the factor (x+a) becomes (-a + a) = 0, and since the factors are being multiplied by each other, the value p(-a) will be 0, since 0 * some value = 0.

The next thing to know is what multiplicity means. It essentially means when you have the same root "multiple times", or in other words it's the degree of the factor. For example: [tex]f(x) = (x+a)^3(x+b)^2(x+c) = (x+a)(x+a)(x+a)(x+b)(x+b)(x+c)[/tex], if you took each factor, you would see that the root -a shows up 3 times, thus the multiplicity is 3, which can also be determined by just looking at the initial degree... 3. The same thing goes for b and c, except for c, the degree isn't explicitly said, it's just 1.

Since we have a zero at x=3 one of the factors will be (x-3) since plugging in 3 to this makes it 0. But this has a multiplicity of 2, so the degree of the this factor is 2. So for we have the polynomial: [tex]p(x) = (x-3)^2[/tex]

Since we have a zero at x=-1, one of the factors will be at (x+1), since plugging in 1 into this makes the value 0. This has a multiplicity of 1, and you can write the degree 1, but if you don't explicitly write it, it can just be assumed to be 1, since a^1=a

So now we have the polynomial: [tex]p(x) = (x+1)(x-3)^2[/tex]

So let's just assume we have an "a" value in front as mentioned in the very beginning, we have the polynomial: [tex]p(x) = a(x+1)(x-3)^2[/tex] and we can solve for this value, using any point except for the zeroes. We can use the y-intercept given to solve for a

Plug in 0 as x (by definition of y-intercept) and set p(x) = -0.9

[tex]-0.9 = a(0+1)(0-3)^2[/tex]

Subtract/add values

[tex]-0.9 = a(1)(-3)^2[/tex]

Simplify

[tex]-0.9 = 9a[/tex]

Divide both sides by 9

-0.1 = a

So now let's plug this into our polynomial to get the final result!

[tex]P(x) -0.1(x+1)(x-3)^2[/tex]

a. Angle BAC is a central angle.

b. Arc BEC is a major arc.

c. Arc BC is a minor arc.

d. m(BEC) = 260°

e. m(BC) = 100°

An arc that has a measure that is greater than 180 degrees or is greater than a semicircle (half a circle) is referred to as a major arc.

An arc that has a measure that is less than 180 degrees or is not up to a semicircle (half a circle) is referred to as a minor arc.

A central angle can be described as an angle with a vertex at the center of a circle and has two radii of the circle at sides.

a. Angle BAC is a central angle.

b. Arc BEC is a major arc.

c. Arc BC is a minor arc.

d. m(BEC) = 360 - 100 [central angle theorem]

m(BEC) = 260°

e. m(BC) = angle BAC = 100° [central angle theorem]

m(BC) = 100°

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Answer: 27°

Step-by-step explanation:

The easiest way to find the measure of angle Z is to know that in a rhombus, the diagonals are perpendicular bisectors of each other. This means that all the four angles in the center are 90°.

Since we know that all angles in a triangle add up to 180°, we can set the sum of z, 63, and 90 to be 180 and solve for z.

[tex]z+63+90=180\\z+153=180\\z=27[/tex]

Hence, z is 27°.

It should be noted that a trial balance is a report which lists the balances of the ledger accounts of a company.

It should be noted that the information is incomplete. Therefore, an overview will be given. It should be noted that the accounts that are reflected on a trial balance are related to the accounting items.

The adjusted trial balance simply lists the general ledger account balances after the adjustments have been made. In such a case, these adjustments typically include prepaid and accrued expenses, and non-cash expenses such as depreciation.

Furthermore, a trial balance is a list of the closing balances of ledger account while adjusted balance is a list of general account. An adjusted trial balance is typically prepared by creating a series of journal entries which are designed to account for any transactions that haven't been completed.

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Answer: 4.6 (rounded to the nearest tenth)

Step-by-step explanation:

I assume that 1.6 is the coefficient of x, which is what we're trying to find out in this case.

Therefore, dividing 1.6 on both sides we get

from

1.6x = 7.37

to

x = 7.37/1.6 = 4.6 (approximately, rounded to the nearest tenth).

The value of b as described in the task content by means of solving the two equations simultaneously is; b= -10.

The given simultaneous equations as indicated have been manipulated to determine the value of a which is; 0.5 in the task content.

Hence, by substituting a= 0.5 into the equation; 5 = 30a + b; we have;

5 = 30(0.5) + b

b = 5- 15 = -10.

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Answer:

a) x + 10 = 45

b) 3 = 6 - x

c) d = s * t

Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.

SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.

This is all we're really doing.

Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.

Just keep doing this with all the equations.

Hope this helped!

The estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

The thickness of a sheet of paper can be measured using a screw gauge or vernier caliper.

If the thickness of a ream of paper, which contains 500 sheets, is given, a sheet will be x/500 thick.

The thickness of 2 sheets of paper will be the thickness of a sheet multiplied by 2.

Number of reams of paper in a box = 5 reams

1 ream = 500 sheets

500 sheets = 5.4 cm thick

The thickness of 2 sheets of paper = 0.0216 cm {5.4cm x 2/500)}

Thus, the estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

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Assume that one ream of paper is 5.4 cm thick.

Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.

The equation is given by:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

In which:

In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

[tex]20 = 10\log{\frac{p}{p_0}}[/tex]

[tex]\log{\frac{p}{p_0}} = 2[/tex]

The logarithm is inverse of the function [tex]10^x[/tex], hence we apply the function to both sides to find the ratio.

[tex]\frac{p}{p_0} = 10^2[/tex]

[tex]\frac{p}{p_0} = 100[/tex]

Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.

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Answer:

  A.  (-1, -4)

Step-by-step explanation:

The vertex can be found by converting the equation from standard form to vertex form.

Considering the x-terms, we have ...

  y = (x^2 +2x) -3

where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...

  y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2

  y = (x +1)^2 -4

Compare this to the vertex form equation ...

  y = a(x -h)^2 +k

which has vertex (h, k).

We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).

On the attached graph, the vertex is the turning point, the minimum.

The number of moles of hydrogen is 185 moles.

We know that the mole refers to the number of elementary entities that make up a substance. According to Avogadro, one mole of a substance contains 6.02 * 10^23 elementary entities which includes atoms, molecules and ions.

Now, we know the number of moles is obtained as the ratio of the mass to the molar mass of the substance.

Thus;

Mass of hydrogen = 370.g

Molar mass of hydrogen = 2 g/mol

Number of moles of hydrogen = 370.g/2 g/mol = 185 moles

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The probability that a person in this income bracket will be audited this year is of 3%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that 30 out of 1000 people are audited, hence the probability that a person in this income bracket will be audited this year is given by:

p = 30/1000 = 0.03 = 3%.

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Answer:

$29765.50

Step-by-step explanation:

Median is the middlemost value (or the average of the 2 middlemost value if there are even number of values) in an ascending order.

First, arrange the salary list in an ascending order.

$21,971 , $25,997 , $27,512 , $32,019 , $38,860 , $43,702

As we can see here, there are even number of values (6), so the median will be the average of the 2 middlemost value, which will be:

Median = [tex]\frac{27512 + 32019}{2}[/tex]

= [tex]\frac{59531}{2}[/tex]

= $29765.50

Answer:

$29,765.50 is the median salary

Step-by-step explanation:

To find the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997

The steps to do this is:

Doing the steps:

This means take the average of $27,512 and $32,019

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Answer:

∠ 3 = 65°

Step-by-step explanation:

∠ 2 and 115° are a linear pair and sum to 180° , that is

∠ 2 + 115° = 180° ( subtract 115° from both sides )

∠ 2 = 65°

∠ 2 and ∠ 3 are corresponding angles and and are congruent , then

∠ 3 = 65°

Using the law of sines, it is found that the distance between the kite and the dog is of 284.77 meters.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

For the situation described, we have that:

Hence:

[tex]\frac{\sin{42^\circ}}{h} = \frac{\sin{87^\circ}}{425}[/tex]

Applying cross multiplication:

[tex]h = 425\frac{\sin{42^\circ}}{\sin{87^\circ}}[/tex]

h = 284.77 meters.

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