The expected number of transmissions if the channel is initially in the Good state is 1/a, and if the channel is initially in the Bad state, it is 1/(1-p).
Let N be the number of transmissions needed to successfully transmit the bit (0) over the channel. We want to find the expected value of N.
If the channel is initially in the Good state, then the probability of successfully transmitting the bit on the first attempt is a. If the transmission is unsuccessful, then the channel switches to the Bad state with probability (1-a)p and to the Good state with probability (1-a)(1-p). In the Bad state, no successful transmission can occur. Therefore, the expected value of N can be written as:
E(N|Good) = 1 + (1-a)p E(N|Bad) + (1-a)(1-p) E(N|Good)
Note that the first term (1) corresponds to the first transmission, and the other terms correspond to subsequent transmissions. We can solve for E(N|Good) as:
E(N|Good) = 1 + (1-a)p E(N|Bad) + (1-a)(1-p) E(N|Good)
E(N|Good) = 1 + (1-a)p E(N|Bad) + (1-a)(1-p) E(N|Good)
E(N|Good) = 1 + (1-a)p E(N|Bad) + (1-a)(1-p) [1 + (1-a)p E(N|Bad)]
E(N|Good) = 1 + (1-a)p E(N|Bad) + (1-a)(1-p) + (1-a)(1-p)(1-a)p E(N|Bad)
E(N|Good) = 1 + (1-a)(1 + (1-a)p + (1-a)(1-p) E(N|Bad))
Similarly, if the channel is initially in the Bad state, then no successful transmission can occur on the first attempt, and the channel remains in the Bad state. Therefore, the expected value of N can be written as:
E(N|Bad) = 1 + (1-p) E(N|Bad)
Solving for E(N|Bad), we get:
E(N|Bad) = 1/(1-p)
Substituting this expression in the equation for E(N|Good), we get:
E(N|Good) = 1 + (1-a)(1 + (1-a)p + (1-a)(1-p)/(1-p))
Simplifying this expression, we get:
E(N|Good) = 1/a
Therefore, the expected number of transmissions if the channel is initially in the Good state is 1/a, and if the channel is initially in the Bad state, it is 1/(1-p).
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The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what are the wavelengths for x-rays with frequency 3 × 1018?
The wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].
What is the wavelength of light ?The distance between the two crests or troughs of the light wave is known as the wavelength of light.
The color of light is determined by its wavelength, and the pitch of sound is determined by its wavelength. The visible spectrum of light has wavelengths between around 700 nm (red) to 400 nm (violet). The range of audible sound wavelengths is roughly 17 mm to 17 m.
To calculate the wavelength of light, we use the equation:
[tex]$\lambda=\frac{c}{\nu}$[/tex]
where,
λ = wavelength of the light
c = speed of light = [tex]$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$[/tex]
ν= frequency of light = [tex]$3 \times 10^{18} s^{-1}$[/tex]
Putting the above value in equation,
[tex]$\lambda=\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{3 \times 10^{19} \mathrm{~s}-1}=1 \times 10^{-10} \mathrm{~m}$[/tex]
Hence, the wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].
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Rewrite each equation without absolute value for the given conditions.
[tex]y=/x-5/+/x+5/ if -5\ \textless \ x\ \textless \ 5[/tex]
Answer: 10
Step-by-step explanation:
If [tex]-5 < x < 5[/tex], then [tex]|x-5|=5-x[/tex] and [tex]|x+5|=x+5[/tex].
So, the expression is equal to 10.
Susie enjoys spending her afternoons kayaking. One afternoon she was kayaking on a river 3 miles upstream, and 3 miles downstream in a total of 4 hours. In still water, Susie can Kayak at an average speed of 2 miles per hour. Based on this information, what a reasonable estimation of the current measured in miles per hour.
Using the relation between velocity, distance and time, it is found that a reasonable estimation of the current is of 1 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Upstream, against the current, he traveled 3 miles in t hours, hence the equation is:
[tex]2 - c = \frac{3}{t}[/tex]
[tex]c = 2 - \frac{3}{t}[/tex]
Downstream, with the current, he traveled 3 miles in 4 - t hours, hence the equation is:
[tex]2 + c = \frac{3}{4 - t}[/tex]
Hence:
[tex]c = \frac{3}{4 - t} - 2[/tex]
Then, taking the two equal equations:
[tex]2 - \frac{3}{t} = \frac{3}{4 - t} - 2[/tex]
[tex]\frac{3}{4 - t} + \frac{3}{t} = 4[/tex]
[tex]\frac{3t + 12 - 3t}{t(4 - t)} = 4[/tex]
12 = -4t² + 16t
4t² - 16t + 12 = 0
t² - 4t + 3 = 0
(t - 3)(t - 1) = 0.
The current is positive, hence:
[tex]c = 2 - \frac{3}{3}[/tex]
c = 2 - 1
c = 1 mph.
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Need this question's answer.
Answer:
1.2
2.4√3÷3
3. x=45, y=15
Step-by-step explanation:
OK,
1. So the first part requires the Pythagoreanism formula which is: b²=a²+c²:
AC²=AB²+BC²====> AC²=(1)²+(√3)²===> AC²=4===> AC=2
2.The second part requires the formula of tan:
tan A=BC÷AB===> tan A=√3÷1===> tan A=√3
tan C=AB÷BC===> tan C=1÷√3===> tan C=√3/3
tan A+tan C=√3+√3/3===> 4√3÷3
3.And the last part requires the equation of angles:
A+B+C=180===>
x+y+x-y+90=180===> 2x=90===> x=45, y=15
ok more of a question not like a equation or anything but when do you know when there is a extraneous answer and how do you solve it (please provide an example equation)
One can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.
What is an extraneous equation?It should be noted that an extraneous equation means a root of a transformed equation that isn't the root of the original equation due to the fact that it's excluded from the domain of the original equation.
In this case, one can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.
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Find the measure of each numbered angle.
Step-by-step explanation:
18z+10z+40z+5+1=360
68z+6=360
68z=360-6
68z=364
z≈5.353
suppose cos(A) = 4/5. use the trig identity sin^2(A)+cos^2(A)=1 to find sin(A) in quadrant IV. round to the ten-thousandth.
a. -0.3954
b. -0.6000
c. 0.6485
d. 0.4500
In quadrant IV, [tex]\sin(A)[/tex] is negative. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \sin(A) = -\sqrt{1-\cos^2(A)} = -\dfrac35 = \boxed{-0.6000}[/tex]
The weight of football players is normally distributed with a mean of 180 pounds and a standard deviation of 20 pounds. what is the probability of a player weighing less than 215 pounds?
Answer:
Given:
mu = 200 lb, the mean sigma = 25 the standard deviation
For the random variable x = 250 lb, the
z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2
From standard tables for the normal distribution, obtain
P(x < 250) = 0.977
Answer: 0.977
There are 450 eighth graders at Wilson Middle School. In the class president election, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris. What percent of eighth graders voted for Luke
Using Percentage, the eighth graders voted for Luke is of 72 percentage or 72%.
According to the question,
They are 450 eighth graders at Wilson Middle School. In the class president, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris.
In order to find the percentage of eighth graders voted for Luke only if 252 divided by 350.
[tex]\frac{252}{350} = 0.72[/tex]
To convert decimal into Percentage multiply 0.72 into 100.
0.72*100 = 72%.
Hence, the percentage of the eighth graders voted for Luke is of 72 percentage or 72%.
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B=(2x+3)(4x^2-6x+9)-2(4^3-1)
The local high school is hosting the last soccer game. They charged adults, x, 5 dollars to enter, and 3 dollars for students, y. It cost the school $300 to pay the referees for the game. The school wants to make a profit on the game, and 75 people attended. This is represented by the system:
5x + 3y > 300
x + y = 75
Which of the following points is a solution to the system?
(20, 15)
(25, 70)
(30, 45)
(40, 35)
IVE HEARD (30, 45) AND (40, 35). PLEASE HELP.
The correct answer is (40, 35) because by plugging in, 40 +35 = 75 and
(40 x 5) + (35 x 3) > 300
How to solve Word Problem ?Word problem can be solved by interpreting the problem into its best fit equation. The equation may be linear, quadratic or simultaneous equations.
Given that
5x + 3y > 300
x + y = 75
Let us first assume that 5x + 3y = 300. That is,
5x + 3y = 300
x + y = 75
Eliminate y by multiplying equation 2 by 3
5x + 3y = 300
3x + 3y = 225
2x = 75
x = 75/2
x = 37.5
Substitute x in equation 2
37.5 + y = 75
y = 75 - 37.5
y = 37.5
The correct answer is (40, 35) because 40 +35 = 75 and
(40 x 5) + (35 x 3) > 300
Therefore, the solution to the system is (40, 35)
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Explain why the following form linearly dependent sets of vectors. (solve this problem by inspection.)
u1 = (3, -l), u2 = (4, 5), u3 = (-4, 7) in r2
A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution
x1 = x2 = .... = xk =0. Then the set {v1,v2,...,vk} is linearly dependent otherwise.
So putting in the formula we get
x1u1 + x2u2 + x3u3 = 0
x1u1 + x2u2 = -x3u3
au1 + bu2 = u3 ∵ (-x1/x3 = a & -x2/x3 = b)
On putting in the values
a(3,-1) + b(4,5) = (-4,7)
(3a+4b,-a+5b) = (-4,7)
On comparing we get
3a + 4b = -4 -(1)
-a + 5b = 7 -(2)
on solving these equations we get
b = 17/19 and a= -48/19
which is non trivial.
Thus the following form linearly dependent sets of vectors.
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Find the surface area of the composite figure. Round to the nearest tenth if necessary.
The surface area of the composite figure is equal to 233.6 square centimeters.
How to determine the surface area of a solid
The surface area is the area of all faces of a solid. Since the surface area of the figure is a combination of triangles and quadrilaterals, we must sum all the areas to determine the surface area of the figure. Now we proceed to determine this:
A = 4 · (1/2) · (3 cm) · (2 cm) + 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (2 cm) + 2 · (8 cm) · (3.6 cm)
A = 233.6 cm²
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The points (-3,2) (5,2) and (5,1) are three vertices of a rectangle what is the fourth vortex?
In a right triangle the length of the hypotenuse is a and the measurement of one of the
acute angle is a. Find the measurement of the other acute angle and the lengths of the
legs.
Answer:
The measure of the acute angle = 90 - a
Leg 1 = a cos(a)
Leg 2 = a sin(a)
Step-by-step explanation:
In a right triangle ,the two acute angles are complementary
We are given that the measure of one of the acute angles is ‘a’
Then
The measure of the other one is ‘90 - a’
Now, we use the law of sine to determine the length of the legs :
Let x and y be respectively the length of the two legs.
[tex]\frac{x}{\sin \left( 90-a\right) } =\frac{a}{\sin \left( 90\right) }[/tex]
[tex]\Longleftrightarrow \frac{x}{\sin \left( 90-a\right) } =a[/tex]
[tex]\Longleftrightarrow x = a \times\sin \left( 90-a\right)[/tex]
[tex]\Longleftrightarrow x = a \times\cos \left( a\right)[/tex]
On the other hand,
[tex]\frac{y}{\sin \left( a\right) } =\frac{a}{\sin \left( 90\right) }=a[/tex]
Then
[tex]y = a \times \sin(a)[/tex]
Select the correct answer from each drop-down menu.
Consider the function represented by this graph.
As the value of x increases, the value of f (x)........ increases or decreases
The x-intercept is the point......
As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)
What is the function?A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.
Functions can also be represented on the graph called graphical representation.
From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.
The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)
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When figuring out the sign of a fraction as a
whole, you use the rules for dividing negatives.
Given the graph of the function, f(x) , what is the value of f (-2)?
The value of f(-2) is 0
How to evaluate the function?The graph of the function is added as an attachment
The graph is given as:
y = f(x)
When x =-2. we have
y = f(-2)
From the graph, we have:
x = -2 and y = 0
So, we have
f(-2) = 0
Hence, the value of f(-2) is 0
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The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -2x + 6. What is the
point-slope form of the equation for this line?
O y-3=-%(x + 8)
y+3=-2(x-8)
y+8=-%(x-3)
D y-8 = -2(x + 3)
Answer: [tex]y-8=-2(x+3)[/tex]
Step-by-step explanation:
See attached image, it's direct formula substitution.
Which of the measurements of triangleBAC are correct
Answer:
yes
no
yes
Step-by-step explanation:
sin C = opp/hyp = 9/15 yes
tan B = opp/adj = 12/9 no
tan B = 12/9; B = tan^-1 12/9 = 53.13°
Please help me
better be worth my 57 points
Answer: a
Step-by-step explanation:
The slope is the rate at which a line goes up or down (i.e., how steep it is). It is measured by the slope formula, which is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where (x1, y1) and (x2, y2) are two points on the line.
Below, (x1, y1) are (c, d) and (x2, y2) are (a, b).
When all variables are plugged in, the slope is
[tex]\frac{b-d}{a-c}[/tex]
29. The table below represents the relationship of the price of carrots to their weight in ounces in a market: Price Weight, in oz. $0.377.4 $0.44 8.8 $0.52 10.4 B Another market sells carrots at a rate of $4.80 for every 3 pounds. Which equation represents the market that sells their carrots at a lower rate per pound? y = 0.8x y = 1.2x ) y = 0,4x y = 1.6x
The proportional relationship that represents the market that sells their carrots at a lower rate per pound is: y = 1.6x.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
From the table, the rate is:
k = $8.8/4.4 = 2.
From the market, the rate is:
k = $4.8/3 = $1.6.
Hence the equation is y = 1.6x.
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In the 30-60-90 triangle below, side s has a length of
length of
30
90°
S
60
OA. 16√3, 5
B. 4√2, 4√2
OC. 4, 4√3
OD. 8.5, 16
OE. 16√3, 16√3
OF. 4, 8√3
and side q has a
Answer:
4, 4√3
Step-by-step explanation:
In a 30-60-90 triangle:
The leg opposite of the 30-degree angle is 1/2 of the hypotenuse: 8/2 = 4
The longer leg is √3 times the shorter leg: 4*√3 = 4√3
Check work: 4^2+(4√3)^2 = 8^2 --> 16+48 = 64 --> 64 = 64
Okey please help me out
Rewrite the second expression as
[tex]\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}[/tex]
and the third expression as
[tex]\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}[/tex]
so the fractions all have the same denominator.
Then combining the fractions gives the desired result,
[tex]\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}[/tex]
Express tan D as a fraction in simplest terms. 40 B 24 32 C
Answer:
[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]
Step-by-step explanation:
Trigonometry ratios:
[tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]
[tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]
The vertex of a parabola is (0,0)and the focus is (1/8, 0) . What is the equation of the parabola?
The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².
How to derive the equation of the parabola from the locations of the vertex and focus
Herein we have the case of a parabola whose axis of symmetry is parallel to the x-axis. The standard form of the equation of this parabola is shown below:
(x - h) = [1 / (4 · p)] · (y - k)² (1)
Where:
(h, k) - Coordinates of the vertex.p - Distance from the vertex to the focus.The distance from the vertex to the focus is 1 / 8. If we know that the location of the vertex is (0, 0), then the standard form of the equation of the parabola is:
x = 2 · y² (1)
The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².
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In ΔPQR, find the measure of ∡P. Hypotenuse is 57.6 and the opposite side is 33.8.
Step-by-step explanation:
pythogoras theorem = Q²=P²+R²
P=P
Q= 57.6
R=33.8 =
(57.8)²=(P)²+(33.8)²
=3,340.84=(P)²+1142.44
=3340.84-1142.44=P²
=2,198.4=P²
[tex] = \sqrt{2198.4} = p \\ = 46.8 = p[/tex]
Nani needs to buy 8 cups of fresh pineapple for a fruit cocktail. the table shows the unit prices of pineapple at different stores. if nani only has $4, from which stores could she purchase her pineapple?
Nani could purchase her pineapple from stores A, D, and E.
Given Information
It is given that Nani needs to purchase 8 cups of pineapple.
The unit prices of pineapple at each store is as follows,
Store A : 0.49
Store B : 0.51
Store C : 0.55
Store D : 0.48
Store E : 0.45
Amount that Nani has = $4
Reason Behind Purchasing From Either A, D, or E
Since Nani has amount of $4, she can purchase pineapple only from the stores where the total cost of 8 pineapple cups adds up to less than $4. The purchase of 8 pineapple cups at each store would be given as,
Store A : 0.49(8) = $3.92
Store B : 0.51(8) = $4.08
Store C : 0.55(8) = $4.40
Store D : 0.48(8) = $3.84
Store E : 0.45(8) = $3.60
As it can be seen, Nani can purchase from the store A, D, and E as it falls within her budget of $4.
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A polypay sheep produces an average $9.9$ pounds of wool annually. This wool is cleaned, spun into yarn and then packaged into skeins of $175$ yards of yarn each. One pound of wool makes $10.95$ miles of yarn. If farmer Bill has a flock of $200$ polypay sheep, to the nearest thousand skeins, how many skeins of yarn is his flock expected to produce in one year
Answer:
218,048. skeins
Step-by-step explanation:
Break down the process into proper order.This question is built to throw you off by not telling you about the information in order.
First, the polypay sheep produces 9.9 pounds of wool.
Then, each pound produces 10.95 miles of yarn.
And finally, the yarn is packaged into skeins that are 175 yards each.
Step 1: Outline the workEach polypay sheep is 9.9 pounds. And we will use that total weight to find the amount of yarn in miles.
Then we will split up that yarn into equal pieces to make skeins.
BUT, the pieces are measured in yards, so we will have to convert the miles of yarn into an equivalent amount in yards as well. (Unmatched units of measurements don't mix well).
So, our equation will look like this:
(#of sheep) [tex]\times[/tex] (9.9 pounds per sheep) [tex]\times[/tex] (10.95 miles per yarn) [tex]\times[/tex] (1760 yards per mile) [tex]\div[/tex] (175 skeins per yard)
Step 2: Plug and ChThe number of sheep Bill has is 200.
So, we plug that into the number model we made.
[tex]200\times9.9\times10.95\times1760\div175[/tex]
We end up with:
218,048.914
The decimal indicates that there is a remaining amount of yarn that couldn't be properly packaged into a skein.
Since, that remainder is not a complete skein, we must ignore its existence.
So the number of skeins expected is:
218,048
The number of skeins of yarn is Bill's flock expected to produce in one year is 1819.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, a polypay sheep produces an average 9.9 pounds of wool annually.
Farmer Bill has a flock of 200 polypay sheeps
So, total weight of wool is 9.9×200
= 1980 pounds
One pound of wool makes 10.95 miles of yarn.
So, the number of yarns = 1980/10.95
= 180.82 miles of yarn
We know that, 1 mile =1760 yards
Then, 180.82 miles
= 318243.2 yards
This wool is cleaned, spun into yarn and then packaged into skeins of 175 yards of yarn each.
Number of skeins = 318243.2/175
= 1819
Therefore, the number of skeins of yarn Bill's flock expected to produce in one year is 1819.
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Use trig to find the height of the hot air balloon. Write an equation and show work. Round answer to the nearest tenth
Answer:
x = 753.6 ft
Step-by-step explanation:
One leg is x.
The other leg is given.
The trig function that relates the two legs of a right triangle is the tangent.
tan A = opp/adj
tan 37° = x/1000ft
x = 1000 ft × tan 37°
x = 753.6 ft
Answer: 753.6 feet
Step-by-step explanation:
The angle, theta, is 37 degrees. However, we're not given the length of the hypotenuse in this case. So sine would be x by the hypotenuse and cosine would be 1,000 by the hypotenuse. In this case, we can use tangent, which is sine/cosine. In this case, tan 37 = x/1,000.
Hence,
tan 37 = x/1,000
x = tan 37 * 1000
x is approximately 753.6, rounded to the nearest tenth.