Molecular communications. Suppose Alice wants to send one bit message (1 or 0) to Bob. If the message is 1, Alice emits molecules, which will be then detected by Bob. If the message is 0, Alice does not emit any molecule. Suppose that given Alice emits molecules, the number of molecules detected at Bob for t minutes, denoted by N(1), follows Poisson distribution N() Poisson(t). Assume that Alice emits molecules. Let T denote the time Bob waits until it detects the first molecule. Find the pdf of T.
Answers
The pdf of T is f(t) = λ \(e^{(-\lambda t)\)for t >= 0.
To find the probability density function (pdf) of T, we need to consider the distribution of the waiting time until the first molecule is detected by Bob.
In this scenario, since the number of molecules detected at Bob, denoted by N(1), follows a Poisson distribution with parameter λ (the average number of molecules emitted by Alice per minute), we can use the properties of the exponential distribution to find the pdf of T.
The waiting time until the first molecule is detected, T, follows an exponential distribution with parameter λ. The pdf of the exponential distribution is given by:
f(t) = λ \(e^{(-\lambda t)\) for t >= 0
where λ is the rate parameter, which in this case represents the average number of molecules emitted per minute.
Therefore, the pdf of T is f(t) = λ \(e^{(-\lambda t)\)for t >= 0.
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Related Questions
I need help, Whats 9+10=
Answers
Answer:
19
Step-by-step explanation:
Answer:
the answer is 19
Step-by-step explanation:
you have 9 things then you added then you will get 19
1. If you roll a single die and get 4 fives in a row, what is the probability that you'll get a five on the
next roll?
2. What is the probability that you'll get 5 fives in a row when rolling a single die?
3. A roulette wheel has 38 numbers. If the "lucky" number 7 comes up twice in a row, what is the
probability it will come up on the very next roll?
4. What is the probability of getting three 7's in a row on a roulette wheel?
5. If I type randint(1,10) on my calculator, I get a random integer between 1 and 10 (inclusive). If I
do this 6 times, what is the probability that all 6 outcomes will be a 1?
6. If I roll a pair of dice, what is the probability of getting a pair of sixes?
7. If I roll a pair of dice, what is the probability of getting any pair?
Answers
1. 1/6 is the probability of rolling a five on the next roll.
2. The probability of getting 5 fives in a row when rolling a single die is 1/7776 .
3. 1/38 is he probability of 7 coming up on the very next spin is
4. 1/54782 is the probability of getting three 7's in a row on a roulette wheel.
5. (1/10)⁶ is the probability of getting a 1 on all six trials.
6. 1/36 is the probability of getting a pair of sixes when rolling a pair of dice is
7. The probability of getting any pair is 1/6
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
1. The probability of rolling a five on a single roll of a fair die is 1/6, since there are six equally likely outcomes: rolling a 1, 2, 3, 4, 5, or 6.
the probability of rolling a five on the next roll is still 1/6, regardless of whether the previous rolls resulted in four fives in a row or not.
2. The probability of getting a five on a single roll of a fair die is 1/6, as there are six equally likely outcomes.
the probability of getting 5 fives in a row when rolling a single die is:
(1/6) × (1/6) × (1/6) × (1/6) × (1/6) = 1/7776
3. The probability of any particular number coming up on a single spin of an American roulette wheel with 38 numbers is 1/38, since there are 38 equally likely outcomes.
As these are independent , the probability of 7 coming up on the very next spin is still 1/38.
4. The probability of getting three 7's in a row on a roulette wheel is:
(1/38) × (1/38) × (1/38) = 1/54,872
5. The probability of generating a 1 on a single trial is 1/10.
The probability of getting a 1 on a single trial by itself six times
(1/10) × (1/10) × (1/10) × (1/10) × (1/10) × (1/10) = (1/10)⁶
The probability of getting a 1 on all six trials is (1/10)⁶
6.
The probability of getting a pair of sixes when rolling a pair of dice is:
1/36
7.
The probability of getting any pair when rolling a pair of dice is:
Number of ways to get a pair / Total number of possible outcomes
= 6 / 36
= 1 / 6
So the probability of getting any pair is 1/6
Hence,
1. The probability of rolling a five on the next roll is 1/6.
2. 1/7776 is the probability of getting 5 fives in a row when rolling a single die.
3. The probability of 7 coming up on the very next spin is 1/38.
4. The probability of getting three 7's in a row on a roulette wheel is 1/54782
5. The probability of getting a 1 on all six trials is (1/10)⁶
6. The probability of getting a pair of sixes when rolling a pair of dice is:
1/36
7. the probability of getting any pair is 1/6
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Based on What you learned about economics of organic produce, explain why buying organic food is so expensive
Answers
Answer:(:
Step-by-step explanation:
Organic food production is usually more labour and management intensive and happens on a smaller scale ie on smaller farms which lack the benefit of economy of scale.
What two equations are in this graph (slope intercept form if you can)
Answers
Answer:
use rise over run! this means "rise" (being the change in y, going up or down) divided by the "run" (being the change in x, going from left to the right).
Step-by-step explanation:
In ΔXYZ and ΔEFG, angles Y and F are right angles. Which set of congruence criteria would be enough to establish that the two triangles are congruent by HL?
Answers
XZ ≅ EG and YZ ≅ FG is enough to make triangles to be congruent by HL. Option b is correct.
Two triangles ΔXYZ and ΔEFG, are given with Y and F are right angles.
Condition to be determined that proves triangles to be congruent by HL.
What is HL of triangle?HL implies the hypotenuse and leg pair of the right-angle triangle.
Here, two right-angle triangles ΔXYZ and ΔEFG are congruent by HL only if their hypotenuse and one leg are equal, i.e. XZ ≅ EG and YZ ≅ FG respectively.
Thus, XZ ≅ EG and YZ ≅ FG are enough to make triangles congruent by HL.
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In ΔXYZ and ΔEFG, angles Y and F are right angles. Which set of congruence criteria would be enough to establish that the two triangles are congruent by HL?
A.
XZ ≅ EG and ∠X ≅ ∠E
B.
XZ ≅ EG and YZ ≅ FG
C.
XZ ≅ FG and ∠X ≅ ∠E
D.
XY ≅ EF and YZ ≅ FG
what are the outside diameters of the three high tension ignition cables in use
Answers
The outside diameter of each cable is 8mm.
If the inner cable has a radius of 2mm, then its diameter is 4mm. Adding the spacing between each cable of 2mm on each side gives a total of 4mm of additional diameter.
Therefore, the diameter of each cable is 4mm + 4mm = 8mm. This assumes that the cables are cylindrical in shape and have no additional insulation or shielding that would increase their overall diameter.
It is important to note that the diameter of high tension ignition cables can vary depending on the specific application and design of the cable.
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Complete question:
what are the outside diameters of the three high tension ignition cables in use given that inner cable have 2mm radius and spacing between each cable is 2mm.
A book is marked down by 28 percent from an original price of $19.50. What is the new price?
Answers
Step-by-step explanation:
First find 28% of $19.50:
($19.50) / (100) × (28) = $5.46
Now minus the 285 from the original price:
($19.50) - ($5.46) = $14.04
The answer is $14.04
Hope it helped :)
Show that if A and B are sets with A ⊆ B, then a. A ∪ B = B b. A ∩ B = A
Answers
If A and B are sets with A⊆B the a) A ∪B = B, b) A∩B = A.
a) Let A⊆B
Let x ∈ A∪B
Then x ∈ A or x ∈ B .....(i)
By definition of union we have
x ∈ A ⇒ x ∈ B .....(ii)
Using (i) and (ii), if x ∈ A, then x ∈ b. If x ∈ B, then clearly x ∈ B.
Thus given A⊆ B, then A∪B = B.
b) First assume A∩B which implies that x ∈ A and x ∈ B.
Hence we can implies the
A∩ B ⊆ A (we started with the element in A∩B and concluded that it is in A) ------(i)
Now, let x ∈ A which implies x ∈ B ( as A⊆ B)
Hence, x ∈ A∩B, which in turn imply
A ⊆ A∩B -----(ii)
From (i) and (ii) we get
A∩B = A
Therefore if A and B are sets with A⊆B, then A ∩B = B and A∩B = A.
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Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
Answers
The theorem that would be included in the proof is: CPCTC theorem.
What is the CPCTC Theorem?CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.
To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:
1. angle D ≅ angle F [given]
2. angle DBE ≅ angle ECF [given]
3. side DE ≅ side EF [given]
4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]
5. DB ≅ FC [by the CPCTC theorem]
With the given proof, we can state that side DB is congruent to side FC.
Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.
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Answer for brainliest
Answers
Answer:
x = 2
Step-by-step explanation:
The measure of minor arc FD is 51x + 1
The measure of major arc FD is 360 - (51x + 1)
m<E = ½[m(major arc FD) - m(minor arc FD)]
36x + 5 = ½[360 - (51x + 1) - (51x + 1)]
72x + 10 = 360 - 51x - 1 - 51x - 1
174x = 348
x = 2
answer to get brainlest ASAP
Answers
Answer:
5.075
Step-by-step explanation:
I think this is the answer. I hope this helps!
Answer:
x=5.075
Step-by-step explanation:
Isolate the variable by dividing each side by factors that dont contain the variable.
find the bearing of the ship for the given values of x and y. round to the nearest tenth of degree. x=9.4 y=10.1
Answers
Using trigonometry we obtain the bearing of the ship ≈ 41.8 degrees.
To obtain the bearing of the ship given the values of x and y, we can use trigonometry.
The bearing represents the angle in degrees measured clockwise from the north direction.
First, we need to determine the angle θ between the positive x-axis and the line connecting the origin (0,0) and the point (x, y).
We can use the inverse tangent function (arctan) to find this angle:
θ = arctan(y/x)
Substituting the values x = 9.4 and y = 10.1 into the equation:
θ = arctan(10.1/9.4)
Using a calculator, we find that θ is approximately 48.2 degrees.
However, this angle corresponds to the angle counterclockwise from the positive x-axis.
To convert it to the bearing (measured clockwise from the north direction), we subtract this angle from 90 degrees:
Bearing = 90 - θ = 90 - 48.2 = 41.8 degrees.
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I’ll give brainlist!!What is the restricted domain of the quadratic(y=x^2 +4) that would ensure that the inverse is a function? Justify the answer
Answers
Finding the Inverse of a Polynomial Function by Restricting the Domain
Substitute y for f(x).Replace x with y.After determining y, rename the function to f−1(x).What is meant by Polynomial Function?When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial. One polynomial with an exponent of 1 is 2x+5, for instance. Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all arithmetic operations that are possible, however division by variables is not one of them. The absence of square roots of variables, fractional or negative powers on the variables, and the absence of variables in any fraction's denominator are specifically required for an expression to qualify as a polynomial term.To learn more about Polynomial Function, refer to:
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Use the given function value and the trigonometric Identities to find the exact value of each indicated trigonometric function
0˚ ≤ ᵝ ≤ 90˚ , 0≤ ᵝ≤π/2 cost(ᵝ)=√11/6
a. sec(ᵝ) 6/11
b. sin (ᵝ) 25/36
c. Cot(ᵝ) 11/5
d. Sih(ᵝ- 90˚) 11/6
Answers
:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately) are the exact values of each indicated trigonometric function.
Given function value is `cos(β) = √11/6` where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.
To find the exact value of each indicated trigonometric function, we need to first find sin(β), tan(β), cos(β), csc(β), sec(β), and cot(β) where `0˚ ≤ β ≤ 90˚` and `0 ≤ β ≤ π/2`.
We know that `sin²(β) + cos²(β) = 1`.So, `sin(β) = ± √(1 - cos²(β))`Since `0˚ ≤ β ≤ 90˚`, `sin(β) = √(1 - cos²(β))`Now, `sin(β) = √(1 - (√11/6)²)` = √(1 - 11/6) = √(6/6 - 11/6) = √(-5/6)
Since the value of β lies in the first quadrant, sin(β) is positive. Therefore, `sin(β) = √(5/6)`We also know that `tan(β) = sin(β)/cos(β)`.So, `tan(β) = (√(5/6))/((√11)/6)`
Now, `tan(β) = (6√5)/11`Similarly, we can find the values of all other trigonometric functions.a. sec(β) = `1/cos(β)` = `1/(√11/6)` = `6/√11` = `6/11`b. sin (β) = `√(5/6)` = `5/6`c. Cot(β) = `1/tan(β)` = `1/((6√5)/11)` = `11/(6√5)` = `(11/6) * (1/√5)` = `11/(6√5)` * `(√5/√5)` = `(11√5)/30` = `(11/5.48)` = `2.01` (approximately)d. Sin(β - 90˚) = `cos(β)` = `√11/6`
Therefore, the exact value of each indicated trigonometric function is:a. sec(β) = `6/11`b. sin (β) = `5/6`c. Cot(β) = `2.01` (approximately)d. Sin(β - 90˚) = `√11/6` = `0.95` (approximately).
Therefore, the options (a), (b), (c), and (d) are (6/11), (25/36), (11/5), and (11/6) respectively.
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How has mawi been inspired by "beetles and angels"?
mawi dreamed that one morning he awoke to find he turned into a beetle.
mawi dreamed of angels.
mawi read a book about beetles and angels.
mawi was helped along the way by many different people
Answers
Mawi, inspired by the book "Beetles and Angels," experienced significant personal growth and transformation. In his dreams, he found himself both turning into a beetle and encountering angels, symbolizing his journey of self-discovery and spiritual enlightenment.
Additionally, Mawi read a book specifically about beetles and angels, which likely provided him with further inspiration and insight. Along his path, Mawi received support and guidance from various individuals who played pivotal roles in his development and progress.
Mawi's experience of dreaming about transforming into a beetle and encountering angels represents a metaphorical journey of self-realization. Just as beetles undergo metamorphosis, Mawi's dreams reflect his own transformation and growth as he navigates through challenges and strives for personal fulfillment. The presence of angels in his dreams suggests a spiritual dimension, indicating that Mawi's journey is not only physical and mental but also deeply connected to his values and beliefs.
The book Mawi read about beetles and angels likely provided him with valuable knowledge and insights. It could have served as a source of inspiration, offering him guidance on his own journey and helping him make sense of the symbolism in his dreams. By immersing himself in this literature, Mawi may have gained a deeper understanding of the potential for personal growth and spiritual exploration.
Crucially, Mawi's progress was not solely self-driven. Throughout his journey, he received support from various individuals who played important roles in his development. These people likely offered guidance, encouragement, and assistance, helping Mawi overcome obstacles and continue on his path of self-discovery. Their collective influence and involvement in Mawi's life further fueled his inspiration and contributed to his personal transformation.
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is this a Function?
Answers
Answer:yes
Step-by-step explanation:
There aren’t any point in the line in the same space
stephen curry, a professional basketball player in the nba, has made 92% of his free throws during the 2018-2019 regular season with the golder state warriors. calculate the probability that curry will make exactly three of his next five free throws.
Answers
The probability of Stephen Curry making exactly three of his next five free throws is 0.3264 or 32.64%.
\(p(x) = nCx * p^x * q^(n-x)\)
where:
n = total number of attempts (5 in this case)
x = desired number of successes (3 in this case)
p = probability of success (0.92 in this case)
q = probability of failure (1 - p, or 0.08 in this case)
Plugging these numbers into the equation gives us:
p(3) = 5C3 * 0.92^3 * 0.08^2 = 0.3264
Stephen Curry is a professional basketball player in the NBA who is known for his incredibly accurate shooting ability. He made 92% of his free throws during the 2018-2019 regular season with the Golden State Warriors. We can calculate the probability of Curry making exactly three of his next five free throws using the binomial probability formula. This formula takes into account the probability of the event (Curry making the free throw) and the number of attempts (five). In this case, the probability of success (Curry making the free throw) is 0.92 and the number of attempts is five. Plugging these numbers into the equation gives us a probability of 0.3264 or 32.64%. This means that Curry has a 32.64% chance of making exactly three of his next five free throws.
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Translate each phrase into an algebraic expression to reveal the three letter code. * Answers must be "ALL CAPS" with no spaces. 19 Four more than the product of three and n 20 Four less than the product of three and n Your answer M P Escape Room #7 4(n+3) N 3n +4 3n-4 Q n +3 21 # Four times a number plus three 03(n-4) R 4n+3
EXAMPLE:MOP
must be capitalized and must be in order 19,20,21
Answers
An expression for the phrase four times a number plus three is 4(n+3).
19) Four more than the product of three and n.
Product of three and n =3n
So, the expression is 3n+4
20) Four less than the product of three and n.
Product of three and n =3n
So, the expression is 3n-4
21) Four times a number plus three.
A number plus three = n+3
So, the expression is 4(n+3)
Therefore, expression for the phrase four times a number plus three is 4(n+3).
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This number line models the division problem 1/4÷5 what is the quotient
15 points!
Answers
Answer: 1/20
Step-by-step explanation:
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What is the derivative of sin x with respect to x?
What is the derivative of cos x with respect to x?
What is the antiderivative of sin x with respect to x?
What is the antiderivative of cos x with respect to x?
Answers
Cosx, -sinx, -cosx + C, sinx + C are the derivative answers to the question.
The derivative of sin x with respect to x is cos x.
The derivative of cos x with respect to x is -sin x.
The antiderivative of sin x with respect to x is -cos x + C, where C is the constant of integration.
The antiderivative of cos x with respect to x is sin x + C, where C is the constant of integration.
1. The derivative of sin(x) with respect to x is cos(x).
2. The derivative of cos(x) with respect to x is -sin(x).
3. The antiderivative of sin(x) with respect to x is -cos(x) + C, where C is the constant of integration.
4. The antiderivative of cos(x) with respect to x is sin(x) + C, where C is the constant of integration.
A derivative in mathematics is a measurement of how much a function alters as its input alters. It refers to how quickly a function alters in relation to its input variable. The slope of the tangent line to the function at a certain point is what it is, in other words.
The limit of the ratio of the change in the output to the change in the input, as the change in the input approaches zero, is known as the derivative of a function, indicated by the symbols f'(x) or \(dy/dx\).
The opposite of differentiation is an antiderivative, usually referred to as an indeterminate integral. It is a function that yields the original function when differentiated. In other words, f(x) follows if \(f'(x) = g(x)\).
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EASY EXTRA POINTS HELP ASAP WILL MARK BRAINLIEST
Answers
Answer:
it should be two
Step-by-step explanation:
I hope this helps!
Can someone please help me
Answers
D.
\(22 - 8 \sqrt{5} \)
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answers
Answer:
12
Step-by-step explanation:
16-4=12
Answer:
3x=12
if you have to solve for x:
x=12/3
x=4
A rectangle has a length of 1 inches and a width of 12 inches whose sides are changing. The length is increasing by 7 in/sec and the width is growing at 4 in/sec. What is the rate of change of the area?
Answers
So, the rate of change of the area is 88 in²/sec.
The area of the rectangle is given by the formula A = lw, where l is the length and w is the width of the rectangle. If the length and width of the rectangle are changing at rates of 7 in/sec and 4 in/sec, respectively, then the rate of change of the area is given by the formula:
dA/dt = l * dw/dt + w * dl/dt
Plugging in the values given in the problem, we get:
dA/dt = 1 * 4 + 12 * 7 = 4 + 84 = 88 in²/sec
So the rate of change of the area of the rectangle is 88 in²/sec.
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a researcher believes that women today weigh less than in previous years. to investigate this belief, she randomly samples 41 adult women and records their weights. the scores have a mean of 111 lbs. and a standard deviation of 12.4. a local census taken several years ago shows the mean weight of adult women was 115 lbs. the obtained value of the appropriate statistic for testing h0 is
Answers
The given problem is concerned with hypothesis testing. The researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The obtained value of the appropriate statistic for testing H0 is t= -2.42.
Given that,
Population mean µ = 115 lbs
Sample mean x = 111 lbs
Sample size n = 41
Standard deviation σ = 12.4 lbs
hypothesis testing
Null hypothesis H0: µ = 115 lbs
Alternate hypothesis H1: µ < 115 lbs
Since the population standard deviation is unknown and the sample size is less than 30, we use a t-distribution to test the hypothesis. The formula for the t-test statistic is,
t= (x- µ)/(s/√n)
Where, x = sample mean, µ = population mean, s = sample standard deviation, and n = sample size
Substituting the given values in the above formula, we get,
t= (111 - 115) / (12.4/ √41)t= -4 / 1.93t= -2.07
The obtained value of the appropriate statistic for testing H0 is t= -2.07.
The calculated t-value is compared with the critical value of t with degrees of freedom (df) = n-1 = 41-1 = 40 at the desired significance level. If the calculated t-value is less than the critical value of t, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
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PLEASE HELPPP ILL DO ANYTHING PLEASE
Answers
Answer:
7 2/3
Step-by-step explanation:
We can divide 23/3 which teh closest whhole number is 7 and we have a remainder of 2. So 7 2/3
Answer: Hello! Your answer should be 7 2/3, hope this helps
Step-by-step explanation:
let x be the charge for an oil change, and let the tax on x be 7% so that the actual charge is 1.07x. let y be the number of containers of oil that are needed, and $2 the price per container. then 2y is the price of the oil itself. the cov(x,y) is 5.6. what is the the cov(1.07x, 2y)? select one:a. 11. 984b. 0.3821c. 2.616d. 7.982
Answers
let x be the charge for an oil change, and let the tax on x be 7% so that the actual charge is 1.07x. let y be the number of containers of oil that are needed, and $2 the price per container. then 2y is the price of the oil itself. the cov(x,y) is 5.6.
The covariance of 1.07x and 2y is 11.984
What is covariance?
Covariance refers to the way two variables shift together. It is a measurement that evaluates how close two variables are to one another. It examines whether they change in the same direction (positive covariance) or in the opposite direction (negative covariance)
.Calculating Covariance:
Given that Cov(X,Y) = 5.6
we need to find Cov(1.07X,2Y)Hence,
Cov(1.07X,2Y) = 2 * 1.07 * Cov(X,Y) = 2.2996 * 5.6 = 11.984
Therefore, the covariance of 1.07x and 2y is 11.984.
Hence option (a) is the correct answer.
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Which western trail stretched 1,300 miles from illinois to utah territory? the mormon trail the santa fe trail the california trail the oregon trail
Answers
The Oregon Trail is a western route that runs 1,000 miles from Illinois to Utah Territory.
In American history, the Oregon Trail, also known as the Oregon-California Trail, was an overland route that connected Independence, Missouri, with Oregon City, which is located close to Portland, Oregon, today, in the Willamette River valley. In the nineteenth century, it was one of two major emigration routes to the American West, the other being the southerly Santa Fe Trail from Independence to Santa Fe (now in New Mexico). A spur of the northerly Oregon route, which was a component of the Oregon Trail, headed to the Great Salt Lake region of what is now northern Utah. Additionally, branches from each main trail provided links to places in California.
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Answer:
I can "Confirm" The answer is not Oregon Trail, I believe the answer is "The Mormon Trail "
Step-by-step explanation:
Or "A"
Have a Joyous Day
x+5y=-5 find x and y intercept
Answers
Answer:
x= (5,0) y= (0,1)
Step-by-step explanation:
The pet store has 6 puppies, 9 kittens, 4 lizards, and 5 snakes. if you select five pets from the store randomly, what is the probability that at least one of the pets is a puppy?
Answers
The probability that at least one of the pets selected is a puppy is approximately 0.7887 or 78.87%.
To calculate the probability that at least one of the pets is a puppy, we can find the probability of the complement event (none of the pets being a puppy) and subtract it from 1.
The total number of pets in the store is 6 puppies + 9 kittens + 4 lizards + 5 snakes = 24.
The probability of selecting a pet that is not a puppy on the first selection is (24 - 6) / 24 = 18 / 24 = 3 / 4.
Similarly, on the second selection, the probability of selecting a pet that is not a puppy is (24 - 6 - 1) / (24 - 1) = 17 / 23.
For the third selection, it is (24 - 6 - 1 - 1) / (24 - 1 - 1) = 16 / 22.
For the fourth selection, it is (24 - 6 - 1 - 1 - 1) / (24 - 1 - 1 - 1) = 15 / 21.
For the fifth selection, it is (24 - 6 - 1 - 1 - 1 - 1) / (24 - 1 - 1 - 1 - 1) = 14 / 20 = 7 / 10.
To find the probability that none of the pets is a puppy, we multiply the probabilities of not selecting a puppy on each selection:
(3/4) * (17/23) * (16/22) * (15/21) * (7/10) = 20460 / 96840 = 0.2113 (approximately).
Finally, to find the probability that at least one of the pets is a puppy, we subtract the probability of the complement event from 1:
1 - 0.2113 = 0.7887 (approximately).
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