Assume that the tunnel in Exercise 3.132 is observed during ten two-minute intervals, thus giving ten independent observations Y1, Y2,..., Y10, on the Poisson random variable. Find the probability that Y > 3 during at least one of the ten two-minute intervals
Answers
Answer: hello the exercise is missing from your question below is the missing exercise for reference
answer:
0.1745
Step-by-step explanation:
Determine P ( Y > 3 )
Given that y follows Poisson distribution with mean
P( Y = y ) = \(\frac{e^{-1} }{y!}\)
assuming that yi represents number of autos that will enter the tunnel and
also let A represent Y > 3 at one of the ten two-minute interval
step 1 : hence finding P(A )
= P(Y > 3 ) = 1 - P( Y≤ 3 )
= 1 - [ \([\frac{e^{-1} }{0!} +\frac{e^{-1} }{1!} +\frac{e^{-1} }{2!} +\frac{e^{-1} }{3!} ]\)
= 0.018988
since the ten observations are independent
P(X≥ 1 ) = 1 - P( X = 0 )
= 1 - \(\left[\begin{array}{ccc}10\\0\\\end{array}\right]\) * (0.018988)^0 ( 1 - 0.018988)^10-0
= 1 - 0.8255 = 0.1745
Related Questions
Solve for x. I attached the question. Pls help me :(
Answers
Answer:
x = 16°
Step-by-step explanation:
What we know:
∠JML = 47°
∠JKL = (7x + 21)°
∠JML is an inscribed angle
∠JKL is an inscribed angle
Inscribed angles are half of the value of their intercepted arc
So if m∠JML = 47° then mArc JL is double that or 94°
And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so
mArc JL + Arc JML = 360°
94 + Arc JML = 360
Subtract 94 from both sides to isolate Arc JML
Arc JML = 266°
So if Arc JML = 266° then it's intercepted inscribed angle is half of that.
Arc JML ÷ 2 = ∠JKL
266 ÷ 2 = ∠JKL
133 °= ∠JKL
Now we can use this value and set it equal to the expression to find the value of x
(7x + 21) = 133
Subtract 21 from both sides to isolate the x
7x = 112
Divide both sides by 7
x = 16
Suppose sam deposited 1000$ every month in the beginning for his retirement fund for 20 years at 5% compounded monthly. What is value of N
Answers
To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.
To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.
Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.
The formula to calculate the future value of a series of monthly deposits is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the investment,
P is the monthly deposit amount,
r is the monthly interest rate, and
n is the number of deposits.
In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.
By rearranging the formula, we can solve for n:
n = log((FV * r) / (P * r + FV)) / log(1 + r)
Plugging in the values, we get:
n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)
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Which division problem is represented with this model?
Responses
15÷2
1 fifth divided by 2
15÷6
1 fifth divided by 6
16÷2
1 over 6 end fraction divided by 2
12÷5
1 half divided by 5
Answers
Answer:
C.
Step-by-step explanation:
We have five unshaded, 1 half of unshaded, and 1 shaded, Thus, It will be showed as \(\frac{1}{6}\) ➗ \(2\)
The blue object (D) has been rotated 270° clockwise about the point (1, 2). Which is the correct image?
Answers
The correct image include the following: B. Green: image A.
What is a rotation?In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.
In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.
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PLZ HELP I WILL MARK BRAINLEST!
Answers
Answer:
Most likely B.}21 inches,
Please mark me brainliest
Answer:
The answer is B, 21 inches
Step-by-step explanation:
You find what happened with the width which is time 3. Then you multiply 7 by 3 to get 21!
Hopefully that helps! Please mark BRAINILEST
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with grams of a radioactive isotope, how much will be left after 4 half-lives?
Answers
After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:
Amount remaining = Initial amount × (1/2)^(number of half-lives)
In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.
So, the equation becomes:
Amount remaining = Initial amount × (1/2)^4
Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.
Simplifying the equation:
Amount remaining = Initial amount × (1/16)
Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
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graph the line with y-intercept 1 and slope 4
Answers
Answer:
y = 4x + 1
Step-by-step explanation:
Let's graph it in slope intercept form y = mx + b
m = the slope
b = y-intercept
m = 4
b = 1
So, the equation is y = 4x + 1
Suppose log5=b , then what is the exact value of log5^4?
Answers
Answer:
4b
Step-by-step explanation:
log(5) = b actually means that
\(10^b = 5\)
The power of 10 is b.
So log(5⁴) means that
\((10^b)^4 = 5^4\)
so the power of 10 is 4b.
Suppose the current cost of gasoline is $3.10 per gallon. Find the current price index number, using the 1975 price of 56.7 cents as the reference value.
The current price index is _____
(Round to one decimal place as needed.)
Answers
The current price index is mathematically given as,
$538.194
This is further explained below.
What is the current price index?The index value may be calculated by taking the ratio of the current value to the reference value and multiplying that ratio by 100.
In regard to this issue, we have that:
Current value = $3.10
Reference value: $0.576
Generally, the Index price for the is mathematically given as,
I = (3.10/0.576)*100
I= $538.194
The current price index number is 538.194
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part of the proceeds from a garage sale was $370 worth of $5 and $20 bills. If there were 4 mote $5 bills and $20 bills, find the number of each denomination
Answers
Answer:
I am confused by this
Step-by-step explanation:
given that -3/2 is one of the root of the equation 2y^2+6y+p=0, find the value of p
Answers
Answer:
p = \(\frac{9}{2}\)
Step-by-step explanation:
given y = - \(\frac{3}{2}\) is a root of the equation , then this value makes the equation true.
substitute y = - \(\frac{3}{2}\) into the equation and solve for p
2( - \(\frac{3}{2}\) )² + 6(- \(\frac{3}{2}\) ) + p = 0
2( \(\frac{9}{4}\)) - 9 + p = 0
\(\frac{9}{2}\) - \(\frac{18}{2}\) + p = 0
- \(\frac{9}{2}\) + p = 0 ( add \(\frac{9}{2}\) to both sides )
p = \(\frac{9}{2}\)
What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
![What is the meaning of "[tex] \varphi (x,y)[/tex] be [tex] y\wedge \phi (x)[/tex] "?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/IEnaK9Mnw3ftGn7VoWymvKjzqCukNTp6.png)
Answers
The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.
The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.
The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.
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Find the relative rate of change at the given value of . Assume is in years and give your answer as a percent
Answers
Answer:
84.37 %.
Step-by-step explanation:
The question is shown in the attached figure.
We have,
\(f(t)=2t^3+10,\ t=3\)
We can find the value of f(t) at t = 3,
\(f(3)=2(3)^3+10\\\\f(3)=64\)
Finding f'(t).
\(f'(t)=6t^2\)
Finding f'(t) at t = 3
\(f'(3)=6(3)^2\\\\=54\)
The relative change is calculated as :
\(\dfrac{f'(t)}{f(t)}=\dfrac{54}{64}\\\\=0.8437\)
In percentage rate of change,
\(\dfrac{f'(t)}{f(t)}=0.8437\times 100\\\\=84.37\%\)
Hence, the required percent change is 84.37 %.
on rectangle DEFG, it D is located at (-1 -1) and F is located at (4 -8), what is the length of GE
Answers
First we have to notice that the lenght GE is the same as the length DF, this comes from the fact that the diagonals in any rectangle have the same length. Now that we know that we have to remember that the distance between two points is given as:
\(d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)In this case we have that:
\(\begin{gathered} d(G,E)=d(D,F)=\sqrt[]{(4-(-1))^2+(-8-(-1))^2} \\ =\sqrt[]{(5)^2+(-7)^2} \\ =\sqrt[]{25+49} \\ =\sqrt[]{74} \end{gathered}\)Therefore the distance between GE is
\(\sqrt[]{74}\)this is appoximately 8.602
(c) Solve by Completing the Square (Round answers to the nearest tenth)
x²+10 x+2=2 x+5
Answers
After solving the equation by Completing the square , the answer is x = 0.4 , x = -8.4 .
In the question ,
it is given that ,
the equation is x² + 10x + 2 = 2x + 5,
rewriting the equation ,
we get ,
x² + 8x - 3 = 0
adding 3 to both sides ,
we get ,
x² + 8x = 3 ,
For the method of completing the square ,
we take half of the second term's coefficient, and square it, then add it to both sides.
that is 8/2 = 4 .
the equation becomes ;
x² + 2*x*4 + 4² = 3 + 4²
(x + 4)² = 3 + 16
(x + 4)² = 19
taking root on both the sides ,
we get ,
x + 4 = ±√19
So , x = -4 + √19 or x = -4 - √19
Simplifying further ,
we get ,
x = 0.35889 or x = -8.35889
rounding to the nearest tenth we get
x = 0.4 or x = -8.4 .
Therefore , the solution of the given equation is x = 0.4 , x = -8.4 .
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If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose
Answers
Answer: 1250 square feet!
Step-by-step explanation:
A (25)=25•(100-2•25)=25•50=1250 Sq Ft
If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall.
Any rectangle's length and width differences must be as small as possible for the area to be maximized.
The largest area you can enclose
A =25×(100-2•25)
A=25•50
A=1250 Sq Ft
Thus, if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.
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I need help please.
Answers
Answer:
Answer is C hope this helps
Step-by-step explanation:
Fred did 600 J of work in 60 seconds. Calculate his power.
O
A. 600 W
B. 100 N
C. 500 N
OD. 10 W
Answers
Answer:
To calculate Fred's power, we can use the formula:
Power = Work / Time
Given that Fred did 600 J of work in 60 seconds, we can substitute the values into the formula:
Power = 600 J / 60 s
Power = 10 W
Therefore, the correct answer is:
D. 10 W
Step-by-step explanation:
Answer:
Power = Work/Time
Power = 600 J/60 s = 10 W
Therefore, the answer is D. 10 W.
Step-by-step explanation:
If I roll two six-sides dice, what is the probability that the sum of the numbers that show up on the dice is 3 or less?
Answers
Answer:
1/12
Step-by-step explanation:
first we have to find all the possibilities of getting a sum of 3 or less: 1+1 or 1+2 and we count the second combination 2 times because the numbers can be on either of the dices so we have a total of 3 possibilities. all the possible pairimg of dice are 6*6=36 because each dice has 6 sides and we can get either of them. so the probability would be the chance of getting a sum of 3 or less divided by all the diff combination which equals 3/36 or 1/12 which is roughly around 8.3%
Find the area of the figure.
Answers
Answer:
1) 143 square inches
2) 32 square inches
3)152 square yards
4) 150 square inches
Step-by-step explanation:
Finding the area:1) Parallelogram:base= 11 in ;height = 13 in
\(\sf \boxed{\text{Area of parallelogram = base * height}}\)
= 11 * 13
= 143 square inches
2) Triangle:base = 8 cm ; height = 8 cm
\(\sf \boxed{\text {Area of triangle = } \dfrac{1}{2}*base * height}\)
\(\sf =\dfrac{1}{2}*8 * 8\\\\= 4 * 8\\\\= 32 \ in^2\)
3) Kite:diagonal = p = 7 + 12 = 19 yd
diagonal 2 = q = 8 + 8 = 16 yd
\(\sf \boxed{\text{Area of kite =} \dfrac{pq}{2}}\)
\(\sf =\dfrac{19*16}{2}\\\\= 19*8\\\\= 152 \ yd^2\)
4)Trapezium:a = 13 in ; b = 12 ; h = 12 in
a,b are the parallel sides of the trapezium.
\(\sf \boxed{\text{Area of trapezium = }\dfrac{(a + b)*h}{2}}\)
\(\sf = \dfrac{(13+12)*12}{2}\\\\\\=\dfrac{25*12}{2}\\\\=25*6\\\\= 150 \ in^2\)
What is the solution to the equation 82 (4x + 2) = 10?
Answers
Answer:
x = -77/164
Step-by-step explanation:
82(4x+2) = 10
328x+164 = 10
328x = -154
x = -77/164
Answer:
\(-\frac{77}{164}\)
Step-by-step explanation:
Apply the distributed property: 82 × 4x = 328x, 82 × 2 = 164Re-write the problem: 328x + 164 = 10Subtract 164 from each side, so it now looks like this: 328x = -154Divide each side by 328 to cancel out the 328 next to x. It should now look like this: \(x = -\frac{77}{164}\)I hope this helps!
Find the scale factor of the figures. Then list all pairs of congruent angles.
DEFG∼PQRS
k=
Answers
9514 1404 393
Answer:
k = 1/3
∠D ≅ ∠P
∠E ≅ ∠Q
∠F ≅ ∠R
∠G ≅ ∠S
Step-by-step explanation:
The scale factor is the ratio of corresponding side lengths. It is convenient to choose one of the sides that has length 1.
k = QR/EF
k = 1/3
__
Corresponding angles are listed in the same order by the similarity statement.
∠D ≅ ∠P
∠E ≅ ∠Q
∠F ≅ ∠R
∠G ≅ ∠S
Find the number if 2/5 of it is 22
Answers
Answer:
22×2/5=8.8
Step-by-step explanation:
Hope it helps you
Answer:
55
Step-by-step explanation:
2/5n = 22
multiply each side by 5/2 to get:
n = 110/2
n = 55
Carol successfully increases her business to 200 customers per day. However, her total cost for doing so is 50% greater than the expected $1,600. What percent greater is the actual marginal cost than the expected marginal cost, to the nearest full percent?
Answers
Carol's Steakhouse, the total cost of serving 150 customers per day is $900. Carol is interested in increasing her business, but is concerned about the effect on marginal cost.
Carol successfully increases her business to 200 customers per day. However, her total cost for doing so is 50% greater than the expected $1,600. What percent greater is the actual marginal cost than the expected marginal cost, to the nearest full perc
Answer:
214
Step-by-step explanation:
We have been given
C1 = $900
Q1 = 259
Then c2 = $1600
Q2 = 200
M = 1600-900/50
= 14
For real,
C1 = 900
C2 = 2400
Q1 = 150
Q2 = 50
1500/50 = 30
30/14 x 100
= 214
It is greater by 214 percent
Name the relationship
Answers
Answer:
A vertical angle!
Step-by-step explanation:
Vertical angles sit across from each other.
Answer:
Its definitely a sexual relationship I would say
(Only the tips tho)
i need the answer to this question
Answers
Answer:
Area of annulus is 40.85cm² to 2d.p
Step-by-step explanation:
Area of shaded part=Area of bigger circle -Area of smaler circle
Area of annulus= πR²- πr²= π(R²-r²)
A=3.142(7²-6²)
A=3.142(49-36)
A=3.142×13
A=40.846cm²
A=40.85cm² to 2d.p
what are the assymptotes of this equation
Answers
4.
During the last year the value of your house decreased by 30%. If the value of your
house is $224,000 today, what was the value of your house last year? Round your
answer to the nearest cent, if necessary.
Answers
Answer:
$320,000
Step-by-step explanation:
70%/100%=224,000/X
(224,000*100)/70=320,000
The value of your house last year was $320,000
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
We are given that During the last year the value of your house decreased by 30%.
If the value of your house is $224,000 today, then we have
70%/100% =224,000/X
Now cross multiplication will be;
x =(224,000*100)/70
x =320,000
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the sum of three consecutive odd integers is 129. find the integers
Answers
Answer:
\(\huge\boxed{\sf 41,\ 43, \ 45}\)
Step-by-step explanation:
Let the three consecutive integers be x, x + 2 and x + 4
So, the given condition is:
x + x + 2 + x + 4 = 129
3x + 6 = 129
Subtract 6 to both sides
3x = 129 - 6
3x = 123
Divide 3 to both sides
x = 123/3
x = 41
So, the integers are:
x = 41
x + 2 = 41 + 2 = 43
x + 4 = 41 + 4 = 45
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807At a school of 900 students, 20% have blue eyes. A student randomly selects 100 students and finds 17% of them have blue eyes. A second student takes another random sample of 90 students and finds 24% of them have blue eyes. Which of the following explains why there is a difference between the two percentages?
a. The sample sizes were both too small.
b.The samples were not random samples.
c. Both samples suffered from non-response bias.
d. Random error; the numbers were different due to variability inherent in sampling.
Answers
Answer:
d.
Step-by-step explanation:
Given that:
In a school;
Population mean = 900
First student:
Sample size = 100
Sample proportion = 0.17
Second student:
Sample size = 90
Sample proportion = 0.24
The difference between the two percentages is a result of the random error because numbers were not the same as a result of variability inherent in sampling.