n is a poisson random variable that represents the number of telephone calls processed in telecommunications switch in 10sec. if the call arrival rate is .5 per second. a) what is the probability that there will be no call processed in 10seconds? b) what is the probability that at least 2 calss will be processed in 2 seconds
Answers
a)The chance that no call will be handled in 10 seconds is 0.0067
b) 0.2642 percent of classes will be processed in two seconds at least.
what is percentage?A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages.
given,
The number of phone calls handled by the communications switch in a 10-second period is represented by the Poisson random variable n.
a)the chance that no call will be handled in 10 seconds is
for 10 sec= λ= 10*0.5 = 5 calls per sec
P(X=0) \(e^{-5}\)(5)° / 0!
P(X=0)= 0.0067
b) percent of classes will be processed in two seconds at least is
for 2 sec =λ = 0.5 *2 = 1
P(X≥2) = 1- P(X<2)
= 1-[P(X=2) + P(X=1)]
=0.2642
a)The chance that no call will be handled in 10 seconds is 0.0067
b) 0.2642 percent of classes will be processed in two seconds at least.
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Related Questions
The hypotenuse of a right triangle is 25 cm, and the shorter leg is 15 cm. Find the length of the other leg.
a.12 √5 cm
b.✓ 10 cm
c.20 cm
Answers
Use the Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 15^2 = 25^2
a^2 + 225 = 625
a^2 = 400
a = 20
Answer: 20 cm
Hope this helps!!
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There are 115 flowers on 7 trees. What is the unit rate of the flowers per tree? How many flowers on 22 trees?
Answers
Answer: 16 flowers per tree, 352 flowers on 22 trees.
Step-by-step explanation:
115 flowers/ 7 trees= 16.4 flowers per tree
Since you can't have partial flowers, round down to 16 flowers per tree.
16 flowers per tree * 22 trees=352 flowers
please help help help
Answers
Answer:
CA=6x-24 and BD = 2x+8
Find CE
CA=BD => 6x-24=2x+8 => x=8
CE=1/2(CA) or 1/2(BD) => 1/2(6x-24)=12
CE=12
CA=24
BD=24
Step-by-step explanation:
What is the slope of this function. f(x)=-3x+5
Answers
Multiply (x+9)2 need help ASAP
Answers
Answer:
2+18
Step-by-step explanation:
(x + 9)2 distribute 2 · x = 2x and 9 · 2 = 18.
2x + 18, is the answer.
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A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15.
Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing?
(–6, –3)
(–3, –1)
(–3, 0)
(–6, –5)
(–6, –3)
(–3, –1)
(–3, 0)
(–6, –5)
Answers
The function is increasing over the interval (-3,-1).
A table with x and f(x) values are given as:
x f(x)
-6 34
-5 3
-4 -10
-3 -11
-2 -6
-1 -1
0 -2
1 -15
We have to check whether this function is increasing or not in the intervals (–6, –3), (–3, –1), (–3, 0), (–6, –5).
A function is said to be increasing over an interval (x, y), if for x < y, it follows that f(x) < f(y).
Consider the intervals one-by-one.
For (-6, -3), we have the function values in between which are 34 > 3 > -10 > -11. So in this interval the function is not increasing but decreasing over the x-values in (-6, -3).
For (-3, -1), the corresponding function values are -11 < -6 < -1. Here the function values are increasing over the x-values in the interval (-3, -1).
For (-3,0), the corresponding function values are -11 < -6 < -1 >-2. Since we got -1 > -2 in the interval (-3,0), the function is not increasing here also.
For (-6,-5), the corresponding function values are 34 > 3. So the function is not increasing but decreasing.
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if a regression line is parallel to the horizontal axis of the scattergram, the slope (b) will be
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If a regression line is parallel to the horizontal axis of a scattergram, it means that there is no relationship between the two variables being plotted. In this case, the slope (b) of the regression line would be zero.
When we perform a linear regression analysis, we are trying to find the best-fitting line that represents the relationship between the independent variable (x) and the dependent variable (y). The slope (b) of this line represents the rate of change between the two variables. If the regression line is parallel to the horizontal axis, it suggests that there is no change in the dependent variable for any change in the independent variable.
The general equation for a linear regression line is:
y = a + bx
Here, "a" represents the y-intercept (the value of y when x is zero) and "b" represents the slope. When the regression line is parallel to the horizontal axis, it means that the line is perfectly horizontal, and the dependent variable (y) does not change as the independent variable (x) changes.
Mathematically, this can be represented as:
y = a + 0x
y = a
In this equation, the slope (b) is zero because there is no change in the dependent variable (y) for any change in the independent variable (x). The value of y remains constant, resulting in a horizontal line parallel to the x-axis.
To further explain, when the slope (b) is zero, it indicates that there is no linear relationship between the two variables. In a scattergram, the points are spread out randomly and do not follow any specific trend or pattern. Each value of x corresponds to a single value of y, and these values do not exhibit any systematic change as x increases or decreases.
Visually, a regression line that is parallel to the horizontal axis will appear as a flat line, with all points lying on the same y-value. This indicates that the dependent variable does not depend on the independent variable and remains constant across all values of x.
In conclusion, when a regression line is parallel to the horizontal axis in a scattergram, the slope (b) of the line is zero. This indicates that there is no linear relationship between the variables being analyzed, and the dependent variable does not change as the independent variable varies. The absence of a slope suggests that the two variables are not related in a linear fashion, and the scattergram does not exhibit any pattern or trend.
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translate the following phrase into an algebraic expression. use the variable c to represent the unknown quantity. the total of the number of cars in the garage and the 6 cars outside
Answers
The algebraic expression for the given phrase would be: c + 6, where c represents the unknown quantity (number of cars in the garage) and 6 represents the number of cars outside.
To translate the following phrase into an algebraic expression, we need to use the variable c to represent the unknown quantity. The phrase is "the total of the number of cars in the garage and the 6 cars outside."
So, the algebraic expression is: c + 6Where "c" represents the number of cars in the garage.
The expression c + 6 represents the total number of cars, which is the sum of the number of cars in the garage and the 6 cars outside.
Example: If there are 10 cars in the garage, then the total number of cars would be: c + 6= 10 + 6= 16.
So, there would be 16 cars in total.
The expression c + 6 would always give us the total number of cars, regardless of the value of "c."
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Christina wanted to fence in her yard. How many feet of fence will be needed? 60 ft 50 ft 40 ft 25 ft
Answers
Christina will need 220 feet of fence to enclose her yard.
What is a Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
To solve this, we need to calculate the perimeter of the rectangular yard:
Perimeter = 2 × (Length + Width)
Plugging in the given dimensions:
Perimeter = 2 × (60 ft + 50 ft)
Perimeter = 2 × (110 ft)
Perimeter = 220 ft
Christina will need 220 feet of fence to enclose her yard.
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Christina wants to fence in her rectangular yard. The length of her yard is 60 feet, and the width is 50 feet. How many feet of fence will she need to enclose the entire yard?
Need help to break this down pleasd
Answers
Answer:
The height of the window is 150 centimeters.
Step-by-step explanation:
Use ratio and proportion to find the height of the window.
\(\frac{h}{60cm} = \frac{210cm}{84cm}\)
Cross multiply
\(h = \frac{210cm(60cm)}{84cm} \\h = \frac{12600cm^2}{84cm} \\h = 150 cm\)
Woodworkers Alex and Brandon make precision pieces for toys. Each toy requires four 9-inch long sticks. Alex cuts four sticks one at a time, and their lengths are independent. Alex’s sticks have mean length 9 inches with a standard deviation 0.17 inches. Brandon clamps four sticks together and cuts them all at once, so that they all have the same length. Brandon’s sticks also have a mean length of 9 inches with a standard deviation of 0.17 inches. Brandon’s four sticks are laid end-to-end. What is the mean of the total length? What is the standard deviation of the total length? The mean of the total length is inches. The standard deviation of the total length is inches.
Answers
The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.
The mean of the total length for both Alex and Brandon can be determined by multiplying the mean length of a single stick by the number of sticks required for each toy. In this case, each toy requires four 9-inch long sticks.
Mean of the total length for both Alex and Brandon: 4 sticks * 9 inches = 36 inches.
Since both Alex and Brandon have sticks with the same mean length and standard deviation, the standard deviation of the total length for both of them remains the same.
Standard deviation of the total length for both Alex and Brandon: 0.17 inches.
Therefore, The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.
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(20 POINTS) Joseph buys a subway pass for $55. Every time he rides the subway, money is deducted from the value of the pass. He rode the subway 5 times and $40 was deducted from the value of the pass. How much was deducted from Joseph's account for each ticket? Write a mathematical expression to represent this situation; then find the answer.
Answers
The amount deducted from Joseph's account for each ticket is $8
The amount deducted from Joseph's account for each ticket?Total cost of subway pass Joseph bought = $55Number of times he rode the subway = 5Total amount deducted from the value of the subway pass = $40The amount deducted from Joseph's account for each ticket = Total amount deducted from the value of the subway pass ÷ Number of times he rode the subway
= $40 / 5
= $8 per ticket
Total amount remaining in the subway pass = Total cost of subway pass Joseph bought - Total amount deducted from the value of the subway pass
y = $55 - $40
= $15
The mathematical equation to represent this situation is y = $55 - $40
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The JASON group and the NIH Advisory Committee to the Director have issued similar recommendations about research integrity that would allow universities and federal agencies to manage undue foreign influence more effectively. What was this recommendation
Answers
The JASON group and the NIH Advisory Committee to the Director have issued recommendations that aim to enhance the management of undue foreign influence in research integrity.
The recommendation put forth by both the JASON group and the NIH Advisory Committee to the Director revolves around strengthening measures to address undue foreign influence in research integrity. This includes enhancing the ability of universities and federal agencies to effectively manage and mitigate the risks associated with foreign influence on research activities.
The specific details of the recommendation may vary, but the overarching goal is to establish robust mechanisms for identifying and addressing potential threats to research integrity posed by undue foreign influence. This may involve implementing stricter oversight, transparency, and disclosure requirements, as well as promoting education interest among researchers.
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A pottery factory kept track of the number of broken plates per shipment Number of broken plates Number of shipments 2 376 2 380 6 567 5 737 2 928 964 3 X is the number of broken plates that a randomly chosen shipment had. What is the expected value of X? Write your answer as a decimal.
Answers
Answer: The expected value of X is 672.75
Expected value can be calculated using the below formula
\(\begin{gathered} \text{Expected value = }\frac{\Sigma fx}{\Sigma f} \\ \Sigma fx\text{ = 376 x 2 + 380 x 2 + 567 x 6 + 737 x 5 + 928 x 2 + 964 x 3} \\ \Sigma fx\text{ = 752 + 760 + 3, 402 + 3, 685 + 1, 964 + 2, 892} \\ \Sigma fx\text{ = 13, 455} \\ \Sigma f\text{ = 2 + 2 + 6 + 5 + 2 + 3} \\ \Sigma f\text{ = 20} \\ \text{Expected value = }\frac{13,\text{ 455}}{20} \\ \text{Expected value = 672.75} \end{gathered}\)Therefore, the expected value of X is 672.75
X is a normally Distributed random variable with a standard deviation of 4.00. Find the mean of X when 64.8% of the area lies to the left of 8.52.
Answers
Answer:
7
Step-by-step explanation:
σ = 4 ; μ =?
8.52 to the left of X
.
P(X < 8.52) = 64.8%
P(X < 8.52) = 0.648
Using the Z relation :
(x - μ) / σ
P(Z < (8.52 - μ) / 4)) = 0.648
The Z value of 0.648 of the lower tail is equal to 0.38 (Z probability calculator)
Z = 8.52 - μ / 4
0.38 = 8.52 - μ / 4
0.38 * 4 = 8.52 - μ
1.52 = 8.52 - μ
μ = 8.52 - 1.52
μ = 7
Find the indefinite integral. (Use C for the constant of
integration.) 8sin xcos x dxFind the indefinite integral. (Use C
for the constant of integratioFind the indefinite integral. (Use C
for the con
Answers
The indefinite integral of 8sin(x)cos(x) dx can be found using the trigonometric identity:
sin(2x) = 2sin(x)cos(x)
Using the trigonometric identity, we can rewrite the integral as:
∫ 8sin(x)cos(x) dx = ∫ 4sin(2x) dx
Now, we can integrate 4sin(2x) with respect to x:
∫ 4sin(2x) dx = -2cos(2x) + C
where C is the constant of integration.
Therefore, the indefinite integral of 8sin(x)cos(x) dx is -2cos(2x) + C.
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How does adding salt to water affect the boiling point?
Answers
When salt is added to water, the boiling point of water is increased. The boiling point elevation depends on the concentration of salt added. The addition of salt increases the boiling point of water.
The extent of the increase in boiling point is directly proportional to the amount of salt added. Boiling point is defined as the temperature at which the vapor pressure of a liquid is equal to the pressure exerted on it by the surrounding atmosphere.
In layman's terms, this means that a liquid boils when its vapor pressure equals atmospheric pressure. Boiling point of a liquid can be increased or decreased by the addition of solutes such as salt.When a solute such as salt is added to water, the boiling point of water increases due to the phenomenon of boiling point elevation.
This is because the solute particles in the water interfere with the formation of water vapor molecules at the surface of the liquid. As a result, more energy is required to boil the water, which means that the boiling point is elevated.
The amount of elevation is directly proportional to the concentration of salt added. In short, the addition of salt to water increases the boiling point of water.
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\(\sqrt{ 6^{2} +(x-2)^{2} }\)
Answers
Answer:
\( \sqrt{36 + x {}^{2} } - (2) {}^{2} \\ 6 + x + - 2 \\ 6 - 2 + x \\ 4 + x \\ \: \:answer = 4 + x \\\)
One side of a triangle is 3 inches and its area is 36 inches. The corresponding side of
a similar triangle is 7 feet. What is the area of the larger triangle?
Answers
its lonmg.answer
Step-by-step explanation:
Of 48 apples harvested, every third apple was too small, every fourth apple was too green, and every tenth apple was bruised. If all other apples were perfect, how many perfect apples were harvested?
Answers
Step-by-step explanation:
48/3 = 16 apples were too small.
48/4 = 12 apples were too green.
48/10 = 4.8 ≈ 4 apples were bruised.
we have to round down to the nearest integer.
because the 10th, the 20th, the 30th and the 40th apples were bruised. there was no 50th. so, only 4 bruised aplles.
and now : there could be a mixture. e.g. a small apple can also be bruised. a bruised apple can also be too green. and so on.
but your teacher did not give any indications or information on that. so, we have to assume that these are disjunct events.
so, we have to deduct all imperfect apples from the total amount.
the number of perfect apples is
48 - 16 - 12 - 4 = 16
Find the units of displacement of the point (4,2) to get the image of (7,7). Chapter (transformation) (coordinates) (translation). Please answer my questions correctly. Unnecessary answers will be reported.
Answers
Answer:
The units of the displacement are (3, 5) → T (x + 3, y + 5)
Step-by-step explanation:
The rules of translation of a point
If the point (x, y) is translated h units to the right and k units up, then its image is (x + h, y + k)If the point (x, y) is translated h units to the right and k units down, then its image is (x + h, y - k)If the point (x, y) is translated h units to the left and k units up, then its image is (x - h, y + k)If the point (x, y) is translated h units to the left and k units down, then its image is (x - h, y - k)∵ Point (4, 2) is translated by (h, k)
∵ Its image is (7, 7)
∴ The x-coordinate of the point is increased from 4 to 7
∴ The point is translated to the right by h units
∵ 4 + h = 7
∴ h = 7 - 4 = 3
∴ The point is translated to the right 3 units
∵ The y-coordinate of the point is increased from 2 to 7
∴ The point is translated up by k units
∵ 2 + k = 7
∴ k = 7 - 2 = 5
∴ The point is translated up 5 units
∴ The point is translated 3 units right and 5 units up
∴ The units of the displacement are (3, 5) → T (x + 3, y + 5)
HELP!! MEEE PLSS
What number completes this pattern?
1, 3, 6, __.
Answers
Identify the following:a) Relative maximum(s):b) Relative minimum(s):c) Increasing interval(s):d) Decreasing interval(s):e) Domainf) Range:g) End Behavior:h) Zerosi) y-intercept:
Answers
relative maximum: (-3,4)
relative minimum: (-1,0)
increasing interval: (-∞,-3) U (-1,∞)
decreasing interval: (-3,-1)
domain: (-∞,∞)
range: (-∞,∞)
end behavior:
as x approaches to infinity, y approaches to infinity
zeros: x = -3, x = -1
y-intercept: y = 4
A corner lot that originally was square lost 185 m² of area when one of the adjacent syreets what is wide by 3 m and the other was widnened by 5 m find the new dimensions of the lot
Answers
The new dimensions of the lot is length = 22 meters and width = 20 meters
The corner lot that originally was square
Consider the side of the lot = x
The area of the square = Length × length
Therefore,
x × x = \(x^2\)
one of the adjacent streets which is widened by 3 m and the other was widened by 5
Therefore
(x-3) × (x-5) = \(x^2\) - 185
open the brackets
\(x^2-5x-3x+15=x^2-185\)
The x square term will cancel each other
-5x-3x = -185-15
-8x = -200
x = 25 meter
The new length of the lot = x-3
= 25-3
= 22 meter
The new width of the lot = 25-5
= 20 meters
Hence, the new dimensions of the lot is length = 22 meters and width = 20 meters
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I NEED HELP ON THIS PLEASE
Answers
Answer:
m<5 = 120* because <5 and 120* are corresponding angles
Step-by-step explanation:
Let x be a discrete random variable. if pr(x<6) = 1/7, and pr(x>6) = 1/4, then what is pr(x=6)?
Answers
Answer:
\(pr(x=6)=\frac{17}{28}\)
Step-by-step explanation:
Well the probabilities should all up to 1. This means pr(x<6) + pr(x=6) + pr(x>6) = 1.
So plugging in the known values we get: \(\frac{1}{7} + pr(x=6) + \frac{1}{4}=1\)
To make things easier, let's multiply the 1/7 by 4/4 and 1/4 by 7/7
\(\frac{4}{28}+pr(x=6)+\frac{7}{28}=1\)
Now combine like terms: \(pr(x=6)+\frac{11}{28}=1\)
Subtract 11/28 from both sides
\(pr(x=6)=\frac{17}{28}\)
Solve for m 5m+35=70
Answers
Answer:
m=7
Step-by-step explanation:
subract 35 from both sides to isolate the variable. Then you should be left with 5m=35. From there, divide both sides to isolate the variable even more, and you should be left with m=35/5 which is 7.
Answer: m=7
Step-by-step explanation:
\(5m+35=70\)
subtract 35 on both sides
\(5m+35-35=70-35\)
\(5m=35\)
divide 5 on both sides
\(35/5=7\)
\(m=7\)
Graph the function g(x)= 1/4x+4
Answers
The given function is
\(g(x)=\frac{1}{4}x+4\)First, we make x = 0.
\(g(0)=\frac{1}{4}\cdot0+4=0+4=4\)Second, we make g(x) = 0.
\(\begin{gathered} 0=\frac{1}{4}x+4 \\ -4=\frac{1}{4}x \\ x=-16 \end{gathered}\)Third, we graph the points (0, 4) and (-16, 0).
At last, we draw the line through the points to get the line.
what is four less then a number
Answers
Answer:
n - 4 :)
Step-by-step explanation:
A number = n
So, 4 less than n is simply n - 4 :)
if a distribution of scores is shown in a bar graph, you know that the scores were measured on a(n) _________ scale of measurement.
Answers
If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.
An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.
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