The probability of exactly 5 occurrences is (Rounding to three Decimal places), we get P(X ≤ 3) ≈ 0.251.
a) The probability of exactly 5 occurrences is given by the Poisson probability mass function:
P(X = 5) = (e^(-λ) * λ^5) / 5! = (e^(-5.1) * 5.1^5) / 120 ≈ 0.1755
Rounding to four decimal places, we get P(X = 5) ≈ 0.1755.
b) The probability of more than 6 occurrences can be calculated as the complement of the probability of 6 or fewer occurrences:
P(X > 6) = 1 - P(X ≤ 6) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6))
Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:
P(X = 0) ≈ 0.006
P(X = 1) ≈ 0.031
P(X = 2) ≈ 0.079
P(X = 3) ≈ 0.135
P(X = 4) ≈ 0.174
P(X = 5) ≈ 0.1755
P(X = 6) ≈ 0.1493
Substituting these values into the formula, we get:
P(X > 6) ≈ 1 - (0.006 + 0.031 + 0.079 + 0.135 + 0.174 + 0.1755 + 0.1493) ≈ 0.249
Rounding to three decimal places, we get P(X > 6) ≈ 0.249.
c) The probability of 3 or fewer occurrences is given by the cumulative distribution function:
P(X ≤ 3) = ∑ P(X = k), for k = 0, 1, 2, 3.
Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:
P(X = 0) ≈ 0.006
P(X = 1) ≈ 0.031
P(X = 2) ≈ 0.079
P(X = 3) ≈ 0.135
Adding these probabilities, we get: P(X ≤ 3) ≈ 0.251
Rounding to three decimal places, we get P(X ≤ 3) ≈ 0.251.
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What is the domain of the function?
The domain of the piecewise function is the set of all real numbers.
(-∞, ∞)
What is the domain of the graphed function?For a function y = f(x), we define the domain as the set of the possible inputs of the function (this is the possible values that x can take)
Here we can see the graph of a piecewise function. To find the domain, we need to look at the horizontal axis of the graph.
We can see that the function covers the whole horizontal axis, then the domain is the set of all real numbers, which means that we can write this as:
D = (-∞, ∞)
Then the correct option is the last one.
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how do I find the inverse of this function??
The inverse function of f(n) is:
g(n) = -(4/7)*n - 8/7
How to find the inverse of the function?Two functions are inverses if the composition is equal to the identity, so if g(n) is the inverse of f(n), we must have that:
f( g(n) ) = n
Replacing the actual function we will get:
-2 - (7/3)*g(n) = n
Now we can solve this for the inverse function g(n), then we will get:
-2 - (7/3)*g(n) = n
(-7/4)*g(n) = n + 2
g(n) = (-4/7)*(n + 2)
g(n) = -(4/7)*n - 8/7.
That is the inverse function.
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please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
The values of all the solutions are,
16) m QT = 142 deg
17) m ∠STR = 23 deg
18) m ∠RSQ = 19 deg
Given that;
A circle is shown.
Now, We can formulate;
16|) The value of m QT is,
m QT = 2 ∠QST
= 2 × 71
= 142 degree
17) The value of m ∠STR is,
m ∠STR = 1/2 m ∠SXR
= 1/2 × 46
= 23 deg
17) Since, ∠ RST = 90°
Then, We get;
m ∠RSQ = 90 - ∠QST
= 90 - 71
= 19 degree
Thus, The values of all the solutions are,
16) m QT = 142 deg
17) m ∠STR = 23 deg
18) m ∠RSQ = 19 deg
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The following data has been collected from the Paper Company. The data collected concerned the employees' favorite cell phone carrier. Of the 500 employees in the company, 200 were surveyed. The results are below:
Verizon: 105
Sprint: 55
AT&T: 40
How many employees were part of the random sampling?
500 employees
150 employees
200 employees
300 employees
Round 7.176 to the nearest hundredth
please answer this question by showing all the steps thank you
Answer:
x = 20°
Step-by-step explanation:
m∠CBA = 360 - 90 - 160 - 30 = 80
It's an isosceles Δ, therefore the base angles are congruent.
m∠CBA = m∠ACB = 80
Sum of interior angles of a Δ = 180
x = 180 - 80 - 80 = 20
heeeeeeeeeeeeeeeeeeelp plssssss
To solve this problem, we need to first convert the distance on the map to actual distance using the map scale.
1 cm on the map represents 50,000 cm (or 500m) in actual distance.
So, 8.5 cm on the map represents 8.5 x 500m = 4,250m in actual distance.
Now, we can use the formula: time = distance ÷ speed
Here, distance = 4,250m and speed = 10km/h = 10,000m/h
So, time = 4,250m ÷ 10,000m/h = 0.425 hours
To convert hours to minutes, we can multiply by 60:
time = 0.425 x 60 = 25.5 minutes
Therefore, it will take Myra 25.5 minutes to run from the park entrance to the beach.
The temperatures at midday on March 1st in five cities are shown in the
bar chart below.
12
a)
Temperature C
10
8
CO
1
London Paris Munich Rome Oslo
What is the
difference in
temperature
between Rome
and Munich?
b) The temperature
in Oslo rises by
5°C over the next
6 hours.
What is the
temperature in
Oslo at 6pm?
The temperature difference between Rome and Munich is [tex]2[/tex]°C in the first case.
a) To find the difference in temperature between Rome and Munich, we compare their respective temperatures on the bar chart. Let's assume the temperatures on the chart are represented by the heights of the bars. From the chart, the temperature in Rome is [tex]10[/tex]°C, and the temperature in Munich is [tex]8[/tex]°C.
The difference in temperature between Rome and Munich can be calculated as the absolute difference between their values:
[tex]\[ \text{Difference in temperature} = |10 - 8| = 2°C \][/tex]
Therefore, the temperature difference between Rome and Munich is [tex]2[/tex]°C.
b) If the temperature in Oslo rises by [tex]5[/tex]°C over the next [tex]6[/tex] hours, we can add this increase to the current temperature in Oslo to determine the temperature at [tex]6[/tex] pm. However, the initial temperature in Oslo is not provided in the information given.
Without the initial temperature, we cannot calculate the specific temperature at [tex]6[/tex] pm.
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To the nearest tenth, what is the value of x?
Answer:
34.1
Step-by-step explanation:
In this case we have supplementary information that is not required to find the length of [tex]x[/tex].
A screenshot is provided below with the other values.
Two lines AB and CD intersect each other at O.If angle AOD = 120 deg . BOC=3y. < BOD = 2x then find (x + y)
The value of x + y = 70 when 2 lines AB and CD intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.
Given that,
AB and CD 2 lines intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.
We have to determine the value of (x + y).
We know that,
In the picture we can see the two lines AB and CD intersect each other at O.
So,
From line AB a straight line has 180°.
Then ∠AOD + ∠DOB = 180°
120° + 2x = 180°
2x = 180° - 120°
2x = 60
x = [tex]\frac{60}{2}[/tex]
x = 30°
Then ∠DOB = 2x = 2(30) = 60°
And by vertically opposite angles ∠AOD = ∠COB
120° = 3y
3y = 120°
y = [tex]\frac{120}{3}[/tex]
y = 40°
Then ∠COB = 120°
So,
Now, x + y = 30 + 40 = 70
Therefore, The value of x + y = 70
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a coin sold for $279 in 1977 and was sold again in 1990 for $434. Assume that the growth in the value V of the collector's item was exponential
Answer: To find the exponential growth of the coin's value over the given period, we can use the formula for exponential growth:
V(t) = V0 × e^(kt)
where V(t) is the value of the coin at time t, V0 is the initial value of the coin, e is the mathematical constant e (approximately equal to 2.71828), k is the growth rate, and t is the time period.
We can use the information given to find the value of k. Let's use 1977 as the initial time period and 1990 as the final time period. The value of the coin in 1977 is V0 = $279, and the value of the coin in 1990 is V(13) = $434 (since 1990 - 1977 = 13 years).
Substituting these values into the formula, we get:
$434 = $279 × e^(k × 13)
Dividing both sides by $279, we get:
e^(k × 13) = $434 / $279
Taking the natural logarithm of both sides, we get:
k × 13 = ln($434 / $279)
Simplifying, we get:
k = ln($434 / $279) / 13
Using a calculator, we find that k is approximately 0.0556.
Now that we have found the growth rate, we can use the formula to find the value of the coin at any time t. For example, to find the value of the coin in 1985 (8 years after 1977), we can use the formula:
V(8) = $279 × e^(0.0556 × 8)
Using a calculator, we find that V(8) is approximately $425.46.
Therefore, we can conclude that the value of the coin grew exponentially at a rate of approximately 5.56% per year, and was worth about $425.46 in 1985.
URGENT
Please help
Will mark brainiest
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X=14), n=19, p=0.8
The probability of obtaining 14 successes in 19 trials with a probability of success of 0.8 is approximately 0.1025.
How to find the probabilitiesUsing the binomial probability formula:
P(X = 14) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials,
p is the probability of success, and
k is the number of successes.
Plugging in the given values, we have:
P(X = 14) = (19 choose 14) * 0.8^14 * (1-0.8)^(19-14)
P(X = 14) = 0.1025 (rounded to four decimal places)
Therefore, the probability of obtaining 14 successes in 19 trials with a probability of success of 0.8 is approximately 0.1025.
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What is the interval in which both f (x) and g(x) are positive?
The interval in which both functions are positive is the one in option C.
(3, ∞)
In which interval are the two functions positive?First, when we have a graph, to identify when the function is positive we need to see when the graph of the function is above the horizontal axis.
So here we just need to see in which interval are both curves (orange one and blue one) are above the horizontal axis.
We can see that from x = 3 and above, both of the curves are above the horizontal axis, then the interval in which both functions are positive is:
(3, ∞)
So the correct option is C.
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On average, Americans consume 13.9 pounds of ice cream per person over an entire year. Ben loves ice cream, but limits himself to one 3-ounce (oz) serving each week. Find the difference between the amount of ice cream that Ben consumes compared to the national average. (1 pound equals to 16 ounces and there are 52 weeks in a year.)
Q6: A fishing boat sails in a direction of 024° for 30 km from a port P, and then in a direction of 114° for 20 km. a) Draw a diagram please.
Select the correct answer. Which logarithmic equation correctly rewrites this exponential equation? 8x = 64 A. log8 64 = x B. log8 x = 64 C. log64 8 = x D. logx 64 = 8 Reset Next
The Exponential equation is 8x = 64. the correct answer is option A: log8 64 = x.
The exponential equation is 8x = 64.
To rewrite the exponential equation in logarithmic form, we use the following format:
log base a of b = c if and only if ac = b
Here, the base is 8 and the result is 64.
So, we can rewrite the equation as:
log8 64 = x
Therefore, the correct answer is option A: log8 64 = x.
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len Love: by Can Themba
Your response should be 80-100 words in length.
The is story about two people who loved each other deeply and had
to hide their feelings. Micheal is black and Dora is coloured.
The two lovers are eventually exposed when Dora's little brother
Bobby is told at his school that his sister is in a relationship with a
native.
A fight follows and Menner Carelse (school teacher) who is in love
with Dora finds out. He tries to convince the Principal that her family
must be told, and much against the Principal's wishes, he goes to
tell the whole community about what they considered "scandal".
Put yourself in Dora's shoes and write TWO diary entries on
how she feels about the meeting between the two families. One
entry must express her feelings. BEFORE Micheal's beating by
Davie and his friends. The other must express how she felt
AFTER Salome presents evidence in the form of love letters
that Davie has written to her.
[20]
CAN SOMEONE PLEASE HELP ME ASAPPPPPPPPP
Answer:
216 in. 3
Step-by-step explanation:
math ...
(Worth 100 Brainly points) After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
1. The table of at least 4 values of the function is
x 0 -6 6 3
y 36 0 0 27
2. The domain is All set of real values and the range: y ≤ 36
3. The x and y intercepts of the rainbow are x = (-6, 0) and (6, 0) y = (0, 36)
1. Creating a table of at least 4 values of the functionGiven that we have
y = -x² + 36
From the graph, we have the following values
x y
0 36
-6 0
6 0
Set x = 3
So, we have
y = -3² + 36
Evaluate
y = 27
So, we have
x y
0 36
-6 0
6 0
3 27
2. The domain and the rangeFrom the graph, we have
Domain: All set of real valuesRange: y ≤ 36These values mean that;
Domain: The time of the dayRange: The height of the sun3. The x and the y-interceptsFor the x and y intercepts of the rainbow, we have
x = (-6, 0) and (6, 0)
y = (0, 36)
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differentiate cosx/sin2x
Answer:
derivative of cosx/sin2x is (1 + secx) / [2sinx cosx].
Step-by-step explanation:
To differentiate cosx/sin2x, we can use the quotient rule of differentiation, which states:
(d/dx) [f(x)/g(x)] = [g(x) * f'(x) - f(x) * g'(x)] / [g(x)]^2
Here, f(x) = cosx and g(x) = sin2x. So we have:
f'(x) = -sinx (differentiation of cosine)
g'(x) = 2cos2x (differentiation of sine2x using chain rule)
Now, using the quotient rule:
(d/dx) [cosx/sin2x] = [sin2x * (-sinx) - cosx * (2cos2x)] / [sin2x]^2
= [-2cos2x cosx + sin2x sinx] / [sin2x]^2
= [-2cosx cos2x + sinx] / [2sinx cosx]^2
= [-2cosx(1-2sin^2(x)) + sinx] / [2sinx cosx]^2
= [-2cosx + 4cosx sin^2(x) + sinx] / [2sinx cosx]^2
= (sinx + 2cosx sin^2(x)) / [2sinx cosx]^2
= sinx / [2sinx cosx]^2 + 2cosx / [2sinx cosx]^2
= 1/[2sinx cosx] + secx/[2sinx cosx]
= (1 + secx) / [2sinx cosx]
Therefore, the derivative of cosx/sin2x is (1 + secx) / [2sinx cosx].
5. Jordan is putting his
blocks away. He measures
one block and discovers it
is 5 cm long, 3 cm wide,
and 1 cm tall. If he is
planning to put all the
blocks into a bin that has a
volume of 370 cm³, how
many blocks will fit?
PLEASE HELP WILL MARK BRAINLIEST
Which measurement is the same for Charles and Jermod?
O median
Orange
Olower quartile
Oupper quartile
1
These dot plots show how many refutes Charles and Jermod spent on homework per day
for three weeks.
W
15 20 25 30 35 40 45 50 55 60
Charles's Homework (minutes per day)
..
15 20 25 30 35 40 45 50 55 60
Jermod's Homework (minutes per day)
Which measurement is the same for Charles and Jermod?
The measurement that is the same for Charles and Jermod is the median
How to find the Which measurement is the same for Charles and Jermod?The dot plots show the distribution of the number of minutes that Charles and Jermod spent on homework per day for three weeks. To determine which measurement is the same for both of them, we need to compare the dot plots.
Looking at the dot plots, we can see that both Charles and Jermod have a dot at 35 minutes, indicating that they both spent 35 minutes on homework on at least one day.
Therefore, the measurement that is the same for Charles and Jermod is the median, since it is the middle value of the data when arranged in order. In this case, the median is not clearly identifiable from the dot plots
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o = 6.5 cm, ∠P=88° and ∠N=83°. Find the area of ΔNOP, to the nearest 10th of a square centimeter.
The area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side. It states that for any triangle ABC, the ratio of the length of a side to the sine of the angle opposite that side is constant, that is;
a/sinA = b/sinB = c/sinC
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.
angle m∠O = 180 - (83 + 88) {sum of interior angles of a triangle}
angle m∠O = 9°
Using the sine rule;
6.5/sin9 = ON/sin88
ON = (6.5 × sin88°)/sin9 {cross multiplication}
ON = 41.5
Area of the triangle = 1/2 × 6.5cm × 41.5cm × sin83
Area of the triangle = 133.9
Therefore, the area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.
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x[tex]x^{2} -12x+36=0[/tex]
[tex]x^2-12x+36=0\\(x-6)^2=0\\x-6=0\\x=6[/tex]
Among 100 college students, 80 said they study 12 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 12 hours per week to those that do not?
Answer: The ratio is 4:1
Lines band care parallel. Which pair of angles are corresponding angles?
A. 23 and 25
B. 21 and 22
OC. 42 and 43
D. 24 and 28
The corresponding angles of the parallel lines are ∠4 and ∠8
Given data ,
Let the parallel lines be represented as b and c
Let the line a be the transversal line
Now , Corresponding angles are equal
Co-interior angles add up to 180°
When two parallel lines are intersected by a transversal, the corresponding angles formed are congruent. Corresponding angles are pairs of angles that are in the same relative position at each intersection.
So , the angles ∠4 and ∠8 are the corresponding angles from the figure
This property of corresponding angles holds true for any pair of corresponding angles formed by intersecting parallel lines with a transversal.
Hence , the corresponding angles are ∠4 and ∠8
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n
The measures of the angles of a triangle are shown in the figure below. Solve for x.
$2°
34
Answer: The angle is 105 degrees
Step-by-step explanation:
In a triangle, there is 180 degrees total. To find x, we can do....
x = 180 - 41 - 34
x = 105
Calcula la medida de la altura de un triángulo equilátero del lado 6
The measure of the height of an equilateral triangle with a side length of 6 is 3√3.
We have,
In an equilateral triangle, all three sides are equal, and all three angles are also equal.
To calculate the height of an equilateral triangle, we can use the formula:
Height = (√3 / 2) x side
Given that the side length of the equilateral triangle is 6, we can substitute this value into the formula to find the height:
Height = (√3 / 2) x 6
Height = (√3) x 3
Simplifying, we have:
Height = 3√3
Therefore,
The measure of the height of an equilateral triangle with a side length of 6 is 3√3.
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The complete question.
Calculate the measure of the height of an equilateral triangle of side 6
Write the equation in standard form for the circle that has a diameter with endpoints
(4,–7) and (–12,–7).
Answer:
To find the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7), we first need to find the center and radius of the circle.
The center of the circle is the midpoint of the diameter, which can be found using the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the diameter.
Using (4,-7) and (-12,-7) as the endpoint coordinates, we get:
Midpoint = ((4 + (-12))/2, (-7 + (-7))/2) = (-4, -7)
So the center of the circle is (-4, -7).
The radius of the circle is half the length of the diameter, which is:
Radius = 1/2 × distance between (4,-7) and (-12,-7)
Radius = 1/2 × (4 - (-12)) = 8
So the radius of the circle is 8.
Now we can write the equation of the circle in standard form:
(x - h)² + (y - k)² = r²
Where (h,k) is the center of the circle and r is the radius.
Substituting the values we found, we get:
(x - (-4))² + (y - (-7))² = 8²
Simplifying this equation, we get:
(x + 4)² + (y + 7)² = 64
Therefore, the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7) is (x + 4)² + (y + 7)² = 64.
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A real estate sells houses for Birr 200,000 plus Birr 400 per one square metre. a Find the function that represents the cost of the house that has an area of x m². Calculate the cost of the house that has an area of 80 m².
Step-by-step explanation:
Cost of house = Birr ( 200 000 + 400 x ) where x is square meters
for 80 m^2 cost = Birr ( 200 000 + 400(80)) = Birr 232000
