Using the Poisson distribution, it is found that there is a 0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.Considering the average of 15 birds every 2 hours during daylight hours, the mean for a 45-minute period is given by:
[tex]\mu = 15 \times \frac{45}{120} = 5.625[/tex]
The probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours is given by:
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.625}(5.625)^{0}}{(0)!} = 0.004[/tex]
[tex]P(X = 1) = \frac{e^{-5.625}(5.625)^{1}}{(1)!} = 0.02[/tex]
[tex]P(X = 2) = \frac{e^{-5.625}(5.625)^{2}}{(2)!} = 0.057[/tex]
[tex]P(X = 3) = \frac{e^{-5.625}(5.625)^{3}}{(3)!} = 0.107[/tex]
[tex]P(X = 4) = \frac{e^{-5.625}(5.625)^{4}}{(4)!} = 0.150[/tex]
[tex]P(X = 5) = \frac{e^{-5.625}(5.625)^{5}}{(5)!} = 0.169[/tex]
Then:
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.004 + 0.02 + 0.057 + 0.107 + 0.15 + 0.169 = 0.507[/tex]
0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.
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Which of the following terminating decimals is equivalent to StartFraction 3 over 8 EndFraction
The 0.375 terminating decimals are equivalent to 3/8 option second is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The fraction is:
= 3/8
After dividing with 8
= 0.375
Thus, the 0.375 terminating decimals are equivalent to 3/8 option second is correct.
The complete question is:
Which of the following terminating decimals is equivalent to 3/8?
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2x − 4y = 40,
−x + 2y = −20
Find x and y intercept
Answer:
The x and y intercept are (20,0)
Step-by-step explanation:
2x-4y=40—eqn1
-x+2y=-20—eqn2
Make x the subject of eqn2
-x=-20-2y
x=20+2y
plug this into eqn 1
2(20+2y)+4y=40
40+4y+4y=40
8y=40-40
y=0
plug y=0 into eqn2
-x+2(0)=-20
-x=-20
x=20
Can someone solve this? please
Answer:
Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]h
Where, l is the lower limit of the modal class
f₁ is the frequency of the modal class
f₀ is the frequency preceding the modal class
f₂ is the frequency succeeding the modal class
h is the class size
From the table,
Maximum frequency = 41
This frequency lies in the class 10000 - 15000
l = 10000
h = 5000
f₁ = 41
f₀ = 26
f₂ = 16
Now, f₁ - f₀ = 41 - 26 = 15
2f₁ - f₀ - f₂ = 2(41) - 26 - 16
= 82 - 42
= 40
[(f₁ - f₀)/(2f₁ - f₀ - f₂)] = 15/40
= 3/8
Now, mode = 10000 + (3/8)(5000)
= 10000 + (15000/8)
= 10000 + 1875
= 11875
Therefore, the modal income is 11875.A sphere has a surface area of 16pi cm³. Find the volume giving your answer in form. Anyone know how to do this question?
Answer:
Your answer should be around 10.7π cm³
Step-by-step explanation:
The surface area formula for a sphere is SA = 4πr^2. The volume formula for a sphere is V=4/3πr^3. Use the given SA to find the value of V.16π=4πr^2 Divide by 4π on both sides. 4 = r^2. r=2 Plug in 2 for r in the equation V=4/3πr^3. Your answer should be around 10.7π cm³
Which graph represents the function f(x) = |-x - 2|-1?
-6-
Answer:
it is the third one
Step-by-step explanation:
third one
Gareth buys two oranges. He pays with a £1 coin and gets 52p change. Work out the cost of one orange.
Answer:
24p
Step-by-step explanation:
£1 - £0.52 = £0.48 ← cost of 2 oranges
cost of 1 orange = £0.48 ÷ 2 = £0.24
Fill in the gaps below:
Answer:
anticlockwise; reflection about x = 0; reflection about y = x - 1
Step-by-step explanation:
To get from A to A', we have to rotate anticlockwise. This rotation would take us around the coordinate plane from the first quadrant to the fourth quadrant to the third quadrant to the second quadrant. Clockwise about (0, -1) would not bring us to A'. To get from A' to A'', we to reflect across the line x = 0. As you can see in the image, the two triangles mirror each other across a vertical line in the center of them, and this vertical line would be x = 0 because both triangles are at least 1 unit away from it (they are equidistant from this line)
A single transformation that could map A onto A'' would be a reflection about y = x - 1. Both triangles happen to meet at this point so you might be able to visualize it. However, we can also test some points to see if this works. First, we can test the right-most point of A (which is the top-most point of A''). This point on A is (6, 0). If this point was reflected across y = x - 1, y would become 6 - 1 or 5, and since y = x - 1 is the same as x = y + 1, x would become 0 + 1 or 1. Indeed, the equivalent point on A'' is (1, 5).
What type of function is shown in the data in the table below?
Answer:
the function is quadratic because it have (2) turning points which is a sign of the ax² in rhe quadratic equation (ax²+bx+c)
-8y=7y-5 direct variation or not
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{-8y = 7y - 5}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathbf{-8y = 7y - 5}[/tex]
[tex]\mathbf{7y - 5 = -8y}[/tex]
[tex]\huge\textbf{SUBTRACT 7y to BOTH SIDES}[/tex]
[tex]\mathbf{-8y - 7y = 7y - 5 - 7y}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{-15y = -5}[/tex]
[tex]\huge\textbf{DIVIDE -15 to BOTH SIDES}[/tex]
[tex]\mathbf{\dfrac{-15y}{-15} = \dfrac{-5}{-15}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{y = \dfrac{-5}{-15}}[/tex]
[tex]\mathbf{y = \dfrac{-5\div-5}{-15\div-5}}[/tex]
[tex]\mathbf{y = \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Met your answer:}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{y = \dfrac{1}{3}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]10 divided by 34352 rounded to the nearest tenth
Answer: 0
Step-by-step explanation:
Answer:
34352.0
Step-by-step explanation:
Can someone please help me on this question
Answer: ? = 72
Step-by-step explanation:
We will set up a proportion to solve.
[tex]\displaystyle \frac{?}{56} =\frac{45}{35}[/tex]
Now, we will cross-multiply.
? * 35 = 56 * 45
35? = 2,520
? = 72
Problem 2
Given: HJ = 5x - 3, JK = 82-9, and KH = 131
Find: x, HJ, and JK
x =
HJ =
JK =
What is the answer.
Answer:
i got 12.2
Step-by-step explanation: (5x-3) +73 =131 is the equation and from that x = 12.2
A.
B.
10. Multiple choice. Determine the area of one face of a cube with a
side length of 14 cm.
A. 196 cm² B. 196 cm³ C. 14 cm²
D. 2744 cm³
Answer:
196cm²
Step-by-step explanation:
14*14=196
area = length of one side * the length of the other side
Use the quadratic formula to find both solutions to the quadratic equation
given below.
The solution of the equation are [tex]x = \frac{7 + \sqrt{61}}{6}[/tex] and [tex]x = \frac{7 - \sqrt{61}}{6}[/tex]
How to determine the solution?The equation is given as:
3x^2 - 7x- 1 = 0
The quadratic equation is represented as:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
So, we have:
[tex]x = \frac{7 \pm \sqrt{(-7)^2 - 4 *3 *-1}}{2*3}[/tex]
Evaluate the expression
[tex]x = \frac{7 \pm \sqrt{61}}{6}[/tex]
Expand
[tex]x = \frac{7 + \sqrt{61}}{6}[/tex] and [tex]x = \frac{7 - \sqrt{61}}{6}[/tex]
Hence, the solution of the equation are [tex]x = \frac{7 + \sqrt{61}}{6}[/tex] and [tex]x = \frac{7 - \sqrt{61}}{6}[/tex]
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Simplify by looking for like terms: 3a – a + 4b – 2b.
Answer:
2a+2b
Step-by-step explanation:
3a - a = 2a
4b - 2b = 2b
Answer:
2a+2b
Step-by-step explanation:
3a – a + 4b – 2b
Combine like terms
3a-a =2a
4b-2b =2b
3a – a + 4b – 2b. = 2a+2b
need help ASAPP and show your work ( will rate 5 starts )
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
How to find sinusoidal functions from a given graph
Sinusoidal functions are periodic trascendent expressions which involves trigonometric functions. There are two kinds of sinusoidal functions:
[tex]y = A \cdot \cos (B\cdot x + C) + D[/tex] (1)
[tex]y = A\cdot \sin (B\cdot x + C) + D[/tex] (2)
Where:
A - AmplitudeB - Angular frecuencyC - Angular phaseD - MidpointFirst, we find the amplitude and the midpoint:
A = [3 - (- 17)]/2
A = 10
D = [3 + (- 17)]/2
D = - 7
Now we find the angular phase and the angular frequency for each model:
Cosine model (x, y) = (0, - 17), (x, y) = (30, 3)
- 17 = 10 · cos C - 7 (3)
3 = 10 · cos (30 · B + C) - 7 (4)
By (3):
- 10 = 10 · cos C
cos C = - 1
C = acos(- 1)
C = - π
And by (4):
3 = 10 · cos (30 · B - π) - 7
10 = 10 · cos (30 · B - π)
cos (30 · B - π) = 1
30 · B - π = acos 1
30 · B - π = 0
30 · B = π
B = π/30
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
Sine model
Obtain the sine model by using trigonometric expressions:
cos θ = sin (θ + π/2) (5)
By (5):
y = - 7 + 10 · sin (π · x/30 - π + π/2)
y = - 7 + 10 · sin (π · x/30 - π/2)
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
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A cab company calculates cab fares using the expression 1.50d + 3, where d is the distance traveled in miles. If a passenger has to pay a $21 fare for a ride, which number from the set {9, 12, 15, 18} is the value of d?
Answer:
12
Step-by-step explanation:
⇒ 21 - 3 = 18 = 1.5a
⇒ a = 12
A country specializes in agricultural production—in particular, pineapples and coconuts. last year, its economy was operating efficiently at point a. to capitalize on its favorable climate for growing these fruits, the country decides to build some islands near its coast to use for growing pineapples and coconuts. which ppc represents the change that results from this decision?
The country will achieve a blue PPC.
What is Production Possibilities Curve (PPC)?
The Production Possibilities Curve (PPC) Sometimes called the production possibilities frontier (PPF) is a model used to show the tradeoffs associated with allocating resources between the production of two goods. The PPC can be used to illustrate the concepts of scarcity, opportunity cost, efficiency, inefficiency, economic growth, and contractions.
Due to the increase in resources of the country, the production capacity for both pineapple & coconut will increase as a result country's PPC will shift rightward/forward. And the country will achieve blue PPC.
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If you anwser the question i give you brainly
The proportional relationship graph that shows the situation is: Graph C.
What is a Proportional Relationship?A proportional relationship is defined as y = kx, where k is the constant of proportionality between x and y, and k = y/x.
Given the equation, M = 3n,
k = 3.
Thus, the graph that has a constant of proportionality (k) of 3, will correspond to the situation.
In graph C, using a point, (400, 1,200), we have:
k = 1,200/400
k = 3
Therefore, the graph that corresponds to the situation is: C.
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A population of a particular yeast cell develops with a constant relative growth rate of 0.4425 per hour. The initial population consists of 3.1 million cells. Find the population size (in millions of cells) after 3 hours. (Round your answer to one decimal place.)
The exponential function is often used to model the growth or decay of a population
The population size of the yeast cell after 3 hours is 6.24 million
The given parameters are:
a = 3.1M --- initial number of cells
r = 0.4425 per hour --- rate
The nth term of an exponential function is:
f(n) = a(1+r)^n-1
After 3 hours; n = 3
So, we have:
f(3) = a(1+r)^3-1
Substitute values for a and r
f(3) = 3.1 (1+0.4425)^3-1
f(3) = 3.1 ( 1.4425)^2
f(3) = 6.24
Hence, the population size of the yeast cell after 3 hours is 6.24 million.
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A motorbike is priced at $945.50 Johnson has $ 5000.
How many motorbikes could he buy?
The number of motorbikes is 5
How to determine the number of motorbikes?The given parameters are:
Motorbike = $945.50
Johnson = $5000.
The number of motorbikes is calculated as:
n = Johnson/Motorbike
So, we have:
n = 5000/945.5
Evaluate
n = 5.29
Remove the decimal
n = 5
Hence, the number of motorbikes is 5
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Can someone help me out on this problem and show work
Answer: 4230.14
Step-by-step explanation:
The amount that the balance is multiplied by each month is
[tex]\frac{2448}{2040}=1.2[/tex].
So, after t months, the balance is [tex]1700(1.2)^{t-1}[/tex].
Substituting in t=6, we get the balance is
[tex]1700(1.2)^{6-1}=\boxed{4230.14}[/tex], to the nearest hundredth.
A tour company charges a given price per ticket based on the number, n, of people who take the tour. the maximum number of people who are allowed to take the tour is 35. the price per ticket is $20 unless more than 10 people take the tour. if more than 10 people take the tour, the price per ticket is given by the expression: 20- n-10/2 b. harper goes on a tour where the ticket price is $10.50. how many people went on this tour? solve algebraically.
Harper goes on a tour where the ticket price is $10.50 along with 29 people according to the given expression. Solving the given expression for 'n' results in the required number.
How to solve an algebraic expression?Solving an expression algebraically involves basic operations like addition, subtraction, multiplication, and division.
In the expression, add/subtract the constant terms on both sidesMultiply/divide the coefficient of the variable on both sidesSolve for the variable.Calculation:Given that,
A tour company charges a given price per ticket based on the number 'n' of people who take the tour.
The maximum number of people who are allowed to take the tour is 35. I.e., n ≤ 35.
The price per ticket is $20 for n < 10 people and the price per ticket is given by the expression 20-(n-10)/2 for n > 10 people.
Harper goes on a tour where the ticket price is $10.50.
Since the price is less than $20, so the number of people who went on this tour is known by the expression 20-(n-10)/2 for n > 10 people.
So, solving the given expression:
20-(n-10)/2 = $10.50
-(n-10)/2 = 10.50 - 20
-(n-10)/2 = -9.5
(n-10) = 9.5 × 2
n -10 = 19
∴ n = 19 + 10 = 29
Therefore, 29 people went on this tour for a ticket price of $10.50.
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find the distance between (0,3) and (0,-6)
Answer:
the answer should be 9
Step-by-step explanation:
,look at a graph count from 0,-6 up to 0,3 . the distance between them is 9
Answer: 9
Step-by-step explanation:
let the two points P (0,3) and Q(0,-6)
We need to find distance PQ
PQ=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
here
x1=x coordinate of P=0
y1=y coordinate of P=3
x2=x coordinate of Q=0
y2=y coordinate of Q=-6
Putting values
[tex]PQ=\sqrt{(0-0)^2+(-6-3)^2}\\[/tex][tex]PQ=\sqrt{(0)^2+(-9)^2} \\PQ=\sqrt{81} \\PQ=9[/tex]
What is the slope of these two equations?
Answer:
8. 0
9. undefined
Step-by-step explanation:
8. 0
> because the y variable is the same for all x-values, this is a horizontal line. Horizontal lines have a slope of 0.
> Thinking of slope as rise over run: we will always rise 0, and run __ from any two points--0 divided by any number is always 0
9. undefined
> because the x variable is always the same, no matter what y variable we graph, we will have the same outcome. So, this would look like a straight line, which have an undefined slope.
> If you think of a slope as rise / run; if you go from any two points, there will be a 0 in the denominator--which is undefined
hope this helps!! have a lovely day :)
What is the length of the longest side of a triangle that has the vertices (-2, 1), (5, 1), and (5, 4)?
OA. 65 units
OB. √58 units
OC. 6√65 units
OD. 5√65 units
Answer:
B
Step-by-step explanation:
To find the length of the longest side of the triangle, first sketch the triangle. A graph paper is not needed here.
In this case we have a right-angled triangle, since the ends of the adjacent side has the same y-coordinate of 1 and the opposite side has the same y-coordinate of 5.
In a right-angled triangle, the hypotenuse side is the longest. The length of the hypotenuse side can be found using 2 methods.
1) Pythagoras' Theorem
a² +b²= c²
(adjacent)² +(opposite)²= (hypotenuse)²
Length of adjacent
= 5 -(-2)
= 7 units
Length of opposite side
= 4 -1
= 3 units
(hypotenuse)²
= 7² +3²
= 58
hypotenuse= [tex] \sqrt{58} [/tex]
2) Distance formula
Since we know that the hypotenuse side is the longest, we can simply find the length of the hypotenuse side instead of calculating the length of each side.
[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]
Length of longest side
= distance between (5, 4) and (-2, 1)
[tex] = \sqrt{(4 - 1) {}^{2} + (5 - ( - 2)) {}^{2} } [/tex]
[tex] = \sqrt{3 {}^{2} + {7}^{2} } [/tex]
[tex] = \sqrt{58} [/tex]
Thus, the length of the longest side is [tex] \sqrt{58} [/tex] units.
I also dont know how to solve this one either. Please help! I just want to know how to solve it so i can do it on my own
Answer:
[tex]z=5[/tex]
Step-by-step explanation:
[tex]-\frac{3}{z}+\frac{7}{4z}=\frac{5}{z-25}\\\\\implies-\frac{12}{4z}+\frac{7}{4z}=\frac{5}{z-25}\\\\\implies-\frac{5}{4z}=\frac{5}{z-25}\\\\\implies125-5z=20z\\\\\implies25z=125\\\\\implies z=5[/tex]
Have a nice day, also mark brainliest please!
does anyone know how to do these??
Answer:
b)
c=140°
a= 40°
b=40°
c)
p= 60°
q= 60°
r= 120°
d)
a= 65 °
b= 65°
c= 65°
d= 115°
e=65°
Step-by-step explanation:
Hope it helps
Combine the radicals 4√7+3√28.
O 10√7
O
4√7
0 -2√7
10√14
Answer:
10sqrt(7)
Step-by-step explanation:
[tex]4 \sqrt{7} + 3 \sqrt{28} \\ \\ 4 \sqrt{7} + 3(2 \sqrt{7} ) \\ \\ 4 \sqrt{7} + 6 \sqrt{7} = 10 \sqrt{7} [/tex]
Can someone please explain what an outlier is? it keeps popping up in all of my math questions and it is really confusing me...
Answer:
An outlier is something that is out of place compared to the rest of the group. For example, If you had the numbers 3,4,5,4,3,4, and 19, 19 would be the outlier.
Step-by-step explanation:
An outlier is a number that's far away from the rest of your data.
For example, if we look at the numbers 3, 2, 4, 5, 27, and 1, you can likely consider 27 to be an outlier because it's so far away from the rest of the data.
The specific definition of how far something has to be from the rest of the data to be an outlier depends entirely on the situation, but in general: if a number obviously sticks out from the rest, it's probably an outlier.