By applying probability method in a Poisson distribution, we find out that the probability that in a given year that area will be hit by fewer than 4 hurricanes is 0.1512 and the probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes is 0.4015.
It is given that -
On an average, Eastern United States is hit by 6 hurricanes in a year.
We have to find out -
(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes
(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes
This is a case of probability which relates to Poisson distribution that provides probability of any random event that occurs within a specific time interval.
Let us assume the number of hurricanes is represented by [tex]X[/tex]. The Poisson distribution can be represented as -
[tex]P(X) = \frac{(lambda)^{X}*e^{-lambda}}{X!}[/tex] -------(1)
Here, [tex]X\\[/tex] = 1,2,3,...
lambda = Average = 6 (in this question)
[tex]e[/tex] = 2.718
(a) Probability that in a given year that area will be hit by fewer than 4 hurricanes
[tex]P(X < 4) = P(X=0) +P(X=1)+P(X=2)+P(X=3)\\= \frac{6^{0}*e^{-6}}{0!}+\frac{6^{1}*e^{-6}}{1!}+\frac{6^{2}*e^{-6}}{2!}+\frac{6^{3}*e^{-6}}{3!}\\=0.0025+0.0149+0.0446+0.0892\\=0.1512[/tex]
Thus, the probability that in a given year that area will be hit by fewer than 4 hurricanes is 0.1512.
(b) Probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes
[tex]P(6\leq X\leq 8)=P(X=6)+P(X=7)+P(X=8)\\=\frac{6^{6}*e^{-6} }{6!}+\frac{6^{7}*e^{-6} }{7!}+\frac{6^{8}*e^{-6} }{8!}\\=0.1606+0.1376+0.1033\\=0.4015[/tex]
Thus, the probability that in a given year that area will be hit by anywhere from 6 to 8 hurricanes is 0.4015.
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A wood board 100 cm long is cut into two pieces. One piece is 26 cm longer than the other. What are the lengths of the two pieces?
Answer:
the little peice (x) is 37 cm
the second piece(x +26) = 37 + 26 = 63 cm
Step-by-step explanation:
think the little or second piece is x
and another piece is (x + 26)
according to question,
x + x+26 = 100
2x + 26 = 100
2x = 100 - 26
2x = 74
x = 74 ÷ 2
x= 37
Find the area and perimeter of a rectangle with vertices at (-1, 2), (3, 2),
(3.-5), and (-1,-5).
The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²
What is rectangle short answer?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.the points (-1 , 2) and (3 , 2 ) form one the of the rectangle w = [tex]\sqrt{( 3 + 1 )^{2} + ( 2 - 2 )^{2} }[/tex]
= [tex]\sqrt{4^{2} + 0 }[/tex]
= √ 16
= 4
The length can be obtained by finding distance between the points (-1,2) and ( -1, - 5) = [tex]\sqrt{( -1 -2 )^{2} + ( -5 + 1)^{2} }[/tex]
= [tex]\sqrt{(-3)^{2} + ( -6)^{2} }[/tex]
= √9 + 36
= √45 = 3√5
The perimeter of the rectangle is: P = 2( w + L) = 2( 4 + 3√5) ⇒ 8 + 6√5 unit
The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²
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. The price of a new TV is £540, which includes 20% VAT.
Find the cost of the TV excluding VAT.
Answer:
450
Step-by-step explanation:
Based on the given conditions, formulate:
Calculate the sum or difference:
Convert decimal to fraction:
Divide a fraction by multiplying its reciprocal:
Cross out the common factor:
Calculate the product or quotient:
Answer:
I need answer to this equation with working ASAP
5.104 ÷ 0.016
Answer:
319
Step-by-step explanation:
hope this helps
It would take 180 minutes to fill a swimming pool using the water from 5 taps.
a) How many minutes will it take to fill the pool if only 3 of the taps are used?
b) An assumption being made in my working
is that all the taps are flowing at the same
It will take 300 minutes to fill the pool if only 3 taps are used
How to determine the number of minutes it will take to fill the pool?From the question, we have the following parameters that can be used in our solution:
Number of taps = 5 taps
Number of minutes = 180 minutes
From the above parameter, we can calculate the constant of proportionality
The constant of proportionality is calculated as
Constant of proportionality = Number of taps * Number of minutes
Substitute the known values in the above equation
So, we have the following equation
Constant of proportionality = 5 * 180
Evaluate the quotient
Constant of proportionality = 900
The number of minutes it will take to fill the pool is then calculated as
Constant of proportionality = Number of taps * Number of minutes
Where
Constant of proportionality = 900
Number of taps = 3
Substitute the known values in the above equation
So, we have the following equation
900 = 3 * Number of minutes
This gives
Number of minutes = 900/3
Evaluate
Number of minutes = 300
Hence, the number of minutes is 300 minutes
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I need help finding the answer too Y= 2.82x + 25.1
Answer:
-8.9 is x and y is -25.1
Step-by-step explanation:
on a hot day, students are lining up to buy ice cream. let l be the number of people in line. write a differential equation for l using the following assumptions.
If a+ 1/a = 5 then find the value of; i) a² + 1/a² ii) a³ + 1/a³
Answer:
23
110
Step-by-step explanation:
We have a + 1/a = 5
(a + 1/a)² = a² + (1/a²) + 2.a.1/a = a² + (1/a²) + 2
But (a + 1/a)² = 5² = 25
So a² + (1/a²) = 25 - 2 = 23
(a + 1/a)³ = a³ + 3a²(1/a) + 3a(1/a)² + (1/a)2
= a³ + 1/a³ + 3a + 3/a
= a³ + 1/a³ + 3(a + 1/a)
= a³ + 1/a³ + 3(5)
= a³ + 1/a³ + 15
But (a + 1/a)³ = 5³ = 125
So
a³ + 1/a³ + 15 = 125
a³ + 1/a³ = 110
Answer:
23 and 110
Step-by-step explanation:
using the expansion
(a + b)² = a² + 2ab + b² , then
a + [tex]\frac{1}{a}[/tex] = 5 ( square both sides )
(a + [tex]\frac{1}{a}[/tex] )² = 5²
a² + 2(a × [tex]\frac{1}{a}[/tex] ) + [tex]\frac{1}{a^2}[/tex] = 25
a² + 2(1) + [tex]\frac{1}{a^2}[/tex] = 25
a² + 2 + [tex]\frac{1}{a^2}[/tex] = 25 ( subtract 2 from both sides )
a² + [tex]\frac{1}{a^2}[/tex] = 23
---------------------------------------------------------------------
using the expansion
(a + b)³ = a³ + b³ + 3ab(a + b) , then
a + [tex]\frac{1}{a}[/tex] = 5 ( cube both sides )
(a + [tex]\frac{1}{a}[/tex] )³ = 5³
a³ + [tex]\frac{1}{a^3}[/tex] + 3(a × [tex]\frac{1}{a}[/tex] )(a + [tex]\frac{1}{a}[/tex] ) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + 3(1)(5) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + (3 × 5) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + 15 = 125 ( subtract 15 from both sides )
a³ + [tex]\frac{1}{a^3}[/tex] = 110
HELP making flowchart
A flowchart is a diagram that shows a workflow or procedure. A diagrammatic explanation of an algorithm or a step-by-step procedure for solving a problem is another definition of a flowchart.
The phases are represented in the flowchart as a sequence of boxes of varying sizes that are connected by arrows in the right order.
This diagrammatic picture depicts a proposed fix for a specific problem. Flowcharts can be used in a range of industries to analyze, create, document, or manage a process or program. Using flowcharts, simple programs or procedures are created and documented. They, like other types of diagrams, help with process visualization. One of the many benefits is the possibility of flaws and bottlenecks becoming apparent. Common primary symbols include the ones listed below.A decision step for the information.The decision based on the information.To learn more about flowchart visit:
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A 16-foot board is to be cut into 4 pleces. Three of the pleces will be the same length, and one piece will be 4 feet
longer than the other three.
Which equation could be used to solve for the lengths?
x+x+x+x+4=16
x+x+x+4x=16
x+x+x+X-4=16
x+x+x+x=16+4
Answer:
I think it's B
Step-by-step explanation:
It's the only one with 3 x's to represent the part where it's cut into four pieces the x represents the 3 numbers and then the 4x means how the x = the number that the 3 represent plus the 4 feet longer
Can someone help me and explain this please. I don’t understand what to do.
Answer:
The answer is 3 or 3/1
Step-by-step explanation:
The equation you use is m=y2-y1/x2-x1
Answer:
Slope = 3
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define two points on the line from the given table:
[tex]\textsf{Let}\:(x_1,y_1)=(2,7)[/tex][tex]\textsf{Let}\:(x_2,y_2)=(4,13)[/tex]Substitute the defined points into the formula:
[tex]\implies \textsf{Slope}=\dfrac{13-7}{4-2}=\dfrac{6}{2}=3[/tex]
Note:
The change between each y-value is 6.The change between each x-value is 2.Therefore, the question may require you to enter 6/2 into the answer boxes. However, the slope of the line is 3.
how dose a value that is greater than 100 of the orangianl value less than1 of the orangilal value copare the oraginal value
If a value that is is greater than 100% of the original value will always be larger than original value.
If a value is less than 1% of the original value will always be less than the original value.
Given,
A value that is greater than 100% of the original value.
And it is 1% less than the original value.
We have to compare these values with the original value;
That is,
A value that is greater than 100% of the original value,
eg;
130% of 20 = 20 × 130/100 = 26
26 is greater than 20.
That is,
If a value that is is greater than 100% of the original value will always be larger than original value.
Next,
It is 1% less than the original value.
eg;
1% of 20 = 1/100 × 20 = 0.2
0.2 is less than 20
That is,
If a value is less than 1% of the original value will always be less than the original value.
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Would be nice if answered soon.
Simplify the expression.
√8r³y
Enter your answer in the box. Enter variables in alphabetical order when within roots.
√8x³y=
Answer:
2√2 x ³y
Step-by-step explanation:
1) Write the number in exponential form with the base of 2
2) Rewrite the exponent as a sum where one of the addends is a multiple of the index
3) Use a m+n m n = a xa to expand the expression
4) Any expression raised to the power of 1 equals itself
5) The root of a product is equal to the product of the roots of each factor
6)Reduce the index of the radical and exponent with 2
Then you get your answer!! Hope this helps
On a standardized exam, the scores are normally distributed with a mean of
150 and a standard deviation of 10. Find the z-score of a person who scored
178 on the exam.
The z-score of the person who scored 178 on the exam is fund as 2.8.
What is defined as the normally distribution?The proper term for just a probability bell curve is the normal distribution.The mean of a normal distribution is zero, as well as the standard deviation is one. It has a skew of 0 and a kurtosis of 3.However all symmetrical distributions are normal, not all normal distributions are symmetrical.Many naturally occurring phenomena resemble the normal distribution.However, most pricing distributions in finance are not perfectly normal.For the given question,
Mean μ = 150
Standard deviation σ = 10
Observed value x = 178.
The z-score is calculated as;
z = (x - μ)/σ
z = (178 - 150)/10
z = 28/10
z = 2.8
Thus, the z-score of the person who scored 178 on the exam is fund as 2.8.
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11. Which of the following equations best represents
the graph below?
A. -2x + 3y = 6
C. 3x - 2y = 6
B. 2x + 3y = 6
D. -3x-2y = 6
Answer: A
Step-by-step explanation:
|2x + 11| = 3
Solve for x
Answer:
x=-4 or -7
Step-by-step explanation:1: 2x+11=3
2x=-8
x=-4
2: -(2x+11)=3
2x+11=-3
2x=-14
x=-7
if -(x-1)=5 find the value of -4x
if 9-6x=45 find the value of x-4
Answer:
value of -4x=16.
value of -4x=10.
cuantos años tiene la luna
Answer: La luna tiene 4.53 billion anos
Step-by-step explanation:
=
Question 2 of 2 (1 point) | Question Attempt: 5 of Unlimited
A manufacturer produces two models of toy airplanes. It takes the manufacturer 32 minutes to assemble model A and 8 minutes to package it. It takes the
manufacturer 20 minutes to assemble model B and 10 minutes to package it. In a given week, the total available time for assembling Is 3200 minutes, and t
total available time for packaging is 960 minutes. Model A earns a profit of $8 for each unit sold and model B earns a profit of $11 for each unit sold. Assum.
the manufacturer is able to sell as many models as it makes, how many units of each model should be produced to maximize the profit for the given week?
Note that the ALEKS graphing calculator can be used to make computations easier.
Answer :
Model A : 0 unit(s)
Model B: 96 unit(s)
In linear equation, Maximize this profit equation: P = 10X + 8Y
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an uncertain variable with only one potential value. One such linear equation in one variable is 9x + 78 = 18.Bounded by (hours): Assembly hours≤ 3200, Packaging hours ≤960
Assembly time (subject to above boundary):
32A + 20B ≤ 3200
Packaging time (subject to above boundary):
8A + 10B ≤960
Maximize this profit equation: P = 10X + 8Y
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Solve the simultaneous equation
y= 9 - x
y= 2x² + 4x + 6
Using substitution method, For the given equations, the value of x is 1/2 or x = -3
Describe substitution.A fundamental operation in computer algebra is substitution. In computer algebra systems, it is frequently abbreviated as "subs" or "subst."
When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.
Given,
y= 9 - x
y= 2x² + 4x + 6
Substituting the value of y from 1 equation to other.
⇒ 9 - x = 2x² + 4x + 6
Now factorizing the equation,
⇒ 2x² + 5x - 3 = 0
⇒ 2x² + 6x - 1x - 3
⇒ 2x(x + 3) -1 (x + 3)
⇒ (2x - 1) (x + 3)
x = 1/2 or x = -3
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Help I’ve forgotten fifth grade math
bobbie spent at least 2.35 on lunch every day for five days in a row. write an equality to show bobbies average lunch cost
Answer:
2.35 x 5 = 11.75
Step-by-step explanation:
We take 2.35 and 5. We put it in a multiplication equation and multiply. We end up with 2.35 x 5 = 11.75
graph the proportion y = -4x
Answer in the attachment
suppose you have a sample of 29 women over 35 who have not previously given birth who exercise daily, and who have an average duration of labor of 17.3 hours and a sample variance of 37.2 hours. you want to test the hypothesis that women over 35 who have not previously given birth and who exercise daily have a different duration of labor than all women over 35 who have not previously given birth.
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.
Standard error sm = 1.634
Test statistic t = 1.102
P-value = 0.28
This is a hypothesis test for the population mean.
The claim is that women who exercise daily have a significantly different duration of labor than all women.
Then, the null and alternative hypothesis are
[tex]H_{0}[/tex] : μ=16
[tex]H_{0}[/tex] : μ≠ 16
The significance level is 0.05.
The sample has a size n=29.
The sample mean is M=17.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.
The estimated standard error of the mean is computed using the formula:
[tex]s_{M}[/tex] = [tex]\frac{s}{\sqrt{n} }[/tex] = [tex]\frac{8.8}{\sqrt{29} }[/tex]= 1.634
Then, we can calculate the t-statistic as
t=(M-μ)/(s/[tex]\sqrt{n}[/tex])=(17.8-16)/1.634)=1.102
The degrees of freedom for this sample size are:
df=n-1=29-1=28
This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):
[tex]P_{value}[/tex]=2.P(t≥1.102)=0.28
As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women
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In a math class with 22 students, a test was given the same day that an assignmentwas due. There were 14 students who passed the test and 13 students who completedthe assignment. There were 6 students who failed the test and also did not completethe assignment. What is the probability that a student chosen randomly from theclass passed the test and completed the homework?
Let:
A = students who passed the test = 14
B = students who completed the assignment = 13
N = Total students = 22
(A⁺ ∩ B⁺) = 6
P(A ∪ B) = 1 - 6/22 = 8/11
P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 14/22 + 13/22 - 8/11 = 1/2
P(A|B) = P(A ∩ B)/P(B) = (1/2)/(13/22) = 11/13 ≈ 0.85 ≈ 85%
through: (4, -3) and (-5, -4)
Find point-slope form of the equation.
Answer:
y + 3 = (1/9) (x - 4)
Step-by-step explanation:
To find slope:y2-y1 / x2-x1
-4 -(-3) / -5 - 4
Double negative switches the # to a positive
-4+3 / 5 - 4
= -1 / -9
Two negatives equal a positive
m=1/9
point-slope form:y-y1=m(x-x1)
y-(-3)=(1/9)(x-4)
Solving:Double negative=positive #
y+3=(1/9)(x-4)
Distribute (1/9) to the x and -4
y+3= (1/9)x - (4/9)
Subtract 3 from both sides
y = -3.4
4. Simplify the radical expression.
Answer: Hello Love I believe the answer is the LAST one
Step-by-step explanation:
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion.
x/-2=-9
The equation x/-2 = -9 has only one solution and is x = 18.
We are given an equation x/-2 = -9 for which we need to check whether it has a solution, no solution or infinite solutions.
For this we first solve this equation.
x/-2 = -9
⇒ x = -9 x -2
⇒ x = 18
So this equation has only one solution and it is unique.
Hence we cannot find two values of to support this conclusion, since x = 18 is the only value which satisfy this equation.
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PLEASE HELP ASAP! THANK YOU!
The scalar factor is of 6.
What is the scalar factor?
A scale factor is the ratio between corresponding measurements of an object and a representation of that object. in simple words how big or small is one object compared to another.
We are given two triangle and the measurements of the corresponding sides of the triangle.
side of one triangle is 4 and side of another triangle is 24.
To find the scalar factor we divide the two
We get the answers as 6
Hence the scalar factor is of 6
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Find the value of r that gives the line passing through (3,2) and (r,-4) a slope that is undefined.
The value of r is calculated as (m/-6) + 3 for the line with undefined slope passing through (3,2) and (r,-4).
Describe slope intercept form using an example.The slope-intercept form of an equation is when the equation of a line is written in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, and the y-intercept is (0, 7).We must determine the value of r that gives the line passing through (3,2) and (r,-4) an undefined slope.
Let,
x₁ = 3
y₁ = 2
x₂ =r
y₂ = -4
slope = m
Using the slope equation we get,
m = (y₂ - y₁)/(x₂ - x₁ )
m = (-4-2)/(r-3)
m/-6 = r - 3
r = (m/-6) + 3
Therefore, the value of r is calculated as (m/-6) + 3 for the line passing through (3,2) and (r,-4) with undefined slope.
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Convert to a decimal. 13 --- 4