Using the Poisson distribution, it is found that:
a) Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.b) 0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.c) 0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.d) 0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.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 successes e = 2.71828 is the Euler number [tex]\mu[/tex] is the mean in the given interval.Item a:
In this problem, we are given the mean during an interval, which is a common event(1.4 every 8 hours), and intervals can be assumed to be independent, hence, the correct option is:
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.Item b:
Mean of 1.4 every 8 hours, hence, every 11 hours, the mean is:
[tex]\mu = 11 \times \frac{1.4}{8} = 1.925[/tex]
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1459 = 0.8541[/tex]
0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.
Item c:
The probability is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]
[tex]P(X = 1) = \frac{e^{-1.925}(1.925)^{1}}{(1)!} = 0.2808[/tex]
[tex]P(X = 2) = \frac{e^{-1.925}(1.925)^{2}}{(2)!} = 0.2703[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1459 + 0.2808 + 0.2703 = 0.697[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.697 = 0.303[/tex]
0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.
Item d:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]
0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.
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Can anyone help thanks
Answer:
First Option, log 3x is equivalent to the expression shown
help me please please
Answer:
its 3 OR C
Step-by-step explanation:
HELP!!!! PLEASE NO LINK SCAM THO
Which graph shows all natural numbers less than 3?
OA)
-4 -3 -2 -1
+
4
o
1
2
3
+
+
OB) -4 -3 -2 -1
+
2 3
o
1
4
+
+
OC) -4 -3 -2 -1
+ +
2 3 4
o
1
OD)
-4 -3 -2 -1
+ +
+
0 1 2 3 4
Answer: C
Step-by-step explanation:
Answer:
The Answer Is B
Step-by-step explanation:
Which of the following equations contains the point (8, 5) and is perpendicular to the line y = 2x − 3?
Answer:
[tex]y = \ -\displaystyle\frac{1}{2}x \ + \ 9[/tex]
Step-by-step explanation:
Given that the reference line is y = 2x - 3, with a slope of [tex]m_{reference} \ = \ 2[/tex].
We know that two non-vertical lines are perpendicular if the slope of one line is the negative reciprocal of the slope of the other. In other words, both slopes can be multiplied together to yield -1. Let [tex]m_{1}[/tex] be the slope of one line and [tex]m_{2}[/tex] be the slope of its corresponding perpendicular line,
[tex]m_{1} \ \times \ m_{2} \ = \ -1 \ \ \ \ \ \ \ \ \ \ \ \mathrm{or} \ \ \ \ \ \ \ \ \ \ \ m_{1} \ = \ \displaystyle\frac{-1}{m_{2}}[/tex].
Thus,
[tex]m_{reference} \ \times \ m_{perpendicular} \ = \ -1 \\ \\ \-\hspace{2.26cm} m_{perpendicular} \ = \ \displaystyle\frac{-1}{m_{reference}} \\ \\ \-\hspace{2.26cm} m_{perpendicular} \ = \ \displaystyle\frac{-1}{2} \\ \\ \-\hspace{2.26cm} m_{perpendicular} \ = \ -\displaystyle\frac{1}{2}[/tex]
Therefore, using the point-slope form for the equation of a line passing through the point [tex](x_{1}, \ y_{1})[/tex] is [tex]y \ - \ y_{1} \ = \ m(x \ - \ x_{1})[/tex]. Given that the perpendicular line passes through the point [tex](8,\ 5)[/tex], the equation of the perpendicular line is
[tex]y \ - \ 5 \ = \ -\displaystyle\frac{1}{2}(x \ - \ 8) \\ \\ y \ - \ 5 \ = \ -\displaystyle\frac{1}{2}x \ + \ 4 \\ \\ \-\hspace{0.85cm} y \ = \ -\displaystyle\frac{1}{2}x \ + \ 9[/tex]
Johnny has a box filled with 10 black marbles and 5 purple marbles.What are the odd he pulls two purple marbles in a row without replacemnet
Answer:
2/21
Step-by-step explanation:
The first purple is 5/15 and the second is 4/14. Multiply them together to get 2/21.
Approximately what portion of the circle is shaded blue?
A. 2/3
B. 2/10 C.2/5
Answer:
2/5
Step-by-step explanation:
Try to make equal sections. The fraction they are asking for has the shaded number of sections on top (this us called the numerator) and the total number of sections on the bottom (this is called the denominator) see image
snowboard is advertised to be 60% of the original price. If the sale price is $180, use a double number line determine the original price.
Step-by-step explanation:
60% of original price X = $180
60/100 × X = $180
60X/100= $180( cross multiply)
60X= 18000
X= 18000÷60
X= $300
B. Analyze the problem below and answer the questions that follow. a monthly salary of Php 18.500 Complete the table below which shows the deductions on Bianca has her payslip Name Bianca Ramos Assistant For the month of September 2020 Basic Salary 18,500 00 Position Financial Allowances Total Earnings 18.500 00 DEDUCTIONS Description SOCIAL SECURITY SYSTEM MEDICARE (PHILHEALTH) PAGIBIG (FUND) BIR (WITHHOLDING TAX) Amount of Deduction (11) (12) (13) (14). Total Deductions (15) NET PAY (16)
The completed table showing Bianca Ramos's tax deduction and NET PAY
is presented as follows;
SOCIAL SECURITY SYSTEM = Php 1,147
MEDICARE (PHILHEALTH) = Php 268.25
PAGIBIG (FUND) = Php 370
BIR (WITHHOLDING TAX) = Php 5,509.19
Total deductions = Php 7,294.44
NET PAY = Php 11,205.56
Reasons:
Based on online search, the tax rate for the items on the table are as follows;
SOCIAL SECURITY SYSTEM = 6.20% of earnings
MEDICARE (PHILHEALTH) = 1.45% of earnings
PAGIBID (FUND) = 2% of salary
BIR (WITHOLDING TAX) = P1,342.47 + 32% over P5,479
Bianca Ramos's basic salary = 18,500.00
Which gives the deduction amount as follows;
SOCIAL SECURITY SYSTEM = 0.062 × 18,500.00 = 1,147
MEDICARE (PHILHEALTH) = 0.0145 × 18,500.00 = 268.25
PAGIBIG (FUND) = 0.02 × 18,500.00 = 370
BIR (WITHHOLDING TAX) = 1,342.47 + 0.32×(18,500 - 5,479) = 5,509.19
Total deductions = 1,147 + 268.25 + 370 + 5,509.19 = 7,294.44
NET PAY = 18,500 - 7,294.44 = 11,205.56
Her net pay = Php 11,205.56
Learn more about tax systems here:
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pls help it is math for 7th grade.
Answer:
36.8 *36 8/10 of 36 4/5
Step-by-step explanation:
2/5x(-1/2)= -2/10
37+(-2/10)=36.8
Which quadrilateral is a trapezoid?
Answer:
Hey mate!Step-by-step explanation:
A trapezoid is a quadrilateral with exactly one pair of parallel sides. (There may be some confusion about this word depending on which country you're in. In India and Britain, they say trapezium ; in America, trapezium usually means a quadrilateral with no parallel sides.)
pls mark me as brainliest!!135% as a fraction or a mixed number fully simplified please 50 POINTS + BRAINILEST
Answer:
27/20
Step-by-step explanation:
135% = 135/100 = (27/20 × 5) = 27/20 = 1 7/20 I think
Of the 600 sixth graders at Melville Middle school, 80% want more field trips. How
Many students want more field trips?
Multiply total students by the percentage:
600 x 80% = 600 x 0.80 = 480
480 students want more field trips.
Adelita, Elena, Betina, and Bianca each work as a doctor, lawyer, teacher, or banker. From these clues, decide who is the doctor.
Answer: betina or adelita
Step-by-step explanation: hope it helps
hii
l have some dought
Answer:
I'm sorry what?
2. Which expression is equivalent to 3ly-6)?
A. 3y - 6
B. 2y - 18+y
c. 5y + 18-2y
D.2y-18-5y
Answer:
pyfoydoye9ye9ye9ts8ts9teo5e
3/4+x=2x−x+_
Make equation have infinite solutions in the blank
Answer:
3/4
Step-by-step explanation:
3/4+x=2x−x+_
2x-x is x
So the equation is now
3/4+x=x+_
So to have infinite solutions, we will have to get both of the sides the same value
Since there is already an x on both sides we don't have to worry about it
Now there isn't a 3/4 on one side so we can just add that to the blank side, thus creating an infinite solution equation
Hope this helps!
Market for flat-screen TVs:
Demand: Qd=2,600-5P
Supply: Qs=-1000 +10P
What would be the amount of shortage if a price ceiling is imposed at price of $205?
Your Answer: 1100
Answer
Answer:
525
Step-by-step explanation:
The demand at a price of 205 is ...
Qd = 2600 -5(205) = 2600 -1025 = 1575
The supply at a price of 205 is ...
Qs = -1000 +10(205) = 2050 -1000 = 1050
The demand exceeds the supply by ...
1575 -1050 = 525
The shortage is 525 units.
Which choice is equivalent to the product below?
14.6
O A. 125
B. 6-28
C. 2-21
D. 28
Answer:
2√21
Step-by-step explanation:
1) Simplify.
√84
2) Simplify √84 to 2√21.
2√21
The radius of a circle is 19 miles. What is the circle's circumference?
Answer:
119.32 miles
Step-by-step explanation:
radius=19 miles
circumference =2×3.14×19 miles
The circle's circumference 119.32 miles
What is circle's circumference ?Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it. If we open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in units, such as cm or unit m.
GIven that, radius of a circle is 19 miles
we know , circumference of circle = [tex]2\pi r[/tex]
= [tex]2\pi \cdot19[/tex]
= 38 (3.14)
= 119.32 miles
Hence, circle's circumference 119.32 miles
To learn more about the circle's circumference here:
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The polygons below are similar. Find the value of y
Answer:
y = 21
Step-by-step explanation:
Devaughn is 15 years younger than sydney. the sun of their ages is 63. what is sydney’s age?
Answer:
39
Step-by-step explanation:
d = s - 15
d + s = 63
Replace d with s - 15
s - 15 + s = 63
2s -15 = 63
2s = 78
s = 39
Find the value for x.
Answer:
4x + 22
Step-by-step explanation:
Little help please...?
Answer: The answer is B
Step-by-step explanation:
It's B because every pound is $14 and for C it looks similar, until you add another pound and then option B becomes $28 per 2 pounds and option C becomes $25 per 2 pounds. Therefore, the answer is B
Please help me answer
Answer: Second Choice
Step-by-step explanation:
You earn $8.45 an hour. How much would you make for a 40-hour week, before taxes are withheld?
giving crown
Answer:
278.5
Step-by-step explanation:
Addie bought 9 candy bars and ate 1/2 of them. Frankie bought 6 candy bars and ate 2/3 of them
Answer:
addie at 4.5 candie bars and frankie had 4
Approximately what portion of the box is shaded blue?
A.1/3
B.1/10
C. 1/6
3. Solve the formula A = 1/2 (b1+ b2))h for h. Show your work.
[tex]A = \dfrac 12 (b_1 + b_2)h\\\\\implies 2A = (b_1+b_2) h\\\\\implies h =\dfrac{2A}{b_1+b_2}[/tex]
r less than one-eighth
Answer:
what did you mean
Step-by-step explanation:
is not a question
108 is what percent of 72
108/72 x 100% = 150%