q1 ).The number of white corpuscles on a slide has a Poisson distribution with mean 4.5.
a. Find the most likely number of white corpuscles om a slide.
b. Calculate correct to three decima places the probability of obtaining this number
c. If such two slides are prepared, what is the probability, correct to three decimals
places of obtaining at least two white corpuscles in total on the two slides?
q2). At a Supermarket 45% of customers pay by credit card. Find the probability that
in a randomly selected sample of fifteen customers.
a. Exactly four pay by credit card
b. More than ten pay by cash
(give answers to 3 decimal places
Answers
The most likely number of white corpuscles om a slide is 4 ,the probability of obtaining this number 4 is 0.190 , probability of obtaining at least two white corpuscles in total on the two slides is 0.999.
Attending to the first question
What is Poison Distribution ?Poisson Distribution is used for an independent event to find its probability in a fixed interval of time .
Let X be the number of white corpuscles on a slide, then X~Pois(4.5)
a) We have to find the most likely number of white corpuscles on a slide , which means expected value of Poise(4.5)
The expected value of Poisson distribution with mean λ is equal to λ.
Therefore the expected value is 4.5.
the number of corpuscles cannot be non-integer,
To find the most likely number in one experiment,
determine it between 4 and 5.
In the common case P(X=k) when X~Poise(λ) is equal to \(\frac {\lambda^{k}} {k!}}e^{-\lambda}\)
,\(\rm e^{-\lambda}\) is a constant in terms of k
so the point is to find out what is greater : \({\frac {4.5^4} {4!}}\) or \({\frac {4.5^5} {5!}}\)
\({\frac {4.5^5} {5!}}={\frac {4.5^4} {4!}} * {\frac {4.5} 5}\)
\({\frac {4.5} 5} < 1\)
So, \({\frac {4.5^4} {4!}}\) is greater
So, the most likely number of white corpuscles om a slide is 4.
b) the probability of obtaining this number 4 is
P(X = 4)
= \({\frac {4.5^4} {4!}}e^{-4.5}=0.190\)
c) Let Y be the total number of corpuscles on two screens.
\(Y=X{\scriptscriptstyle 1}+X{\scriptscriptstyle 2}Y=X1+X2\) ,
where \(X{\scriptscriptstyle 1}, X{\scriptscriptstyle 2}\) - number of corpuscles on the first and second slide respectively.
Then Y = Poise(4.5 + 4.5) = Poise(9)
the probability, correct to three decimals places of obtaining at least two white corpuscles in total on the two slides
The goal is to find P(Y ≥ 2)
Therefore the probability less than 2 will be subtracted from the total probability i.e. 1
P(Y ≥ 2 ) = 1 - P (Y=0) - P(Y=1)
= \(1-{\frac {9^0} {0!}}e^{-9}-{\frac {9^1} {1!}}e^{-9}=1-10e^{-9}=0.999\)
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Related Questions
Bryan invests $6500 in two different accounts. The first account paid 11 %, the second account paid 7 % in interest. At the end of the first year he had earned $519 in interest. How much was in each account?
$ at 11 %
$ at 7 %
Answers
Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.
The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).
According to the problem, the total interest earned after one year is $519. So we can set up the equation:
0.11x + 0.07(6500 - x) = 519
Simplifying the equation:
0.11x + 455 - 0.07x = 519
0.04x + 455 = 519
0.04x = 64
x = 64 / 0.04
x = 1600
Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
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4325 as a product of its prime factors
Answers
Answer:
5*5*173=4325
Step-by-step explanation:
please mark brainiest hope it works out for you
Answer:
5²×173
Step-by-step explanation:
4325 as a product of its prime factors
5²×173
Find the value of 3a when a = -4.
(b)- 7
(d) -12
(a) 7
(c) 12
Answers
Answer:
(d) -12
Step-by-step explanation:
3a = _____
a = -4
3(-4) = ___
3(-4) = -12
The answer is (d) -12
Please help!!
Thankyou!!
Answers
The scale factor is: 1.8
because of :
\(\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8\)
At a sale this week, a suit is being sold for $217. This is a 38% discount from the original price. What is the original price?
Answers
Answer:
List price (original price) = $350
Discount amount ($ saved) = $133
Step-by-step explanation:
The list price is the sale price ($217) divided by the difference of 1 minus the result of the discount (38%) divided by 100.
help me plis What is the exact measurement of the line segment? A. B. C. D.
Answers
Answer: where is the line segment
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Which point is a solution of x^2 + y^2 > 49 and y ≤ –x^2 – 4 ?
A. (–8, –1)
B. (–3, 1)
C. (1, –9)
D. (0, –6)
Answers
Answer:
C. 1, -9
Step-by-step explanation:
I just put it on desmos
(1, –9) is a solution of \(x^{2} +y^{2} > 49\), \(y\) ≤ \(-x^{2} -4\).
What is inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Given inequalities
\(x^{2} +y^{2} > 49\)..............(1)
\(y\) ≤ \(-x^{2} -4\)...............(2)
Option (A)
(–8, –1)
Substitute x = -8, y = -1 in equation 1
\(x^{2} +y^{2} > 49\)
⇒ \((-8)^{2}+(-1)^{2} > 49\)
L.H.S = 65
R.H.S = 49
65 > 49
It is true
Substitute x = -8, y = -1 in equation 2
\(y\) ≤ \(-x^{2} -4\)
-1 ≤ \(-(-8)^{2} -4\)
L.H.S = -1
R.H.S = -68
-1 ≤ -68
It is false.
It is not suitable solution.
Option (B)
(–3, 1)
Substitute x = -3, y = 1 in equation 1
\(x^{2} +y^{2} > 49\)
⇒ \((-3)^{2}+(1)^{2} > 49\)
L.H.S = 10
R.H.S = 49
10 > 49
It is false
Substitute x = -3, y = 1 in equation 2
\(y\) ≤ \(-x^{2} -4\)
1 ≤ \(-(-3)^{2} -4\)
L.H.S = 1
R.H.S = -13
1 ≤ -13
It is false.
It is not suitable solution.
Option (C)
(1, –9)
Substitute x = 1, y = -9 in equation 1
\(x^{2} +y^{2} > 49\)
⇒ \(1^{2}+(-9)^{2} > 49\)
L.H.S = 82
R.H.S = 49
82 > 49
It is true
Substitute x = 1, y = -9 in equation 2
\(y\) ≤ \(-x^{2} -4\)
-9 ≤ \((-1)^{2} -4\)
L.H.S = -9
R.H.S = -5
-9 ≤ -5
It is true.
Hence, (1, –9) is a solution of \(x^{2} +y^{2} > 49\), \(y\) ≤ \(-x^{2} -4\).
Option (D)
(0, –6)
Substitute x = 0, y = -6 in equation 1
\(x^{2} +y^{2} > 49\)
⇒ \(0^{2}+(-6)^{2} > 49\)
L.H.S = 36
R.H.S = 49
36 > 49
It is false
Substitute x = 0, y = -6 in equation 2
\(y\) ≤ \(-x^{2} -4\)
-6 ≤ \(-(0)^{2} -4\)
L.H.S = -4
R.H.S = -6
-4 ≤ -6
It is false.
It is not suitable solution.
Hence, (1, –9) is a solution of \(x^{2} +y^{2} > 49\), \(y\) ≤ \(-x^{2} -4\).
Option C is correct.
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ANSWER ALL QUESTIONS
1. In a class of 28 pupils, 13 have pencils, 9 have erasers and 9 have neither pencils nor erasers. How
many pupils have both pencils and erasers?
2. A universal set, U consists of prime numbers with P and Q as subsets of U. If P and Q are given by
P = {n: 3(n + 1) = 2(n + 10)}, and Q = {n: 7<n<31}, list the elements of P n Q.
Answers
1. 3
29-9=19
13+9=22
22-19=3
I don't know number 2, sorry.
Prove the Converse of the Pythagorean Theorem
In this activity, you will prove and apply the converse of the Pythagorean theorem. Recall that the
converse states that if the square of the length of the longest side of a triangle is equal to the sum of
the squares of the other two sides, then the triangle is a right triangle.
Open the GeoGebra activity to complete each step below. For help, watch these short videos about
using GeoGebra to measure and create points, lines, and anglese.
Question 1
Part A
Draw AABC with vertices at A(1,6), B(1, 1) and C(5,1). In this triangle, AB²+ BC² = AC².
Next, use the GeoGebra tools to draw ADEF such that AB = DE, m/E
Paste a picture of your drawing in the answer box.
= 90°, and EF
BC.
B I U X² X2 15px
AVA
E E g = = 三 四 V 田
=
Answers
The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.
To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.
AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5
BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4
AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)
Now, let's check if AB^2 + BC^2 = AC^2:
AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41
AC^2 = (2sqrt(10))^2 = 4(10) = 40
Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.
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A circle has a diameter of 10 centimeters.
What is the best approximation of its area?
Use 3.14 to approximate for π.
15.7 cm²
31.4 cm²
78.5 cm²
314 cm²
Answers
Answer:
78.5 (please put brainliest)
Step-by-step explanation:
r = diameter / 2 = 5
area = π * r^2 = 25 * 3.14 = 78.5
Answer:
78.5 m^2
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answers
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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Beron wants to buy a new sound system for $145. He already has $65. He receives $20 for
each lawn that he cuts. Write an equation for how many lawns he must cut in order to have
enough money.
What is the variable?
Answers
Answer:
he would need to cut 4 lawns
Step-by-step explanation:
if you take 145-65 if would need 80 left. if you take 80 divided by 20 you get 4.
. do you need to use sd to estimate the sd of the population? no, we're given the sd of the population, we don't need to estimate it. yes, because with only 20 observations the sample sd is not a great estimate of the true population sd.
Answers
The measure of the spread of scores within a set of data is termed as standard deviation. Usually, we are interested in the standard deviation of a population. since, we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation.
When to use the sample or population standard deviation ?
Population standard deviation is of great intrest because our population contains all the values we are interested in. Therefore, we would normally calculate the population standard deviation In two cases first when we have the entire population or second we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize our findings to the population. but, in statistics, a sample is presented from which we wish to estimate (generalize to) a population, and the standard deviation is no exception to this.
Thus it can be concluded that, if we have all is a sample, but we wish to make a statement about the population standard deviation from which the sample is drawn, we need to use the sample standard deviation. There a Confusion can often arise as to which standard deviation to use due to the name "sample" standard deviation incorrectly being interpreted and not the estimate of the population standard deviation based on the sample.
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Chris is making pancakes. The recipe makes four servings. the recipe calls for 3/4 cup of flour. He wants to make enough for six servings. How many cups of flour does he need?
Answers
Answer:
Step-by-step explanation:
a little over one cup
1.2500
so like 1 1/2
7th grade math need help ASAP will mark brainlist
Answers
Answer:
615
Step-by-step explanation:
14x14= 196,
3.14x196= 615
Answer:
area of the circle= pi×radius²
area of the circle=3.14×14²
area of the circle=3.14×196
area of the circle=615.44m²
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.
Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
Answers
Answer:
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.
Step-by-step explanation:
hope its right
20 Per Question, Algebra 2, Thanks :)
Answers
The answer to the expression is (x+3)/(x-1)
What is a quadratic expression?You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0
The given expressions are
(x² - 3x - 18) / (x²- 7x +6
(x²-6x +3x +19) / (x²-x -6x +6)
This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}
⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]
This means that [(x+3)(x-6)] / [(x-6)(x-1)]
Dividing by (x-6) to have
Therefore the value of the expression is (x+3)/(x-1)
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The 10 passengers on a small airplane have paid a total of $1,580 for the flight.
If an economy ticket cost $135 and a first-class ticket costs $250 , how many economy tickets were bought?
Answers
Answer:
8 people bought economy and 2 bought first class
Step-by-step explanation:
there are 10 person and total is 1580 so 250+ 9(135)=1460 which is wrong so we gonna try adding 2(250) and 8(135) which got us 1580
To find the distance AB across a river, a distance BC=290 is laid off on one side of the river. It is found that B=117degrees and C=24degrees. Find AB.
Answers
The value of distance AB is 187.5 units
What is sine rule?Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other.
sine rule can be expressed as;
a/sinA = b/sinB = c/sinC
The opposite side to angle A is BC
the opposite side to angle C is AB
therefore;
A = 180-( 117 +24)
A = 180- 141
A = 39°
290/sin 39 = x/ sin24
xsin39 = 290 × sin24
0.629x = 117.95
x = 117.95/0.629
x = 187.5
therefore the distance AB is 187.5
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Please look at the photo for the question. Thank you!
Answers
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
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A percentage is another way to write a _________________.
Answers
Answer:
Ratio, Decimal or Fraction
Step-by-step explanation:
Answer:
it's another way to write a fraction:)
Write an equation.
A line that has a slope of 4 and goes through the point (3,7).
Answers
Answer:
y=4x+c now put (-3,7) into the equation to find the y intercept. 7=4×−3+c. 7=−12+c. c=19.
Step-by-step explanation:
y=mx++c is the general equation with m as the slope.
y is inversely proportional to the square of x
y = 8 when x = 3.5
Answers
Step-by-step explanation:
y = k/x^2
substitute 8 and 3.5 to get the value of k.
k= 98
are u just looking for k? or the question is missing
The hexagonal prism below has a height of 9 units and a volume of 216.9 units. Find the area of one of its bases.
Answers
Answer:
The answer is 24.1 unit²
Step-by-step explanation:
Volume of prisms=cross sectional area×h
cross sectional area=Volume of prisms/height
A=216.9/9
A=24.1 unit²
what is the ordered pair for -5, 6
Answers
The ordered pair for -5, 6 is (-5, 6)
How to determine the ordered pair for -5, 6?The expression is given as:
-5, 6
Ordered pairs are often represented by the parenthesis i.e. ( , )
Where the variables x and y are in the parenthesis
So, the proper representation of an ordered pair is
(x, y)
Substitute -5, 6 for x and y in (x, y)
(-5, 6)
Hence, the ordered pair for -5, 6 is (-5, 6)
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Help plzzzzzzz!! Thanks
Answers
Answer:
m > 1
Step-by-step explanation:
m+6 > 7
m > 7-6
m > 1
Jeff and Eric roommates and enjoy talking about sports. They mainly discuss their favorite professional soccer teams. Jeff enjoys European soccer whereas Eric prefers American teams. Outside soccer they do not discuss much. Their lack of range of talking to it fall into which category?
Answers
0°
EXPLANATION:In each figure below find m∠1 and m∠2, if a||b. Show your work with statements.
====================================
If you have any questions feel free to ask me^^
Have a nice and great day!
Cayler#PilipinasAngBayanKo
0°
Sana Maka help ako tnx
The owner of Animal Lovers Pet Shop just got a delivery of 315 bags of cat food and you need to put the bags on 9 shelves. How many bags will be put on each shelf? Explain the long division steps you used to find your answer
Answers
Answer:
Sample Response: Divide 9 into 31, multiply 9 and 30 to get 270, subtract 270 from 315 and get 45. Divide 9 into 45, multiply 9 and 5 and get 45, subtract 45 from 45 and get 0. The answer is 35.
Step-by-step explanation:
heres the sample response <3
Divide 9 into 31, multiply 9 and 30 to get 270, subtract 270 from 315 and get 45. Divide 9 into 45, multiply 9 and 5 and get 45, subtract 45 from 45 and get 0. The answer is 35.
Step-by-step explanation:
i did the test on edge
I need help to find the slope of the line the answers are
A: 4
B:-1/4
C:-4
D:1/4
Answers
Answer:
-1/4
Step-by-step explanation:
Take two points on the line
(-4,-1) and (0,-2)
Using the slope formula
m = (y2-y1)/(x2-x1)
= ( -2 - -1)/( 0 - -4)
= (-2+1)/ ( 0+4)
-1/4
Why did the troll give us the clues
We had no money in our pockets
He was nice
So we can get confused
Answers
Answer:
lol
Step-by-step explanation:
im laughing in class