The diameter of a particle of contamination (in micrometers) is modeled with the probability density function for . Determine the following (round all of your answers to 3 decimal places): (a) Enter your answer in accordance to the item a) of the question statement .972 (b) Enter your answer in accordance to the item b) of the question statement .0123 (c) Enter your answer in accordance to the item c) of the question statement .028 (d) Enter your answer in accordance to the item d) of the question statement .972 (e) Determine such that . Enter your answer in accordance to the item e) of the question statement
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a [tex]P(X < 5) = 0.960[/tex]
b [tex]P(X > 8) = 0.016[/tex]
c [tex]P(6 < x < 10) = 0.018 [/tex]
d [tex] P(X < 6 or X > 10 ) = 0.982 [/tex]
e [tex]X = 2[/tex]
Step-by-step explanation:
From the question we are told that
The probability density function is [tex]f(x) = \frac{2}{x^3}[/tex] for x > 1
Considering question a
[tex]P(x < 5) = \int\limits^5_1 {\frac{2}{x^3} } \, dx[/tex]
=> [tex]P(X < 5) = [-\frac{1}{x^2} ]| \left \ 5} \atop {1}} \right.[/tex]
=>[tex]P(X < 5) = - \frac{1}{25} + \frac{1}{1^2}[/tex]
=> [tex]P(X < 5) = 0.960[/tex]
Considering question b
[tex]P(x > 8) =1 - \int\limits^6_1 {\frac{2}{x^3} } \, dx[/tex]
=> [tex]P(X > 8) =1- [-\frac{1}{x^2} ]| \left \ 8} \atop {1}} \right.[/tex]
=>[tex]P(X > 8) = 1 - [- \frac{1}{64} + \frac{1}{1^2}][/tex]
=>[tex]P(X > 8) = 0.016[/tex]
Considering question c
[tex]P(6 < x < 10) = \int\limits^{10}_{6} {\frac{2}{x^3} } \, dx[/tex]
=> [tex]P(6 < x < 10) = [-\frac{1}{x^2} ]| \left \ 10} \atop {6}} \right.[/tex]
=>[tex]P(6 < x < 10) = [- \frac{1}{100} + \frac{1}{36}][/tex]
=>[tex]P(6 < x < 10) = 0.018 [/tex]
Considering question d
[tex] P(X < 6 or X > 10 ) = 1 - P(6 < x < 10) = 1 - \int\limits^{10}_{6} {\frac{2}{x^3} } \, dx[/tex]
=> [tex] P(X < 6 or X > 10 ) =1- [-\frac{1}{x^2} ]| \left \ 10} \atop {6}} \right.[/tex]
=> [tex] P(X < 6 or X > 10 ) =1- [- \frac{1}{100} + \frac{1}{36}][/tex] [/tex]
=> [tex] P(X < 6 or X > 10 ) = 0.982 [/tex]
Considering question e
[tex]P(X < x ) = \int\limits^x_1 {\frac{2}{x^3} } \, dx = 0.75[/tex]
[tex]P(X < x ) = [- \frac{1}{x^2} ]| \left \ x } \atop {1}} \right. = 0.75[/tex]
[tex]P(X < x ) = - \frac{1}{x^2} - [- \frac{1}{1^2} ]= 0.75[/tex]
[tex]P(X < x ) = - \frac{1}{x^2} + 1 = 0.75[/tex]
[tex] - \frac{1}{x^2} = -0.25[/tex]
[tex]X = 2[/tex]
Related Questions
How many three-digit even numbers are possible if the leftmost digit cannot be zero?
Answers
Answer:
450
Step-by-step explanation:
There are 900 3-digit numbers in the range 100–999. Of those, exactly half are even numbers.
There are 450 even three-digit numbers.
Mei tapes two pieces of paper together that each measure 30.45
centimeters. They then cut off 10.42 centimeters.
Answers
Step-by-step explanation: 30.45 x 2 (cuz theres 2 pieces of paper) = 60.9
60.9 - 10.42 = 50.48
Solve the formula for the specified variable v=ypu for y
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Step-by-step explanation:
[tex]v = ypu \\ v = y \times p \times u \\ dividing \: both \: sides \: by \: p \times u \\ we \: get \\ \frac{v}{p \times u} = \frac{y \times p \times u}{p \times u} \\ by \: simpliphying \\ \frac{v}{pu} = y \\ hence \\ y = \frac{v}{pu} [/tex]
Reword the expression using the distributive property. Explain your answer or show your work. 6(x-4)
Answers
you have to multiple the 6 by the number in the parentheses
The lines represented by the equations y = -X – 3 and
5y + 5x = -15 are
neither parallel nor perpendicular
Submit Answer
the same line
parallel
perpendicular
What is the answer?
Answers
Answer:
The lines represented by the equations y = -X – 3 and
5y + 5x = -15
Step-by-step explanation:
neither are parallel nor perpendicular
Submit Answer
the same line
parallel
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Enya walked 2km 309m from school to the store. Then, she walked from the store to her home. If she walked a total of 5km, how far was it from the store to her home?
Answers
Answer:
2 km 691 m
Step-by-step explanation:
5 km - 2 km 309 m
= 5000 m - 2309 m
= 2691 m
= 2 km 691 m
Pleasee helpp
Write a^3 •a^4 without the exponents
Answers
Answer:
a x a x a x a x a x a x a
Step-by-step explanation:
a^3 is three a's being multiplied by each other. a^4 is four a's being multiplied by each other
thanks again for the help everyone
Answers
Answer:
[tex]\sf{ (z-7)(z-2)}[/tex]
explanation:
[tex]\sf z^2 - 9z + 14[/tex]
break down, (7 * 2) = 14
[tex]\sf z^2 - 7z - 2z + 14[/tex]
collect in parenthesis
[tex]\sf z ( z - 7 ) -2(z - 7)[/tex]
collect in groups
[tex]\sf{ (z-7)(z-2)}[/tex]
Can someone help me plzz I need the answer plzzz
Answers
Answer:
translation of 8 units to the left
Step-by-step explanation:
the x coordinate change by -8 so that is 8 units to the left
Please help with this problem.
Answers
Step-by-step explanation:
you should have measured the lengths of the sides and added that information here to the picture.
because we here cannot measure this from a picture that is inclined and has no size scale.
I can give you a hint how to get the angles, when you have all 3 sides :
start with the extended Pythagoras for non right-angled triangles:
c² = a² + b² - 2ab×cos(C)
with c being the side opposite of the angle you are aiming for.
then
2ab×cos(C) = a² + b² - c²
cos(C) = (a² + b² - c²)/(2ab)
for example, to get the angle at T, its opposite side is SE.
cos(T) = (ST² + ET² - SE²)/(2×ST×ET)
you can do the same thing for all 3 angles (you need to always pay attention to what sides you have to use in what combination for the angle).
or you can switch after getting the first angle to the laser of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides and the disposing angles are always opposite of each other.
for your triangle that looks like
ET/sin(S) = ST/sin(E) = SE/sin(T)
from there (once you have one angle via the Pythagoras approach) you get all other angles.
Determine if the three lengths can be the measures of the sides of a triangle.
20 ft, 16 ft, 38 ft
Answers
Answer:
No
Step-by-step explanation:
No because if you have 38 on the bottom, 20 and 16 do not add up to 39 or more.
Help please and show work
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Answer: i think that jacks volume would be 24 i think jills is 882 i believe but i may be wrong
Step-by-step explanation:
If the millers spend $1400 on housing, then what is their total budget?
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Answer:
need more detail
Step-by-step explanation:
PLZZZZZ HELP ME I WILL MAKE YOU BRAINLIEST ANWER PLZZZZZ THANKYOU!!!!!!
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Answer:
Step-by-step explanation:
For the first one here is the answer:
Given.
Transitive property of equality- this is becasue the rule is if A=b and B=c then A=c. IN this situation its saying that a is parrelel to b and b is parralel to c therfore a is parrelel to c.
line A and d cross over at 90 degree angles making them perpendicular. -There should be a rule for this and if there is then write that rule down
Second answer:
Given.
Definition of a supplementary angle.
Definition of a supplementary angle
Definition of supplementary angles.
Alternate Exterior Angles Theorem
C=D
-Srry for the definiton of supplementary angles thing but thats the best answer for those.
Hope i helped
49. Find the m
a. 60°
c. 300
b = 13
b. 75°
d. 73°
47
B.
c=17
Answers
Answer:
C. 30°
Step-by-step explanation:
thank you for the points make me brainliest please.
if i use elmer's glue for my fake nails will they stay
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Answer: Yes maybe for about 3-4 days then they will fall off
Step-by-step explanation: my little sis did it
Find the degree of this polynomial.
-7d
Answers
Hey there!
The degree is the exponent.
Let me explain with examples.
Suppose we have a polynomial 4d.
Its degree is 1 (it's a first degree polynomial)
What is the degree of the polynomial 4d²?
That's right, this is a second-degree polynomial.
And so on...
Let's look at our polynomial.
We have
-7d.
What is the degree of the polynomial?
That's right, 1.
Hence, -7d is a
[tex]\boxed{\boxed{\bold{first-degree~polynomial}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
[tex]\bold{Don't~give~up...}[/tex]
Do this word document and just add it into the question please it's urgent
Answers
• State whether the figure appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry and state their number.
•State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry.
yes,oneyes, 5NoNoyes ,8 ,45°nonoyes ,one ,180°2x+3y=11
10x+5y=20
Simple equation
Answers
Answer:
2x+3y=11. x=4 and y=1.
10x+5y=20. x=1 and y=2.
Use a graphing calculator or other technology to answer the question.
Which quadratic regression equation best fits the data set?
yˆ=1568.064x2−115.264x+2.608
yˆ=2.608x2−115.264x+1568.064
yˆ=2.608x2+115.264x+1568.064
yˆ=2.608x2+112.909x+1568.064
x y
15 423
17 398
19 308
20 255
21 297
25 365
29 401
Answers
Answer:
yˆ=2.608x2−115.265x+1568.065
Step-by-step explanation:
I took the test.
The quadratic regression equation best fits the data set is 2.608x² -155.264x + 1568.064 option second is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
Let's suppose the quadratic regression equation best fits the data set:
y = Ax² + Bx + C
From the data set, we can calculate the value of the A, B and C:
A = 2.608
B = -155.264
C = 1568.064
y = 2.608x² -155.264x + 1568.064
Thus, the quadratic regression equation best fits the data set is 2.608x² -155.264x + 1568.064 option second is correct.
Learn more about the line of best fit here:
brainly.com/question/14279419
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3/8 + 1/8 - 2/7 + 1/4 equals
Answers
Answer:
Step-by-step explanation: 37/56
the price of gasoline rose from $3.59 to $3.71 in one week. By what percentage did the gas price rise?
Answers
Directions For the following set of triangles, fill in the blanks with the correct measure. Enter your answers as numbers only. Tip: Label all parts in the diagram first. ДАВС вы дXYZ A Х 5 3 9.01 B 37 CZ 4. Y
Answers
Answer:
Step-by-step explanation:
First, you have to find the degress for m<A.
m<A+ 90+37=180
m<A+ 127=180
then you subtract 127 from both sides.
So, m<A= 53 degress, We already know that m<B is 90,
So let's solve for m<C.
m<C + 53+ 90= 180
m<C+ 143=180
m<C= 37 degress.
Since the triangles are both the same and has the same length and are congruent polygons
m<X=53 degress, m<Y= 90 degress, and m<Z= 37 degress
Rashaad owns a small business selling used books. He knows that in the last week 13 customers paid cash, 50 customers used a debit card, and 53 customers used a credit card. Based on these results, express the probability that the next customer will pay with a debit card as a fraction in simplest form.
Answers
Answer:
25/58
Step-by-step explanation: Ok, your step one should be to add all the previous customer values together to see what the total pool of values is. 13+50+53=116, this becomes your denominator. Then, you see that out of these 116 customers in the past week, 50 used a debit card. So based on this data, we can assume that 50 out of every 116 customers will use a debit card. The fraction is thus 50/116. Then it needs to be simplified. Divide the numerator and denominator by 2, and BAM 25/58 is your final answer.
Probability that next customer will pay with debit card is (25 / 58) (simplest fraction form).
What is probability?" Probability is defined as the ratio of number of favourable outcomes to the total number of outcomes for a given event."
Formula used
Probability = [tex]\frac{Number of favourable outcomes}{Total number of outcomes}[/tex]
According to the question,
Given,
Number of customers paid through cash = 13
Number of customers paid through debit card = 50
Number of customers paid through credit card = 53
Total number of customers = 13 + 50 + 53
= 116
Substitute the value in the formula we get,
Required probability = (50 / 116)
= (25 / 58) (simplest fraction form)
Hence, probability that next customer will pay with debit card is (25 / 58) (simplest fraction form).
Learn more about probability here
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Pls help me
Question 4 Part C (3 points): Based on the composite function you created in part A, determine how many trees Carlos can expect to have after 22 days. Click the included image to refer back to Part A as needed.
The composite function is 20d-(80) = 67
A.86 trees in 22 days
B.440 trees in 22 days
C.1340 trees in 22 days
D.1360 trees in 22 days
Answers
Answer:
C) 1340 days
Step-by-step explanation:
The composite function you have given is incorrect.
The composite function for this question is:
t(d) = 60d + 20
(as I have proven in a previous question)
Substitute d = 22 into the function:
t(22) = 60(22) + 20
= 1320 + 20
= 1340 days
determine the rate of change from the two points (3,4)(5,8)
Answers
Answer: 2
Step-by-step explanation:
8 - 4 = 4
5 - 3 = 2
4/2 = 2
Answer:
2Step-by-step explanation:
the rate of change or slope from the given two points is rise over run.
(3, 4) (5, 8)
slope = (y2 - y1) / (x2 - x1)
= (8 - 4) / (5 - 3)
= 4 / 2
= 2
Х
If two lines do not intersect, then
they are parallel.
Answers
Please answer the following question:
A pen costs $2.09. It costs $0.45 less than a marker. Ken paid for one pen and one marker with a five-dollar bill. What is his change? If you can answer this thank you, you may use a tape diagram with caculations to determine his change.
Answers
Answer:
His change would be $1.27 because he paid $3.73 for the pen and marker.
Step-by-step explanation:
Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).
a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcherâs contention.
b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience a population standard deviation of Ï = $1600 may be assumed. What is the p-value?
c. At α = .05, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.
Answers
Answer and Step-by-step explanation:
Solution:
Develop hypothesis:
H₀ : µ ≥ 1056
H₁ < 1056
Given:
n = 400
ẋ = 910
∂ = 1600
a = 0.05
The sampling distribution of sample means µ and standard deviation ∂ / √n.
Z = ẋ-µ /∂ / √n.
= 910 – 1056 / 1600 /√400.
= - 1.83
Probability: p = p(z< -1.83) = 0.033
At a = 0.05
If p value is smaller than significance level a, then hypothesis is rejected.
P < 0.05 its means H0 rejected.
Hypothesis test using critical value:
The critical value corresponding to probability of 0.05:
Z = -1.645
The rejection region, then contains all values smaller than -1.645.
If value of test statistics is within the rejection region, then null hypothesis rejected.
-1.83 < -1.645
Rejected H
Can someone please help me with this.
Suppose that hothotdogs came in packs of 6 and buns came in packs of 9. Deon bought the same number of hotdogs as buns. It was the least number for which this is possible.
How many hotdogs did he buy?
How many packs of hotdogs did he buy?
How many packs of buns did he buy?
Answers
Answer:
54
Step-by-step explanation:
First we multiply 6 x 9 to get 54 so that's all.