Answer:
[tex]\begin{array}{cc}X&P(X)\\0&0\\1&0.3333\\2&0.6667\end{array}[/tex]
E(X)= 1.667
Step-by-step explanation:
The question asks for the probability distribution and the expected value of X.
The possible values for the number of defective cameras (X) are 0, 1 or 2.
The probability distribution for X is:
[tex]P(X=0)=0[/tex]
Since there is only one camera in the box that is not defective, it is impossible for no camera to be defective when picking 2.
[tex]P(X=1)=\frac{1}{6}*\frac{5}{5}+\frac{5}{6}*\frac{1}{5}\\ P(X=1)=0.3333[/tex]
[tex]P(X=2)=\frac{5}{6}*\frac{4}{5}\\ P(X=2) =0.6667[/tex]
The probability distribution is:
[tex]\begin{array}{cc}X&P(X)\\0&0\\1&0.3333\\2&0.6667\end{array}[/tex]
The expected value of X is:
[tex]E(X) = 0.3333*1+0.6667*2\\E(X) = 1.667[/tex]
The expected value is 1.667 defective cameras.
Clara did not want to tell Carl how old she was. All she said was that every year on her birthday, her Mom put as many coins in her money box as how old she turned that day. Carl roughly estimated the number of coins in the box as not less than 110 but not more than 130 coins. How old is Clara?
The volume of a cantaloupe is approximated by Upper V equals four thirds pi font size decreased by 5 r cubed . The radius is growing at the rate of 0.5 cm divided by week, at a time when the radius is 6.4 cm. How fast is the volume changing at that moment?
Answer:
308.67 cm ^ 3 / week
Step-by-step explanation:
A cantaloupe is approximately a sphere, therefore its approximate volume would be:
V = (4/3) * pi * (r ^ 3)
They tell us that dr / dt 0.5 cm / week and the radius is 6.4 cm
if we derive the formula from the volume we are left with:
dV / dt = (4/3) * pi * d / dr [(r ^ 3)]
dV / dt = (4/3) * pi * 3 * (r ^ 2) * dr / dt
dV / dt = 4 * pi * (r ^ 2) * dr / dt
we replace all the values and we are left with:
dV / dt = 4 * 3.14 * (6.4 ^ 2) * 0.6
dV / dt = 308.67
Therefore the volume is changing at a rate of 308.67 cm ^ 3 / week
find the value of x
m<2= x + 122
Answer:
x= -14
Step-by-step explanation:
Please see attached picture for full solution.
Crane Company reports the following for the month of June.
Date
Explanation
Units
Unit Cost
Total Cost
June 1 Inventory 150 $4 $600
12 Purchase 450 5 2,250
23 Purchase 400 6 2,400
30 Inventory 80
Assume a sale of 500 units occurred on June 15 for a selling price of $7 and a sale of 420 units on June 27 for $8.
Calculate cost of goods available for sale.
Calculate Moving-Average unit cost for June 1, 12, 15, 23 & 27. (Round answers to 3 decimal places, e.g. 2.525.)
Answer:
Crane CompanyJune Financial Reports
a) Cost of goods available for sale = $5,250
b) Moving-Average unit cost for:
i) June 1: = $5
ii) 12: = $4.75
iii) 15: = $4.75
iv) 23: = $5.75
v) 27: = $5.25
Step-by-step explanation:
a) Calculations:
Date Explanation Units Unit Cost Total Cost Moving Average Cost
June 1 Inventory 150 $4 $600 $4.000
12 Purchase 450 5 2,250 4.750
15 Sale 500 7 3,500 4.750
23 Purchase 400 6 2,400 5.750
27 Sale 420 8 3,360 5.250
30 Inventory 80
Cost of goods available for sale = Cost of Beginning Inventory + Cost of Purchases = $5,250 + ($600 + 2,250 + 2,400)
b) Moving-Average unit cost for:
i) June 1: Cost of goods available/Units of goods available = $5 ($600/150)
ii) 12: Cost of goods available/Units of goods available = $4.75 ($600 + 2,250/600)
iii) 15: Cost of goods available/Units of goods available = $4.75 ($475/100)
iv) 23: Cost of goods available/Units of goods available = $5.75 ($475 + 2,400)/500
v) 27: Cost of goods available/Units of goods available = $5.25 ($420/80)
20x=60y What is x in terms of y? (Hope this isn't illogical)
Answer:
x=3y
Step-by-step explanation:
divide both sides by 20
20x = 60y
------ -------
20 20
x=3y
Answer:
x = 3y
Step-by-step explanation:
20x = 60y
Divide 20 into both sides.
20x/20 = 60y/20
1x = 6/2y
x = 3y
A school district performed a study to find the main causes leading to its students dropping out of school. Thirty cases were analyzed, and a primary cause was assigned to each case. The causes included unexcused absences (U), illness (I), family problems (F), and other causes (O). The results for the thirty cases are listed below:
U U U I F O O U I F F O U I I F I I O U I F F U U I I O F U
Required:
Construct a table summarizing the frequency distribution of the primary causes leading to student dropout.
Answer:
See below for the table.
Step-by-step explanation:
The results for the thirty cases are listed below:
U U U I F O O U I F F O U I I F I I O U I F F U U I I O F U
The table summarizing the frequency distribution of the primary causes leading to student dropout is:
[tex]\left|\begin{array}{c|c}$Cause&$Frequency\\----------&----\\\\$Unexcused absences (U)&9\\$Illness (I)&9\\$Family problems (F)&7\\$Other causes (O)&5\\-----------&---\\$Total&30\end{array}\right|[/tex]
Suppose that the lenghth between 911 calls to a ceration police stattion is exponentially distribution with an average of 5 minutes between calls. What is the probability that they receive 10 calls in the next hours?
Answer:
0.1048
Step-by-step explanation:
The computation of probability that they receive 10 calls in the next hours is shown below:-
Average which is given in the question 5 minutes between calls = 5/60 calls an hour so it becomes 12 calls per hour
So,
P(X = 10)
[tex]= \frac{e^{-12}12^{10}}{10!}[/tex]
= 0.1048
Therefore for computing the probability that they receive 10 calls in the next hours we simply applied the above formula.
Find the slope on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer:
Step-by-step explanation:
(-2,2) (2,-4)
(-4-2)/(2+2)= -6/4= -3/2 is the slope of the graph
There are 3 white counters and 1 black counters in a bag I take one of the counters at random what is the probability??
Answer:
0.25
Step-by-step explanation:
Out of the 4 counters only 1 is black so the probability is 1/4 or 0.25.
Answer:
0.25
Step-by-step explanation:
Since there are four marbles 100/4 =25 in this 100 is 1 thus the answer is 0.25
What is the slope of the line on the graph below? On a coordinate plane, a line goes through points (negative 2, negative 3), (negative 1, negative 1), (0, 1) and (1, 3). –One-half One-half 1 2 plz
Answer:
slope = 2
Step-by-step explanation:
All four points lie on the same line.
Taking the first and fourth points, the slope can be found by the formula
slope, m = (y2-y1)/(x2-x1) = (3- -3) / (1- -2) = 6/3 =2
See attached diagram.
Answer:
2
Step-by-step explanation:
edge 2020
A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes
Answer:
19.49% probability that no more than 16 of them are strikes
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 30, p = 0.626[/tex]
So
[tex]\mu = E(X) = np = 30*0.626 = 18.78[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*(1-0.626)} = 2.65[/tex]
What is the probability that no more than 16 of them are strikes
Using continuity correction, this is [tex]P(X \leq 16 + 0.5) = P(X \leq 16.5)[/tex], which is the pvalue of Z when X = 16.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16.5 - 18.78}{2.65}[/tex]
[tex]Z = -0.86[/tex]
[tex]Z = -0.86[/tex] has a pvalue of 0.1949
19.49% probability that no more than 16 of them are strikes
The diagram shows the first four patterns of a sequence. Find an expression for the numbers of squares in the nth pattern of the sequence.
Answer:
n^2+3
Step-by-step explanation:
As we can see in the diagram
1st pattern consists from 1 square 1x1 +3 squares 1x1 each
2nd pattern consists from 1 square 2x2 +3 squares 1x1 each
3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each
4-th pattern consists from 1 square 4x4 + 3 squares 1x1 each
We can to continue :
5-th pattern consists from 1 square 5x5+3 squares 1x1 each
So the nth pattern consists from 1 square nxn+3 squares 1x1 each
Or total amount of 1x1 squares in nth pattern N= n^2+3
The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
What is nth term of a sequence?"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."
From the given diagram
We can see that every term is made up with a square which side is n and three small square side is 1.
So,
1st term is 1 × 1 + 3 = 4
2nd term is 2 × 2 + 3 = 4
3rd term is 3 × 3 + 3 = 12
4th term is 4 × 4 + 3 = 19
So, nth term is [tex]n^{2} +3[/tex]
Hence, The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
Learn more about nth term of a sequence here
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The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a maximum of 12.75 ounces of soda. Every can that has more than 12.75 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process?
Answer:
0.1587
Step-by-step explanation:
According to the situation, the solution and the data provided is as follows
mean = 12.45 ounces
Standard deviation = 0.30 ounces
maximum = 12.75 ounces
More than ounces of soda = 12.75
Based on the above information, the probability is
[tex]Z=\frac{X-\mu }{\sigma } \\\\Z=\frac{12.75-12.45 }{0.30 } \\\\\Z=\frac{0.30 }{0.30 } \\\\Z= 1 \\\\P(X> 12.75)=1-P(X< 12.75) \\\\\P(X> 12.75)=1-P(Z< 1) \\\\[/tex]
As we know that
P(Z<1) = 0.8413
So,
P (X > 12.75) = 1 - 0.8413
= 0.1587
50 random teenagers were asked how many hours a day they use their phone. They spent an average of 7 hours a day with a standard deviation of 1.3. Based on the results, what is the margin of error for the true mean number of hours a teenager spends on their phone?your margin of error on a 95% confidence level, round your answer to the nearest tenth
Answer:
The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.
Step-by-step explanation:
We have the standard deviation of the saple, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2\frac{1.3}{\sqrt{50}} = 0.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.
Lisa surveyed 60 students at her school and found that 0.85 of the students she surveyed said their favorite class is math. Another 15% of the students she surveyed reported that their favorite class is science. How many more students in the survey prefer math over science?
Answer:
42
Step-by-step explanation:
Number of students whose favorite class is Math:
60*0.85=51
Number of students whose favorite class is Science:
15% is equal to 0.15.
60*0.15=9
Subtract number of students who like science from number of students who like math.
51-9=42
42 more students in the survey prefer math over science.
Answer:
42
Step-by-step explanation:
85% math
15% science
Subtract
85-15 = 70
The difference is 70 %
70% of 60 students
.70 * 60 = 42
There is a 42 student difference
The following lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men. Has Lung Disease/smoker 0.1, No Lung Disease/Smoker 0.17, Lung Disease/Nonsmoker 0.03, No Lung Disease/Nonsmoker 0.7. One 60-to-65 year old man is selected at random. What is the probability of the following event: He has lung disease given that he does not smoke?
Answer:
4.11% probability that he has lung disease given that he does not smoke
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Does not smoke
Event B: Lung disease
Lung Disease/Nonsmoker 0.03
This means that [tex]P(A \cap B) = 0.03[/tex]
Lung Disease/Nonsmoker 0.03
No Lung Disease/Nonsmoker 0.7
This means that [tex]P(A) = 0.03 + 0.7 = 0.73[/tex]
What is the probability of the following event: He has lung disease given that he does not smoke?
[tex]P(B|A) = \frac{0.03}{0.73} = 0.0411[/tex]
4.11% probability that he has lung disease given that he does not smoke
Probabilities are used to determine the chances of an event.
The probability that he has lung disease given that he does not smoke is 0.231
The required probability is calculated as:
[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]
From the question, we have:
[tex]\mathbf{P(Lung\ Disease\ and\ Non\ Smoker) = 0.03}[/tex]
[tex]\mathbf{P(Lung\ Disease) = P(Has Lung Disease/smoker) + P(Lung Disease/Nonsmoker)}[/tex]
[tex]\mathbf{P(Lung\ Disease) = 0.1 + 0.03}[/tex]
[tex]\mathbf{P(Lung\ Disease) = 0.13}[/tex]
So, we have:
[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]
[tex]\mathbf{P = \frac{0.03}{0.13}}[/tex]
[tex]\mathbf{P = 0.231}[/tex]
Hence, the probability that he has lung disease given that he does not smoke is 0.231
Read more about probabilities at:
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I will Give brainliest to who ever can show me how to solve this killer!!!!!!! Using Descartes Rule and the rational zeros of polynomial equation, find the root (positive, negative and imaginary) of x^5-2x^4+x^3+x^2-2x+1=0
see if other people has already answered this question
Answer:
-1
1
1/2(1±i√3)
Step-by-step explanation:
x^5-2x^4+x^3+x^2-2x+1=0x^3(x^2-2x+1)+(x^2-2x+1)=0(x^3+1)(x-1)^2=0(x+1)(x^2-x+1)(x-1)^2=01. x+1=0 ⇒ x= -1
2. x-1= 0 ⇒ x= 1
3. x^2-x+1=0
x^2- 2*1/2x+1/4= -3/4(x-1/2)^2= -3/4x-1/2= ±√-3/4 ⇒ x-1/2=±i√3/2 ⇒ x= 1/2 ± i√3/2= 1/2(1± i√3)In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each participant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree," and these are assigned the numbers 1 or −1, respectively. Participant’s responses to the survey are encoded as a vector in R4, where coordinates correspond to their answers to each question. Here are the questions:
The question is incomplete. Here is the complete question.
In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:
Question #1: I prefer outdoor activities, rather than indoor activities.
Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.
Question #3: I prefer texting, rather than talking on the phone.
Question #4: I prefer living in a small town, rather than in a big city.
Here are the results for the questionaire, with a group of 5 participants:
Question1 Question2 Question3 Question4
participant A 1 1 -1 -1
participant B -1 1 1 1
participant C -1 -1 1 1
participant D 1 -1 -1 -1
participant E 1 -1 1 1
Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".
(a) Which pairs of paricipants are compatible?
(b) Which pairs of participants are incompatible?
(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only
allowing "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?
Answer: (a) Participants A and D; B and C; C and E.
(b) Participants A and B; A and C; A and E; B and D; C and D;
Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.
Vectors form angles between themselves and can be found by the following formula:
cos α = [tex]\frac{A.B}{||A||.||B||}[/tex]
which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.
For the compatibility test, find the angle between vectors:
1) The vectors magnitude:
Magnitude of a vector is given by:
||x|| = [tex]\sqrt{x_{i}^{2} + x_{j}^{2}}[/tex]
Since all the vectors have value 1, they have the same magnitude:
||A|| = [tex]\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}[/tex] = 2
||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2
2) The dot product of vectors:
A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{1}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]
The angle that has cosine equal -1/2 is 120°, so incompatible
A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4
cos [tex]\alpha _{2}[/tex] = -1
Angle = 180° --------> incompatible
A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2
cos [tex]\alpha _{3}[/tex] = 1/2
Angle = 60° ---------> COMPATIBLE
A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{4}[/tex] = -1/2
Angle = 120° --------> incompatible
B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha _{5}[/tex] = 1/2
Angle = 60° -------------> COMPATIBLE
B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4
cos[tex]\alpha_{6}[/tex] = -1
Angle = 180° -----------> incompatible
B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0
cos[tex]\alpha _{7}[/tex] = 0
Angle = 90° -------------> may or may not
C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2
cos[tex]\alpha_{8} =[/tex] -1/2
Angle = 120° ---------------> Incompatible
C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha_{9}[/tex] = 1/2
Angle = 60° ---------------> COMPATIBLE
D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0
cos [tex]\alpha_{10}[/tex] = 0
Angle = 90° -----------------> may or may not
(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.
11. If 4 < x < 14, what is the range for -x - 4?
Answer:
-18 < -x-4 < -8
Step-by-step explanation:
We start with the initial range as:
4 < x < 14
we multiplicate the inequation by -1, as:
-4 > -x > -14
if we multiply by a negative number, we need to change the symbols < to >.
Then, we sum the number -4, as:
-4-4> -x-4 > -14-4
-8 > -x-4 > -18
Finally, the range for -x-4 is:
-18 < -x-4 < -8
Need help solving for x
Answer:
9.2
Step-by-step explanation:
The given triangle is a right angled triangle. To solve for any of the side length of such triangle, apply the trigonometry ratio formula which can easily be remembered as SOHCAHTOA.
SOH is Sin θ = opposite/hypothenuse,
CAH is Cos θ = Adjacent/hypotenuse
TOA is Tan θ = Opposite/adjacent
Thus, in the right triangle given, we have:
θ = 38°
Opposite side to the given angle = x
Hypotenuse = 15
We're going to use, sin θ = opposite/hypotenuse
Sin(38) = x/15
Multiply both sides by 15 to solve for x
15*sin(38) = x
15*0.616 = x
9.24 = x
x ≈ 9.2 (to nearest tenth)
4x+1/15=2x/10 PLEASE HELP
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
Cross multiply.
10(4x + 1) = 15(2x)
Expand brackets.
40x + 10 = 30x
Add -30x and 10 on both sides.
40x - 30x = -10
10x = -10
Divide both sides by 10.
10/10x = -10/10
x = -1
If AB= X and x=4, then the transitive property states
Answer:
AB=4
Step-by-step explanation:
The transitive property states if A=B and B+C than A+C Next substitute
AB=x and x=4 so AB=4
Hope this helps, if it did, please give me brainliest, it helps me a lot. :)
Have a good day!
HELP WITH THESE QUESTIONS!!
An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 51% of passengers have no checked luggage, 33% have one piece of checked luggage and 16% have two pieces. We suppose a negligible portion of people check more than two bags.
Required:
a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.
b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation? Note any assumptions you make and if you think they are justified.
Answer:
The average revenue per passenger is about $13.85
μ = $13.85
The corresponding standard deviation is $14.51
σ = $14.51
The airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.
Expected revenue = $1,662 ± 14.51
Step-by-step explanation:
An airline charges the following baggage fees:
$25 for the first bag and $35 for the second
Suppose 51% of passengers have no checked luggage,
P(0) = 0.51
33% have one piece of checked luggage and 16% have two pieces.
P(1) = 0.33
P(2) = 0.16
a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.
The average revenue per passenger is given by
μ = 0×P(0) + 25×P(1) + 35×P(2)
μ = 0×0.51 + 25×0.33 + 35×0.16
μ = 0 + 8.25 + 5.6
μ = $13.85
Therefore, the average revenue per passenger is about $13.85
The corresponding standard deviation is given by
σ = √σ²
Where σ² is the variance and is given by
σ² = (0 - 13.85)²×0.51 + (25 - 13.85)²×0.33 + (35 - 13.85)²×0.16
σ² = 97.83 + 41.03 + 71.57
σ² = 210.43
So,
σ = √210.43
σ = $14.51
Therefore, the corresponding standard deviation is $14.51
b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation?
For 120 passengers,
Expected revenue = 120×$13.85
Expected revenue = $1,662 ± 14.51
Therefore, the airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.
Create a bucket by rotating around the y axis the curve y=5 ln(x-2) from y=0 to y=4. If this bucket contains a liquid with density 760 kg/m3 filled to a height of 3 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity.
Answer:
The work will be "1909212.015 J". The further explanation is given below.
Step-by-step explanation:
The given values are:
Liquid's density
= 760 kg/m³
Height
= 3 meters
Gravity
g = 3.8 m/s²
Value of y is:
y = 5 log (x-2)
y = 0
y = 4
As we know,
⇒ [tex]\Delta V=\pi r^2 \Delta y[/tex]
⇒ [tex]y =5log(x-2)[/tex]
⇒ [tex]\frac{y}{5} =log (x-2)[/tex]
⇒ [tex]e^{\frac{y}{5}}=(x-2)[/tex]
⇒ [tex]x=e^{\frac{y}{5}}+2[/tex]
Now,
[tex]\Delta F=ma[/tex]
[tex]=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y[/tex]
So that,
⇒ [tex]\Delta W = \Delta F.distance[/tex]
[tex]=\Delta F(4-y)[/tex]
The required work will be:
⇒ [tex]W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy[/tex]
[tex]=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}][/tex]
[tex]=760\times 9.8 \pi[81.455][/tex]
[tex]=1909212.015 \ J[/tex]
16. How much money will I need to have at retirement so I can withdraw $60,000 a year for 20 years from an account earning 8% compounded annually? a. How much do you need in your account at the beginning b. How much total money will you pull out of the account? c. How much of that money is interest?
Answer:
starting balance: $636,215.95total withdrawals: $1,200,000interest withdrawn: $563,784.05Step-by-step explanation:
a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.
The principal P that must be invested at rate r for n annual withdrawals of amount A is ...
P = A(1+r)(1 -(1 +r)^-n)/r
P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95
__
b) 20 withdrawals of $60,000 each total ...
20×$60,000 = $1,200,000
__
c) The excess over the amount deposited is interest:
$1,200,000 -636,215.95 = $563,784.05
Tanya can wash a car and vacuum its interior in 2 hours. Pat needs 5 hours to do this same job. If Tanya and Pat work together, how many hours will it take them to clean a car??
Answer:
It will take 1.43 hours for them to clean the car.
Step-by-step explanation:
The together rate is the sum of each separate rate.
In this problem:
Together rate: 1/x
Tanya's rate: 1/2
Pat's rate: 1/5
Together rate = Tanya's rate + Pat's rate
[tex]\frac{1}{x} = \frac{1}{2} + \frac{1}{5}[/tex]
[tex]\frac{1}{x} = \frac{5 + 2}{10}[/tex]
[tex]\frac{1}{x} = \frac{7}{10}[/tex]
[tex]7x = 10[/tex]
[tex]x = \frac{10}{7}[/tex]
[tex]x = 1.43[/tex]
It will take 1.43 hours for them to clean the car.
7.22. (a) A fair coin is tossed 100 times. Estimate the probability that the number of heads is between 40 and 60. Estimate the probability that the number is between 50 and 55.
Answer:
the probability that the number of heads is between 40 and 60 is 0.9535
the probability that the number of heads is between 50 and 55 is 0.3557
Step-by-step explanation:
From the given information:
A fair coin is tossed 100 times.
Let consider n to be the number of time the coin is tossed, So n = 100 times
In a fair toss of a coin; the probability of getting a head P(Head) = 1/2 = 0.5
If we assume X to be the random variable which follows a binomial distribution of n and p; therefore , the mean and the standard deviation can be calculated as follows:
Mean μ = n × p
Mean μ = 100 × 1/2
Mean μ = 100 × 0.5
Mean μ = 50
Standard deviation σ = [tex]\sqrt{n \times p \times (1-p)}[/tex]
Standard deviation σ = [tex]\sqrt{100 \times 0.5 \times (1-0.5)}[/tex]
Standard deviation σ = [tex]\sqrt{50 \times (0.5)}[/tex]
Standard deviation σ = [tex]\sqrt{25}[/tex]
Standard deviation σ = 5
Now, we've made it easier now to estimate the probability that the number of heads is between 40 and 60 and the probability that the number is between 50 and 55.
To start with the probability that the number of heads is between 40 and 60 ; we have:
P(40 < X < 60) = P(X < 60)- P(X < 40)
Applying the central limit theorem , for X is 40 which lies around 39.5 and 40.5 and X is 60 which is around 59.5 and 60.5 but the inequality signifies less than sign ;
Then
P(40 < X < 60) = P(X < 59.5) - P(X < 39.5)
[tex]P(40 < X < 60) = P( \dfrac{X - \mu}{\sigma}< \dfrac{59.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{39.5 - 50 }{5})[/tex]
[tex]P(40 < X < 60) = P( Z < \dfrac{9.5 }{5}) - P( Z< \dfrac{-10.5 }{5})[/tex]
[tex]P(40 < X < 60) = P( Z <1.9}) - P( Z< -2.1)[/tex]
[tex]P(40 < X < 60) =0.9713 -0.0178[/tex]
[tex]P(40 < X < 60) =0.9535[/tex]
Therefore; the probability that the number of heads is between 40 and 60 is 0.9535
To estimate the probability that the number is between 50 and 55.
P(50 < X < 55) = P(X < 55)- P(X < 50)
Applying the central limit theorem , for X is 50 which lies around 49.5 and 50.5 and X is 55 which is around 54.5 and 55.5 but the inequality signifies less than sign ;
Then
P(50 < X < 55) = P(X < 54.5) - P(X < 49.5)
[tex]P(50 < X < 55) = P( \dfrac{X - \mu}{\sigma}< \dfrac{54.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{49.5 - 50 }{5})[/tex]
[tex]P(50 < X < 55) = P( Z < \dfrac{4.5 }{5}) - P( Z< \dfrac{-0.5 }{5})[/tex]
[tex]P(50 < X < 55) = P( Z <0.9}) - P( Z< -0.1)[/tex]
[tex]P(50 < X < 55) =0.8159 -0.4602[/tex]
[tex]P(50 < X < 55) =0.3557[/tex]
Therefore; the probability that the number of heads is between 50 and 55 is 0.3557
Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?
Answer:
65%
Step-by-step explanation:
Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?
3 gallons of 80% juice solution contains this amount of juice:
80% * 3 gal = 0.8 * 3 gal = 2.4 gal
1 gallon of 20% juice solution contains this amount of juice:
20% * 1 gal = 0.2 * 1 gal = 0.2 gal
The total amount of juice in the final juice solution is
2.4 gal + 0.2 gal = 2.6 gal
The total amount of juice solution made is 3 gal + 1 gal = 4 gal
The 4 gal juice solution contains 2.6 gallons of juice.
2.6 gallons is what percent of 4 gallons?
2.6/4 * 100% = 0.65 * 100% = 65%
Answer: 65%
Answer:
65% i got the answer right on the question
Step-by-step explanation:
What is the measure of x?
Answer:
x= 9 inches
Step-by-step explanation:
Hello
I can help you with this.
in this case, we have two similar triangles, let's see
Step 1
identify the rigth triangles.
1) the first triangle has these dimensions
hypotenuse( remember, the longest side)= unknown=H
adjacent side(the horizontal)=6 +x
opposite side(the vertical)=10
2) the second triangle has these dimensions
hypotenuse( remember, the longest side)= unknown=h
adjacent side(the horizontal)=6
opposite side(the vertical)=4.
As these triangles keep the same proportion and in both cases we know the length of the legs, we can establish a relationship
Step 2
establish a relationship
let's compare the opposite side and the adjacent side
triangle 1 (the bigger)
[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{10}{6+x}[/tex]
Triangle 2
[tex]proportion= \frac{opposite\ side}{adjacent\ side}\\proportion= \frac{4}{6}\\proportion=\frac{2}{3}[/tex]
were the proportions are equal, so
[tex]\frac{10}{6+x}=\frac{2}{3}[/tex]
at this point, just isolate x to find its value
Step 3
isolate x
[tex]\frac{10}{6+x}=\frac{2}{3}\\multiply\ both\ sides\ by\ 3\\\frac{10*3}{6+x}=\frac{2*3}{3}\\\frac{30}{6+x} =2\\\\Multiply\ both\ sides\ by (6+x)\\\frac{30(6+X)}{6+x} =2(6+x)\\30=12+2x\\30-12=2x\\18=2x\\so\\x=\frac{18}{2} \\x=9[/tex]
remember the units of measure ( Inches)
x= 9 inches
I really hope it helps, have a nice day.