alice and bob arrange to meet for lunch on a certain day at noon. however, neither is known for punctuality. they both arrive independently at uniformly distributed times between noon and 1:48 pm on that day. each is willing to wait up to minutes for the other to show up. what is the probability they will meet for lunch that day?
Answers
For the arrival of both Bob and alice independently at uniformly distributed times on that day. The probability they will meet for lunch that day is equals to the 0.4514.
Let X = arrival time (in minutes past noon) of the first-to-arrive person and
Y = arrival time (in minutes past noon) of the second-to-arrive person. Then, we have X and Y are independent implies their joint probability = product of their individual probabilities .... (1)
Probability density function, Pdf of X is : (1/60)dx [noon to 1 pm is 60 minutes and X ~ Uniform ....(2)
Similarly, Pdf of Y is: (1/60)dy [noon to 1 pm is 60 minutes and Y ~ Uniform] ...(3)
The two will meet for lunch on that day if
Y = X ± 15...(4)
To expand equation (4), further,
If X ≤ 15, 0 ≤ Y ≤ x + 15If 15 ≤ X ≤ 45, x – 15 ≤ Y ≤ x + 15If 45 ≤ X ≤ 60, x – 15 ≤ Y ≤ 60.P(The two will meet for lunch on that day) = A + B + C, ...(5)
where \(A = \int_{0}^{15}(\frac{1}{60}\int_{0}^{x +15}\frac{1}{60}dy)dx\)
\(B = \int_{15}^{45}(\frac{1}{60}\int_{x- 15}^{x +15}\frac{1}{60}dy)dx \\ \)
\(C= \int_{45}^{60}(\frac{1}{60}\int_{x- 15}^{60}\frac{1}{60}dy)dx \)
Now, we solve the above integrales one by one, \(A = \int_{0}^{15} \frac{1}{3600} (x + 15)dx\)
\(A =\frac{1}{3600}[x^{2}+15x]_{0}^{15}\)
\(= \ \frac{1}{3600}[15^{2} + 15 \times 15 - 0]\)
A = \( \frac{775}{7200} = 0.1076 \)
\(B= \int_{15}^{45} \frac{1}{3600} [(x + 15) - (x - 15)]dx \\ \)
\(= \int_{15}^{45} \frac{1}{3600}[30]dx \)
= \( \frac{1}{3600}[30x]_{15}^{45} \\ \)
\(= \frac{30}{3600} [ 45 - 15 ]\)
\( \frac{900}{3600} \: = 0.25\)
\(C = \int_{45}^{60} \: \frac{1}{3600}(60 - x + 15)dx\)
\(= \int_{45}^{ 60} \: \frac{1}{3600}(75 - x )dx\)
\(= \frac{1}{3600}[75x - \frac{x²}{2}]_{45}^{ 60} \)
\(= \frac{1}{3600}[75 \times 60 - \frac{{60}^{2}}{2} - 75 \times 45 + \frac{ {45}^{2}}{2}] \\ \)
\(= \frac{1}{3600}[ 1125 - 787.5] \)
= \( \frac{337.5}{3600} = 0.0938\)
From Required probability = 0.1076 + 0.25 + 0.0938 = 0.4514
Hence, required probability is 0.4514.
For more information about probability, visit:
https://brainly.com/question/25870256
#SPJ4
Related Questions
Determine if the vectors ([1],[-2],[3]),([2],[-2],[0]) and ([0],[1],[7]) are a linearly independent set.
Answers
The vectors \(([1],[-2],[3]),([2],[-2],[0])\) and \(([0],[1],[7])\) are a linearly independent set.
To determine if the vectors are a linearly independent set, we can use the determinant method. The determinant of a 3x3 matrix is given by:
\(\begin{bmatrix}a_1 & a_2 &a_3 \\ b_1& b_2 &b_3 \\ c_1&c_2 &c_3 \end{bmatrix}\)
We can create a 3x3 matrix using the given vectors as the columns of the matrix:
\(\begin{bmatrix}1 & 2 &0 \\ -2& -2 &1 \\ 3&0 &7 \end{bmatrix}\)
Now, we can find the determinant of this matrix using the formula:
\(det(\begin{bmatrix}1 & 2 &0 \\ -2& -2 &1 \\ 3&0 &7 \end{bmatrix})\)
\(= 1(-2*7 - 1*0) - 2(-2*7 - 1*3) + 0(-2*0 - 1*-2)\)
\(= -14 - 0 - 4(-14) - 6 + 0\)
\(= -14 + 56 - 6\)
\(= 36\)
Since the determinant is not equal to zero, the vectors are linearly independent.
Therefore, the vectors\(([1],[-2],[3]),([2],[-2],[0])\) and \(([0],[1],[7])\) are a linearly independent set.
See more about linear independence at: https://brainly.com/question/10725000
#SPJ11
What is the slope of the line?
A.) 1
B.) 1/2
C.) -2
D.) 2
Answers
Answer:
D
Step-by-step explanation:
Two similar figures have a side ratio of 2:5. What is the ratio of their volumes?
Answers
Answer: The ratio of the side lengths of two similar figures is 2:5.
Let's assume that the dimensions of the smaller figure are 2x, 2y, and 2z, where x, y, and z are some constants. Then, the dimensions of the larger figure will be 5x, 5y, and 5z.
The ratio of the volumes of two similar figures is the cube of the ratio of their corresponding side lengths.
So, the ratio of the volumes of the smaller and larger figures will be:
(2x)^3 : (5x)^3
8x^3 : 125x^3
We can simplify this ratio by dividing both sides by the common factor of x^3:
8 : 125
Therefore, the ratio of the volumes of the smaller and larger figures is 8:125.
Step-by-step explanation:
Find the length of the hypotenuse
on a right triangle with legs of 15
Inches and 7 Inches. NEED ANSWER NOW!!!
Answers
awscalculate mse for each region. is the variability·around the fitted regression line approxi- mately the same for the four regions? discuss.
Answers
In order to calculate the Mean Squared Error (MSE) for each region, you will need to have a dataset with values for each region.
Once you have this dataset, you can calculate the MSE using the following formula:
MSE = 1/n x ∑(yi - ŷi)²
where n is the number of data points in the region, yi is the actual value for the ith data point, and ŷi is the predicted value for the ith data point. Once you have calculated the MSE for each region, you can compare the values to determine if the variability around the fitted regression line is approximately the same for each region.
If the MSE values are similar for each region, then the variability around the fitted regression line is approximately the same. If the MSE values are different for each region, then the variability around the fitted regression line is not the same for each region.
You can learn more about Mean Squared Error at: brainly.com/question/29662026
#SPJ11
Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. f(x) = 3x + 4, X<-3
2x2 + ax + b. X>-3
Answers
The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.
To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.
On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.
Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.
Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.
Learn more about piecewise
brainly.com/question/28225662
#SPJ11
Which of the following equations has the solution set {0}?
A.) -14m - 7m + 1 = -7m + 1
B.) -14m + 7m + 1 = -7m + 2
C.) 14m - 7m - 1 = -7m + 1
Answers
Answer:
Option A
Step-by-step explanation:
\(-14m-7m+1=-7m+1\\\\-14-7m+1-(-7m+1)=-7m+1-(-7m+1)\\\\-14m=0\\\\-14m/-14=0/-14\\\\\boxed{m=0}\)
Answer:A
Step-by-step explanation:
-14m-7m+1=-7m+1
then
-14m-7m+7m=1-1
-14m=0
m=0
I also need help on this one
Answers
Answer:
A
Step-by-step explanation:
27-9=18
18=18
5(27)=135
135=135
What are the slope and the y-intercept of the linear function that is represented by the equation Y --10x+1?
BARE
O The slope is -10, and the y-intercept is -1.
O The slope is -10, and the y-intercept is 1.
The slope is -1, and the y-intercept is -10.
O The slope is 1, and the y-intercept is -10.
Answers
Answer:
The slope is -10, and the y-intercept is 1.
Step-by-step explanation:
Assuming that the equation is y = -10x+1, the easiest way to identify slope and the y-intercept is by knowing the equation for slope-intercept (y = mx+b)
Equation for slope-intercept (y = mx+b) explained:
The equation is y = mx+b, let's break it down.
y = The line
m = The slope
b = The y-intercept
Now that we know the equation and broke it down you can identify them in your equation
Slope (m)= -10
y-intercept = 1
Conclusion: The slope is -10, and the y-intercept is 1.
in two or more complete sentences, describe choices that a consumer can make that could lead to financial irresponsibility.
Answers
Choices made by consumer leads to financial irresponsibility are as follow:
Spend money on emotional feelingDon't save money for emergency purposeSpending money without knowing your limitsSpending money doing comparisonAs given in the question,
Choices made by consumer leads to financial irresponsibility are as follow:
Spend money on emotional feelingWhen a person is spending money just on emotional feeling and buying large gifts for children which is beyond the budget. Due to this habits a person may have to take debt.
Don't save money for emergency purposeWhen a person is not saving enough money for the time of emergency, it can be a medical emergency then it is financial irresponsible behavior.
Spending money without knowing your limitsWhen you are not making any budget and spending money ,it might possible at the end of the month or some time you have to face financial crises.
Spending money doing comparisonDon't compare yourself with anyone, this might lead you to take loan or debts which lead your life in facing financial trouble.
Therefore, choices made by consumer leads to financial irresponsibility are as follow:
Spend money on emotional feelingDon't save money for emergency purposeSpending money without knowing your limitsSpending money doing comparisonLearn more about choices here
brainly.com/question/23417375
#SPJ1
In the u.s., shoe sizes are defined differently for men and women, but in europe, both genders use the same shoe size scale. the accompanying histogram shows the european shoe sizes of 269 male and female college students, converted from their reported u.s. shoe sizes. what might be the problem with either the standard deviation or the iqr as a measure of spread?
Answers
The problem with using the mean or median as a measure of center is that the distribution of the data is bimodal, indicating that there are two distinct groups of shoe sizes. The correct answer is A
The histogram shows that one group has shoe sizes from 38 to 40, while the other group has shoe sizes from 44 to 49. This suggests that the two groups have roughly the same mean shoe size, but different distributions.
Therefore, the mean or median are not good measures of center because they do not accurately reflect the underlying distribution of the data. It would be more useful to report the modes instead, which represent the most frequent shoe sizes in the data.
Your question is incomplete but most probably your full question is
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both sexes use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. What might be the problem with either the mean or the median as a measure of center?
a. The distribution is bimodal, so it is more useful to report the modes than the mean or median.
b. The distribution does not have any modes, because it is uniform.
c. The distribution has one mode from 44 to 49. This is due to the students having noughly the same mean shoe size.
d. The distribution has one mode from 38 to 40. This is due to the students having noughly the same mean shoe size.
For more questions like Mean click the link below:
brainly.com/question/8074804
#SPJ4
Peter bought 8 lemons for $ 6. Each lemon was the same price.
What was the cost for 1 lemon?
Answers
Answer:
$0.75
Step-by-step explanation:
the total was 6 dollars, and there were 8 lemons. so 6/8 = 3/4 = 0.75
hope this helps!! :)
Answer:
.75 cents each
Step-by-step explanation:
if you divided the 6 dollars by the 8 lemons then you get 0.75
How many minutes in 420 seconds?
Answers
Answer: 7 minutes
Step-by-step explanation:
There is 1 minute every 60 seconds
So if we divide the amount of seconds by 60 we will get the answer.
Therefore our equation is: 420/60
420/60=7
SO the answer is 7 minutes
Hope this helps! :)
An airplane travels 4,000miles in 8 hours. What is the speed?
Answers
Answer:500 mile per hour
Step-by-step explanation: 4000/8=500
Answer: 500mi/h
Step-by-step explanation: Speed = distance/time.
distance = 4000mi(miles)
Time =8h(hours)
4000mi/8h = 500mi/h
Transcribed image text: The probability distribution for the random variable x follows. x f(x) 20 0.30 25 0.15 30 0.20 35 0.35 (a) Is this probability distribution valid? Explain. Since f(x) 0 for all values of x and rx) = 1 , this is a proper probability distribution. (b) What is the probability thatx30? (c) What is the probability that x is less than or equal to 25? (d) What is the probability that x is greater than 30?
Answers
a. The probability distribution is valid because the probabilities (f(x)) are non-negative for all values of x, and the sum of all probabilities is equal to 1.
b. The probability that x 30 is 20%.
c. The probability that x is less than or equal to 25 is 45%.
d. The probability that x is greater than 30 is 35%.
(a) The probability distribution is valid because the probabilities (f(x)) are non-negative for all values of x, and the sum of all probabilities is equal to 1. This is indicated by the statement "rx) = 1", which means the sum of all probabilities is 1.
(b) The probability that x = 30 is given by f(30) = 0.20. Therefore, the probability that x = 30 is 0.20 or 20%.
(c) To find the probability that x is less than or equal to 25, we need to sum the probabilities of all values of x that are less than or equal to 25. In this case, we need to sum the probabilities of x = 20 and x = 25:
P(x ≤ 25) = f(20) + f(25) = 0.30 + 0.15 = 0.45 or 45%.
(d) To find the probability that x is greater than 30, we need to sum the probabilities of all values of x that are greater than 30. In this case, we need to sum the probability of x = 35:
P(x > 30) = f(35) = 0.35 or 35%.
Therefore, the probability that x is greater than 30 is 0.35 or 35%.
Learn more about probability at https://brainly.com/question/15135952
#SPJ11
While hiking, Diego drank 2¼ liters of water. Lin drank 1⅗ liters of water. How much more did Diego drink than Lin?
Answers
Answer: 13/20
Step-by-step explanation:2 1/4 - 1 3/5 = 13/20
Answer:
13/20
Step-by-step explanation:
The following spinner has four sections. There are equal sections for 1, 4, and 3. The section for 2 is twice as large as each of the other sections. 1 2 4 3
Answers
Answer:
it would be 39t for the extra 8s
Step-by-step explanation:
Solve: 493x = 3432x + 1. a. x = –3 b. x = 1 c. x = 3 d. no solution
Answers
On solving the mentioned equation, the correct answer for value of x will be d. no solution.
We will begin with converting the base to same numbers. As per the fact, 49 is the square of 7 and 323 is the cube of 7. So, the equation will be -
\( {7²}^{3x} = {7³}^{(2x + 1)} \)
Now, performing the multiplication of both exponents on both sides of the equation
\( {7}^{6x} = {7}^{(6x + 3)} \)
As the bases are equal, hence will be the exponents.
6x = 6x + 3
6x is common on both sides and hence x will not exist. Thus, no solution is possible.
Learn more about exponent -
https://brainly.com/question/2456547
#SPJ4
The correct question is -
Solve: \( {49}^{3x} = {343}^{(2x + 1)} \). a. x = –3 b. x = 1 c. x = 3 d. no solution
Answer:
It's D, No solution.
Step-by-step explanation:
I did the assignment.
In the given figure ABCD, prove that
angleBCD= angleBAD+ angle ABC+angle ADC.
[Hint: Join A and C then extended AC to the point E]
Answers
We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:
Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.
Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.
Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).
Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.
Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).
Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.
Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.
Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.
Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.
Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
For more questions on Angle .
https://brainly.com/question/31615777
#SPJ8
Given: Quadrilateral \(\displaystyle\sf ABCD\)
To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)
Proof:
1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).
2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).
3. In triangle \(\displaystyle\sf ACD\):
- \(\displaystyle\sf \angle ACD = \angle BAD + \angle ADC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).4. In triangle \(\displaystyle\sf BCE\):
- \(\displaystyle\sf \angle BCE = \angle BAD + \angle ABC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):
- \(\displaystyle\sf \angle BCE = \angle BCD\).6. Combining the equations from steps 3 and 4:
- \(\displaystyle\sf \angle BCD = \angle ACD = \angle BAD + \angle ADC\). - \(\displaystyle\sf \angle BCD = \angle BCE = \angle BAD + \angle ABC + \angle ADC\).Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
in a large city, you pick a sample of 30 of lawn mowings during summer whose standard deviation is 7.7. the margin of error for a 90% confidence interval will be
Answers
2.388 is the margin of error for a 90% confidence interval will be standard deviation.
What does the standard deviation of the sample mean?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.Sample size n=30
Sample standard deviation s= 7.7
t critical at alpha =0.10, for 29 d.f. is 1.699
Margin error = t critical ×s/√n
=1.699×7.7/√30 = 2.388
Margin error =2.388
Learn more about standard deviation
brainly.com/question/16555520
#SPJ4
Becca made 2 trays of rolls and bisouits. Each tray had 12 folls and 6 biscuits. How many total rols and bisouits did Beca make?
Answers
Becca made a total of 24 rolls and 12 biscuits.
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.
Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:
Total rolls = 2 trays × 12 rolls per tray = 24 rolls
Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits
know more about multiply here;
https://brainly.com/question/30875464
#SPJ11
find the greatest 4 digit number which becomes divisible by 24 and 28 when 100 is added to it
Answers
Answer:
9912 is the biggest 4 digit number divisible by 24 and 28.
Step-by-step explanation:
Answer:
9812
Step-by-step explanation:
To find it, you start with the prime factors of 24 and 28 to find the lowest common multiple, which is 168.
Any multiple of 168 will also be a multiple of 24 & 28.
I hope it helps you.....
please explain how to solve this
(12+5i) - (9-2i)
i have answers but dont understand
Answers
Answer: 3 + 7i
Step-by-step explanation:
Equation expanded: 12 + 5i - 9 + 2i // now simplfy
12 - 9 = 3
5i + 2i = 7i
// together, we get
3 + 7i
Answer:
10i
Step-by-step explanation:
(12+5i) - (9-2i)
(17i) - (7i)
10i
The peanuts cost $2.70 for 1 pound. How
much does 3.5 pounds of peanuts cost?
Answers
Answer: $9.45
Step-by-step explanation:
Set up a proportion of 2.70/1 = x/3.5. To solve, multiply 2.70 by 3.5 and divide by 1. 2.70*3.5 = 9.45/1 = 9.45.
Take 2.70 times 3.5 and you get your answer.
pllsssssssssss neeed this done so i can go to sleep
:(
Answers
Answer:
r is greater then 5
Step-by-step explanation:
if it's pointing from say 3 up to 10 the number is bigger then the answer
charlie ran 5 laps around the track. each lap was 400 meters how many total kilometers did charlie?
Answers
5 laps
400 meters each lap.
So, to answer this we have to multiply the number of laps by the length of each lap:
400 m x 5 = 2,000 meters
Then we have to convert into kilometers.
Since 1 km= 1000 meters
We have to divide the value in meters by 1000:
2,000 / 1,000 = 2 km
2 kilometers
Answer:
5 laps x 400m = 2000m = 2km
answer is 2 kilometres
Step-by-step explanation:
What is the y-intercept of the line whose equation is y=−3x ?
Answers
Answer:
y=mx+b
b is the y intercept
b=0, so 0 is the y intercept
Step-by-step explanation:
50 POINTS! Please Help!
Answers
Jason drove 180 miles in 4 hours and Ali drives 75 miles in 1.5 hours. Who is driving faster
Answers
The equation of the line with a slope of zero and passes through the point (-5, 2)
Answers
Answer:
The equation is y=2
Step-by-step explanation:
Well if it has a slope of 0 this means that its a horizontal line
the point (-5, 2)
The x is -5 and the y is 2
so y=2