Answer:
(a) Probability that at most 3 cars per year will experience a catastrophe is 0.2650.
(b) Probability that more than 1 car per year will experience a catastrophe is 0.9596.
Step-by-step explanation:
We are given that the distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with variance = 5.
Let X = the number of cars per year that will experience the catastrophe
SO, X ~ Poisson([tex]\lambda = 5[/tex])
The probability distribution for Poisson random variable is given by;
[tex]P(X=x) = \frac{e^{-\lambda} \times \lambda^{x} }{x!} ; \text{ where} \text{ x} = 0,1,2,3,...[/tex]
where, [tex]\lambda[/tex] = Poisson parameter = 5 {because variance of Poisson distribution is [tex]\lambda[/tex] only}
(a) Probability that at most 3 cars per year will experience a catastrophe is given by = P(X [tex]\leq[/tex] 3)
P(X [tex]\leq[/tex] 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= [tex]\frac{e^{-5} \times 5^{0} }{0!} +\frac{e^{-5} \times 5^{1} }{1!} +\frac{e^{-5} \times 5^{2} }{2!} +\frac{e^{-5} \times 5^{3} }{3!}[/tex]
= [tex]e^{-5} +(e^{-5} \times 5) +\frac{e^{-5} \times 25 }{2} +\frac{e^{-5} \times 125}{6}[/tex]
= 0.2650
(b) Probability that more than 1 car per year will experience a catastrophe is given by = P(X > 1)
P(X > 1) = 1 - P(X [tex]\leq[/tex] 1)
= 1 - P(X = 0) - P(X = 1)
= [tex]1-\frac{e^{-5} \times 5^{0} }{0!} -\frac{e^{-5} \times 5^{1} }{1!}[/tex]
= 1 - 0.00674 - 0.03369
= 0.9596
If a graphical solution to a linear equation
results in the point of intersection (8. 13), then
the solution to the equation is _____
Answer:
The solution to the equation is (8,13).
Step-by-step explanation:
A linear system of equations is composed by two lines.
The solution of the system is the point where the two lines intersect, that is.
In this question:
Point of intersection (8,13).
So
The solution to the equation is (8,13).
PLEASE HELP Last year Lenny had an annual earned income of $58,475. He also had passive income of $1,255, and capital gains of $2,350. What was Lenny’s total gross income for the year?
a.
$58,475
b.
$59,730
c.
$60,985
d.
$62,080
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
For 90:
9 10p coins
7 10p coins and 1 20p coin
5 10p coins and 2 20 p coins
3 10p coins and 3 20p coins
For 60:
6 10p coins
4 10p coins and 1 20p coin
2 10p coins and 2 20p coins
3 20p coins
Step-by-step explanation:
Answer:
For 90 is having each containing both the 20 and10 for 2 boxes then the rest each a 20&10
For 60 is two 20s and two10
Step-by-step explanation:
Hope it helps
A stack of 4 identical books is 6.28 high. What is the heigh of 30 of these books?
Answer:47.1
Step-by-step explanation:6.28/4=x/30
188.4=4x
47.1=x
Answer:
47.1
Step-by-step explanation:
height of 1 book=6.28÷4=1.57
height of 30 books=1.57×30=47.1
4. The 92 million Americans of age 50 and over control 50% of all discretionary income. AARP estimates that the average annual expenditure on restaurants and carryout food was $1,873 for individuals in the age group. Suppose this estimate is based on a sample of 80 persons and that the sample standard deviation is $550. a. At 95% confidence, what is the margin of error
Answer:
$120.52
Margin of error M.E = $120.52
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
Where M.E = margin of error
M.E = zr/√n
Given that;
Mean x = $1,873
Standard deviation r = $550
Number of samples n = 80
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
M.E = (1.96 × $550/√80) = 120.5240639872
M.E = $120.52
Margin of error M.E = $120.52
A florist currently makes a profit of $20 on each of her celebration bouquets and sells a average of 30 bouquets every week
Answer:
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW;
A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.
CHECK THE ATTACHMENT FOR THE GRAPH
EXPLANATION;
FIRST QUESTION:
From the graph maximum profit is the value gotten where p(X) has maximum value, and the maximum value is observed at y- axis at P(X)to be 675.
Thefore, maximum profit the florist will earn from celebration bouquet is $675.
SECOND QUESTION:
Break even is the exact point that profit p(x) is observed as zero.
Checking the given g graph the point where there is zero value of p(X) is observed at x=20 and x= -10 but we can only pick the positive value which is x=20
Therefore, the florist will break even after 20 one- dollar decreases
THIRD QUESTION;
The interval of number of one dollar decreases can be observed at the point where we have the value of P(x) been more than zero, looking at the given graph, the P(x) has its value greater than zero at the interval 0 to 20.Therefore, it can be concluded that the interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)
Answer:
Step-by-step explanation:
The freezer contains vanilla and chocolate ice cream. Chocolate ice cream contains 12 servings less than vanilla. How many servings of vanilla ice cream are in the freezer if there are a total of 40 servings of ice cream? (Solve by building an equation)
Answer:
26 servings
Step-by-step explanation:
Let the number of servings of vanilla ice cream be x.
Number of servings of chocolate ice cream
= x -12
(since it has 12 servings less than vanilla)
Total servings= servings of chocolate+ vanilla
x + x-12= 40
2x -12 =40 (simplify)
2x= 40 +12 (+12 on both sides)
2x= 52 (simplify)
x= 52 ÷2
x= 26
Therefore, there are 26 servings of vanilla ice cream in the freezer.
If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.
88 degrees
89 degrees
90 degrees
91 degrees
Answer:
89 degrees
Step-by-step explanation:
The angle 1 is the same as angle 3.
Angle 2 is the same as angle 4.
The sum of these four angles is 360 degrees.
We have that:
Angle 2 = Angle 4 = 7x - 14
Angle 3 = Angle 1 = 5x + 14
Finding x:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
2*(5x + 14) + 2*(7x - 14) = 360
10x + 28 + 14x - 28 = 360
24x = 360
x = 15
Angle 1:
5x + 14 = 5*15 + 14 = 89 degrees
Answer:
I think it is B
Step-by-step explanation:
15=3(2x+4)-3 prove x=1
Answer:
X=1
Step-by-step explanation:
6x+12-3=15
6x+9=15
6x+9-9=15-9
6x=6
X=1
Answer:
see below
Step-by-step explanation:
15=3(2x+4)-3
Distribute
15 = 6x +12 - 3
Combine like terms
15= 6x +9
Subtract 9 from each side
15 -9 = 6x+9-9
6 = 6x
Divide each side by 6
6/6 = 6x/6
1 =x
What’s the correct answer for this question?
Answer: 3/20
Step-by-step explanation:
p(A)=the day selected in Monday =1/5
p(B)=student is absent
P(A∩B)=it is Monday AND a student is absent =3/100
Events A and B are independent so
P(A∩B) = P(A) · P(B)
3/100=1/5*p(B)
p(B)=3/20
The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass?
Required:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Answer:
Answers below
Step-by-step explanation:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Accident rate data y1, ...., y12 were collected over 12 consecutive years t=1,2,...12. At over 12 consecutive years t = 1,2,..., 12. At the end of the 6th year, a change in safety regulations occured. FOr each of the following situations, set up a linear model of the form y=XB+E. Define X and B appropriately.
a. The accident rate y is a linear function of t with the new safety regulations having no effect.
b. The accident rate y is a quadratic function of t with the new regulations having no effect.
c. The accident rate y is a linear function of t. The slope for t>= 7 is the same as for t<7. However there is a discrete jump for t=7.
d. The accident rate y is a linear function of t. After t=7, the slope changes, with the two lines intersecting at t=7.
Answer:
The correct option is;
The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7
Step-by-step explanation:
The given parameters are;
Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂
Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂
Accident rate equation is a linear model given as follows;
y = X·B + E
Where:
y = Accident rate
X = Slope of linear model
B = Year
E = y intercept of model
At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;
Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁
After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂
Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)
Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."
A parabola has a focus of (6,–6) and a directrix of y = –2. Which of the following could be the equation of the parabola?
Answer:
[tex]-8(y+4) =(x-6)^{2}[/tex]
Step-by-step explanation:
The standard form of a parabola is given by the following equation:
[tex](x-h)^{2} =4p(y-k)[/tex]
Where the focus is given by:
[tex]F(h,k+p)[/tex]
The vertex is:
[tex]V=(h,k)[/tex]
And the directrix is:
[tex]y-k+p=0[/tex]
Now, using the previous equations and the information provided by the problem, let's find the equation of the parabola.
If the focus is (-6,6):
[tex]F=(h,k+p)=(6,-6)[/tex]
Hence:
[tex]h=6\\\\k+p=-6\hspace{10}(1)[/tex]
And if the directrix is [tex]y=-2[/tex] :
[tex]-2-k+p=0\\\\k-p=-2\hspace{10}(2)[/tex]
Using (1) and (2) we can build a 2x2 system of equations:
[tex]k+p=-6\hspace{10}(1)\\k-p=-2\hspace{10}(2)[/tex]
Using elimination method:
(1)+(2)
[tex]k+p+k-p=-6+(-2)\\\\2k=-8\\\\k=-\frac{8}{2}=-4\hspace{10}(3)[/tex]
Replacing (3) into (1):
[tex]-4+p=-6\\\\p=-6+4\\\\p=-2[/tex]
Therefore:
[tex](x-6)^{2} =4(-2)(y-(-4)) \\\\(x-6)^{2} =-8(y+4)[/tex]
So, the correct answer is:
Option 3
Calculate g(x)=f(x+1) when f(x) =4x-2
Answer:
g(x)= 2/5
Step-by-step explanation:
g(xl=f(4x-2)+1
5×-2
5x/5
x=2/5
Find the area of a circle with diameter, D = 8.1m.
Give your answer rounded to 1 DP (One decimal point)
The photo is attatched below
Answer:
51.5m
Step-by-step explanation:
half 8.1 to get the radius (4.05)
then times pi by 4.05 squared
your answer is 51.5 (rounded)
An amount was invested at r% per quarter. What value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
25.75 % interest rate
Step-by-step explanation:
Given:
Amount was invested = r% per quarter
Amount invested = P
Rate of interest = r % per quarter
Time (n) = 4 Quarters
Computation:
A = P(1 + r/100)ⁿ
According to question.
⇒ A = P + 1.5P = 2.5P
⇒ 2.5P = P(1 + r/100)⁴
⇒ 2.5 = (1 + r/100)⁴
⇒ 1 + r/100 = 1.2575
⇒ r/100 = 0.2575
⇒ r = 25.75
25.75 % interest rate
16. Convert 55° to radians.
Answer:
0.96 radians
Step-by-step explanation:
Formula
1° = [tex]\frac{\pi }{180}[/tex] radians
Multiplying both sides by 55, It becomes
55° = [tex](\frac{\pi }{180} )*55[/tex]
55° = [tex]\frac{55\pi }{180}[/tex]
= 172.8/180
= 0.96 radians
Mariah spent $9.50 on 9 pounds of limes and pears. Limes cost $0.50 per pound and pears cost $1.50 per pound. Let l be the number of pounds of limes and let p be the number of pounds of pears.
The system of linear equations that models this scenario is:
l + p = 9
0.5l + 1.5p = 9.5
How many pounds of each type of fruit did she buy?
Answer:
4 pounds of lime and 5 pounds of pears
Step-by-step explanation:
I + P = 9
0.5l + 1.5P = 9.5
I = 9 - P
0.5(9 - P) + 1.5P = 9.5
4.5-0.5P + 1.5P = 9.5
4.5 + P (1P) = 9.5
P = 9.5-4.5 = 5
I = 9 - 5 = 4
Answer: 4 pounds of lime and 5 pounds of pears
Please answer this correctly
Answer:
326
Step-by-step explanation:
l x w
7x8
25x6
4x30
326
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 260.5-cm and a standard deviation of 1.6-cm. For shipment, 8 steel rods are bundled together.Find the probability that the average length of a randomly selected bundle of steel rods is greater than 260.2-cm.P(M > 260.2-cm) = Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Answer:
P(M > 260.2-cm) = 0.702
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 260.5, \sigma = 1.6, n = 8, s = \frac{1.6}{\sqrt{8}} = 0.5657[/tex]
P(M > 260.2-cm)
This is 1 subtracted by the pvalue of Z when X = 260.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260.2 - 260.5}{0.5657}[/tex]
[tex]Z = -0.53[/tex]
[tex]Z = -0.53[/tex] has a pvalue of 0.298.
1 - 0.298 = 0.702
So
P(M > 260.2-cm) = 0.702
Dominique is thinking about buying a hosue for 286000
Answer:
is this supposed to be a question?
Answer:
yah so
Step-by-step explanation:
sider F and C below. F(x, y, z) = yz i + xz j + (xy + 4z) k C is the line segment from (1, 0, −2) to (6, 4, 1) (a) Find a function f such that F = ∇f. f(x, y, z) = xyz+2z2+c (b) Use part (a) to evaluate C ∇f · dr along the given curve C.
Answer:
a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]
b) The value of the integral is 18
Step-by-step explanation:
a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that
[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]
From here, we have that
[tex] yz = \frac{\partial f}{\partial x}[/tex]
if we integrate both sides with respect to x, we get that
[tex] f(x,y,z) = xyz+ g(y,z)[/tex]
where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is
[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]
This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form
[tex] f(x,y,z) = xyz+g(z)[/tex]
If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get
[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]
This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]
So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]
b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is
[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]
What is the answerrrrrrrrrrrr :(((((((((((
Answer: The answer is choice 3
Step-by-step explanation:
i think the answer is c
Step-by-step explanation:
i don't think u would want a whole explanation
Find the volume of the cone below.
Answer:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
Step-by-step explanation:
For this case we know that the volume of the cone is given by:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
What is the midpoint of the vertical line segment graphed below? (2,4) (2,-9)
Answer is A
Midpoint
[tex] \frac{x \: a xis}{2} . \frac{y \: axis}{2} [/tex]
[tex] \frac{2 + 2}{2} . \frac{4 + ( - 9)}{2} [/tex]
[tex](2. - 2.5 )[/tex]
Maddie is packing moving boxes. She has one 3 cubic-foot box and one 6 cubic-foot box. How many cubic feet of clothing can she fit in the two boxes?
8 9 10 12
Answer:
She can fit 9 cubic feet of clothing in the two boxes.
Step-by-step explanation:
She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.
3 + 6 = 9
Answer:
9 cu ft.
Step-by-step explanation:
That is the sum of the capacities of the 2 boxes
= 3 + 6
= 9 cu ft.
Erin has previously recorded all credit card activity manually using the Expense transaction screen and reconciled the account using the Reconciliation Tool. After connecting her credit card in the Banking Center, she doesn’t see any matches for the transactions she previously entered and reconciled.
Answer:
The steps Erin has to take for the reconciliation of her account and activities is as follows: Select the reconciled transactions, Select Batch actions, and Modify the selected ones.
Step-by-step explanation:
Solution
Since Erin could not detect any matches for the transactions she has entered before and enrolled, she needs to take the following processes to reconcile back all her credit activities which is stated below:
Process 1 :Select the reconciled transactions
Process 2 :Batch Actions
Process 3: Modify Selected
From the process stated above Erin can first of all choose the reconciled transactions, after that she can select the batch actions and lastly modify the ones that was selected with the aim of putting or adding them back in the account reconciliation.
Which of the following represents "two times the sum of a number and fifteen is equal to six times the number?"
A. 2(6N + 15) = N
B. 2N + 15 = 6N
C. 2(N + 15) = 6N
A study of consumer smoking habits includes A people in the 18-22 age bracket (B of whom smoke), C people in the 23-30 age bracket (D of whom smoke), and E people in the 31-40 age bracket (F of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes.
The correct question is:
A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes
Answer:
The probability of getting someone who is age 23-30 or smokes = 0.575
Step-by-step explanation:
We are given;
Number consumers of age 18 - 22 = 167
Number of consumers of ages 22 - 30 = 148
Number of consumers of ages 31 - 40 = 85
Thus,total number of consumers in the survey = 167 + 148 + 85 = 400
We are also given;
Number consumers of age 18 - 22 who smoke = 59
Number of consumers of ages 22 - 30 who smoke = 31
Number of consumers of ages 31 - 40 who smoke = 23
Total number of people who smoke = 59 + 31 + 23 = 113
Let event A = someone of age 23-30 and event B = someone who smokes. Thus;
P(A) = 148/400
P(B) = 113/400
P(A & B) = 31/400
Now, from addition rule in sets which is given by;
P(A or B) = P (A) + P (B) – P (A and B)
We can now solve the question.
Thus;
P(A or B) = (148/400) + (113/400) - (31/400)
P(A or B) = 230/400 = 0.575
choose the most convenient method to graph the line y=−3
Answer:
the line just goes straight up the y-axis. so, place your dot at -3 and draw the line straight up
Step-by-step explanation:
The line is shifted downward by 3 units from the x-axis, and the slope of the line is zero. The intercept of the line is at (0, -3).
What is the graph of the function?The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the line is given below.
y = –3
The line y = –3 is parallel to the x-axis.
The slope of the line is zero.
The line is shifted downward by 3 units from the x-axis.
The intercept of the line is at (0, -3).
The graph of the line y = –3 is given below.
More about the graph of the function link is given below.
https://brainly.com/question/9834848
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