First Bank of Springdale operates a one-lane drive-in ATM machine. Cars arrive according to a Poisson distribution at the rate of 12 cars per hour. The time per car needed to complete the ATM transaction is exponential with mean 6 minutes. The lane can accommodate a total of 10 cars. Once the lane is full, other arriving cars seek service in another branch. Determine the following:(a) The probability that an arriving car will not be able to use the ATM machine because the lane is full.(b) The probability that a car will not be able to use the ATM machine immediately on arrival.(c) The average number of cars in the lane.
Answers
Answer:
a) 0.19
b) 0.9689
c) ≈ 6 cars
Step-by-step explanation:
Rate at which cars arrive = 12 cars/hour = 1/5 cars/minute
time needed by each car to complete ATM transaction = 6 minutes = 1/6 car/minute
capacity of lane = 10 car
n = 10
a) Calculate the probability of an arriving not using the ATM because the line is full
p ( not using the ATM ) = 0.19
b) probability that a car will not be able to use the ATM machine immediately on arrival
P ( n > 0 ) = 1 - Po
= 1 - 0.0311 = 0.9689
c) Average number of cars in the lane
Lq = 5.74 ≈ 6 cars
attached below is the detailed solution
Related Questions
All vectors and subspaces are in RnR n. Mark each statement True or False. Justify each answer.
a. Not every linearly independent set in RnR n is an orthogonal set.
b. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be computed without row operations on a matrix.
c. If the vectors in an orthogonal set of nonzero vectors are normalized, then some of the new vectors may not be orthogonal.
d. A matrix with orthonormal columns is an orthogonal matrix.
e. If L is a line through 0 and if ˆyy^ is the orthogonal projection of y onto L, then ∥ˆy∥∥ y^ ∥ gives the distance from y to L.
Answers
Answer:
a. True
b. True
c. False
d. False
e. False
Step-by-step explanation:
The matrix with orthonormal column must be in square for that it forms orthogonal matrix. Every orthonormal set of non zero vector is linearly independent. This statement is correct because there is linear combination of non zero vectors.
the passing of heart through a material is called _____
Answers
Answer:
hardening of the arteries.
12. Which of these is not a characteristic (property) of a polygon?
A. A closed shape
B. Parallel faces
C. Made of straight lines
D. Two-dimensional
Answers
B. Parallel faces
Not all sides need to be parallel and a polygon has only 1 face unless cut
he first date went well. You are still dating the same person and still looking for a great person to spend your life with. You are cautiously moving forward with the relationship and know that if they are a great match, their likelihood of being kind to animals is 0.9 whereas their likelihood of being kind to animals if they are not a great match is 0.7. You see that your prospective spouse is kind to animals. What is the probability that they are a great match now?
Answers
Answer:
0.125 = 12.5% probability that they are a great match now.
Step-by-step explanation:
To solve this question, we need the probability of a person being a great match, which i will use 0.1.
This question is solved using conditional probability.
Conditional Probability
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: Is kind to animals.
Event B: Is a great match.
Probability of being kind to animals:
0.9 of 0.1(Is a great match).
0.7 of 1 - 0.1 = 0.9(is not a great match). So
[tex]P(A) = 0.9*0.1 + 0.7*0.9 = 0.72[/tex]
Probability of being kind to animals and a great match:
0.9 of 0.1. So
[tex]P(A \cap B) = 0.9*0.1 = 0.09[/tex]
What is the probability that they are a great match now?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09}{0.72} = 0.125[/tex]
0.125 = 12.5% probability that they are a great match now.
1. One of the acute angles of a right triangle is 28°, the other acute angle is?
Answers
Answer:
no idea
Step-by-step explanation:
cuz I don't
1.) At a pet store, there are 30 aquariums. Of the 30, 20 have fresh water with 15
fish each. The other 10 aquariums have salt water with 6 fish each. Write an
equation that could be used to find f, the total number of fish at the pet store?
(Equations Review)
Your answer
Answers
Answer:
f = (20 × 15) + (10 × 6)
Step-by-step explanation:
You are just find how many fish are salt water and how many freshwater and adding them together. The total number of aquariums is irrelevant in this case.
Answer:
20 x 15 = A A= 300
10 x 6 = B B=60
A + B = F F= 360
300 + 60 = F
300 + 60 =360
Step-by-step explanation:
Pleasee marrkk me blainist
Help pleaseeeeeeeeeeee
Answers
Answer;
Mark traveled at the highest velocity to Charleston
Simplify.
10/-4 - √3
Answers
Answer:
here you go. hope this helps
Answer:
-4.23205080...
Step-by-step explanation:
A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now wants to determine whether the number of unique listeners per day has changed. Before the change in format, the site averaged 131,520 unique listeners per day. Now, beginning three months after the format change, the site manager takes a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. Using the data provided below, calculate the p-value for the following hypothesis test:
H0:μ=131,520
Ha:μ≠131,520
Listeners after change
125,020
139,250
101,590
94,800
83,700
84,380
139,170
89,380
91,410
139,570
138,980
102,710
124,600
144,770
156,920
131,100
140,020
139,250
118,800
128,380
168,370
133,140
106,930
129,630
120,820
125,250
122,860
122,500
135,230
148,870
Answers
Answer:
The p value is: 0.0301
Step-by-step explanation:
Given
[tex]\mu = 131520[/tex]
[tex]\bar x = 124247[/tex]
[tex]n = 30[/tex]
Required
Determine the p value
First, calculate the standard deviation of the given data.
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(83700 - 124247)^2 + (84380- 124247)^2 + (89380- 124247)^2 + ..... + (156920- 124247)^2 + (168370- 124247)^2}{30}}[/tex]
[tex]\sigma = \sqrt{\frac{13427820070}{30}}[/tex]
[tex]\sigma = \sqrt{447594002.333}[/tex]
[tex]\sigma = 21156[/tex]
The test statistic is then calculated as:
[tex]t = \frac{\bar x - \mu}{\sigma/\sqrt n}[/tex]
[tex]t = \frac{124247 - 131520}{21156/\sqrt{30}}[/tex]
[tex]t = \frac{-7273}{21156/5.48}[/tex]
[tex]t = \frac{-7273}{3860.58}[/tex]
[tex]t = -1.88[/tex]
The p value is calculated as:
[tex]P(Z > -1.88)[/tex]
[tex]P(Z>-1.88) = 0.030054[/tex]
[tex]P(Z>-1.88) = 0.0301[/tex] --- approximated.
Hence, the p value is: 0.0301
A car travels 45 feet in 1 second. At this rate, how many miles will it travel in 1 hour?
Answers
Answer:
256 i did it before
Step-by-step explanation:
In feet the car will travel 162,000 ft. In miles it will be 30.7 rounded original is 30.68 miles. I hope this helps.
i need help ASEP please help me
Answers
Answer:
5
Step-by-step explanation:
it is 5 because you do 1+4=5
Sebastian says that the graph below shows the solution set of the inequality 2.5x≥−20. Do you agree?
Answers
Answer:
There is not a graph.
Step-by-step explanation:
You forgot to include the screenshots.
Jacob Lee is a frequent traveler between Los Angeles and San Diego. For the past month, he wrote down the flight times in minutes on three different airlines. The results are:
Goust Jet Red Cloudtran
51 50 52
51 53 55
52 52 60
42 62 64
51 53 61
57 49 49
47 50 49
47 49
50 58
60 54
54 51
49 49
48 49
48 50
Required:
a. Use the α =0.05 significance level and the six-step hypothesis-testing process to check if there is a difference in the mean flight times among the three airlines.
b. Develop a 95% confidence interval for the difference in the means between Goust and Cloudtran
Answers
Solution :
We know that
[tex]$H_0: \mu_1 = \mu_2=\mu_3$[/tex]
[tex]$H_1 :$[/tex] At least one mean is different form the others (claim)
We need to find the critical values.
We know k = 3 , N = 35, α = 0.05
d.f.N = k - 1
= 3 - 1 = 2
d.f.D = N - k
= 35 - 3 = 32
SO the critical value is 3.295
The mean and the variance of each sample :
Goust Jet red Cloudtran
[tex]$\overline X_1 =50.5$[/tex] [tex]$\overline X_2 =50.07143$[/tex] [tex]$\overline X_3 =55.71429$[/tex]
[tex]$s_1^2=19.96154$[/tex] [tex]$s_2^2=14.68681$[/tex] [tex]$s_3^2=36.57143$[/tex]
The grand mean or the overall mean is(GM) :
[tex]$\overline X_{GM}=\frac{\sum \overline X}{N}$[/tex]
[tex]$=\frac{51+51+...+49+49}{35}$[/tex]
= 52.1714
The variance between the groups
[tex]$s_B^2=\frac{\sum n_i\left( \overline X_i - \overline X_{GM}\right)^2}{k-1}$[/tex]
[tex]$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$[/tex]
[tex]$=\frac{127.1143}{2}$[/tex]
= 63.55714
The Variance within the groups
[tex]$s_W^2=\frac{\sum(n_i-1)s_i^2}{\sum(n_i-1)}$[/tex]
[tex]$=\frac{(14-1)19.96154+(14-1)14.68681+(7-1)36.57143}{(14-1)+(14-1)+(7-1)}$[/tex]
[tex]$=\frac{669.8571}{32}$[/tex]
= 20.93304
The F-test statistics value is :
[tex]$F=\frac{s_B^2}{s_W^2}$[/tex]
[tex]$=\frac{63.55714}{20.93304}$[/tex]
= 3.036212
Now since the 3.036 < 3.295, we do not reject the null hypothesis.
So there is no sufficient evidence to support the claim that there is a difference among the means.
The ANOVA table is :
Source Sum of squares d.f Mean square F
Between 127.1143 2 63.55714 3.036212
Within 669.8571 32 20.93304
Total 796.9714 34
GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)
Answers
Answer:
.7880
Step-by-step explanation:
Answer:
pretty sure it's 0.7880 !!! good luck, this stuff is super tough :(
Step-by-step explanation:
For a quadratic equation where: 2++=0
a
x
2
+
b
x
+
c
=
0
Where: 2−4<0
b
2
−
4
a
c
<
0
How many solutions do you have?
State whether the solutions are rational, irrational, or non-real. Explain why.
Answers
Answer: No real solution
Step-by-step explanation:
Given
For the quadratic equation
[tex]ax^2+bx+c=0[/tex]
It is given that [tex]b^2-4ac<0[/tex]
[tex]D=b^2-4ac[/tex]
If [tex]D=0[/tex] roots are real and equal
If [tex]D>0[/tex] roots are real and distinct
If [tex]D<0[/tex] roots are imaginary
In this case, [tex]D<0[/tex]
So, there is no real solution for the given quadratic equation.
Gavmans
add me on pinterest
Answers
Answer:
I would also add you...but i just don't WANT to
Find the area of the figure.
6 in.
6 in.
8 in.
4 in.
Answers
Answer:
92 inches squared
Step-by-step explanation:
6x6=36
4x(8+6)=56
56+36=92
8x/2 = 24, what value for x makes this equation true?
Answers
Answer:
x=6
Step-by-step explanation:
8x/2= 24
8x = 24× 2
8x= 48
8x÷8 = 48÷8
x= 6
Answer:
6
Step-by-step explanation:
multiply both sides by 2/8 to isolate x.
8/2x=24
2/8(8/2)x=2/8(24)
x=48/8
x=6
What is the range of y = 7x^2 + 14x – 9?
Answers
Answer:
-1,-16
Step-by-step explanation:
y=ax^2+box+c
The diagram shows the radius of the circular
opening of a metal soup can.
3 in
Soup
Which of the following is closest to the area of
the opening in square centimeters?
A.
9.42 in?
C. 18.75 in?
Need Help?
B.
28.27 in
D. 113.1 in
Answers
Answer:
B. 28.27
Step-by-step explanation:
What is Bc and what is ac
Answers
Answer:
Before and after current era
Find the value of the expression below when x = 27, y = - 4 , and z = 64 . 2 * root(3, x) - 5sqrt(x) + y ^ 2 answer
Answers
Answer:
-18Step-by-step explanation:
x = 27, y = - 4, z = 64Expression:
2∛x - 5√z + y² = 2∛27 - 5√64 + (-4)² = 2(3) - 5(8) + 16 = 6 - 40 + 16 = -18Is 1/2 equal , less than or greater than 9/10
Answers
Answer:
1/2 is less than 9/10
Step-by-step explanation:
1/2 =0.5
9/10=0.9
Answer:
1/2 is less than 9/10
Step-by-step explanation:
When you change the denomenator to be equal the other denominator, 1/2 will change to 5/10. 1 x 5 = 5. 2 x 5 = 10.
So, since 9/10 is greater than 5/10, 1/2 would be less than 9/10.
Determine the slope and the y- intercept of the line 7x +3y = -8
Answers
Answer:slope is -7/3 and x=0 y=-8/3
Step-by-step explanation:
The slope of the line is -7/3
The y-intercept of the line is -8/3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
7x + 3y = -8
3y = -8 - 7x
3y = -7x - 8
y = (-7/3)x - 8/3
This is in the form of y = mx + c
Now,
Slope = -7/3
y-intercept = -8/3
Thus,
The slope is -7/3 and the y-intercept is -8/3.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ2
Graph triangle JKL and its image after a reflection in the line x=2 J(1,-1), K(3,0), L(0,-4)
Answers
Answer:
I need more information to help you on this question.
Step-by-step explanation:
The points after image reflection in the line x = 2 will be k'(1, 0), L'(4, -4) and J'(3, -1).
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given information in the question,
Here mirror (x = 2) is vertical, hence only x-coordinate changes vertical distance from x-axis will not change.
For point k(3, 0)
It is one unit right side or x = 2. So, its image point will be one unit left side that is k'(1, 0).
For point L(0, -4)
It is two unit left side, so L' will be 2 unit right side of x = 2, so the point will be L'(4, -4)
Similarly, point J(1, -1) will become J'(3, -1).
To know more about Graph:
https://brainly.com/question/17267403
#SPJ2
6. Which TWO sets of numbers
have a difference of 5?
A. 12 and 7
B. 13 and 6
C. 11 and 8
D. 14 and 9
Answers
Answer:
A and D
Step-by-step explanation:
A: 12-7=5
B: 13-6=7
C: 11-8=3
D 14-9=5
Have a Fantastic Day! :D
Explanation:
Difference is the result of subtracting
12 - 7 = 5
13 - 6 = 7
11 - 8 = 3
14 - 9 = 5
Write integer to describe each situation. A. Charge of 24$ is debited from a bank account
Answers
Answer:
-24
Step-by-step explanation:
To represent a charge of $24 debited from a bank account, this type of transaction being described as a debit means that a sum of $24 was deducted from the account, meaning the total amount in the account will reduce after this transaction takes place. Hence a charge of $24 being debited will take a negative sign as could be represented by the integer - 24
ASAP!! simplify x^-2 show work
Answers
Answer:
1/x^2
Step-by-step explanation:
exponent rule: a^-b = 1/a^b
x^-2 = 1/x^2
Answer:
[tex] \frac{1}{ {x}^{2} } [/tex]
Step-by-step explanation:
1) Remove parentheses.
[tex] {x}^{ - 2} [/tex]
2) Use negative power rule: x^-a = 1/x^a.
[tex] \frac{1}{ {x}^{ 2} } [/tex]
hence, the answer is 1/x^2.
Help Please!! Struggling with this for a while
Answers
Answer:
Area of triangle ABC = 6 square units
Step-by-step explanation:
By applying Pythagoras theorem in right triangle ADC,
AC² = AD² + CD²
3² = (1.8)² + CD²
9 - 3.24 = CD²
CD = √5.76
CD = 2.4 units
By applying mean ratio theorem,
[tex]\frac{AD}{CD}=\frac{CD}{DB}[/tex]
CD² = AD × DB
(2.4)² = 1.8 × DB
DB = [tex]\frac{5.76}{1.8}[/tex]
DB = 3.2 units
AB = AD + DB
AB = 1.8 + 3.2
AB = 5 units
Since, area of a triangle ABC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(\text{AB})(\text{CD})[/tex]
= [tex]\frac{1}{2}(5)(2.4)[/tex]
= 6 square units
What linear expression would you add to -4y+2 to have a sum of y
Answers
Answer:
4
Step-by-step explanation: