2-55 Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability that a call takes
The question is incomplete. Here is the complete question.
Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. find the probability that a call takes
a) 3 minutes or less
b) 4 minutes of less
c) 5 minutes of less
d) Longer than 5 minutes
e) Longer than 7 minutes
Answer: a) P(X<3) = 0.882
b) P(X<4) = 0.908
c) P(X<5) = 0.928
d) P(X>5) = 0.286
e) P(X>7) = 0.174
Step-by-step explanation: Exponential distribution is related with teh amount of time until some specific event happens.
If X is a continuous random variable, probability is calculated as:
[tex]P(X<x) = 1-me^{-mx}[/tex]
in which:
m is decay parameter, given by: [tex]m=\frac{1}{mean}[/tex]
For the Nite Time Inn calls:
[tex]m=\frac{1}{4}[/tex]
m = 0.25
(a) P(X<3)
[tex]P(X<3) = 1-0.25e^{-0.25.3}[/tex]
[tex]P(X<3) = 1-0.25e^{-0.75}[/tex]
[tex]P(X<3) = 1-0.25*0.472[/tex]
P(X < 3) = 0.882
The probability the call takes less than 3 minutes is 0.882.
(b) P(X<4)
[tex]P(X<4) = 1-0.25e^{-0.25.4}[/tex]
[tex]P(X<4) = 1-0.25e^{-1}[/tex]
P(X < 4) = 0.908
The probability the call takes less tahn 4 minutes is 0.908.
(c) P(X<5)
[tex]P(X<5) = 1-0.25e^{-0.25.5}[/tex]
[tex]P(X<5) = 1-0.25e^{-1.25}[/tex]
P(X < 5) = 0.928
The probability of calls taking less than 5 minutes is 0.928.
(d) P(X>5)
Knowing that the sum of probabilities of less than and more than has to equal 1:
P(X<x) + P(X>x) = 1
P(X>x) = 1 - P(PX<x)
[tex]P(X>x) = 1-(1-me^{-m*x})[/tex]
[tex]P(X>x)=me^{-mx}[/tex]
For P(X>5):
[tex]P(X>5) = 0.25e^{-1.25}[/tex]
P(X > 5) = 0.286
The probability of calls taking more than 5 minutes is 0.286.
(e) P(X>7)
[tex]P(X>7)=0.25e^{-0.25.7}[/tex]
[tex]P(X>7)=0.25e^{-1.75}[/tex]
P(X > 7) = 0.174
The probability of calls taking more than 7 minutes is 0.174.
If 9 is subtracted from a certain number and the difference is divided by 3, the result is 1 more than
1/7 of the original number. Find the original number.
Answer:
Let the number be x.
(x-9)/3= (x/7)+1
(x-9)/3= (x+7)/7
Cross multiplying
7x-63= 3x+21
4x= 84
x= 42
Hope this will help :-)
a table is on sale for 72% off. the price is $246.40. What is the regular price
Answer:
$68.99
Step-by-step explanation:
This is called percentage decrease:
(100 - 72)% = 28%
246.40 × 28/100
= $68.99
Cynthia besch wants to buy a rug for a room that is 20 ft wide and 33 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 378 ft² of carpeting. What dimensions should the rug have?
Answer:
Length of rug = 14 ft
Width of rug = 27 ft
Step-by-step explanation:
Given:
Length of rug = 20 ft
Width of rug = 33 ft
Area she afford = 378 ft²
Find:
New sides
Computation:
Assume;
Uniform strip = x
So,
Length of rug = 20 - x ft
Width of rug = 33 - x ft
Ares = l × b
[20-x][33-x] = 378
660 - 20x - 33x + x² = 378
x² - 53x + 282
x² - 47x - 6x + 282
x(x-47) -6(x-47)
So,
x = 6 and x = 47
X = 47 not be taken, So x=6
Length of rug = 20 - 6 ft
Width of rug = 33 - 6 ft
Length of rug = 14 ft
Width of rug = 27 ft
Please, can you do this step-by-step.... 2 1/3 + 6 3/5
Answer:
8 14/15
Step-by-step explanation:
Step 1:
2 1/3 + 6 3/5
Step 2:
2 5/15 + 6 9/15
Answer:
8 14/15
Hope This Helps :)
Answer:8 14/15
Step-by-step explanation:
convert to lcd, 2 5/15 6 9/15
add them and you get that
A post is put every 6 feet along a fence around a rectangular field that is 42 feet long and 36 feet wide. What is the total number of feet around the field? *
Answer:
26 posts
Step-by-step explanation:
find perimeter:
42+42+36+36= 156
divide by 6
156/6=26
Solve the formula for the specified variable A= P+Prt for r
Answer:
R=a/pt-1/t
Step-by-step explanation:
r= a/pt-1/t
Step-by-step explanation:
The width of kevin's yard is three times the width of his garage, increased by 12 feet. What expression describes the width of kevin's yard if g represents the width of his garage?
Answer:
The expression that describes the width of Kevin’s yard is (3g + 12) feet
Step-by-step explanation:
This is an expression problem.
From the question, we are made to know that the width of the yard is 3 times the width of the garage increased by 12 feet.
Now, we are told that the width of the garage is g feet and we want to find the width of the yard.
The width of the yard will be g feet * 3 + 12
Mathematically that would be 3g + 12 feet
Which of the expressions has a sum of 15.41? Select all that apply. A. 11 . 38 + 4 . 03 B. 10 + 5 . 41 C. 12 . 38 + 2 . 93 D. 9 . 2 + 6 . 21 E. 7 . 54 + 6 . 87
Answer: A. 11 . 38 + 4 . 03
B. 10 + 5 . 41
D. 9 . 2 + 6 . 21
Step-by-step explanation:
Step 1
Compute the sum of the given options
a) 11 . 38 + 4 . 03 = 15.41
b) 10 + 5 . 41= 15.41
c) 12 . 38 + 2 . 93= 15.31
d) 9 . 2 + 6 . 21 =15.41
e) 7 . 54 + 6 . 87=14.41
Step 2
Eliminate the expressions that do not give a sum of 15.41 , we have
a) 11 . 38 + 4 . 03 = 15.41
b) 10 + 5 . 41= 15.41
d) 9 . 2 + 6 . 21 =15.41
Therefore, the expressions with sum of 15.41 are A, B and D
.8787... as a fraction
Step-by-step explanation:
Write 0.8787 as
0.8787/1
Multiply both numerator and denominator by 10 for every number after the decimal point
0.8787 × 10000
1 × 10000
=
8787/10000
Reducing the fraction gives
8787/10000
Which graph is generated by this table of values? x –5 –3 –1 4 y 2 4 1 0 On a coordinate plane, points are at (negative 5, 2), (negative 3, 4), (negative 1, 1), and (4, 0). On a coordinate plane, points are at (negative 5, negative 2), (negative 3, negative 4), (negative 1, negative 1), and (4, 0). On a coordinate plane, points are at (0, 4), (1, negative 1), (2, negative 5), and (4, negative 3). On a coordinate plane, points are at (1, negative 1), (3, negative 4), (4, 0), and (5, negative 2).
Answer:
The answer is A
Step-by-step explanation:
All you must do is find the correct values in the graph.
The graph which is generated by the table of values x -5,-3,-1,4 and y=2,4,1,0 is on coordinate plane points are at (-5,2) ,(-3,4) ,(-1,1) ,(4,0).
What is function?A function is a relationship between two or more variables having each value of x corresponding to y values. Values of x are known as domain and values of y are known as codomain.
How to graph function?We have been given the following table as under:
x y
-5 -3
-3 4
-1 1
4 0
We have to plot the points -5 ,-3,-1,4 on x axis and corresponding-3,4,1,0 on y-axis.
Hence the graph of given table of values is that on coordinate plane points are at (-5,2) (-3,4)(-1,1)(4,0).
Learn more about function at https://brainly.com/question/10439235
#SPJ2
Which of the following is an odd function??
O g(x) = x2
O g(x) = 5x - 1
O g(x) = 3
O g(x) = 4x
Step-by-step explanation:
An odd function is where g(x) = -g(-x).
Therefore the answer is g(x) = 4x, as it passes through the origin and g(x) is positive when x is positive, and g(x) is negative when x is negative.
The odd function will be g(x) = 4x. Then the correct option is D.
What is an odd function?A true function f(x) is said to be an odd function if the output value of f(-x) is the same as the negative of f(x) for all values of x in the domain of f.
The equation should be stored in an odd function:
f(-x) = -f(x)
Let's check all the options.
A. The function is g(x) = x².
Substitute x = -x, then we have
g(x) = (-x)²
g(x) = x²
This is an even function.
B. The function is g(x) = 5x – 1.
Substitute x = -x, then we have
g(x) = 5(–x) – 1
g(x) = – (5x + 1)
This is a neither even nor odd.
C. The function is g(x) = 3.
Substitute x = -x, then we have
g(x) = 3
This is an even function.
D. The function is g(x) = x.
Substitute x = -x, then we have
g(x) = -x
g(x) = x
This is an odd function.
Then the correct option is D.
More about the odd function link is given below.
https://brainly.com/question/14264818
#SPJ2
Suppose f(x) = 2x-1 and g (x) = x + 1/a. Which value(s) of a would make the composite functions commutative? A. 0 B. 2 C. any value of a D. no value of a
Answer:
2
Step-by-step explanation:
A commutative function means that when you insert one function in space of x in the other function, they will equal x. The equation is f(g(x)) = g(f(x)) = x
So, 2([tex]\frac{x+1}{a}[/tex]) - 1 = [tex]\frac{(2x-1)+1}{a}[/tex]
If you multiply both sides by a, you get 2a([tex]\frac{x+1}{a}[/tex]) - a = (2x-1)+1
Simplify it 2a([tex]\frac{x+1}{a}[/tex]) - a = 2x
Add a to both sides 2a([tex]\frac{x+1}{a}[/tex]) = 2x +a
The two as on the left cancel out 2(x+1)=2x+a
Distribute the 2 2x+2=2x+a
Then subtract 2x from both sides 2 = a
Therefore, a = 2
Hope this helps!
Answer:2
Step-by-step explanation:
number sets of the square root of 15
Answer:
the square root is 15=5
(-1.5)(0.8) need the answers asap
Answer:
what do u look like
Step-by-step explanation:
this is true or false? and why.
PLEASE HELPPP ON THIS ONE TOO
Out of 340 racers who started the marathon, 302 completed the race, 26 gave up, and 12 were disqualified. What percentage did not complete the marathon?
Answer:
11.18%
Step-by-step explanation:
Total = 340
Completed = 302
Not completed = 340 - 302 = 38
Not completed% = 38/340*100% = 11.18%
Trevor picked 5 ⅗ pounds of cherries. He distributed them evenly into 12 containers. How many pounds of cherries were in each container?
Answer:
7/15
Step-by-step explanation:
For me, it is easier to take the 3/5 and put it in decimal form which is .6 and add the 5 to it, making 5.6, and then in a calculator put in 5.6 divided by 12 and you should get a big decimal that's pretty big but if you have a graphing calculator and convert that to a fraction and you should get 7/15, This is a pretty lazy way of me doing it but that's how I did it.
Mx-y when m=2,x=7. And y= 5
Answer:
9
Step-by-step explanation:
mx - y (m = 2, x = 7, y = 5)
(2*7) - 5
= 14 - 5
= 9
The ages of an audience at a concert were recorded as follows:
12, 14, 13, 11, 10, 16, 17, 13, 12, 10, 10, 14, 15, 15, 12, 15, 17, 15
(a) Create a frequency table with the above information.
look at the image and show work 4) translation: 6 units left K, J, I, L
Answer:
K (-5, 2); J (-2, 3); I (-1, 1); L (-5, -3)
Step-by-step explanation:
Translating the shape 6 units to the left means that every point/vertex will be moved 6 units to the left of where it is originally drawn.
Point K is at (1, 2). Since we are only moving it left (on the x-axis), the y value will not change. To move K left 6, we have to subtract 6 from its current x-value, 1. We get -5 for the new x-value. Because the y value didn't change, the new location of K is (-5, 2).
Point J is at (4, 3). Subtracting 6 from 4 (the x value) gives us the new x value of -2. Again, the y value does not change and so our new location for J is (-2, 3).
Point I is at (5, 1). If we subtract 6 from 5, we get -1. This is our new x value for I. The new point is (-1, 1). (Once again, the y value does not change).
Point L is at (1, -3). By subtracting 6 from the original x value, 1, we get our new x value: -5. The new point for L is (-5, -3).
Here is a central angle that measures 1.5 radians. Select all true statements. Question 1 options: A) The area of the whole circle is 1.5 times the area of the slice. B) The radius is 1.5 times longer than the length of the arc defined by the angle. C) The ratio of radius to arc length is 1.5. D) The length of the arc defined by the angle is 1.5 times longer than the radius. E) The ratio of arc length to radius is 1.5. F) The circumference of the whole circle is 1.5 times the length of the arc formed by the angle.
Answer:
D, E
Step-by-step explanation:
The applicable formula is ...
s = rθ
so, for θ = 1.5, the arc length is 1.5 times the radius. The true statements are ...
D) The length of the arc defined by the angle is 1.5 times longer than the radius.
E) The ratio of arc length to radius is 1.5.
Express the following in scientific notation:
10,030,400,000
Answer:
1.00304 * 10^10
Step-by-step explanation:
The first one dark blue I think
Please help me solve the problem
Answer:
Probability of getting a green marble=5/15=3/5
Probability of getting a black marble=5/15=3/5
If 2.5 pounds of strawberries cost $10, how much do 8 pounds of strawberries cost? Question 17 options: $3.13 $32.00 $40.00 $2.00
Answer:
32 dollars for 8 pounds
Step-by-step explanation:
1. 2.5 times 3 = 7.5
2. 10 times 3 = 30
3. 2.5 divided by 5 = .5
4. 10 divided by 5 = 2
5. 7.5 + .5 equals 8
6. 30 + 2 = 32.
hope this helps you:)
Answer:
$32.00
Step-by-step explanation:
i took 10 divided by 2 and got its $4 a pound then take 8 times 4 and got 32
If the spread of data on one side of the median of a data set is much greater than the spread of data on the other side, then what shape does the data distribution have? Explain.
Irene's grandfather arrived in Sydney from Athens at 10 pm on Friday after a 25-hour trip. The flight began at 12 noon on Thursday, Athens time. What is the time difference between Athens and Sydney?
The question is incomplete:
Irene's grandfather arrived in Sydney from Athens at 10 pm on Friday after a 25-hour trip. The flight began at 12 noon on Thursday, Athens time. What is the time difference between Athens and Sydney?
A. Athens time is 9 hours behind Sydney time.
B. Athens time is 9 hours ahead of Sydney time.
C. Athens time is 15 hours behind Sydney time.
D. Athens time is 15 hours ahead of Sydney time.
Answer:
A. Athens time is 9 hours behind Sydney time.
Step-by-step explanation:
The statement indicates that the flight began at 12 noon on Thursday, Athens time and that it lasted 25 hours. So, you can calculate the Athens time when he arrived after 25 hours which would be 1 pm on Friday. Also, the statement says that Irene's grandfather arrived in Sydney at 10 pm on Friday and now we know that at that moment it was 1 pm on Friday, Athens time. From these, you can calculate the difference between 1 pm and 10 pm that would be 9 hours. Because of this, the answer is that the time difference between Athens and Sydney is that Athens time is 9 hours behind Sydney time.
Is 1/2 rational or a not whole interger
Answer:
Every integer is a rational number, numbers like 1/2,and -3/7 are also rational, It is an Rational number
Step-by-step explanation:
*PLEASE ANSWER ASAP, ILL CHOOSE BRAINLIEST* Julie is playing a game where she must flip 3 coins. If Julie flips all 3 coins and gets heads all three times, she wins. If Julie does not get heads all three times, she loses. This information was used to create the following tree diagram.
Answer:
It is fair.
See the chart?
On all coins, there is a 50/50 chance it will be wrong or right.
There are 6 sides.
Half of them are H, and the other half T.
So, there are 3 heads and 3 tails.
3 to 3 is equal, so it is fair.
Hope this helped :)!
Answer:
No, the game is not fair because Julie does not have equal probabilities of winning or losing.
Step-by-step explanation: