Answer:
V=π(d/2)^2·h
=π·(10/2)^2 · 20
≈1570.79633in³
this is the correct answer!!!
The approximate volume of the cylinder is 1570.796 inches³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
A cylinder is a geometrical shape has two circular bases which are parallel and they are connected with a curved surface.
Given that,
Height of the cylinder = 20 inches
Diameter of the base = 10 inches
Radius = Diameter / 2 = 10/2 = 5 inches
Volume of the cylinder = π r² h, where r is the radius and h is the height.
Volume = π (5)² (20)
= 500π
= 1570.796 inches³
Hence the volume is approximately 1570.796 inches³.
Learn more about Volume here :
https://brainly.com/question/16134180
#SPJ3
21=b/-19 solve for b
Answer:
-399
Step-by-step explanation:
21=b/-19
b=21 x -19
b=-399
Answer:
-399
explanation
b=21×-19
b=-399
2. Which number is a solution of the inequality?
x(7 - x) > 8
A 8
B 2
C-1
D 0
Answer:
B
Step-by-step explanation:
x * ( 7 - x ) > 8
Substitute the number and if the expression is True then that number is a solution.
A substitute x=8
x * ( 7 - x ) > 8
8 * ( 7 - 8 ) > 8
8 * ( -1 ) > 8
-8 > 8
This statement is FALSE so the number is not a solution of the inequality.
B substitute x=2
x * ( 7 - x ) > 8
2 * ( 7 - 2 ) > 8
2 * ( 5 ) > 8
10 > 8
This statement is True so the number is a solution of the inequality.
C substitute x=-1
x * ( 7 - x ) > 8
-1 * ( 7 - -1 ) > 8
-1 * ( 7 + 1 ) > 8
-8 > 8
This statement is FALSE so the number is not a solution of the inequality.
D substitute x=0
x * ( 7 - x ) > 8
0 * ( 7 - 0 ) > 8
0 * ( 7 ) > 8
0 > 8
This statement is FALSE so the number is not a solution of the inequality.
Students are going through a three-step process to obtain their ID cards. Each student will spend 2 minutes at the registration desk before going to one of three cashiers to pay a fee for the ID card. After that, he/she will visit one of four ID processing stations to have his/her picture taken and ID card printed. Visits to the cashier and ID processing station take 10 and 20 minutes respectively. If the demand rate is 0.125 student per minute, how long does it take to process 20 students assuming the system is full?
A. 100 minutes
B. 152 minutes
C. 160 minutes
D. 184 minutes
Answer:
C. 160 minutes
Step-by-step explanation:
The calculation to be made will be to process 20 students
We have, according to the exercise, the following data:
For process 1: Registration table, Number of servers = 1, Time spent = 2 minutes
For process 2: cashier, number of servers = 3, time spent = 10 minutes
For process 3: ID processing station, number of servers = 4, time spent = 20 minutes
Demand rate = 0.125
To solve it, we will look for the capacity that the server has of the previously mentioned processes, calculating the following:
Capacity = Number of students served per minute
We can say that at the registration table we observe:
Time needed to serve 1 student = 2 minutes
Capacity = 0.5 students per minute
With the cashier we analyze the following:
Time needed to serve 1 student = 10 minutes
Number of servers = 3
Capacity = 0.3 students per minute
ID processing station
Time needed to serve 1 student = 20 minutes
Number of servers = 4
Capacity = 0.2 students per minute
When comparing the processes, it is definitely found that the bottleneck is the ID processing station, where it takes more time to serve a student, which leads us to infer that the capacity of the process is comparable to the capacity of the process bottleneck
Process capacity = 0.2 students per minute
Given, demand rate = 0.125 students per minute
We observe that the demand rate is less than the capacity of the process, therefore we can infer that the number of students served during each minute is the same as the demand rate.
In this way we find that:
Number of students served per minute = 0.125
Time needed to serve 1 student = 1 / 0.125 = 8 minutes
Time needed to serve 20 students = 8 x 20 = 160 minutes.
We conclude that the answer is that it will take 160 minutes to serve 20 students.
.
Answer:
C) 160 minutes
Explanation:
Given:
Time spent at registration desk = 2mins
Time spent at the cashier = 10 mins
Time spent at the ID processing station = 20 mins
Number of registration desk = 1
Number of cashiers = 3
Number of ID processing stations = 4
Let's calculate the capacity of each process using the expression: number of agents / process time
Therefore,
Capacity of registration desk =
[tex] \frac{1}{2} = 0.5 students per min[/tex]
Capacity of cashiers =
[tex] \frac{3}{10} = 0.3 students per min [/tex]
Capacity of ID processing stations =
[tex] \frac{4}{20} = 0.2 students per min[/tex]
The process capacity is equal to the bottleneck process. Here, the bottleneck process is the process with the longest time per minute which is the ID processing station.
Therefore, given a rate of 0.125 student per min and Process capacity of 0.2 student per min, we'll take 0.125 as the number of students per minute since it is lower than the process capacity.
Therefore, time taken to serve one student = [tex] \frac{1}{0.125} = 8mins [/tex]
Time taken to serve 20 students would be = 20 * 8 = 160 minutes
Eat For 10 Hours. Fast For 14. This Daily Habit Prompts Weight Loss, Study Finds This is the title of an NPR article about a 2019 study that recruited 19 overweight adults diagnosed with metabolic syndrome (elevated blood sugar, elevated cholesterol levels, high blood pressure). Participants were asked to restrict any eating to a period of just 10 hours each day. The study found a statistically significant reduction in body weight after 12 weeks of this eating pattern.
Define the parameter in this hypothesis test as a sentence in context.
Answer:
Step-by-step explanation:
The parameter in this hypothesis test describes the entire population. So in this test, the parameter is looking into the summary number for instance like an average of all overweights who after undergoing this pattern/daily habits exhibits weight loss.
circle O with chords AB and CD intersecting at E if CE= 20 ED=12 and Ae =8 Determine the length of EB
Answer:
12+20+8=40
Step-by-step explanation:
1tu5gtv445567164r7f+5824++
dane used a ruler and a protractor to draw a rhombus with a side of 4 cm inlength and an angle that measures 110 degrees choose the angle measure that is missing
Answer:
70 °
Step-by-step explanation:
We have that one side of the rhombus is equal to 4 cm and an angle of the rhombus is 110 degrees. We know that the adjacent sides of a rhombus are supplementary, which means that the sum of the angles must be 180 degrees.
We can assume that the other angle is x.
110 ° + x = 180 °
x = 180 ° -110 °
x = 70 °
The measure of the missing angle on the diagram will be 70 °.
helpp degrees, minutes, and seconds
Answer:
3) 174°15'18"
4) 34.859722...(repeating)°
5) 434°, -286°
Step-by-step explanation:
There are 60 minutes in a degree, and 60 seconds in a minute.
3) To find minutes, multiply fractional degrees by 60:
.255° = 0.255°×(60'/1°) = 15.3'
To find seconds, multiply fractional minutes by 60:
0.3' = 0.3'×(60"/1') = 18"
Then the whole angle is ...
174.255° = 174° 15' 18"
__
4) The conversion works the other way, too.
34° 51' 35" = 34° +51(1/60)° +35(1/3600)° = (34 619/720)°
= 34.8597222...° (a repeating decimal)
__
5) Add or subtract multiples of 360° to get co-terminal angles.
74° +360° = 434°
74° -360° = -286°
f(x)=-9x^2-2x and g(x)=3x^2+6x-9, find (f-g)(x) and (f-g)(-4)
Answer:
[tex](f-g)(x) = -12x^{2} - 8x + 9[/tex]
(f-g)(-4) = -151
Step-by-step explanation:
To find f-g(x) we subtract the common terms. So
[tex]f(x) = -9x^{2} - 2x[/tex]
[tex]g(x) = 3x^{2} + 6x - 9[/tex]
(f-g)(x)
[tex](f-g)(x) = f(x) - g(x) = -9x^{2} - 2x - (3x^{2} + 6x - 9) = -9x^{2} - 2x - 3x^{2} - 6x + 9 = (-9 - 3)x^{2} + (-2 - 6)x + 9 = -12x^{2} - 8x + 9[/tex]
(f-g)(-4)
[tex](f-g)(x) = -12x^{2} - 8x + 9[/tex]
We replace x by -4
[tex](f-g)(-4) = -12(-4)^{2} - 8(4) + 9= -151[/tex]
(f-g)(-4) = -151
A device that continuously measures and records seismic activity is placed in a remote region. The time, T, to failure of this device is exponentially distributed with mean 3 years. Since the device will not be monitored during its first two years of service, the time to discovery of its failure is X = max(T, 2).
Answer:
E[X]= [tex]2 + 3 e^{(-2/3)[/tex]
Step-by-step explanation:
The objective of this question is to determine E[X].
T is defined (0,infinity)
X=max(c,T)
where; c=constant
E[X]=c+function (c,infinity) Sf(t)dt
E[X] =[tex]e^{-t/3[/tex]
E[X]=2+function (2,infinity)[tex]e^{-t/3[/tex]dt
E[X] =[tex](2+e^{-t/3})/(1/3)[/tex] function (2,infinity)
E[X]= [tex]2 + 3 e^{(-2/3)[/tex]
If X = T if T ≥ 2 and X = 2 if 0 ≤ T < 2,
So Since T is exponentially distributed with mean 3, the density function of T is [tex]f(t) = (1/3)e^{(-t/3)[/tex]
A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap.
Part A Write an equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.
Part B Write an equation to relate the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.
Answer:
a) 2b = 3g
b) 3p = b
Step-by-step explanation:
Given:
Fire hydrant with a blue cap, b, provides water at a rate = 1500 gallons per min
Fire hydrant with a green cap, g, provides water at a rate = 1000 gallons per min
Fire hydrant with a purple cap, p, provides water at a rate = ½g = [tex] \frac{1}{2}*1000 = 500 [/tex]
a) The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.
Given flow of blue hydrant, b = 500
Simplifying, we have:
b = 3*500
[tex] b = 3 * \frac{1000}{2} [/tex]
Since the flow rate of green hydrant, g, is 1000, let's replace 1000 with g above.
Therefore,
[tex] b = 3 * \frac{g}{2} [/tex]
[tex] b = \frac{3}{2}g [/tex]
Cross multuply
[tex] 2b = 3g [/tex]
The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g is 2b=3g.
b) An equation to relate the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.
Given flow rate of purple hydrant, p = 500
It could also be re-written as:
[tex] \frac{3}{3} * 500 [/tex]
[tex] p = \frac{1500}{3} [/tex]
Since the flow rate of blue hydrant, b, is 1500, let's replace 1500 with b above.
[tex] p = \frac{b}{3} [/tex]
Cross multiply
3p = b
The relation between the flow of water between different caps is required.
The relations are b = (3/2)g and p = (1/3)b
Rateb = Rate of water flow through blue cap = 1500 gallons per minute
g = Rate of water flow through green cap = 1000 gallons per minute
p = Rate of water flow through purple cap = 1000/2 = 500 gallons per minute
We have the relation
[tex]1000\times 1.5=1500[/tex]
[tex]\Rightarrow g1.5=b[/tex]
[tex]\Rightarrow b=\dfrac{3}{2}g[/tex]
For second part
[tex]500 \times 3=1500[/tex]
[tex]\Rightarrow p3=b[/tex]
[tex]\Rightarrow p=\dfrac{1}{3}b[/tex]
Learn more about rate:
https://brainly.com/question/527553
01:11:0
What is the final step in solving the inequality -2(5 - 4x)<
6x – 4?
o x < -3
x> 3
Step-by-step explanation:
-10 + 8x < 6x - 4
Bringing like terms on one side
8x - 6x < - 4 + 10
2x < 6
x < 6/2
x < 3
You have a summer job that pays double for working overtime. Overtime is determined as the
number of hours over 20 hours you work in ane week. Your regular pay is $5 per hour for the
first 20 hours you work in one week.
Write a piecewise function to represent the amount of your weekly paycheck p(h)
Answer:
Step-by-step explanation:
For 20 hours a week, I earn $15 per hour, and I earn $15,600 annually. As noted on my W-4 form, I can assert my exemptions. Every year the Internal Revenue Service declares allowances for exemptions. A single person's current allowance for one exception is $3,950. I may assert another exemption for a partner of $ 3,950. At $3,950 each, I can also assert exemptions for any dependents. Suppose my contribution is 10 percent to a 401(k) retirement plan: $15,600-$1,560 = 14,040 dollars I am single, so on my W-4 form, I claimed one exemption which I submitted to my employer: 14,040-3,950 dollars = 10,090 dollars My gross revenue (minus exemptions and deductions) is therefore $ 10,090. Currently based on $10,090, I can measure the federal income tax, social security, and other withholdings My employer withholds federal tax, tax on social security, and tax on Medicare cash. For 2015, the federal income tax brackets are as follows: Tax Rate Taxable Income Levels 10% $0–$9,225 15% $9,226–$37,450 25% $37,451–$90,750 28% $90,751–$189,300 33% $189,301–$411,500 35% $411,501–$413,200 39.60% Above $413,200 The tax bracket for my income is 15 percent. However, I am not taxed 15 percent on the entire amount. I will be taxed 10 percent for the first $9,225 dollars earned. Then, I will be taxed 15 percent on the remaining amount: 10 percent of 9,225 = $922.50 15 percent of ($10,090 – $9,225) = $129.75 Total income tax = $1,522.25 Thus, my income minus federal tax ($10,090 – $1,522.25) is $9,037.75. The Social Security tax is 6.2 percent, and the Medicare tax is 1.45 percent. These taxes are calculated based on my gross income: 6.2 percent of $15,600 = $967.20 1.45 percent of $15,600 = $226.20 Thus, my net pay will be: $9,037.75 – (967.20 + 226.20) = $7,844.35.
Type the missing number in this sequence: 1, 2, 4, 8, , 32
Answer:
1,2,4,8,"16",32
Step-by-step explanation:
we are times by 2 on each one
The missing number in the sequence is 16.
The given sequence follows a pattern where each number is obtained by multiplying the previous number by 2.
Starting with 1:
1 × 2 = 2
2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
So, the missing number in the sequence is 16.
To learn more on Sequence click:
https://brainly.com/question/21961097
#SPJ6
(50 POINTS!) The figure is transformed as shown in the diagram. Describe the transformation.
A) dilation, then reflection
B) reflection, then rotation
C) rotation, then translation
D) translation, then reflection
Answer:
The solution is rotation, then translation. The figure has been rotated about the origin by 90° and then translated 6 units to the right.
Use the diagrams below to derive the formula for the volume of a hemisphere.
What is the formula for the volume of a hemisphere?
πr3
πr3
πr3
πr3
Answer:
2/3 [tex]\pi[/tex]r²
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What is the solution to the system of
equations shown below?
Answer:
Where's the picture?
is 1/2 greater than 3/6
Answer:
they're equal. 3/6 simplifies to 1/2
Step-by-step explanation:
Answer:
It is the same!
Step-by-step explanation:
think about it this way. 3/6 simplified is 1/2. there are two pies, one is cut into two equally and the other is cut into six equally. You eat one on the first one and 3 on the second one. you ate halves of both pies.
The table of values below shows data for a five-word spelling test. Number of Letters vs. Percentage who Spelled Correctly Word Number of letters in the word Percentage of students who spelled the word correctly 1 7 48 2 9 12 3 5 73 4 6 59 5 8 27 Which describes how the data for word 2 should be plotted on a coordinate grid? From the origin, go 2 units to the right and 9 units up. From the origin, go 2 units to the right and 12 units up. From the origin, go 9 units to the right and 12 units up. From the origin, go 12 units to the right and 9 units up.
Answer:
I'm pretty sure it would be B; go 2 units to the right and 12 units up.
Step-by-step explanation:
the question is asking for the percentage that got it right not the number of letters in the word, and 9 is the number of letters, and 12 is the number that got it right.
The correct data for 2 in coordinate grid will be from the origin, go 9units to the right and 12units up.
How to locate a point on graph?
To locate a point having coordinate (x,y) in graph, we have to go x direction right or left depending on the sign of x-coordinate(for right +,for left -), then we have to go y direction up or down depending on the sign of y-coordinate(for up +,for down -).
The graph is done by taking Number of letters in the word in x axis and Percentage of students who spelled the word correctly in y axis.
According to the table, it is clear that for data 2 Number of letters in the word is 9. so x=9
And Percentage of students who spelled the word correctly is 12
so y=12
So the coordinate of the point for data 2 is (9,12)
To locate the point (9,12) in coordinate grid we have to go 9units to the right in x axis and then we have to go 12units up in y axis direction.
Therefore The correct data for 2 in coordinate grid will be from the origin, go 9units to the right and 12units up.
Learn more about the location of point in graph
here: https://brainly.com/question/26865
#SPJ2
1) The Pet Company has recently discovered a type of rock which, when crushed, is extremely absorbent. It is expected that the firm will experience (beginning now) an unusually high growth rate (20%) during the period (3 years) when it has exclusive rights to the property where this rock can be found. However, beginning with the fourth year the firm's competition will have access to the material, and from that time on the firm will assume a normal growth rate of 8% annually. During the rapid growth period, the firm's dividend payout ratio will be relatively low (20%), to conserve funds for reinvestment. However, the decrease in growth will be accompanied by an increase in dividend payout to 50%. Last year's earnings were $2.00 per share (E0) and the firm's cost of equity is 10%. What should be the current price of the common stock?
Answer:
$ 71.83
Step-by-step explanation:
This year's earnings=last year's earnings*(1+growth rate)=$2*(1+20%)=$2.4
This year's dividend=2.4 *payout ratio=2.4 *20%=$0.48
Next year's earnings=$2.4*1.2=$2.88
Next year's dividend=2.88 *0.2=$ 0.58
Year 3 earnings=$2.88*1.2=$ 3.46
Year three dividend= 3.46*0.2=$0.69
year 4 earnings =$3.46*1.08=$ 3.74
Dividend from year 4 onward= 3.74 *0.5=1.87
From year 4 terminal value=1.87 /(cost of equity-growth rate)=1.87/(10%-8%)=$93.5
Share price is present value of the above dividends amnd terminal value=0.48/(1+0.1)^0+0.58/(1+0.1)^1+0.69/(1+0.1)^2+93.5/(1+0.1)^3=$ 71.83
481+114=__-116 need help
Answer:
711
Step-by-step explanation:
595=x-116
x=711
Therefore, 711
I hope this helped and have a good rest of your day!
a truck carrying grapefruit juice, apple juice, and pear juice bottles in a ratio of 1:9:2. If there are 16 grapefruit juice bottles, then how many apple juice bottles are there?
Answer:
yeah
Step-by-step explanation:
Answer:
There are 144 apple juices
Step-by-step explanation:
1 = 16
9 = ?
2 = ?
16 x 9 = 144
16 x 2 = 32
2. A hotel has 18 floors. The hotel owner believes the number 13 is
unlucky. The first 12 floors are numbered from 1 to 12. Floor 13 is
numbered 14, and the remaining floors are numbered from 15 to 19.
The hotel manager starts on the top floor of the apartment building. He
rides the elevator two floors down. The doors open and a hotel guest
gets in. They ride the elevator three floors down. The hotel guest gets
off the elevator. The hotel manager rides the elevator the remaining
floors down to the first floor. On what floor did the hotel guest get off the elevator? Explain.
What is the answer for B?
Answer:
See below
Step-by-step explanation:
The manager rides down 2 floors from 19 floor which means he stops at floor 17, the floor he rides down as negative integer = -2. Then, he rides down 3 floors and it means he stops at floor 14. This means the number of floors he rides down from there = -3
then he rides to the first floor as there is no number 13 floor it means he rides down 12 floor = -12
the addition expression using negative integers to show the number of total floors the hotel manager rode down the elevator = -2 + (-3) + (-12) = -17
Let C(t) be the concentration of a drug in the bloodstream. As the body eliminates the drug, C(t) decreases at a rate that is proportional to the amount of the drug that is present at the time. Thus C 0 (t) = −2kC(t), where 2k is a positive number. Here is it is half of the elimination constant of the drug. (a) If Co is the concentration at time t = 0, find the concentration at time . (b) If the body eliminates half the drug in 30 hours, how long does it take to eliminate 80% of the drug?
Answer:
See explanation below
Step-by-step explanation:
In this case, let's answer this by parts:
a) Concentration at time t when Co is concentration at t = 0:
In this case, we will use the initial expression but without the 2, so:
C(t) = -kC
In this case, we want to know the concentration at time t so:
C'(t) = -kC(t) derivating:
dC/dt = -kC
dC/C = -kdt From here, we can do integrals so:
lnC = -kt + C₁ (1)
Now, it's time to replace t = 0 and C = C₀:
lnC₀ = -k(0) + C₁
lnC₀ = C₁ (2)
Replacing (2) in (1) we have:
lnC = -kt + lnC₀
lnC - lnC₀ = -kt
ln(C/C₀) = -kt
C/C₀ = e^(-kt)
C(t) = C₀ e^(-kt) (3)
This is the expression for C at given time t.
2. time to eliminate 80% of the drug:
With the first data, we need to calculate the value of k, which will be constant at any given time so:
C(t) = C₀ e^(-kt)
0.5C₀ = C₀ e^(-30k)
0.5 = e^(-30k)
ln(0.5) = -30k
k = 0.02310
Now with this value we can calculate the time to eliminate 80% of the drug or simply in other words, that we just have a remaining of 0.2C₀:
0.2C₀ = C₀ e^(-0.0231t)
ln(0.2) = -0.0231t
-ln(0.2) / 0.0231 = t
t = 69.67 h
This is the time to eliminate 80% of the drug
You need to make 9 sourdough loaves, one sourdough loaf requires 500 grams of dough How many kilograms of dough do you need
Answer:
4.5 Kg
Step-by-step explanation:
Given that 500 gms of dough is required to make one sourdough loaf.
And we need 9 such loaves.
We can find the required weight of dough simply by adding 500 gms , 9 times.
i.e. 500 gms + 500 gms + 500 gms + 500 gms + 500 gms + 500 gms + 500 gms + 500 gms + 500 gms = 4500 gms.
Or we can simply multiply 500 gms by 9 to get 4500 gms.
We know that 1 kilogram = 1000 grams.
So, dividing 4500 grams by 1000 to convert into kilogram.
[tex]\Rightarrow \dfrac{4500} {1000}\\\Rightarrow 4.5 kg[/tex]
So, the required weight of dough for making 9 sourdough loaves is 4.5 kg.
Which angles are alternate exterior angles with angle 11?
5 and 13
7 and 15
6 and 16
8 and 14
The above questions answer is 8 and 14
Lucy places five cards that are labeled 1 to 6 face down on the table and mixes them up. What is the likelihood that her friend Harry will draw an even numbered card?
Answer:
1/2 or 0.5
Step-by-step explanation:
Within 1 to 6,
Even numbers are 2, 4, 6
While odd numbers are 1, 3, 5
Assuming cards are mixed up properly and the probabilities of drawing a card with any number from 1 to 6 is constant,
Probability of drawing even number cards = number of units of even number cards ÷ total number of units of cards from 1 to 6 aka total number of cards
= 3 / 6
= 1 / 2
The probability of drawing even number cards is 1/2.
What is probability?Probability is "possibility that deals with occurrence of random events".
According to the question,
Lucy places five cards that are labeled 1 to 6 face down on the table and mixes them up.
Numbers of space = 1,2,3,4,5,6
Even numbers are 2, 4, 6 and odd numbers are 1, 3, 5.
To find Probability of drawing even number cards is equal to number of units of even number cards is divided by total number of units of cards.
Probability of even numbers of cards = 3/6
= 1/2
Hence, Probability of even numbers of cards is 1/2.
Learn more about probability here
https://brainly.com/question/16881470
#SPJ2
According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day. Suppose for a particular office the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is nine. (Round your answers to four decimal places.)
A. What is the probability of receiving no emails during an hour?B. What is the probability of receiving at least three emails during an hour?C. What is the expected number of emails received during 15 minutes?D. What is the probability that no emails are received during 15 minutes?
Answer:
a) 0.0065 = 0.65% probability of receiving no emails during an hour.
b) 0.1212 = 12.12% probability of receiving at least three emails during an hour
c) The expected number of emails received during 15 minutes is 1.2604.
d) 0.2835 = 28.35% probability that no emails are received during 15 minutes
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
In this question.
121 emails per day.
A day has 24 hours, so per hour, 121/24 = 5.0417, which means that [tex]\mu = 5.0417n[/tex], in which n is the number of hours.
A. What is the probability of receiving no emails during an hour?
n = 1, so [tex]\mu = 5.0417[/tex]
This is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]
0.0065 = 0.65% probability of receiving no emails during an hour
B. What is the probability of receiving at least three emails during an hour?
Either you receive less than three emails during an hour, or you receive at least 3. The sum of the probabilities of these events is decimal 1. So
[tex]P(X < 3) + P(X \geq 3) = 1[/tex]
We want [tex]P(X \geq 3)[/tex]
Then
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]
[tex]P(X = 1) = \frac{e^{-5.0417}*(5.0417)^{1}}{(1)!} = 0.0326[/tex]
[tex]P(X = 2) = \frac{e^{-5.0417}*(5.0417)^{2}}{(2)!} = 0.0821[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0065 + 0.0326 + 0.0821 = 0.1212[/tex]
0.1212 = 12.12% probability of receiving at least three emails during an hour
C. What is the expected number of emails received during 15 minutes?
15 minutes is a fourth of an hour, so n = 1/4 and [tex]\mu = \frac{5.0417}{4} = 1.2604[/tex]
The expected number of emails received during 15 minutes is 1.2604.
D. What is the probability that no emails are received during 15 minutes?
[tex]P(X = 0) = \frac{e^{-1.2604}*(1.2604)^{0}}{(0)!} = 0.2835[/tex]
0.2835 = 28.35% probability that no emails are received during 15 minutes
The farmer has a problem with too many mice in his barn. He brought in 363636 cats to catch the mice. Each cat caught 111 mice, but there were still 222222 mice left in the barn.
How many mice were in the barn at the start?
Answer:
40585818
Step-by-step explanation:
thats an insane amount of anything but like, dam n
363636*111 to find out how many were caught, then that number plus 222222
ome Spring 2020
Englis
Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
x + y = 29, 5x + 2y = 100
38 x + y = 100, 5x + 2y = 29
5x + y = 29, 2y + x = 100
2x + y = 100, 5y + x = 29
Answer:the first choice
Step-by-step explanation:
The test has 29 problems. That means x problems + y problems =29
The x problems are worth 5 points. So that’s 5x. The y problems are worth 2 points. So that’s 2y. The total the points add up to is 100. So 5x+2y=100
The first answer choice shows that
Answer:
A
Step-by-step explanation:
x + y = 29, 5x + 2y = 100
HELP ME NOW PLS!!!!!
Answer:
1
Step-by-step explanation:
A rectangle is formed with opposite unique sides , the rectangle formed can only be 1.
See the diagram attachment for you to get the picture;