Answer:
It should be 60 feet following the pattern!
It would cast a 60 foot shadow following the pattern but depending on how far the trees are apart the 30 foot tree could also cast a 40 foot shadow:)
Each airline passenger and his or her luggage must be checked to determine whether he or she is carrying weapons on to the airplane. Suppose that at O’hare International Airport, an average of 10 passengers per minute arrive (interarrival times are exponential). To check passengers for weapons, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. A checkpoint can check an average of 12 passengers per minute (the time to check a passenger is exponential). Under the assumption that the airport has only one checkpoint, answer the following questions:
a. What is the probability that a passenger will have to wait before being checked for weapons?
b. On the average, how many passengers are waiting in line to enter the checkpoint?
c. On the average, how long will a passenger spend at the checkpoint?
Answer:
a
[tex]P_k = 0.83[/tex]
b
[tex]N_{\mu} \approx 4 \ passengers[/tex]
c
[tex]T_{\lambda} = 0.5 \ minutes[/tex]
Step-by-step explanation:
From the question we are told that
The average number of passengers that arrive per minute is [tex]\lambda = 10[/tex]
The average number of check that can be carried out in one minute is [tex]\mu= 12[/tex]
Generally the probability that a passenger will have to wait before being checked for weapons is mathematically represented as
[tex]P_k = \frac{\lambda }{ \mu }[/tex]
=> [tex]P_k = \frac{10 }{ 12}[/tex]
=> [tex]P_k = 0.83[/tex]
Generally the number of passengers are waiting in line to enter the checkpoint is mathematically represented as
[tex]N_{\mu} = \frac{\lambda^2}{\mu (\mu -\lambda) }[/tex]
=> [tex]N_{\mu} = \frac{10^2}{12 (12 -10) }[/tex]
=> [tex]N_{\mu} \approx 4 \ passengers[/tex]
Generally the average time a passenger spend at the checkpoint is mathematically represented as
[tex]T_{\lambda} = \frac{ \frac{\lambda}{(\mu - \lambda)} }{ \lambda}[/tex]
=> [tex]T_{\lambda} = \frac{ \frac{ 10}{(12 - 10)} }{10}[/tex]
=> [tex]T_{\lambda} = 0.5 \ minutes[/tex]
Erasers cost 45 cents a piece. Notebooks cost 90 cents a piece . Karla spent $18 for a total of 28 erasers and notebooks . How many did she buy ?
Answer:
12 Notebooks And 16 Erasers
Step-by-step explanation:
Let x represent the number of notebooks and y represent the number of erasers. (x+y=28) Then, input the cent numbers into the equation. (90x+45y=1800) The 1800 represents the amount of dollars spent. Then simplfy the equation, which gives you 12 notebooks and 16 erasers.
The diameter of a circle is 6 millimeters. What is the circle's area?
d=6 mm
Use 3.14 pi
Answer:
28.26 mm
Step-by-step explanation:
The equation used to solve for the area of a circle is;
A=pi x r^2.
The radius is half the diameter, 6mm/2= 3mm.
A= 3.14 x 3^2
3^2= 9
3.14 x 9 = 28.26 mm
or you could just type 3.14 x (3^2) = 28.26mm
Ben’s favorite deli says the average serving time is 12 minutes. Ben notices that the wait time at the deli varies at different times of day, before and after noon. His observations when the wait time is as advertised can be represented by the equation 2|x − 2| − 12 = 0. Solve for the times when the serving time is as advertised, relative to noon. Group of answer choices (THERES ALOT OF ANSWERS BE PREPARED) SELECT ALL THE ANSWER CHOICES.
4pm,
8pm,
9am,
3pm,
noon,
11am,
6pm,
9pm,
7am,
1pm,
2pm,
5pm,
10pm,
10am,
8am,
7pm,
6am,
Answer:
8 pm and 8 am
Step-by-step explanation:
Let us solve the equation
[tex]2|(x-2)|-12=0[/tex]
There is a modulus in the equation this means that one value of the modulus will be positive and the other will be negative
Let us solve for the positive first
[tex]2(x-2)-12=0\\\Rightarrow 2x-4-12=0\\\Rightarrow x=\dfrac{16}{2}\\\Rightarrow x=8[/tex]
Now we add this value with 12 noon
So
[tex]12+8=8\ \text{pm}[/tex]
Let us solve for the negative
[tex]2(-(x-2))-12=0\\\Rightarrow 2(2-x)-12=0\\\Rightarrow 4-2x-12=0\\\Rightarrow x=-\dfrac{8}{2}\\\Rightarrow x=-4[/tex]
So
[tex]12-4=8\ \text{am}[/tex]
The times when the serving time is as advertised is 8 pm and 8 am.
help pls this is due today:(
Answer:
5cm
Step-by-step explanation:
a^2+b^2=c^2
9+16=x^2
25=x^2
x=5
Hope this helps!
Enter an Integer to represent the situation.
a $535 profit
Answer:
67
Step-by-step explanation:
Took a test
Help me plzzz i need help.
Answer:
Perimeter: 7.8Area: 3.1Step-by-step explanation:
Perimeter = all sides added up together2.8 + 2.8 + 1.1 + 1.1 = 7.8Area = L × W2.8 × 1.1 = 3.08Round 3.08 to the nearest tenth: 3.08 → 3.1I hope this helps!
1 point
6. Precipitation for the month of March was 4 inches less than average. In
April the precipitation was 14 inches less than average. How many inches
below average was the precipitation for both March and April?
Answer:
4 inches because March was 4 so april has to be 4 too
Step-by-step explanation:
The value of 100 pennies is ___% of the value of a dollar
Answer:
The type of coins =pennies has = 100 pennies.
servant has a total number of 100 coins
The sum of the percentage and pennies = $100
Let us represent the number of nickels as which is _% = 55.4
The number of pennies as y
Step-by-step explanation:
Which are equivalent expressions for root(3, 27 ^ 2) Select all that apply.
Answer:
the second one gives the same answer as the one in the question
12 cookies for 3 students rate and unit rate
Answer:
3:12 1:4
Step-by-step explanation:
Hope this helps! (^-^)
Answer: 4 cookies per student.
Step-by-step explanation:
his is a fraction equal to
12 cookies ÷ 3 students
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 3
12 cookies ÷ 3
3 students ÷ 3
=
4 cookies
1 student
=
4 cookies
student
= 4 cookies per student
17 times the sum of a number, n, and 31 is 300. Write as an equation.
Answer:
17(n+31)=300
Step-by-step explanation:
17 times the sum of a number, n and 31 is 17(n+31)
and then set that equal to 300
If N(k) is the inverse of K(n) and N(12) = 4, then K(4) = 12
Answer:True
Step-by-step explanation:
46% of the students that were surveyed like to eat at McDonald's if 351 students do not like to eat at McDonald's how many people were surveyed
Answer:650 people were surveyed
What should be subtracted from 538 to get reminder 3 when divided by 11
Answer:
4
Step-by-step explanation:
Answer: 7
Step-by-step explanation: 538÷11=48 + 10
so to get remainder 3 subtract 7 from 538
Figure ABCD is a parallelogram.
Parallelogram A B C D is shown. The length of A B is 3 y minus 2, the length of B C is x + 12, the length of D C is y + 6, and the length of A D is 2 x minus 4.
What are the lengths of line segments AB and BC?
AB = 4; BC = 16
AB = 4; BC = 8
AB = 10; BC = 20
AB = 10; BC = 28
The lengths of line segments AB and BC are AB = 10; BC = 28
What are parallelograms?Parallelograms are shapes with parallel and equal opposite sides
The given parameters are:
AB = 3y - 2
BC = x + 12
DC = y + 6
AD = 2x - 4
The above means that:
AB = DC
BC = AD
So, we have:
AB = DC
3y -2 = y + 6
Collect like terms
3y - y = 2 + 6
2y = 8
Divide by 2
y = 4
Also, we have:
BC = AD
x + 12 = 2x - 4
Collect like terms
2x - x = 4 + 12
x = 16
The lengths AB and BC are given as:
AB = 3y - 2
BC = x + 12
So, we have:
AB = 3*4 - 2
AB = 10
BC = x + 12
BC =16 + 12
BC = 28
Hence, the lengths of line segments AB and BC are AB = 10; BC = 28
Read more about parallelograms at:
https://brainly.com/question/24056495
Answer:
D
Step-by-step explanation:
What is 40x52 To the 7 power
Answer:
168,439,267,742,187,520,000,000
Step-by-step explanation:
40*52=2080
2080^7=168,439,267,742,187,520,000,000
can anyone just explain how to do a distant rate time problems because I'm confused about them
Answer:
The formula for distance problems is: distance = rate × time or d = r × t. Things to watch out for: Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.
Step-by-step explanation:
Here is an example.
Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?
After t hours the distances D1 and D2, in miles per hour, travelled by the two cars are given by
D1 = 40 t and D2 = 50 t
After t hours the distance D separating the two cars is given by
D = D1 + D2 = 40 t + 50 t = 90 t
Distance D will be equal to 450 miles when
D = 90 t = 450 miles
To find the time t for D to be 450 miles, solve the above equation for t to obtain
t = 5 hours.
5 am + 5 hours = 10 am
PLEASE NEED HELP URGENTLY!
Raul tried to find the midpoint between 5 & 3i and 12 + 7i. Check his work below.
Sum=(5+(-3))+(12+7)i
=2+19i
so the midpoint is 1+ 19over2 i
What mistake did Raul make?
AHe subtracted the values instead of adding them.
BHe did not add the corresponding parts of the complex numbers.
CHe found the sum instead of the average because he forgot to divide by two.
DHe added the numbers in the wrong order.
Answer:
B.He did not add the corresponding parts of the complex numbers.
Step-by-step explanation:
A mid point is a point that is of equal distance to two reference points.
Given: Find the midpoint of 5+(-3)i and 12+7i.
These expressions have two parts: the value and complex number parts.
Thus the addition ought to have been;
(5+(-3i)) + (12+7i) = (5 - 3i) + (12 + 7i)
= (5 + 12) + (-3i + 7i)
= 17 + 4i
The midpoint can be determined as:
[tex]\frac{(17 +4i)}{2}[/tex]
Thus it can be observed that Raul did not add the corresponding parts of the complex numbers.
Answer:
bbbbbbbbb
Step-by-step explanation:
Which number line shows the solution to the inequality 5x + 3> - 17
(I'm not going to get an answer in time, but this is for people in the future who are going to need it)
Which reigon represents the solution to the given system of inequalities
Answer:
I think the answer is B.
This exponential function has a base of 1.4 and an initial amount of 17. Its graph
is shifted 3 units left and 5 units up.
Answer:
-2.4 and 22
Step-by-step explanation:
How do you solve these angles again?
Answer:
(2x+2)
=98
(x+34)
=82
Step-by-step explanation:
a straight line adds up to 180
(2x+2)+(x+34)=180
x+2+x+34=180
(2x+x)+(2+34)=180(Combine Like Terms)
3x+36=180
3x+36=180
Step 2: Subtract 36 from both sides.
3x+36−36=180−36
3x=144
Step 3: Divide both sides by 3.
3x/3=144/3
x=48
Now you have your x just substitute it in
(2x+2)
=98
(x+34)
=82
If answers not right i am sorry but i tried
Ryleigh receives her pay monthly. Her deductions include $112 in Federal Income Tax, State Tax of 3.5% of gross, City Tax of 2.5% of gross, as well as Social Security and Medicare taxes. This month her paycheck is $5,161.28. What is Ryleigh's monthly gross pay?
9514 1404 393
Answer:
$6,106.87
Step-by-step explanation:
The total of percentage deductions is ...
state tax + city tax + social security + medicare
= 3.5% +2.5% +6.2% +1.45% = 13.65%
Then Ryleigh's take-home pay is ...
gross(1 -13.65%) -112 = 5161.28
gross = (5161.28 +112)/0.8635 = 6106.87
Ryleigh's monthly gross is $6,106.87.
Answer:
Hey!! ✿Step-by-step explanation:
ₜₕₑ ₐₙₛwₑᵣ ᵢₛ $₆,₁₀₆.₈₇!! ᵢ ₘᵢgₕₜ bₑ ₗₐₜₑ ᵢ'ₘ ₛₒ ₛₒᵣᵣy ♥The expression 2y + 2.7 is equal to for y = 4.
Answer:
10.7
Step-by-step explanation:
i am not certain but since y is the 4 you will have 2(4) + 2.7 so you get 8+2.7 since you do 2x4 then you add 8 and 2.7 to get 10.7
Sarah has saved 254 pound coins. She puts the pound coins into bags.
There are 20 pound coins in each full bag of coins. Sarah is going to take all her full bags of coins to the bank.
She can only take up to 5 full bags of coins to the bank each day.
Sarah wants to go to the bank on as few days as possible.
On how many days will Sarah need to go to the bank?
Answer:
Step-by-step explanation:
So for the fewest days it would be 3 days. The reason for that is because she has 254 pound coins. And she can inly take 5 bags to the bank a day, all of those 5 bags have 100 pound coins in them. If she take 2 days and get 200 pound coins to the bank. Then on the third day she would only have to bring three bags. So your answer for the fewest days possible is three days!
Hope it helps
David bought 3 1/3 fabric . How much is this in feet?
Answer:10 feet, I think
Step-by-step explanation:
please please help me!!
Answer:
slope is 4
Step-by-step explanation:
slope of the line is the diference in y /diference in x between any 2 points that belong to the line
slope=(10-2) / (3-1) = 8/2 =4
The perimeter of a rectangle is 212. The length is 16 more than 5 times the width.
Answer: Length is 15 and width is 91
Step-by-step explanation:
If the length is 16 more than 5 times the width, that means:
let's say
x=length
y=width
2x+2y=212
If the length is 16 more times than 5 times the width, that means
y=5x+16
now we can substitute all y's for 5x+16:
2x+(5x+16)2=212
=2x+10x+32=212
=12x+32=212
=12x=180
x=15
If the length is 15, the width is
15*2+2y=212
=30+2y=212
=182/2
y=91
Answer:
width 91 length 15
Step-by-step explanation:
2l+2w=212
l=5w+16
2l+2w=212, l=5w+16
substitute
2(5w+16)+2w=212
12w+32=212
12w=180
w=15
L=5w+16
L=5(15)+16
L=91
please someone help me out on this
Answer:
I think it is C
Step-by-step explanation:
im sorry if i am wrong
Answer:
I think it is supplementary, I may be wrong but I googled supplementary angles and the examples kinda looked like that.