Answer:
(a) Explained below.
(b) 0.0294
(c) 0.0173
(d) 0.09827
(e) 0.0452
Step-by-step explanation:
The complete question is:
According to an airline, flights on a certain route are on time 80% of the time. Suppose 25 flights are randomly selected and the number of on-time flights is recorded.
(a) Explain why this is a binomial experiment.
(b) Find and interpret the probability that exactly 16 flights are on time.
(c) Find and interpret the probability that fewer than 16 flights are on time.
(d) Find and interpret the probability that at least 16 flights are on time.
(e) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time.
Solution:
(a)
Let the random variable X be defined as the number of on-time flights.
A Binomial experiment has the following properties:
There are a fixed number of trials (n). Each trial are independent of the others. Each trial has only two outcomes: Success and Failure Each trial has the same probability of success (p).If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
All of these properties can be confirmed for the random variable X.
Thus, this is a binomial experiment.
(b)
Compute the probability that exactly 16 flights are on time as follows:
[tex]P(X=16)={25\choose 16}(0.80)^{16}(0.20)^{25-16}[/tex]
[tex]=2042975\times 0.0281475\times 0.000000512\\=0.029442375072\\\approx 0.0294[/tex]
Thus, the probability that exactly 16 flights are on time is 0.0294.
(c)
Compute the probability that fewer than 16 flights are on time as follows:
[tex]P(X<16)=\sum\limits^{15}_{x=0}{{25\choose x}(0.80)^{x}(0.20)^{25-x}}[/tex]
[tex]=0.0000+0.0000+....+0.011777\\=0.0173[/tex]
Thus, the probability that fewer than 16 flights are on time is 0.0173.
(d)
Compute the probability that at least 16 flights are on time as follows:
[tex]P(X\geq 16)=1-P(X<16)[/tex]
[tex]=1-0.0173\\=0.9827[/tex]
(e)
Compute the probability that between 14 and 16 flights, inclusive, are on time as follows:
[tex]P(14\leq X\leq 16)=\sum\limits^{16}_{x=14}{{25\choose x}(0.80)^{x}(0.20)^{25-x}}[/tex]
[tex]=0.004+0.0118+0.0294\\=0.0452[/tex]
Thus, the probability that between 14 and 16 flights, inclusive, are on time is 0.0452.
-f-6-2f=8
I need help
Answer:
f= -14/3
Step-by-step explanation:
-f-6-2f=8
(given)
-3f-6=8
(combine like terms)
-3f=14
(add 6 to both sides)
f= -14/3
Line f has a slope of -3/4 line g is perpendicular to f. What is the slope of like g
Answer:
Slope of line g = [tex]1\frac{1}{3}[/tex]
Step-by-step explanation:
Line f has a slope of [tex]-\frac{3}{4}[/tex] Line g is perpendicular to f* Mathematics rule: If two lines are perpendicular to each other, then the product of their slopes is equal to -1 .
∴ [tex]-\frac{3}{4}[/tex] × slope of line g = -1
Slope of line g = -1 ÷ [tex]-\frac{3}{4}[/tex] = 4/3 = [tex]1\frac{1}{3}[/tex]
A factory produces 150 plastic compounds per hour. How many components does the factory produce per minute?
Answer:
2.5 components but if you need to round 2
Answer:
150 per 60 mins would be 2.5 per 1 min
Step-by-step explanation:
150/60 = 2.5
Need Help with this Appreciate!
Answer:
Whatever problem choice is equivalent to 2
Step-by-step explanation:
what is the slope between the points (1,19) and (-2,-7) simplify
Find the value of the expression below
8(15-4)/4^2-5
Answer:
8 IS YOUR ANSWERStep-by-step explanation:
HAVE A GREAT DAYGiven: PS=RT, PQ=ST
Prove: QS=RS
Answer:
I) Eq(1) reason: sum of segments of a straight line
II) Eq(2) reason: Given PQ = ST & PS = RT
III) Eq(3) reason: sum of segments of a straight line
IV) Eq(4) reason: Same value on right hand sides of eq(2) and eq(3) demands that we must equate their respective left hand sides
V) Eq(5) reason: Usage of collection of like terms and subtraction provided this equation.
Step-by-step explanation:
We are given that;
PS = RT and that PQ = ST
Now, we want to prove that QS = RS.
From the diagram, we can see that from concept of sum of segments of a straight line we can deduce that;
PQ + QS = PS - - - - (eq 1)
Now, from earlier we saw that PQ = ST & PS = RT
Thus putting ST for PQ & PS for RT in eq 1,we have;
ST + QS = RT - - - - (eq 2)
Again, from the line diagram, we can see that from concept of sum of segments of a straight line we can deduce that;
RS + ST = RT - - - - -(eq 3)
From eq(2) & eq(3) we can see that both left hand sides is equal to RT.
Thus, we can equate both left hand sides with each other to give;
ST + QS = RS + ST - - - (eq 4)
Subtracting ST from both sides gives;
ST - ST + QS = RS + ST - ST
This gives;
QS = RS - - - - (eq 5)
Thus;
QS = RS
Proved
5.
Evaluate f(x) = -2x2 -4 for x = 3.
O -10
O -18
10
-22
Answer:
-22
Step-by-step explanation:
f(x) = -2x^2 - 4 for x = 3
f(3) = -2(3)^2 - 4
f(3) = -2(9) - 4
f(3) = -18 - 4
f(3) = -22
Answer: -22
Answer:
-22
Step-by-step explanation:
what is the ratio of students to adults ? complete the statement the ratio of students to adults is ? 20 to 4 is the awnser
Answer:
20 to 4
Step-by-step explanation:
is the answer because it is the amount of students to adults.
A tennis racket normally costs $70. The tennis racket is on sale for 30% off. What is the sale price of the tennis racket?
PLS I NEED THIS LIKE TODAY
Consider an example of a deck of 52 cards:
The dealer in a card game draws 3 cards from a deck of 52 cards and places them face up on a table. Select all of the correct probabilities.
Answer:
please be more specific
−7x − 7y = −14 2x +7y = 19
Answer:
(-1, 3)
I hope this helps
if you could, feel free to mark me Brainliest it would be much appreciated :D
put the following numbers in order from smallest to largest
548654
550654
1547521
1485554
1547656
1256441
995841
Answer: 548654, 550654, 995841, 1256441, 1485554, 1547521, and 1547656
Hope this helps
6. Which of the following is true about the
graph of the equation y = -5x + 10?
A. The graph would increase from left to right.
B. The graph would pass through the origin.
C. The graph would have a positive y-intercept.
Answer:
C
Step-by-step explanation:
The graph would have a positive y-intercept
The y-intercept is when x = 0
To find the y-intercept, plug in 0 for x
y = -5(0) + 10
y = 0 + 10
y = 10
10 is a positive number
Y-intercept is positive
In a batch of pedometers, are believed to be defective. A quality-control engineer randomly selects units to test. Let random variable Xthe number of defective units that are among the units tested. The probability mass function f(x)P(Xx) is given below. f(x){(0,), (1,), (2,), (3,)} Recall that the mean of a discrete random variable X with probability mass function f(x)P(Xx) is given by . Find for the probability mass function above. What does this number represent?
Answer:
The mean for the probability mass function is 0.64287.
Step-by-step explanation:
The complete question is:
In a batch of 28 pedometers, 3 are believed to be defective. A quality-control engineer randomly selects 6 units to test. Let random variable X = the number of defective units that are among the units tested.
The probability mass function f (x) is:
f (x) = {(0, 0.47009), (1, 0.42308), (2, 0.10073), (3, 0.00611)}
Solution:
The mean of a discrete random variable X with probability mass function f (x) is:
[tex]\mu=\sum\limits^{n}_{x=1}{x\times f(x)}[/tex]
Compute the mean for the probability mass function above as follows:
[tex]\mu=\sum\limits^{n}_{x=1}{x\times f(x)}[/tex]
[tex]=(0\times 0.47009)+(1\times 0.42308)+(2\times 0.10073)+(3\times 0.00611)\\=0+0.42308+0.20146+0.01833\\=0.64287[/tex]
Thus, the mean for the probability mass function is 0.64287.
This values represents the expected number of defective units for every 6 units tested.
5b.) Use this equation to write the area A in terms of the perimeter p.
Henry is playing a new game app where he needs to navigate through a maze without touching the walls. each player stars with 1,000 points, and 5 points are deducted each time a wall is touched.
What type of relationship most appropriately models this situation?
A. Exponential Decay
B. Linear Decrease
C. Exponential Growth
D. Linear Decrease
Answer:
Step-by-step explanation:
Linear decrease
The average person takes in 900 breaths per hour. How many breaths does an average person take in 6 hours?
A 1,500 breaths1,500 breaths
B 4,500 breaths4,500 breaths
C 5,400 breaths5,400 breaths
D 54,000 breaths54,000 breaths
Answer:
C 5,400 breaths
Step-by-step explanation:
900 breaths per hour x 6 hours = 5,400 breaths in 6 hours
Solve the following system of equations using the elimination method. x – y = 11 2x + y = 19 Question 5 options: A) (–3,9) B) (10,–1) C) (–9,6) D) (–10,2)
Answer:
B.(10,-1)
Step-by-step explanation:
10-(-1)=11
2(10)+(-1)=19
20+(-1)=19
I need help please
-24+to the power of 3
Answer:
-13824
Step-by-step explanation:
Which prime number do the prime factorization of 130 and 165 have in common?
Answer:
They both have the #5 and they both have 3 #'s that are prime?
Step-by-step explanation:
Elaine drove 3 miles forward, then 3 miles backward. How many miles did she drive?
Answer:
6 miles
Step-by-step explanation:
3 plus 3= 6
Answer:
6 miles
Step-by-step explanation:
3 miles + 3 miles = 6 miles
What is the slope of a line perpendicular to the line whose equation is x−3y=12. Fully reduce your answer.
Answer:
m perpendicular = - 3
Step-by-step explanation:
To start with, we need to find the slope of the given line, by solving for y in the equation
x - 3 y = 12
x = 3 y + 12
x - 12 = 3 y
divide by 3 both sides:
y = x/3 - 12/3
y = (1/3) x - 4
then, the slope of the given line is 1/3, and according to the property of perpendicular lines, a perpendicular slope will be the 'opposite of the reciprocal" of the slope of the original line. That is: the value - 3.
Then the slope of the perpendicular line is: m = - 3.
Answer:
3
Step-by-step explanation:
the sum of the measures of the angles of the interior angles of a triangle is 180. Write and solve an equation to find the value of the variable
Answer:
look on khan academy
Step-by-step explanation:
answer fast plz.........................
Answer:
180 customers
Step-by-step explanation:
72/100 × x/250
cross multiply
72 × 250 = 100 × x
18000 = 100x
divide both sides by 100
180 = x
Answer:
180
Step-by-step explanation:
72% of 250 is 180 :)
△ABC and △CDE similar right triangles. The coordinates of all the vertices are integers.
A: The relationship between the slope of AC¯¯¯¯¯ and the slope of CE¯¯¯¯¯ cannot be determined, because the triangles are congruent.
B:The slope of AC¯¯¯¯¯ is equal to the slope of CE¯¯¯¯¯ . This this because ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC¯¯¯¯¯ as for CE¯¯¯¯¯
C:The slope of AC¯¯¯¯¯ is greater than the slope of CE¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for AC¯¯¯¯¯ than for CE¯¯¯¯¯ .
D:The slope of AC¯¯¯¯¯ is less than the slope of CE¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for AC¯¯¯¯¯ than for CE¯¯¯¯¯ .
Answer:
Option B.
Step-by-step explanation:
Slope of the line AC = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{\text{AB}}{\text{BC}}[/tex]
= [tex]\frac{4}{6}[/tex]
= [tex]\frac{2}{3}[/tex]
Slope of the line CE = [tex]\frac{\text{DC}}{\text{DE}}[/tex]
= [tex]\frac{2}{3}[/tex]
Therefore, slope of the line AC = Slope of the line AC
And this is because ratio of change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC as for CE.
Option B. is the answer.
Ronnie buys 2 pairs of shoes for $50. Write an equation relating the total cost y to the number of pairs of shies x
Joanne and Ed Greenwood built a new barn with an attached arena. To finance the loan, they paid $1,326 interest on $47,600 at 4%. What was the time, using exact interest? (Do not round intermediate calculations. Round up your answer to the nearest day.)
Answer:254 days
Joanne and Ed Greenwood built a new barn with an attached arena. To finance the loan, they paid $1,326 interest on $47,600 at 4%. What was the time, using exact interest? (Do not round intermediate calculations. Round up your answer to the nearest day.)
Step-by-step explanation
Note that
Interest is represented by I=1326
The principal is represented by P=47,600
Rate is R =4%
And Time is year
Interest is calculated using the formulae,
I =PRT/100
From the above formulae, time can be calculated as
T=100I/PR
T= 100×1326/(47600×4)
T= 132600/190400
T= 0.6964 years
To convert to days, multiply by 365(since those no of days make a year)
T= 0.6964×365=254 days
This was approximated to the nearest day
Answer is 254 days
4/5% of 192?
show work please
Answer:
153.60
Step-by-step explanation:
This will help you and make me burillan
