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.
20 twenty-sevens minus 1 twenty-seven
Answer:
-100
Step-by-step explanation:
27-127=-100
3/5 + -7/5
Answer fast please
Answer:
-0.8
Step-by-step explanation:
hope this helps :3
Answer:
-4/5 for fraction or -0.8 for decimal
Step-by-step explanation:
9. (04.03 LC)
Given a polynomial f(x), if (x - 2) is a factor, what else must be true?
f(0) = -2
f(-2) = 0
f(2) = 0
f(0) = 2
show work pls
Answer:
f(2)=0. The third option is correct.
Step-by-step explanation:
Suppose we have a polynomial called f(x) and we know (x-2) is a factor of f. This means that we can express f(x) as:
f(x)=(x-2)\cdot g(x)
Being g(x) another unknown function.
Option 1: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=-2. Incorrect
Option 2: f(-2)=(-2-2)\cdot g(-2)=-4\cdot g(-2). Since we don't know the value of g(-2), we cannot assure f(-2)=0. Incorrect
Option 3: f(2)=(2-2)\cdot g(2)=0\cdot g(0)=0. Regardless of the value of g(0), f(0) must be 0. Correct
Option 4: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=2. Incorrect
what is the slope of this line?
Answer:
-5/2
Step-by-step explanation:
Find the slope of each line.
Answer:
It is 1/2
Step-by-step explanation:
the rise is 2
the run is 4
2 over four simplifies to one half
Can someone help me with this question please?
Answer:
I believe the answer is C
Step-by-step explanation:
66.5 divided by 19 is 3.5 and 7/2 = 3.5
hope this helps
12. Which of the following sets of ordered
pairs represents a function?
A. {(0,3), (2, 6), (7, 12), (0, -3))
B. {(6, 1), (6,2), (6,3), (6,4)}
C. {-12,0), (-13, -1), (-14, -2), (-14, -3))
D. {(1, 6), (2, 6), (3, 6), (4, 6)
Answer:
D
Step-by-step explanation:
D represents a function because the input (x) is not repeating itself.
Dan orders supplies for the science lab. Each of the 30 stations in the chemistry lab needs 5 feet of rubber tubing. If rubber tubing sells for $8.25 per yard, how much will it cost to equip all stations?
It will cost $412.50 for equipment for all stations.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Dan orders supplies for the science lab. Each of the 30 stations in the chemistry lab needs 5 feet of rubber tubing. If rubber tubing sells for $8.25 per yard.
The cost will be calculated as below,
3 feet = 1 yard
5 x 30 = 150 feet
8.25 per yard = cost
150/ 3 = 50 yards (total tubing needed)
50 x 8.25 = $ 412.50
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According to Siri every 5 inches of the map represents 3 miles of trails in the park how many inches on the map represents 9 miles on the park trails
Answer:
15 inches
Step-by-step explanation:
If 3 miles represents 5 inches and you want to know what represents 9 miles Just multiply 5*3 to get 15
Each of the 25 students in Mr. McDonald class sold 16 raffle tickets if each ticket cost $15 how much money did Mr. McDonald’s students raise PLEASE HELP
Answer:
Mr. McDonald's class raised $6,000 dollars.
Step-by-step explanation:
So they're are 25 students in the class and they each sold 16 raffle tickets. The easiest way to do this problem is to first find the amount of raffle tickets sold and then multiply that by 15. You could also just do 25*16*15 but that doesn't make much sense just thinking about it. So the first operation we have to do is 25*16 because multiplication is repeated addition so we're basically doing 16+16 25 times to see how much raffle tickets were sold. So that is 400 and then we multiply by 15 because each ticket sold for 15 dollars so if we sold 400 raffle tickets for 15 dollars each, again multiplication is repeated addition so we do 15+15 400 times which is 400*15=6,000. So Mr.McDonald's class raised $6,000 dollars.
please help on that excercise
Step-by-step explanation:
16. d-4 = -7
or, d = -7+4
or, d = -3
therefore, d = -3.
17. c-34 = 20
or, c = 20+34
or, c = 54
therefore, c = 54
18. a-4 = -18
or, a = -18 + 4
or, a = -14
therefore, a = -14
19. r-3 = 8
or, r = 8+3
or, r = 11
therefore, r = 11
20. z-100 = 100
or, z = 100+100
or, z = 200
therefore, z = 100
21. 5 = d - 1
or, 5+1 = d
or, 6 = d
or, d = 6
therefore, d = 6
To solve -6x + 4 = -20, what steps would you perform? Subtract 4. Divide by -6.
Answer:
x = 4
Step-by-step explanation:
Original Equation:
-6x + 4 = -20
Subtract 4 from both sides.
-6x = -24
Divide both sides by -6
x = 4
Hope I helped :)
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Answer:
To solve -6 x + 4 = -20, what steps would you perform?
Subtract
4.
Divide by
-6.
Step-by-step explanation:
Similar Sides
The two triangles shown are similar. Find the value of
a
b
2.1
1.4
Answer:
It’s 1.5
Step-by-step explanation:
Just divide 2.1 and 1.4
Olivia chose 10/21 . How did she get that answer?
Can someone help me please
Answer:
16 units
Step-by-step explanation:
The perimeter is the sum of the lengths
Add up the lengths as shown
3+2+1+2+3+1+1+3
16 units
The diameter of a semicircle is 10 feet what is the semicircle radius
Answer:
the radius is 5 ft.
Step-by-step explanation:
radius = 1/2 diameter
10/2 = 5
R= 5
Answer: 5 feet
This one is easy. Because the radius of a circle (or a semicircle) is half of the diameter, you can simply divide the diameter by 2.
Write the number that is 10 times smaller than 600
Use the given x and y values to write a direct variation equation
x=5, y=30
Answer:
The direct variation equation is y = 6x
Step-by-step explanation:
The direct variation equation is y = kx, where
k is the constant of variationTo find the value of k, use the initial values of x and y
∵ y = 5, y = 30
∵ y = k x
→ Substitute the values of x and y to find k
∵ x = 5 and y = 30
∴ 30 = k (5)
∴ 30 = 5k
→ Divide both sides by 5
∴ [tex]\frac{30}{5}=\frac{5k}{5}[/tex]
∴ 6 = k
→ Substitute it in the form of the equation
∴ y = 6x
The direct variation equation is y = 6x
Each of the 25 students in Mr. McDonald’s class sold 16 raffle tickets. If each ticket costs $15, how much money did Mr. McDonald’s students raise.
Answer:
$6,000
Step-by-step explanation:
Basically just multiply 25*16 to see how many raffle tickets the class sold in total (400). Then to find the amount of money they raised, multiply 400*15 (6,000).
What is the value of each expression?
-37-8
Answer:
if it is -37 * -8 the answer is 296
Bush Middle school is selling spirit sticks, 4 for $5.00. What is the cost of one spirit stick? *
Answer:
1.25
Step-by-step explanation:
because 4 is 5 dollars so thats mean u divide 5 to 4 which that give u 1.25
Which number is the greatest? Which is the least
NEVER MIND DON'T DO THIS
BUT I DO NEED POINTS SO COMMENT
Answer:
Huh?
Step-by-step explanation:
A box contains 180 wooden cubes. You open the top of the box and count 9 cubes across the front and 4 cubes along a side. How many layers of wooden cubes are in the box?
Answer:
5
Step-by-step explanation:
9 x 4 = 36
180/36 = 5
PLZ HELP I WILL MARK BRAINLEST!
Answer:
Most likely B.}21 inches,
Please mark me brainliest
Answer:
The answer is B, 21 inches
Step-by-step explanation:
You find what happened with the width which is time 3. Then you multiply 7 by 3 to get 21!
Hopefully that helps! Please mark BRAINILEST
Find the slope of the line that passes through the points: (1, 1) and (7, 5) . If you get stuck , try plotting the points on graph paper and drawing the line through them with a ruler.
Answer:
2,3
Step-by-step explanation:
The slope of the line that passes through points (1, 1) and (7, 5) is 2/3.
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
The formula for slope of a line that passes through two points (x₁.y₁) and (x₂,y₂) is,
y₂ - y₁ = m(x₂ - x₁)
The given points are, (1, 1) and (7, 5).
The slope of the line is given by formula m = (y₂-y1)/(x₂-x₁)
m= (5-1)/(7-1)
m = 4/6
m = 2/3
The slope of the line that passes through points (1, 1) and (7, 5) is 2/3.
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A bag contains 12 red marbles the ratio of red marbles to blue marbles is 3:4 find the number of blue marbles in the bag
Answer:
16
Step-by-step explanation:
If the ratio is 3 red marbles to 4 blue marbles we can solve this using the following:
[tex]\frac{12}{b} = \frac{3}{4}[/tex]
[tex]12 * 4 = 3b\\48 = 3b\\\frac{48}{3} = b\\b = 16[/tex]
So we have 16 blue marbles.
Based on the ratio of red to blue marbles, the number of blue marbles in the bag is 16 marbles.
The bag has red marbles to blue marbles in a ratio of 3:4.
If there are 12 red marbles, the number of blue marbles can be found by direct proportion:
3 : 4
12 : x
Cross-multiply:
3x = 48
x = 48/3
x = 16 blue marbles
In conclusion, there are 16 blue marbles in the bag.
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what is the answer? pls help
Answer:
The answer is Not a line (no constant slope)
Step-by-step explanation:
21/7
-2/-1
78/26
-105/-35
The slope is always different, therefore there is no constant slope!
Hope this helps!
HELP ME SOLVE THE LAST ONE, IF THEYRE ALL WRONG CORRECT THEM, TYYYYYY
Answer:
they are right
Step-by-step explanation:
Answer:
you have the 4 and 7 backwards and the last one they r losing about .75 gallons hope this helps
Andrew made $625 mowing lawns. He worked for 5 consecutive days and earned the same amount of money each day. How much money did Andrew earn per day?
Answer:
625 / 5 = 125 per day
Step-by-step explanation:
If this helped can I get brainliest I need to rank up.
The coefficients in the expansion of (x + y)4
are
O A. 1, 4, 6, 4, 1
OB. 0, 1, 4, 6, 4, 1, 0
C. 0, 4, 6, 4,0
D. 1, 4, 6, 6, 4, 1
Answer:
A
Step-by-step explanation:
Notice: The literal factors are all the combinations of a and b where the sum of the exponents is 4: a4, a3b, a2b2, ab3, b4.
The degree of each term is 4.
The first term is actually a4b0, which is a4 · 1.
Thus to "expand" (a + b)5, we would anticipate the following terms, in which the sum of all the exponents is 5:
(a + b)5 = ? a5 + ? a4b + ? a3b2 + ? a2b3 + ? ab4 + ? b5
The question is, What are the coefficients?
They are called the binomial coefficients. In the expansion of
(a + b)4, the binomial coefficients are
1 4 6 4 1
The coefficients in the expansion are 1, 4, 6, 4, 1.
What is Binomial Expansion?The sum of exponents of x and y is always n. The binomial coefficients which are equidistant from the beginning and from the ending are equal i.e. [tex]^nC_0[/tex]= [tex]^nC_n[/tex], [tex]^nC_1[/tex]= [tex]^nC_{n-1}[/tex], [tex]^nC_2[/tex]= [tex]^nC_{n-2}[/tex] ,….. etc.
The expansion of [tex](x+ y)^4[/tex]
= [tex]x^4[/tex] + 4x³y + 6x²y² + 4xy³ + [tex]y^4[/tex]
So, the highest degree is 4.
and, The literal factors are all the combinations are [tex]x^4[/tex], 4x³y, 6x²y², 4xy³,[tex]y^4[/tex]
Hence, the coefficients in the expansion are 1, 4, 6, 4, 1.
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