Bob tardó 55 minutos en limpiar el garaje, por lo que debemos convertir ese tiempo a segundos para saber cuánto tiempo tardó exactamente.
Sabemos que 1 minuto tiene 60 segundos, por lo que podemos utilizar esta información para convertir los 55 minutos a segundos. La fórmula para realizar esta conversión es:
Segundos = Minutos * 60
Aplicando esta fórmula a los 55 minutos que Bob tardó en limpiar el garaje, obtenemos:
Segundos = 55 * 60
Segundos = 3300
Por lo tanto, Bob tardó 3300 segundos, o aproximadamente 55 minutos, en limpiar el garaje.
Es importante destacar que la conversión de tiempo de minutos a segundos es una operación común en matemáticas y cálculo, y es útil para resolver problemas en los que es necesario trabajar con diferentes unidades de tiempo. Además, entender la relación entre diferentes unidades de tiempo es esencial para realizar cálculos precisos y resolver problemas de manera efectiva.
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I really need help, please help me!
for a subset of patients it has been shown that a certain type of skin lesion will develop into cancer in 34% of patients if left untreated. there is a drug on the market that currently reduces this event rate to 28%. a pharmaceutical company is developing a new drug to treat these lesions but this would be worthwhile only if the new drug can reduce this further to 23%. in planning for a randomized clinical trial, how many evaluable participants are needed to have 80% power to detect a difference of 28% and 23% in the progression to cancer between the current and new drug?
At least 174 participants for the clinical trial, with half of them assigned to the current drug group and half assigned to the new drug group.
To answer this question, we need to consider some statistical concepts. The event rate, or the percentage of patients who progress to cancer, is a key factor in this scenario. The current drug has an event rate of 28%, while the new drug is expected to reduce this further to 23%. We want to detect a difference between these two rates, which is 5 percentage points.
The power of a statistical test is the probability of detecting a true difference between two groups, given that such a difference exists. In this case, we want the power to be at least 80%, which means that we want to have an 80% chance of detecting a true difference of 5 percentage points between the current and new drugs.
To calculate the sample size needed for the clinical trial, we need to consider the expected event rates, the desired power, and the level of statistical significance. The level of significance is typically set at 5%, which means that we are willing to accept a 5% chance of making a type I error (i.e., rejecting the null hypothesis when it is actually true).
Assuming a two-sided test (i.e., testing for a difference in both directions), we can use a formula or an online calculator to determine the sample size. The formula is:
n = (Zα/2 + Zβ)² [p₁(1-p₁) + p₂(1-p₂)] / (p₁ - p₂)²
where n is the sample size, Zα/2 is the critical value of the standard normal distribution at the 2.5% level (for a two-sided test), Zβ is the critical value of the standard normal distribution at the desired power (in this case, 80%), p₁ is the event rate for the current drug (28%), p₂ is the event rate for the new drug (23%), and (p₁ - p₂) is the expected difference in event rates.
Plugging in the values, we get:
n = (1.96 + 0.84)² [(0.28)(0.72) + (0.23)(0.77)] / (0.28 - 0.23)²
n = 173.2
Rounding up to the nearest whole number, we get a sample size of 174 participants.
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Write a matrix to represent the following system: -x+5y=7, 7x-2y=3
[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3
What is Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
The system of linear equations
-x + 5y = 7
7x - 2y = 3
can be represented in matrix form as:
[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex]
The matrix on the left represents the coefficients of the variables x and y, and the matrix on the right represents the constants on the right-hand side of each equation.
The vector on the left contains the variables x and y, and the vector on the right contains the constants.
Hence, [tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3
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one card is randomly selected from a standard deck of 52 cards. what is the probability of randomly selecting a(n) jack or 4? enter your answer as a reduced fraction.
the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.
In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.
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Determine whether the pair of figures is similar. If so, find the scale factor. Explain your reasoning.
OA) no; ZBCD # ZFCG
OB) no; BD #CO
OC) Yes: A BDC-A FGC because ZB
OD) Yes: A BDC-A FGC because ZB
4
LO
ZF. ZD
ZF. ZD
5
D 3
C
25
5
20
BD
ZG. ZBCD ZFCG, and C=
FG
ZG, ZBCD = ZFCG, and
BD
=
DC
CB
The pair of figures is similar by SSS
How to determine if the pair of figures is similarThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Triangles BDC and FGC
When the side lengths of the triangle are compared, we have:
Side lengths of FGC are 5/3 multiplied by the side lengths of BDC
This means that the triangles are similar
And the similarity statement is SSS
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i need help with this for math class
The expression that shows an equivalent expression include the following:
1/4(14x - 8 + 6x) = 5x - 2.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression:
1/4(14x - 8 + 6x)
By opening and expanding the bracket, we have the following mathematical expression:
1/4(14x - 8 + 6x) = 1/4(20x - 8)
1/4(20x - 8) = 5x - 2
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When buying a car Esther can choose a 2 door or 4-door car with leather or cloth interiors in black,silver, or white
The number of possible combinations are 12.
What is a combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.
Given that, Esther can choose a 2 or 4 door car with leather or cloth interiors in black, silver, or white.
Now, C(3, 1)×C(2, 1)×C(2, 1)
= 3×2×2
= 12
Therefore, the number of possible combinations are 12.
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"Your question is incomplete, probably the complete question/missing part is:"
When buying a car, Esther can choose a 2 or 4 door car with leather or cloth interiors in black, silver, or white. How many possible combinations of her car selection?
The robotics club has a budget of
$400. They spent $180 on
equipment. What percent of their
budget was spent on equipment?
gwen has £7 a litre of cola costs £1.25 gwen buys as much as literes as she can. how much money does she have left?
Gwen has £0.75 money left over, as per linear equation if a litre of cola costs £1.25.
"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."
It is given that Gwen has a £5 note and a £2 coin.
Therefore, she has a total of £(5 + 2) = £7
A liter of cola costs £1.25.
Therefore, (7 ÷ 1.25) = 5.6
Therefore, Gwen can buy a total of 5 liters of cola.
Now, Gwen has left money of £[7 - (5 × 1.25)] = £0.75
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Complete question is:
Gwen has a £5 note and a £2 coin
a litre of cola cost £1.25
gwen buys as many liter bottles of cola as she can
how much money will she have left over
a Find: i the number of games played Goals 0 1 2 3 4 5 6 7 8
Frequency 6 11 5 11 4 0 2 0 1
ii the mode iii the median
iv the mean number of goals.
b Maha asked: ‘What is the average number of goals?’
Which would be the best average to use to answer this question? Give a reason for your answer.
1) The mean of the data is 4.45.
2) The mode of the data is 11.
3) The median of the data is 4.
What are the mean, mode, and median?The mean of the data is the ratio of the sum of the given data and the number of the count of the data.
The mode of the data is the number that is repeated maximum number of times. The median of the data is when the data is arranged in an increasing order then the middle most value will be the median of the data.
Given data is 6 11 5 11 4 0 2 0 1.
The mean of the data is,
Mean = ( 6 + 11 + 5 + 11 + 4 + 0 + 2 + 0 + 1 ) / 9
Mena = 4.45
Mode = 11
Median:- 0,0,1,2,4,5,6,11,11
Median = 4
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The amount of time required to download a song from Michael's computer to his music player is the same for each song he downloads.
A linear model of this situation contains the values (138 , 96.6) and (238 , 166.6), where x represents the number of songs he wants to download to his music player, and y represents the total amount of time, in minutes, it will take him to download the songs.
What is the rate of change in this linear model?
A.
100 minutes per song
B.
0.35 of a minute per song
C.
1.4 minutes per song
D.
0.7 of a minute per song
This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).
What is a linear model?A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.
A linear equation is so named because plotting the graph of a given linear model yields a straight line.
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Please read the photo
The average rate of change over the interval [3,4] is given as follows:
3.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The numeric values for the ends of the interval are given as follows:
f(3) = 29.f(4) = 32.Then the change in the output is of:
32 - 29 = 3.
The change in the input is of:
4 - 3 = 1.
Hence the rate is of:
r = 3/1
r = 3.
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Solve the right triangle by completing the table below
The values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:
A + B + C = 180° {sum of interior angles of a triangle}
49° + B + 90° = 180°
B = 180° - 139°
B = 41°
sin49 = a/12.7 {opposite/hypotenuse}
a = 12.7 × sin49 {cross multiplication}
a = 9.5848
cos49 = b/12.7 {adjacent/hypotenuse}
b = 12.7 × cos49 {cross multiplication}
b = 8.3319
Therefore, the values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°..
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which sampling type will yield a representative sample? (choose one or more) group of answer choices stratified random snowball sample convenience simple random
Sampling type which will yield a representative sample is stratified random sampling.
A representative sample is a subset of a population that seeks to accurately reflect the characteristics of the larger group. For example, a classroom of 30 students with 15 males and 15 females could generate a representative sample that might include six students: three males and three females.
This method uses stratified random sampling to help identify its components. Other methods can include random sampling and systematic sampling. A representative sample seeks to choose components that match with key characteristics in the entire population being examined.
Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.
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A spinner and a fair number cube are used in a game. The spinner has an equal chance of landing on 1 of 6 colors: red, purple, blue, green, white, or orange. The faces of the cube are labeled 1 through 6. What is the probability of a player spinning the color green and then rolling an even number?
The probability of a player spinning the color green and then rolling an even number is 1/12.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Spinner:
= {red, purple, blue, green, white, orange}
Cube:
= {1, 2, 3, 4, 5, 6}
Now,
The sample space of spinning and rolling a cube.
= {red, purple, blue, green, white, orange} x {1, 2, 3, 4, 5, 6}
The number of outcomes.
= 6 x 6
= 36
Now,
The outcome of spinning a green and an even number.
= (green, 2), (green, 4), (green, 6)
Number of outcomes = 3
Now,
The probability of a player spinning the color green and then rolling an even number.
= 3/36
= 1/12
Thus,
The probability of a player spinning the color green and then rolling an even number is 1/12.
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A room measures 10m by 6m by 3m the volume of airspace needed for one person is 5m3 find the maximum number of person who may use the room at the same time
The number of persons that can use the room at the same time is 36.
The volume of the cuboid = length x width x height
The room is a cuboid.
Volume of the room = length x width x height
L = 10m, W = 6m, Height = 3m.
Volume = 10 x 6 x 3 = 180 cubic meter.
If each person takes 5 cubic meter of air space,
Then the total person who can occupy the room at the same time is 180/5 = 36.
A cuboid is a three-dimensional geometric shape that is bounded by six rectangular faces, where each face is a parallelogram. It is also known as a rectangular prism. The faces of a cuboid are called its base and lateral faces. The base of a cuboid is the top and bottom rectangular faces, while the lateral faces are the four rectangular faces that connect the base.
Cuboids have eight vertices or corners, where three edges meet, and 12 edges, which are the straight lines that connect the vertices. The length, width, and height of a cuboid are the dimensions of the three pairs of parallel sides of its rectangular faces, and these measurements are usually denoted by l, w, and h, respectively.
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Answer probability question PLSSSSS
Answer:a is 3:9 B is 6:9
Step-by-step explanation:
Sarah earned a 4% commission on all of her sales in December. Her total sales for December were $80,000. How much money did she cam in commission?
On solving the provided question, we can say that Amount of commission = Total sales value x Rate of commission = 3,200
what is amount ?aggregate attempting to calculate the time required, total number or quantity. The quantity at hand or under consideration is incredibly energetic. the overall result, importance, or import. Principal, interest, and a third accounting. amounts, amounting, and amounted are word forms. flexible noun The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by.
[tex]Amount of commission = 3,200\\Total sales value = 80,000//[/tex]
Rate of commission = 4% on sales
Amount of commission = Total sales value x Rate of commission
Amount of commission = 80,000 x 4%
Amount of commission = 3,200
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Mr. Titus travels from Charlotte to New York City and back 12 times each year. The total distance for each round trip is 623 miles. What is the total number of miles Mr. Titus travels from Charlotte to New York City and back each year? Enter your answer in the box.
Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.
The total distance will be calculated as:-
Distance = 12 x 623
Distance = 7476 miles
Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.
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The Lupines, a family of werewolves, are heading off for a vacation in the woods of Transylvania. Uncle Harry Lupine has rented a total of 12 horror movie videos and gory games on CDs to amuse the kids, Freddy and Lenore, on the trip. The kids want to know how many games and movies they have. Uncle Harry wants Freddy and Lenore to do some math on the trip, so he tells them, "Games rent for $4. 50 each and movies for $3. 99 each. The total was $49. 92 before tax. Now you can figure out the answer. "
Uncle Harry rented 4 games, and using that he also rented 8 movies.Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.
What is word problem?
A word problem is a type of mathematical problem that is presented using words instead of or in addition to mathematical symbols and equations. Word problems often describe a real-world scenario or situation, and they require the solver to use math skills and critical thinking to identify the relevant information, determine the mathematical operation or operations required, and arrive at a solution to the problem.
Let's assume that the number of movies Uncle Harry rented is "m" and the number of games is "g". We want to find the values of "m" and "g".
From the problem statement, we know that:
The total number of movies and games rented is 12: m + g = 12
The cost of each movie is $3.99: 3.99m
The cost of each game is $4.50: 4.5g
The total cost before tax is $49.92: 3.99m + 4.5g = 49.92
We can use the first equation to express "m" in terms of "g":
m = 12 - g
Substituting this expression for "m" in the second equation, we get:
3.99(12 - g) + 4.5g = 49.92
Expanding the brackets and simplifying, we get:
47.88 - 3.99g + 4.5g = 49.92
0.51g = 2.04
g = 4
So Uncle Harry rented 4 games, and using the first equation, we find that he also rented 8 movies.
Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.
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Can someone help me pleaseee :(
Select all the equations where x=3 is a solution
A: x+4=7
B:x/9=3
C: 5-4=2
D:8x=32
E:x-10=7
Answer:
A
Step-by-step explanation:
A is correct because 3+4 = 7
B is incorrect because 9/3=3 ,not 3/9
There is no x in C
D is incorrect because 8×3=24
E is incorrect because 3-10= -7 (negative)
hope this helped :)
The graph of g(x) = |x – h| + k is shown on the coordinate grid. What must be true about the signs of h and k?
Both h and k must be positive.
Both h and k must be negative.
h must be positive and k must be negative.
h must be negative and k must be positive.
On solving the provided question we can say that from the graphs,
y = f(x) = |x| and g(x) = |x-h| + k
What is graphs?Mathematicians use diagrams to logically bring facts or values using visual representations or charts. A graph point usually reflects a contact between two or more things. Nodes or vertices and corner form a graph, which is a nonlinear data construction. We often glue knots together called vertices. This graph has vertices V=1, 2, 3, 5 and edges E=1, 2, 1, 3, 2, 4 and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) are graphical representations of expanding growth. Logarithmic graph in the format of a triangle
from the graphs,
y = f(x) = |x|
y = f(x) + k
y = f(x+h)
g(x) = |x-h| + k
now, it will be
k>0 and h<0
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volume of prism
25cm 40cm
Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.
Answer:
The volume of a rectangular prism with length 25 cm and width 40 cm can be calculated as follows:
Volume = Length * Width * Height
Since the height is not given, we cannot calculate the exact volume.
Step-by-step explanation:
Find the perimeter of a rectangle whose length and breadth are 150 cm and 2 m respectively.
Step-by-step explanation:
150x 2m =300 m4679096x 56885666-1480+(34464757/A circular arc has measure 8 ft and is intercepted by a central angle of 2.9 radians. Find the radius r of the circle.
Do not round any intermediate computations, and round your answer to the nearest tenth.
The radius of the circle is 2.8feet (nearest tenth)
What is length of an arc?Arc length is the distance between two points along a section of a curve.
The length of an arc is expressed as ;
L = (tetha) / 360 × 2πr
L is the length of the arc
tetha is the angle made by the two radii and the arc.
In radian 360° = 2π
therefore ;
8 = 2.9/ 2π × 2πr
8 = 2.9 r
r = 8/2.9
r = 2.76 ft
therefore the radius of the circle is 2.8 feet( nearest tenth) .
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[tex]\frac{-3x+6}{x-2}[/tex] = 0
solve for x. if there is no solution, write no solution.
Answer:
there is no solution
Step-by-step explanation:
suppose there are three cards, a, b, and c. two of them will be drawn one by one with replacements. what is the probability of getting (a, b), i.e. the first card is a and the second card is b?
the probability of getting (a, b), i.e. the first card is a and the second card is b is 2/3 by conditional probability.
The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is computed by dividing the likelihood of the earlier occurrence by the likelihood of the subsequent, or conditional, event.
This is where the independent event and dependent event notion is used. Consider a student who misses class twice each week, omitting Sunday. What are the possibilities that he will take a leave of absence on Saturday of the same week if it is known that he will be absent from school on Tuesday? It has been noted that situations where the outcome of one event influences the outcome of a subsequent event are termed as conditional probability
We can work this out directly from the definition of conditional probability,
[tex]P(G_1|G_2)=P(G_1nG_2)/(P(G_1)[/tex]
Exactly one of the three cards has sides, so
P(G1∩G2)=1/3
and P(G1)=1/2
THEN
the probability of getting (a, b), i.e. the first card is a and the second card is b IS = 1/3÷1/2 = 2/3
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14-3(8-3)+10=? can someone please answer that for me i keep on getting 11 but its supposed to be 9 i js have to show my work
FLIPPING COINS There are 2³
possible outcomes for flipping a
penny three times. There are 2⁹
possible outcomes for flipping a
penny nine times. How many times
more possible outcomes are there for
flipping a penny 9 times than flipping a
penny three times?
Answer:
504
Step-by-step explanation:
2 to the power of 9 is 512 2 to the power of 3 is 8 so 512-8 is 504 (hope w this helps!)
Answer:
504
Step-by-step explanation:
2^9 = 512
2^3= 8
512-8=504
the probability of successfully landing a plane using a flight simulator is given as 0.80. nine randomly and independently chosen student pilots are asked to try to fly the plane using the simulator. (a) what is the probability that all the student pilots successfully land the plane using the simulator? (b) what is the probability that none of the student pilots successfully lands the plane using the simulator? (c) what is the probability that exactly eight of the student pilots successfully land the plane using the simulator?
(a) The probability that all the student pilots successfully land the plane using the simulator is 43%
(b) The probability that none of the student pilots successfully lands the plane using the simulator is 0.0026%
(c) The probability that exactly eight of the student pilots successfully land the plane using the simulator is 30.1%
Probability is a measure of the likelihood of an event occurring.
(a) What is the probability that all the student pilots successfully land the plane using the simulator?
Probability of all pilots successfully landing
=> 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = 0.43 or 43%
So, the probability that all the student pilots successfully land the plane using the simulator is 0.43 or 43%.
(b) What is the probability that none of the student pilots successfully land the plane using the simulator?
The probability of each pilot failing to land the plane is 0.20. We can use the multiplication rule again to calculate the probability of none of the pilots successfully landing the plane.
Probability of all pilots failing to land = 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 x 0.20 = 0.000026 or 0.0026%
So, the probability that none of the student pilots successfully land the plane using the simulator is 0.0026% or 0.000026.
(c) What is the probability that exactly eight of the student pilots successfully land the plane using the simulator?
where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success in one trial, and nCk is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.
In this case, we have n=9, k=8, p=0.80, and (1-p)=0.20. So, the probability of exactly eight pilots successfully landing the plane is:
P(X=8) = 9C8 * 0.80^8 * 0.20^(9-8) = 0.301 or 30.1%
So, the probability that exactly eight of the student pilots successfully land the plane using the simulator is 0.301 or 30.1%.
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