5 students are choose at random and there is 4 options (A, B, C and D)


1. What is the probability none choose option B

2. What is the probability all choose option A

3. What is the probability 3 students choose option C

Answers

Answer 1

The probability none choose option is [tex]\frac{243}{1024}[/tex]  , the probability all choose option A is [tex]\frac{1}{1024}[/tex] , the probability 3 students choose option C is [tex]\frac{15}{256}[/tex]  

What do you mean by Probability?

Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.

Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.

Probabilities can be calculated using various methods, such as counting, Bayes' theorem, and simulation. In general, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

To find the probability that none of the 5 students choose option B, we need to find the probability that each student chooses one of the other 3 options (A, C, or D) and then multiply these probabilities. Since each student has the same choices, the probability that each student chooses one of the other options is 3/4. So, the probability that none of the 5 students choose option B is (3/4)^5 = 243/1024.To find the probability that all 5 students choose option A, we need to find the probability that each student chooses option A and then multiply these probabilities. The probability that each student chooses option A is 1/4. So, the probability that all 5 students choose option A is (1/4)^5 = 1/1024.To find the probability that 3 students choose option C, we can use combinations. There are C(5,3) = 10 ways to choose 3 students out of 5. For each of these combinations, the probability that the chosen 3 students choose option C is (1/4)^3, and the probability that the remaining 2 students choose options other than C is (3/4)^2. So, the total probability is 10 * (1/4)^3 * (3/4)^2 = 15/256.

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Related Questions

Which ordered pair represents point F?

Responses

(0, 5)

(0, -5)

(5, 0)

(-5, 0)

Answers

Answer:

(-5, 0)

Step-by-step explanation:

Answer:

D (-5,0)

Step-by-step explanation:

OOOOOOOOOOOOOOOOOOOOOOOO

Higher the weight of the variable in a standardized predictor environment, we can say that the particular variable has a higher discriminating power. True or False?

Answers

False. The weight of a variable in a standardized predictor environment does not necessarily indicate that the variable has a higher discriminating power.

Discriminating power is determined by the correlation of a predictor variable with the outcome variable. We can calculate the correlation between a predictor variable and an outcome variable using Pearson's correlation coefficient, which is represented by the formula:

r = (NΣXY - (ΣX)(ΣY)) / √[(NΣX2 - (ΣX)2)(NΣY2 - (ΣY)2)].

In this formula, N is the sample size, ΣX is the sum of the predictor variable, ΣY is the sum of the outcome variable, ΣXY is the sum of the products of the predictor and outcome variables, and ΣX2 and ΣY2 are the sums of the squares of the predictor and outcome variables, respectively. The Pearson's correlation coefficient ranges from -1 to +1, with +1 indicating perfect positive correlation, 0 indicating no correlation, and -1 indicating perfect negative correlation. A higher correlation coefficient indicates a higher discriminating power.

Therefore, the weight of a variable in a standardized predictor environment does not indicate whether or not the variable has a higher discriminating power; this is determined by the correlation between the predictor and outcome variables.

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the general form of a large-sample (1) 100onfidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest.true or false

Answers

True, the general form of a large-sample 100% confidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest.

The general form of a large-sample 100% confidence interval for a population proportion p is given by the formula:

p ± z(standard error of p)

where p is the sample proportion of observations with the characteristic of interest and z is the critical value from a standard normal distribution corresponding to the desired level of confidence (e.g. z = 1.96 for a 95% confidence interval). The standard error of p is calculated as the square root of (p(1-p)/n), where n is the sample size.

This formula is based on the central limit theorem and the assumption that the sample is random and large enough (n > 30). In this case, the distribution of p is approximately normal and the confidence interval provides a range of plausible values for the true population proportion.

Correct Question :

The general form of a large-sample 100% confidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest. True or false.

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What is the measure of y

Answers

[tex]3 \sqrt{13} [/tex]

Evelyn went shopping for a new pair of pants. Sales tax where she lives is 4%. The price of the pair of pants is $33. Find the total price including tax. Round to the nearest cent.

Answers

The total price of the pair of pants is 34.32 dollars.

How to find the total price of the pants?

Evelyn went shopping for a new pair of pants. Sales tax where she lives is 4%. The price of the pair of pants is $33. Therefore, the total price of the pants including the sales tax can be calculated as follows:

Therefore,

sales tax in dollars = 4% of 33

sales tax in dollars = 4 / 100 × 33

sales tax in dollars = 132 / 100

sales tax in dollars = 1.32 dollars

Therefore,

total price3 of the pants = 33 + 1.32

total price3 of the pants = 34.32 dollars

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you want to watch a play, the ticket for which costs $100. you have just arrived at the theater to buy your ticket and discover that you have lost a $100 bill from your wallet. do you buy a ticket and see the play anyway?

Answers

This is a difficult decision that you have to make. On the one hand, you really want to see the play and have come all this way to do so.

On the other hand, you have lost a $100 bill and may not be able to afford a ticket. Ultimately, it is your decision to make. If you have the financial means, you could consider buying a ticket and seeing the play. Alternatively, you could look for discounted tickets if available or wait until you have the funds available before buying a ticket.

The cost of a ticket to watch a play depends on the venue, seating arrangements, and other factors. Generally speaking, tickets for a play can range from around $10 to upwards of $100, depending on the show and its popularity.

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This question is designed to be answered without a calculator. If f(x) = x2 and g(x) = x - 4, what is the domain of g(f(x))? O all real numbers O all real numbers x 20 O all real numbers x 24 O all real numbers x 22

Answers

If the function f(x) = x² and function g(x) = √(x - 4) , then the domain of g(f(x)) is (d) all real numbers |x| ≥ 2 .

The Domain of a function is defined as the set of all input values for which the function is defined and produces a valid output.

⇒ The domain of f(x) = x² is all real numbers because squaring any real number results in a valid result .

⇒ The domain of g(x) = √(x - 4) ; we know that the square root of a number must be non-negative.

The square root is taken of (x - 4), so (x - 4) must be ≥ 0 . This means that x must be ≥ 4.

The domain of g(f(x)), we need to substitute f(x) into g(x).

So, g(f(x)) = g(x²) = √(x² - 4).

The domain of this expression is all real numbers x such that

⇒ x² - 4 ≥ 0 and

⇒ |x| ≥ 2. This is because x² must be ≥ 4, and taking the square root of a positive number results in a valid result .

Therefore , the domain of g(f(x)) is (d) all real numbers |x| ≥ 2 .

The given question is incomplete , the complete question is

If f(x) = x² and g(x) = √(x - 4) , what is the domain of g(f(x)) ?

(a) all real numbers

(b) all real numbers x ≥ 0

(c) all real numbers x ≥ 4

(d) all real numbers |x| ≥ 2 .

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A culture begin with 3,800 bacteria. After one hour, the count i 10,000. A. Write an exponential equation in the form y=ab^x that model the number of bacteria after x hour

B. How many bacteria are preent after 6 hour

Answers

The function is y = 3800 * (2.63)^x

There are 1257529 bacteria after 6 hours.

The function of the scenario

A. Let y be the number of bacteria after x hours.

We know that y=10,000 when x=1 and

y=3,800 when x=0.

So we can write the equation as follows:

y = 3800 * (10,000/3,800)^x

Evaluate

y = 3800 * (2.63)^x

The bacteria after 6 hours

B. To find the number of bacteria after 6 hours, we substitute x=6 into the equation above:

y = 3800 * (2.63)^6

Evaluate

y = 1257529

So, there are 1257529 bacteria after 6 hours.

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Can anyone answer this question?

Answers

The line that represents the axis of symmetry will be the lines m, h, and g. When the figure is rotated by 120 degrees, 240 degrees, and 360 degrees then the figure remains the same.

What is the axis of symmetry?

Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.

The reflection does not change the shape and size of the geometry. But flipped the image.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The line that represents the axis of symmetry will be the lines m, h, and g. When the figure is rotated by 120 degrees, 240 degrees, and 360 degrees then the figure remains the same.

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Calculate the integral approximations T6 and M6 for?(a=1)(b=2)x^6dx.T6 =M6 =

Answers

The approximate values for the definite integral of x⁶ over the interval [1, 2].

An integral is a mathematical tool used to calculate the total amount of some quantity that changes continuously over a given interval.

The Trapezoidal rule approximates the definite integral of a function by dividing the interval of integration into a number of smaller subintervals, and then using trapezoids to approximate the area under the curve.

The formula for T6 is:

T6 = (b-a) * (f(a) + f(b)) / 2,

where a and b are the limits of integration, and f(x) is the function being integrated.

However, instead of using trapezoids, the Midpoint rule uses rectangles to approximate the area under the curve.

The formula for M6 is:

M6 = (b-a) * f((a + b) / 2)

To calculate T6 and M6 for the integral (a=1)(b=2)x⁶dx, we need to use the formulas above and plug in the appropriate values for a, b, and f(x). The function f(x) is x⁶, so:

T6 = (2 - 1) x (1⁶ + 2⁶) / 2 = 1 x (1 + 64) / 2 = 32.5

M6 = (2 - 1) x (2⁶)¹/₂ = 1 x (64)¹/₂ = 8

So, T6 = 32.5 and M6 = 8.

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Сильные слабые стороны человека

Answers

Answer:

Сильные:

Упорный, нацеленый на результат

Уверен в себе

Трудолюбивый

Общительный

Организованный

Самостоятельный

Дисциплинированный

Слабые:

Излишне стеснительный

Чрезмерно эмоциональный

Раздражительный и даже агрессивный

Не обладающий силой воли

Не умеющий вовремя промолчать

Гиперактивный

Принципиальный

a random sample is to be selected from a population. for which combination of n and p is it reasonable to assume that the sampling distribution of the sample proportion p will be approximately normal?

Answers

For the combination of n = 25 and p = 0.5 it is reasonable to assume that the sampling distribution of the sample proportion p will be approximately normal.

As per the given data:

A random sample is to be selected from a population

Here we have to determine for which combination of n and p is reasonable to assume that the sampling distribution of the sample proportion p will be approximately normal.

For this we have to multiply the value of n and the value of p.

Option (A):

n = 10 and p = 0.4

np = 10 × 0.4

np = 4

Option (B):

n = 25 and p = 0.5

np = 25 × 0.5

np = 12.5

Option (C):

n = 30 and p = 0.2

np = 30 × 0.2

np = 6

Option (D):

n = 40 and p = 0.1

np = 40 × 0.1

np = 4

Option (E):

n = 100 and p = 0.05

np = 100 × 0.05

np = 5

Compare all the combinations of np.

Option (B) is correct because it has the highest value of np.

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A random sample is to be selected from a population. For which combination of n and p is it reasonable to assume that the sampling distribution of the sample proportion p will be approximately normal?

(A) n = 10 and p = 0.4

(B) n = 25 and p = 0.5

(C) n = 30 and p = 0.2

(D) n = 40 and p = 0.1

(E) n = 100 and p = 0.05

4. a rate constant is found to triple when the temperature is increased from 275 k to 300. k. at what temperature will the rate constant be five times greater than the rate constant at 275 k? report your answer in k.

Answers

The temperature at which the rate constant becomes five times greater than the rate constant at 275 K is 325 K.

Let's say that temperature is represented by t and the rate constant is represented by r.

Let' say r₁ = R, r₂ = 3R, t₁ = 275 K and t₂ = 300 K.

considering the relationship between rate constant and temperature is linear.

t - 300 = [(300 - 275)/(3R - R)](r -  3R)

t - 300 = (25/2R)(r - 3R)

We are asked to determine the temperature at which the rate constant becomes five times greater than the rate constant at 275 K.

t - 300 = (25/2R)(5R - 3R)

t - 300 = (25/2R)(2R)

t - 300 = 25

t = 325 K

Hence, the temperature at which the rate constant becomes five times greater than the rate constant at 275 K is 325 K.

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Given: m/X = m/Y, m/X = 4x + 18,
and m¿Y = 78°
Prove: x = 7
Statement:
1. m/X = m/Y
2. m/X= 4x+18
3. m2Y = 78°
4.4x+18= 78
5.4x=60
6.x=15
Reason:
1. Given
2. Given
3. Given
4.[? ]
5.
6. Division Property
of Equality
Select the reason that best
supports Statement 4 in the
given proof.
A. Addition Property of Equality
B. Multiplication Property of Equality
C. Given
D. Substitution

Answers

The reason that best supports Statement 4 in the

given proof is option A. Addition Property of Equality

How does it support statement 4?

The statement 4, "4x + 18 = 78," is an equation that is being derived from the previous statements in the proof. The left side of the equation (4x + 18) represents the value of m/X, which was given as 4x + 18 in statement 2.

The right side of the equation (78) represents the value of m2Y, which was given as 78° in statement 3.

Therefore, statement 4 is derived by substituting the known values of m/X and m2Y into the equation m/X = m2Y, which was given as statement 1.

The reason for this substitution is the Addition Property of Equality, which states that if you add the same value to both sides of an equation, the two sides remain equal.

In this case, the same value (4x + 18) is being added to both sides of the equation m/X = m2Y, resulting in the equation 4x + 18 = 78.

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es urgentee ayuda porfa

Answers

De acuerdo con la información, se puede inferir que la respuesta correcta es la opción C. Solo III, debido a que las otras afirmaciones están erradas.

¿Cómo identificar las afirmaciones correctas?

Para identificar las afirmaciones correctas debemos evaluar cada una de ellas tendiendo en cuenta la información principal. En el caso de la primera afirmación es falsa debido a que 21 monedas representan un cuarto del dinero total entonces habría 84 monedas en total, no 27.

En el caso de la segunda afirmación es falsa debido a que el enunciado dice que hay 12 monedas de 5$ por lo que habría más monedas de las que dice en la opción.

En el caso de la tercera afirmación es verdadera debido a que el dinero total sí equivale a $600 como se muestra a continuación:

12 * $5 = $60

9 * $10 = $90

$90 + $60 = $150

$150 * 4 = $600

Por lo anterior, la afirmación III es verdadera, entonces la opción C sería la única correcta.

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The Tasty as Pi Bakery has two locations! Each location offers the same flavors. Both locations display one pie of each flavor in a rectangle.

The downtown location has $4$ rows in its display. The uptown location has $6$ rows in its display. If one of the locations has a square display, how many pies are in each of the other location's rows?

Answers

Answer:

dd osama

Step-by-step explanation:

if x equals to 1 by x = 5 find the value of x square + 1 divided x square

Answers

Given x = 1 to x = 5, the value of x^2 + 1 divided by x^2 can be calculated as follows:

For x = 1, x^2 + 1 divided by x^2 = (1^2 + 1) / (1^2) = 2/1 = 2

For x = 2, x^2 + 1 divided by x^2 = (2^2 + 1) / (2^2) = 5/4 = 1.25

For x = 3, x^2 + 1 divided by x^2 = (3^2 + 1) / (3^2) = 10/9 = 1.11

For x = 4, x^2 + 1 divided by x^2 = (4^2 + 1) / (4^2) = 17/16 = 1.06

For x = 5, x^2 + 1 divided by x^2 = (5^2 + 1) / (5^2) = 26/25 = 1.04

So, the value of x^2 + 1 divided by x^2 changes from x = 1 to x = 5.

I need help with maths please

Answers

Answer:

Below

Step-by-step explanation:

Perimeter A = 2 (x+2 +x) = 4x + 4

Perimeter B = 2 ( 4x+2x) = 12x

now,equate them

4x+4 = 12x    solve for x   ....subtract 4x from both sides

4 = 8x

x = 1/2

52 cm - 13.1 cm = ? (Choose all correct answers.)
223 cm
39 cm
39.1 cm
223 mm
40 cm
400 mm
390 mm
030 cm
0391 mm

Answers

As per the given measurement, the value of 52 cm - 13.1 cm is 39 cm.

The term in math measurement is defined as quantifies the characteristics of an object or event, which we can compare with other things or events which is the most commonly used word, whenever we deal with the division of a quantity.

Here we have given the expression 52 cm - 13.1 cm.

As we have to subtract the expression then we have written as,

=> 52 - 13.1

When we subtract is then we get the difference as 38.9

Now, we have to round off the value then we get the result as 39 cm.

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An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 800 meters, and Plane B was at an altitude of 360 meters. Plane A is gaining altitude at 15 meters per second, and Plane B gaining altitude at 25 meters per second . Let x be the number of seconds that have passed

Answers

a) The expressions are given as follows:

Plane A: A(t) = 800 + 15t.Plane B: B(t) = 360 + 25t.

b) The will be at the same altitude at a time of: 44 seconds.

How to model the situation?

The situation is modeled by linear functions in slope-intercept format, as follows:

y = mx + b.

In which:

The slope m represents the rate at which the planes are gaining altitude.The intercept b represents the initial altitude.

Hence the functions are defined as follows:

Plane A: A(t) = 800 + 15t.Plane B: B(t) = 360 + 25t.

The planes will have the same altitude when:

A(t) = B(t)

Hence:

800 + 15t = 360 + 25t

10t = 440

t = 44 seconds.

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a jar contains 18 red, 12 blue, 20 yellow, 14 green marbles. what is the ratio of blue marble to the total number of marbles

Answers

The ratio of blue marbles to the total number of marbles is; 3:16.

The total number of marbles in the jar is 18 red + 12 blue + 20 yellow + 14 green = 64.

So, the ratio of blue marbles to the total number of marbles can be expressed as 12:64.

This ratio can be simplified by dividing both the numerator and denominator by the greatest common factor, which in this case is 4.

So, the simplified ratio becomes 12/4 : 64/4 = 3:16.

This means for every 16 marbles in the jar, 3 of them are blue.

The simplified ratio of 3:16 can be understood as a fraction, where the numerator represents the number of blue marbles and the denominator represents the total number of marbles in the jar.

This fraction can be converted to a percentage by multiplying it with 100, which gives 18.75%.

Therefore, the ratio of blue marbles to the total number of marbles is 12:64, which simplifies to 3:16.

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The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what is the probability that a student scored greater than 65?
Multiple Choice
0.7611
−0.714
0.2611
0.2389

Answers

the probability that a student scored greater than 65 is 0.2389.

The probability that a student scored greater than 65 can be calculated using the standard normal distribution and the z-score. The z-score represents the number of standard deviations a value is from the mean, and can be calculated as follows:

z = (x - mean) / standard deviation

Where x is the score of interest (65)

Mean is the average score of the students (70)

Standard deviation is the standard deviation of the scores (7).

Plugging in the values, we get

z = (65 - 70) / 7 = -0.714.

Using a standard normal distribution table, we can find the probability that a student scored greater than 65 by finding the area to the right of the z-score. The probability of a student scoring greater than 65 is approximately 0.2389, or 23.89%.

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How do I covert yard into feet with fractions?

Answers

Answer:    x/3

Step-by-step explanation:

Say "x" is the number of yards you are given.

remember that one yard = 3 feet.

in order to convert x amount of yards into feet, you must divide x by three.

giving you=  x/3

what is the area under the normal curve between z = -1.0 and z = -2.0? 0.0228 0.1359 0.4772 0.3413

Answers

The area under the curve between z = −2.0 and z = −1.0 is 0.1359.

We can use tables to find the area under the normal curve between two values of z.

However, tables give areas from z = 0 to z = 3.9 (beyond which there is literally no change). But as the normal curve is symmetric at z = 0, we can use it to find between any two given z values.

For example, for the area under the curve between z = −2.0 and z = −1.0, we can take values for z = 2.0 and z = 1.0; their difference will give the area between z = −2.0 and z = −1.0.

From tables for z = 1.0, we have 0.8413 and for z = 2.0, we have 0.9772 and

Hence, the Area under the curve between z = −2.0 and z = −1.0 is 0.9772−0.8413 = 0.1359.

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What is the quotient of (x4 − 3x3 + 6x2 − 12x + 8) ÷ (x − 1)?

Answers

The quotient of the division is  x^3 - 2x^2 + 4x - 8

How to determine the quotient

From the question, we have the following parameters that can be used in our computation:

quotient of (x4 − 3x3 + 6x2 − 12x + 8) ÷ (x − 1)?

Using the long division method of quotient, we have

x - 1 | x^4 - 3x^3 + 6x^2 - 12x + 8

The division steps are as follows

          x^3 - 2x^2 + 4x - 8

x - 1 | x^4 - 3x^3 + 6x^2 - 12x + 8

        x^4 - x^3

------------------------------------------------

             -2x^3 + 6x^2 - 12x + 8

             -2x^3 + 2x^2

------------------------------------------------

                         4x^2 - 12x + 8

                         4x^2 - 4x

------------------------------------------------

                                       -8x + 8

                                       -8x + 8

----------------------------------------------------

Hence, the quotient is  x^3 - 2x^2 + 4x - 8

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Jace is going to an amusement park. The price of admission into the park is $15, and once he is inside the park, he will have to pay $5 for every ride he rides on. How much money would Jace have to pay in total if he goes on 5 rides? How much would he have to pay if he goes on rr rides?

Answers

The amount of money that Jace would have to pay in total if he goes on 5 rides is; $40

The amount of money that Jace would have to pay in total if he goes on r rides is; 5r + 15

How to solve Algebra Word problems?

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, Since the price of admission into the park is $15, it means that it is the y-intercept. Thus, c = $15

He pays $5 for every ride and as such this will be the slope. Thus;

Total cost = 5x + 15

where x is number of rides

For 5 rides;

Y(5) = 5(5) + 15

= $40

For r rides, the total cost is;

y(r) = 5r + 15

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Please answer 1 SIMPLE question.

Answers

Answer: Maybe B

Step-by-step explanation:

Guess from heart.

Identify the inital amount (a) and the rate of growth a a prevent y=100000(1. 09)^3

Answers

To identify the initial amount (a) and rate of growth in the equation y=100000(1.09)^3, you can use algebra to isolate the variables.

First, divide both sides of the equation by 100000 to get y/100000=(1.09)^3. Then, take the cube root of both sides of the equation to get y/100000=1.09.

Finally, multiply both sides of the equation by 100000 to get y=109000. Therefore, the initial amount (a) is 100000, and the rate of growth is 1.09.

The initial amount, also known as the starting point or the base value, is the value of a variable at the beginning of a given period.

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12 more than the product of 5 and a number 2 PLEASE HELP!!!

Answers

Answer: (12+5)+2

Step-by-step explanation:

12+5=17

17+2=19

Answer:

12+(5+2)

Step-by-step explanation:

you must do 5 plus 2 first because you are adding 12 to their product. which is the answer to an addition problem. so you are given...

What is the equation of the line that is perpendicular to the line 5x - 3y = 2 and passes through the point (- 1/4, 3/5) ?

Answers

Answer:

y= -3/5x+9/20

I graphed it to be sure it works. Hope this helped!

Step-by-step explanation:

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