Jake tossed a paper cup 50 times and recorded how it landed. the table shows the results:

position open side up closed side up landing on side

3 7 40



based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). show your work

It is true that statistical sampling uses Monte Carlo simulation, where a greater number of trials are employed to obtain a precise answer.

A mathematical method or statistical sampling called Monte Carlo simulation is used to forecast all potential outcomes of any unknown event.

As it relies on historical data to forecast future results, the accuracy increases with the number of trials.

You can review more old data to anticipate the first month's sales of any newly launched product, for instance.

It aids in more precise probability calculations.

As a result, more trials are necessary for an accurate result in Monte Carlo simulation statistical sampling.

Therefore, it is true that statistical sampling uses Monte Carlo simulation, where a greater number of trials are employed to obtain a precise answer.

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Answer:

60 yan po Sana makatutulong

Answer:

1. 56

2. 56

Step-by-step explanation:

edge 2021

The measure of the arcs of the circle is given by

a) The difference of arc measures mAC - mDE = 56°

b) The measure of angle 2(∠ABC ) = 56°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

θ/360 * πr²

where;

θ is the central angle of the sector

r is radius

Now, looking at the given options we can say that the only one that represents the area of the sector is;

A = n/360 * πr²

where n is the central angle of the sector'

Given data ,

Let the measure of the arcs of the circle be

The measure of angle ∠ABC = 28°

The measure of arc mAC = 80°

The measure of arc mDE = 24°

So , the difference of arc measures mAC - mDE = 80 - 24

The difference of arc measures mAC - mDE = 56°

And , measure of angle 2(∠ABC ) = 56°

Hence , the measures of arcs of circle is solved

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Answer:

x = 25 , y = 19

Step-by-step explanation:

Since the triangle has 3 congruent sides then it is equilateral

The 3 angles are also congruent, with each angle = 60° , then

2x + 10 = 60 ( subtract 10 from both sides )

2x = 50 ( divide both sides by 2 )

x = 25

and

3y + 3 = 60 ( subtract 3 from both sides )

3y = 57 ( divide both sides by 3 )

y = 19

The probability that out of 20 randomly chosen students entering college, less than 3 drop out = 0.11674

Let X be a random variable representing the number of students drop out from college such that X follows binomial distribution.

A binomial distribution deals with two possibilities in 'n' trials -  success or  failure. Here the case of success is being drop out from college.

The probability distribution function of a binomial distribution is,

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ , where n is the number of trials,

p - the probability of success

Here, n = 20 since 20 students are selected randomly.

Since 20% of the students entering college drop out before receiving their diplomas, probability of being drop out = 20/100 = 0.2

Probability that less than 3 students = P(X<3)

                                                            = P( X = 0 or 1 or 2)

                                                            = P(X= 0) + P(X= 1) + P(X= 2)

Now, P(X=0) = ²⁰C₀ (0.2)⁰ (1-0.2)²⁰⁻⁰

                     = 1 x 1 x 0.01153

                     = 0.01153

P(X = 1) = ²⁰C₁ (0.2)¹ (1-0.2)²⁰⁻¹

            = 20 x 0.2 x 0.8¹⁹

            = 0.05765

P(X = 2) = ²⁰C₂ (0.2)² (1-0.2)²⁰⁻²

            = 66 x (0. 2)² x 0.8¹⁸

            = 0.04756

Therefore, The probability that out of 20 randomly chosen students entering college, less than 3 drop out = P(X= 0) + P(X= 1) + P(X= 2)  

                                                               = 0.01153 +  0.05765 + 0.04756

                                                               = 0.11674

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Answer:

5

Step-by-step explanation:

NAAAAAA git trippen

Michael can expect to draw a diamond 5 times.

It is a branch of mathematics that deals with the occurrence of a random event.

The probability of drawing a diamond from a standard deck of 52 cards is 13/52 or 1/4.

Since Michael draws 20 cards with replacement, each draw is independent and follows a binomial distribution with n=20 and p=1/4.

The expected number of times Michael will draw a diamond is given by:

E(X) = n×p

= 20 × (1/4)

= 5

Therefore, Michael can expect to draw a diamond 5 times.

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Answer:

1464.84375

Step-by-step explanation:

The n th term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = 6 and r = 15 ÷ 6 = 2.5, thus

\(a_{7}\) = 6 × \((2.5)^{6}\) = 6 × 244.140625 = 1464.84375

The seventh term of the geometric progression will be 1464.84375

When there is a constant between the two successive numbers in the series then it is called a geometric series.

The nth term of a geometric sequence is

\(a_n =a_1(r)^{n-1}\)

where a₁ is the first term and r is the common ratio

Here a₁ = 6 and r = 15 ÷ 6 = 2.5, thus

\(a_7=6\times (2.5)^{6}\)  = 6 × 244.140625 = 1464.84375

Therefore the seventh term of the geometric progression will be 1464.84375

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Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

(-0.5 , 0.5)

Step-by-step explanation:

Midpoint = \((\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\)

               \(= (\frac{-3+2}{2},\frac{4-3}{2})\\\\=(\frac{-1}{2},\frac{1}{2})\\\\=(-0.5, 0.5)\)

Answer:

800 + 150 = 950

Step-by-step explanation:

The answer is 950 because if you have $800 and your mom gives you $150 more. You will have a total of $950.

Answer:

800+150=950

Step-by-step explanation:

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

Given: y = -0.8x + 0.4

As we know that the slop-intercept form of the equation of a line is given by: y = mx + c, where

On comparing the given equation of line with the above form of equation of line, we get: m = -0.8 and c = 0.4.

Hence, The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

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7.59 inches and 3x-3 width

Answer:

18

Step-by-step explanation:

here,

circumference of the circle = 90

\(S = r\theta\)

in above equation, S is the length of arch, r is the radius and theta is the angle formed by arc at the center,

As you can see, in a circle of given radius,

\(S \propto \theta\)

therefore,

\(\dfrac{S_1}{S_2} = \dfrac{\theta_1}{\theta_2}\)

we have the arc length for angle 360 (circumference of the circle).

let S1 be the length of minor arc, S2 be the arc formed by full circle (360 degree),

\(\dfrac{S_1}{90} = \dfrac{72}{360}\)

solving the above equation, we get

\(S_1 = 18\)

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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The budget of at least $10k allocated to each medium. The Linear programming model is to maximize Z = 15x + 10y subject to x + y ≤ 30, x ≥ 10, y ≥ 10, x, y ≥ 0. The graphical solution procedure is used. The additional budget indicates social media advertising is more effective. The speech introduces LP as a mathematical technique and encourages senior citizens to join.

Objective To allocate the budgeted amount between social media and TV in a way that maximizes the number of people reached.

Constraints

The total budget is $30k.

At least $10k must be allocated to each medium.

The amount allocated to social media and TV cannot exceed the total budget.

The amount allocated to each medium must be non-negative.

Decision variables

Let x be the amount allocated to social media and y be the amount allocated to TV.

LP model

Maximize Z = 15x + 10y

Subject to:

x + y ≤ 30

x ≥ 10

y ≥ 10

x, y ≥ 0

Graphical solution procedure

Plot the constraints on a graph and find the feasible region.

The feasible region is the shaded region

LP Graphical Solution

The objective function 15x + 10y is a straight line with slope -1.5 and intercepts (0, 0) and (20, 0). Find the corner points of the feasible region and evaluate the objective function at each corner point.

Corner point A (10, 20): Z = 15(10) + 10(20) = 350

Corner point B (20, 10): Z = 15(20) + 10(10) = 400

Corner point C (20, 10): Z = 15(20) + 10(10) = 400

Corner point D (30, 0): Z = 15(30) + 10(0) = 450

The maximum value of the objective function is 450 at corner point D (30, 0). Therefore, the optimal solution is to allocate $30k to social media and $0 to TV.

The worth per additional $1k of budget for social media is 15 people, which means that for every additional $1k spent on social media, the company can reach 15 more people. This result shows that social media advertising is more effective than TV advertising in reaching people. Therefore, if the company wants to allocate additional budget to reach more people, they should allocate it to social media advertising rather than TV advertising.

Speech

Good morning everyone, thank you for having me here today. My name is [Your Name] and I'm here to introduce you to the world of linear programming.

Linear programming is a mathematical technique that helps us optimize a given objective while satisfying a set of constraints. It has wide applications in business, economics, engineering, and many other fields.

The basic idea of linear programming is to find the best possible solution from all the feasible solutions that satisfy the given constraints.

The course we're offering will teach you how to formulate a problem as an LP model and how to solve it using various methods such as graphical solution, simplex method, and others. You don't need to have any prior knowledge of mathematics.

If you're a senior citizen who is passionate about lifelong learning and has worked in various industries before retirement, this course is perfect for you. It will not only enhance your problem-solving skills but also help you understand the mathematical concepts behind real-life problems.

In conclusion, linear programming is a powerful tool that can help us optimize our decisions and achieve our goals. I encourage you all to sign up for the course and join us in this exciting journey.

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The point (9, 16) is on the line.

Given,

The equation of the line = y = 4/3x + 4

We have to find whether the given points are on this line or not.

For that substitute the points into the equation.

That is,

Point (6, 13)

x = 6 and y = 13

Equation;

y = 4/3x + 4

13 = 4/3 x 6 + 4

13 = 8 + 4

13 ≠ 12

That is, the point (6, 13) is not in the line.

Next,

Point (9, 16)

x = 9 and y = 16

Equation;

y = 4/3x + 4

16 = 4/3 x 9 + 4

16 = 12 + 4

16 = 16

Therefore, the point  (9, 16) is in the line.

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By the binomial theorem,

(1 + x)⁴ = 1 + 4x + 6x² + 4x³ + x⁴

(1 + 2x)³ = 1 + 6x + 12x² + 8x³

In the expansion of (1 + x)⁴ (1 + 2x)³, we get an x⁴ when multiplying

• x⁴ and 1 to get x⁴;

• 4x³ and 6x to get 24x⁴;

• 6x² and 12x² to get 72x⁴; and

• 4x and 8x³ to get 32x⁴.

Add these up:

x⁴ + 24x⁴ + 72x⁴ + 32x⁴ = 129x⁴

Answer:

23

Step-by-step explanation:

Answer:

37.5%

Step-by-step explanation:

to get a percentage you take the fraction 3/8 then times 100

Answer:

37.5%

Step-by-step explanation:

3/8 equals to .375 then multiply .375 by 100 to get the percentage, which is 37.5

Answer:

Step-by-step explanation:

MIXED NUMBER: Convert to a mixed number by placing the numbers to the right of the decimal over 10.Reduce the fraction

8 4/5

SIMPLFIED FRACTION: Convert to a mixed number by placing the numbers to the right of the decimal over 10.Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

44/5

The p-value for testing H0 (null hypothesis) versus Ha (alternative hypothesis) is 0.0038. We need to determine whether H0 would be rejected at different significance levels: α = 0.10, α = 0.05, α = 0.01, and α = 0.001.

To make the decision, we compare the p-value with the chosen significance level. If the p-value is less than or equal to the significance level, we reject H0. Otherwise, we fail to reject H0.

At α = 0.10: Since the p-value (0.0038) is less than 0.10, we reject H0.

At α = 0.05: Since the p-value (0.0038) is less than 0.05, we reject H0.

At α = 0.01: Since the p-value (0.0038) is greater than 0.01, we fail to reject H0.

At α = 0.001: Since the p-value (0.0038) is greater than 0.001, we fail to reject H0.

In summary:

H0 would be rejected at α = 0.10 and α = 0.05.

H0 would not be rejected at α = 0.01 and α = 0.001.

Please note that the decision to reject or fail to reject the null hypothesis depends on the chosen significance level, and different levels of significance can lead to different conclusions.

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On solving the provided question, we can say that - Jeff's and Amber's cities will have the same temperatures after 12 hours

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Ax+By=C is the typical form for linear equations with two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts (x and y) for an equation of this type is not too difficult.

the temperature in both cities is the same after x hours.

The city of Jeff's temperature now varies with time as follows:

\(T_1 = 0.5t + 58\\\)

in Amber's city, we have -

\(T_2 = 0.25t + 61\)

Now , at time x temperature of both city is same .

So ,

\(0.5x + 58 = 0.25x + 61\)

0.25x = 3

x = 12 hours

Therefore, Jeff's and Amber's cities will have the same temperatures after 12 hours. This is the necessary remedy as a result.

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Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

i just got the biggest brain ever

Answer:

x: $20 an hour independent variable

y: total amount dependent variable

y = $20x

The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.

According to the statement

we have to explain about the function in which cryptography takes a string of any length as input and returns a string of any requested variable length.

So, For this purpose,

we know that the

A sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length.

So from definition and its working process it is clear that for this purpose the sponge function is used.

this function returns the string of any variable length.

So, The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.

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Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

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6/5x8/5

6x8 5x5

48/5x5

48/25

Decimal (1.92)

Answer:

The simplest form would be 1 23/28.

Step-by-step explanation:

Khan academy : >

The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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