find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. hint [see example 1.] the sum is 4, given that the green one is either 3 or 2.

Stochastic simulations use random variables or probability distributions to model uncertainty in the system being simulated.

The type of simulation that is defined over a theoretically infinite time frame is called a "steady-state simulation".

In a steady-state simulation, the system being modeled is assumed to have reached a stable state where the behavior of the system does not change over time. The simulation is then run for a long period of time, allowing the outputs to converge to a steady state. The quantities to be estimated are defined over this theoretically infinite time frame.

On the other hand, terminating simulations have a fixed end time, and the simulation is terminated when that time is reached. Discrete simulations model systems where the state changes only at discrete points in time. Stochastic simulations use random variables or probability distributions to model uncertainty in the system being simulated.

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The kicker's ability to punt the ball any distance from the goal line means that the domain is unlimited in range.

As a transformation of f(x), g(x) carries the same infinity of values within its range as well with a limit up to 25.

Decidedly opening downwards, f(x)'s parabola possesses a vertex located at (30, 25). For playing according to territory: representing the kicker’s goal line, x = 30 houses the vertex of f(x) , so punting happens closer there.

In sum, while f(x) equips football players to strategically understand their field posisioning ranging  across all heights, trajectory of direction & ranges, executing effective plays based on the available resources; along with g(x) which offers a modified visual representation- they both obey the constraints of physics-based rules.

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Answer:

2 g

Step-by-step explanation:

She has a total of

5 1/2 + 11 1/4 =

= 5 2/4 + 11 1/4

= 16 3/4

She needs a total of 18 3/4.

She needs an additional

18 3/4 - 16 3/4 = 2

Answer: 2 g

The perimeter of the triangle with sides 3x + 4, x² and 19 cm is is x² + 3x + 23 centimetres.

The perimeter of the triangle is the sum of the whole sides of the triangle. A triangle have three sides. Therefore, let's sum the sides of the triangle to find the perimeter of the triangle.

Hence,

perimeter of the triangle = x² + 3x + 4 + 19

perimeter of the triangle = x² + 3x + 23

Therefore, the perimeter of the triangle is x² + 3x + 23 centimetres.

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The equation of the line in point slope form and slope intercept form are y + 4 = -10 (x + 5) and y = -10x - 19 respectively.

Given that,

A line passes through the point (-5, -4) and the slope is -10.

The equation of the line in point slope form can be written as,

y - y' = m(x - x')

where m is the slope and (x', y') is the point on the line.

Substituting,

y - -4 = -10(x - -5)

y + 4 = -10 (x + 5), which is the point slope form.

Simplifying,

y + 4 = -10x - 15

y = -10x - 19, which is the slope intercept form

Hence the point slope form is y + 4 = -10 (x + 5) and the slope intercept form is y = -10x - 19.

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Answer: The student will need to save about 416.66 dollars a month.

Step-by-step explanation:

Step 1. Find out how much the student will need to pay themselves.

20,000 - 10,000 (grandparents) - 5,000 (scholarship) = 5,000

Step 2. Divide the student's cost by the number of months

5,000/12 = about 416.66

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

Let's first define the terms and state the Secant-Tangent Segment Theorem.

1. Equation: A mathematical statement that shows the equality of two expressions.

2. Secant: A line that intersects a circle at two points.

3. Tangent: A line that touches a circle at only one point, without crossing it.

Secant-Tangent Segment Theorem: If a secant and a tangent are drawn from a point outside a circle, the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

Let's represent the given lengths as follows:
- Length of tangent segment = a
- Length of secant segment (inside the circle) = 12
- Length of the external part of the secant segment (outside the circle) = x

According to the Secant-Tangent Segment Theorem, the equation is:
(a)(a) = (12)(x + 12)

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

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The next step in solving the equation, if the first step was to subtract 5, is to A. add x.

To solve the equation -x + 6 = 5 - 3x, given that its first step is "subtract 5", one should move on to the next step which requires adding x to both sides of the equation.

Upon completing this newly introduced action, the resulting equation can be viewed as follows:

-x + 6 - 5 = 5 - 3x - 5

-x + 1 = -3x

-x + x + 1 = -3x + x

1 = -2x

By isolating x term on the right side of the equation through addition, resolving for x will become much more manageable and feasible in the succeeding steps.

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Answer:

Step-by-step explanation:

Les opinions des 450 élèves d'un lycée quant à savoir s'ils soutiennent le candidat A à la présidence du corps étudiant sont présentées ci-dessous. Masquez et mélangez toutes les valeurs. Prenez un échantillon aléatoire de 25 valeurs de la population. Sur la base de cet échantillon, trouvez la proportion de l'échantillon et utilisez cette valeur pour créer un intervalle de confiance à 95 % pour la véritable proportion de la population qui soutient le candidat A, en arrondissant au millième le plus proche.

Échantillon Oui : 19 Échantillon N° : 6 Échantillons : 25

Based on the mentioned informations, the farmer is calculated to have 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.

The farmer starts with 1800 chickens.

He sells 2/5 of the total, which is:

(2/5) x 1800 = 720 chickens.

So he has 1080 chickens left.

He then sells 5/6 of the remaining chickens, which is:

(5/6) x 1080 = 900 chickens.

So he has 180 chickens left.

Unfortunately, 37 chickens die, so the final number of chickens he has left is:

180 - 37 = 143 chickens.

Therefore, the farmer has 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.

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The complete question is :

A farmer has to sell 1800 chickens, first he sells 2/5 of the total, then 5/6 of the rest and if 37 chickens die, how many chickens does he still have left?

The requried, (6x10¹) + (9x10¹) in scientific notation is 1.50x10²

To add (6x10^1) + (9x10^1) in scientific notation, we need to first make sure that the exponents of 10 are the same.

Now we can add the two numbers:

6.0x10¹ + 9.0x10¹ = 15.0x10¹

To express the result in scientific notation, we need to write 15.0 as 1.50 and move the decimal point one place to the left, which gives:

1.50x10²

Therefore, (6x10¹) + (9x10¹) in scientific notation is 1.50x10².

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The example of systematic sampling is option c) in a population of 1000 at a school, every 64th person is chosen.

In systematic sampling, the population is first divided into a sampling frame (for example, a list or a map) and then every kth individual is selected from the list. In this example, every 64th person is chosen from the list of 1000 individuals, which is an example of systematic sampling. In the example given, there is a list of 1000 individuals, and every 64th person is chosen from the list. This means that the sampling interval k is 64, and the first individual is selected randomly from the first 64 individuals in the list. From then on, every 64th individual is selected to be included in the sample. For instance, if the first individual selected is number 8, then the individuals selected for the sample would be 8+64=72, 8+264=136, 8+364=200, and so on.

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The correct answer is c. Yes, because the evidence was not strong enough to suggest that average reading and writing scores differ.

In hypothesis testing, we use a significance level to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the alternative hypothesis.

Based on the results of the hypothesis test, if we failed to reject the null hypothesis (which is the case in this question), then we cannot conclude that the average reading and writing scores differ. Therefore, it is reasonable to expect a confidence interval for the average difference between the reading and writing scores to include 0. A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. Since we cannot conclude that the average scores differ, it is possible that the true population parameter is 0, and thus 0 could be included in the confidence interval.

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The side x of the given right angle triangle is: 24.388

The six trigonometric ratios that we have are:

sine (sin)

cosine (cos)

tangent (tan)

cotangent (cot)

cosecant (cosec)

secant (sec).

In geometry, trigonometry is defined as a branch of mathematics that caters for the sides and also the angles of right-angled triangles. Thus, trigonometric ratios are evaluated considering the sides and angles

The three main trigonometric ratios are expressed as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We want to find the side x of the given right angle triangle.

Thus:

16/x = cos 49

x = 16/cos 49

x = 24.388

Thus, we can say that is the value of x

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61

Why my answer is sixty one Because the Triangle ls the same size Of the other sixty one

Answer:

61

Step-by-step explanation:

Answer:

10h+6b=£48

5h+2b=£19

12h+9b=£60

Step-by-step explanation:

10h+6b=(3h+1b)+(7h+5b)

5h+2b=(7h+5b)-(2h+3b)

12h+9b=(10h+6b)+(2h+3b)

h=handles

b=bolts

The number of ordered quadruplets of non-negative integers that satisfy the given condition is:
|A| - |B| = 161,700 - 16,215 = 145,485

To solve this problem, we need to use the Principle of Inclusion-Exclusion (PIE). Let A be the set of all quadruplets (a1,a2,a3,a4) of non-negative integers that satisfy the equation a1+a2+a3+a4=100, and let B be the set of all quadruplets where all four integers are odd. Then the number of quadruplets that satisfy the given condition is given by:
|A| - |B|
To find |A|, we can use stars and bars. If we consider 100 stars and 3 bars, we can partition the stars into 4 groups, corresponding to the four integers. There will be 99 gaps between the stars and bars, and we need to choose 3 of them to place the bars. This gives us:
|A| = (99 choose 3) = 161,700
To find |B|, we can use a similar approach. If all four integers are odd, then they must be of the form 2k+1, where k is a non-negative integer. Substituting this into the equation a1+a2+a3+a4=100, we get:
2k1 + 1 + 2k2 + 1 + 2k3 + 1 + 2k4 + 1 = 100
Simplifying this equation, we get:
k1 + k2 + k3 + k4 = 48
This is now an equation in non-negative integers, which we can solve using stars and bars. We need to partition 48 stars into 4 groups, and there will be 3 bars separating them. This gives us:
|B| = (47 choose 3) = 16,215.

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The resulting cross section of the prism will be a parallelogram.

When a right rectangular prism is sliced in a way such that the plane passes through the prism at a slant, the resulting cross section is a parallelogram. This is because the intersection of a plane and a rectangular prism that is not parallel to any of its faces is always a parallelogram.

The shape and size of the parallelogram will depend on the orientation of the plane and the dimensions of the prism. Since the prism is a right rectangular prism, the opposite faces are parallel and congruent, and so are the opposite edges of the parallelogram cross section.

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The answer is 0.0034 (rounded to four decimal places). According to the Empirical Rule, 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean in a normal distribution.

However, the given value Z > 2.72 is beyond the scope of the Empirical Rule, so we'll need to use a Z-table to find the probability.

Using a Z-table, we find that the area to the left of Z = 2.72 is approximately 0.9966. Since we want the probability of P(Z > 2.72), we'll subtract this value from 1:

P(Z > 2.72) = 1 - 0.9966 = 0.0034

So, the probability of Z > 2.72 is approximately 0.0034.

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The values of the variables x and y for the cyclic quadrilateral are 85° and 100° respectively.

The figure is a cyclic quadrilateral since it four side vertices lie on the circumference of the circle. The sum of the interior angles of a cyclic quadrilateral is also 360°. Also opposite angles of a cyclic quadrilateral add up to 180°

Thus;

x + 95° = 180° {opposite angles of a cyclic quadrilateral}

x = 180° - 95° {collect like terms}

x = 85°

Also;

y + 80° = 180°

y = 180° - 80°

y = 100°.

Therefore, the values of the variables x and y for the cyclic quadrilateral are 85° and 100° respectively.

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The slope of the function have been solved below

The the slope/rate of change of Function A is 0.

Function B:

x | y

0 | 0

1 | 1

2 | 4

3 | 3

4 | 9

Function B between f(0) and f(1)?

(y1 - y0) / (x1 - x0)

= (1 - 0) / (1 - 0)

= 1/1 = 1

Function B between f(1) and f(2)?

(y2 - y1) / (x2 - x1)

= (4 - 1) / (2 - 1)

= 3/1 = 3

(y3 - y2) / (x3 - x2)

= (3 - 4) / (3 - 2)

= -1/1 = -1

The slope of Function A is 0.

Function B does not have constant slope

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The general solution for: 3.2.1 sinx. (2 cos x - 1) = 0​ is:  x = nπ or x = ±π/3 + 2πn.

The zero product property which asserts that at least one of the components must be zero if the product of two factors equals zero must be used to answer this problem. So,  we must determine the values of x that bring each factor to zero:

3.2.1 Either x sin or x cos - 1 = 0

When x is a multiple of or when x = n, where n is an integer. we can see that sinx = 0 for the first component. We can find cos x by solving for the second factor:

2 cos x - 1 = 0

2 cos x = 1

cos x = 1/2

Where n is an integer, x is equal to /3 + 2n.

So, x = nπ or x = ±π/3 + 2πn, where n is an integer.

Therefore the solution is x = nπ or x = ±π/3 + 2πn.

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(a) The answer of the question "What is the interval's margin of error (Round your answers to 3 decimal places.)" to part (b) is B = 0.978.

(b) margin of error = 1.96*(10/sqrt(385)) = 0.978

(a) To find the sample size needed to construct a 95% confidence interval with a margin of error of 1, we use the formula:

margin of error = z*(standard deviation/sqrt(sample size))

where z is the critical value from the standard normal distribution for a 95% confidence level, which is approximately 1.96.

Plugging in the given values and solving for the sample size, we get:

[tex]1 = 1.96*(10/sqrt(sample size))[/tex]

[tex]sqrt(sample size) = 1.96*10/1[/tex]

[tex]sample size = (1.96*10)^2 = 384.16[/tex]

Rounding up to the nearest whole number, we need a sample size of 385.

Therefore, the answer to part (a) is 385.

(b) To calculate the 95% confidence interval for the population mean given a sample size of 385 and a sample mean of 295, we use the same formula as above with the values we have:

1 = 1.96*(10/sqrt(385))

Solving for the margin of error, we get:

margin of error = 1.96*(10/sqrt(385)) = 0.978

The 95% confidence interval for the population mean is then:

295 - 0.978 to 295 + 0.978

or

(294.022, 295.978)

Therefore, the answer to part (b) is B = 0.978.

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The correct answer is e) no, it is not a function because it does not pass the horizontal line test.

A function must have only one output for every input, and the horizontal line test checks for this by seeing if any horizontal line intersects the graph more than once. This graph has multiple points where a horizontal line would intersect it more than once, indicating that it does not represent a function. The fact that it contains a quadratic and linear relation or has two open circles is not relevant to determining whether it is a function or not.
C) Yes, it is a function because it passes the vertical line test.

A graph represents a function if and only if it passes the vertical line test. This means that for any given x-value, there is only one corresponding y-value. The horizontal line test is used to determine if a function has an inverse that is also a function, which is not relevant to this question. The presence of a quadratic and linear relation or open circles does not necessarily mean that the graph does not represent a function.

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Yes, the Penders are living within their monthly net income.

To determine the monthly living cost, you have to add up the monthly fixed and variable costs. Next, you will subtract these from the monthly net income, if there is a remainder, or none, then they are living within their monthly income.

However, if there is a deficit from the calculation, we can arrive at an answer that shows that the Penders are living above their monthly net income. Subtracting the expenses from the income of $2,600 shows a controlled budget.

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The test statistic is z = 2.75. Since the test statistic is greater than 1.96, we reject the null hypothesis and conclude that the proportion of the population in favor of candidate a is significantly more than 70%.

To calculate the test statistic, we first need to find the proportion of the sample that favored candidate a:
Proportion = 80/111 = 0.72
Next, we calculate the standard error of the proportion:
SE = sqrt[(0.7)(0.3)/111] = 0.045
Finally, we calculate the test statistic using the formula:
z = (Proportion - Hypothesized Proportion) / SE
z = (0.72 - 0.7) / 0.045 = 2.75
Since the test statistic is greater than 1.96 (the critical value for a two-tailed test at the 5% level of significance), we reject the null hypothesis and conclude that the proportion of the population in favor of candidate a is significantly more than 70%.

To determine whether the proportion of the population in favor of candidate A is significantly more than 70%, we'll use the test statistic formula for proportions:
Test statistic = (Sample proportion - Hypothesized proportion) / Standard error
In this case, a random sample of 111 people was taken, and 80 of them favored candidate A. We are interested in finding if the proportion favoring candidate A is more than 70% (0.7).
First, calculate the sample proportion:
Sample proportion = Favored candidate / Total sample
Sample proportion = 80 / 111 ≈ 0.7207
Next, calculate the standard error using the formula:
Standard error = √(p(1-p)/n), where p is the hypothesized proportion and n is the sample size.
Standard error = √(0.7 * (1-0.7) / 111) ≈ 0.0452
Finally, calculate the test statistic:
Test statistic = (0.7207 - 0.7) / 0.0452 ≈ 0.4581
The test statistic for determining whether the proportion of the population in favor of candidate A is significantly more than 70% is approximately 0.4581.

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[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]

Area of the biggest circle:

[tex]\pi r^{2}=\pi \times 6^{2}=\pi \times 36 \ cm^2[/tex].

Area of the rectangle:

[tex]4 \times (2+2+2+2) = 4 \times 8 = 32 \ cm^2[/tex].

Area of the 6 semicircles:

[tex]6 \times \dfrac{1}{2} \times \pi \times r^2 = 3 \times \pi \times 2^2 = \pi \times 12 \ cm^2.[/tex]

Total shaded area:

Biggest circle area - rectangle area - 6 semicircles area

[tex]= \pi \times 36 - 32 - \pi \times 12\\= \pi \times (36-12) - 32\\= \pi \times 24 - 32\\= 3.14 \times 24 - 32\\= 75.36 - 32\\= \boxed{43.36 \ cm^2}[/tex]

Therefore, the shaded part area is [tex]43.36 \ cm^2[/tex].

[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\bold{answered \: by: \: akbarsdtazm}}}[/tex]

It took Amy a total of 18 1/4 minutes (or 18 minutes and 15 seconds) to run her slowest and fastest miles combined, rounded to the nearest 1/4 of a minute.

To find out how long it took for Amy to run her slowest and fastest mile combined, we need to first determine her slowest and fastest mile times.

From the frequency table, we can see that the slowest mile time recorded is 9 2/4 (which can be simplified to 9 1/2) and it occurred once. The fastest mile time recorded is 8 3/4 and it occurred twice.

To find the total time it took for Amy to run her slowest and fastest miles combined, we need to add these two times together.

9 1/2 + 8 3/4 = 18 1/4

Therefore, it took Amy a total of 18 1/4 minutes (or 18 minutes and 15 seconds) to run her slowest and fastest miles combined, rounded to the nearest 1/4 of a minute.

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Here is the complete question:

Amy ran 8 miles. She recorded how long it took her to run each mile, rounded to the nearest 1/4 of a minute?

TIME                                                  FREQUENCY

8 3/4                                                     2

9                                                            3

9 1/4                                                      2

9 2/4                                                      1

How long did it take army to run her slowest and fastest mile combined?

A line plot for the data is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 9 because it has the highest frequency of 4.

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The hypothesis test would give a binary answer of whether or not the proportions are significantly different, while the confidence interval estimate would provide a range of plausible values for P1.

The null hypothesis for the hypothesis test is that the proportion of people with the common attribute in the first population (P1) is equal to the proportion of people with the common attribute in the second population (P2). The alternative hypothesis is that P1 is not equal to P2.

When conducting the hypothesis test with a 0.01 significance level, we would calculate the test statistic and compare it to the critical value from a t-distribution with degrees of freedom equal to the sum of the sample sizes minus two. If the test statistic falls outside of the critical region, we would reject the null hypothesis and conclude that the proportions are significantly different.

On the other hand, the 99% confidence interval estimate of p would provide a range of values that P1 could fall within with 99% confidence. We would calculate the confidence interval by taking the difference in proportions (P2 - P1) and adding/subtracting the margin of error, which is based on the sample sizes and the level of confidence desired.

Overall, comparing the results from the hypothesis test and the confidence interval estimate would provide different information about the proportions in the two populations.

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