Slope of the line pls helpppppp

In the given problem, we are provided with a p.d.f. for the random variable X as ce^(-6x) for x >= 0. Let's use this information to solve the questions:

(a) We know that the total area under the p.d.f. must be equal to 1. Therefore, we can set up the following integral and solve for c:

int0 to infinity = 1

=> c * int0 to infinity = 1

=> c * [(-1/6)*e^(-6x)] from 0 to infinity = 1

=> c * (0 - (-1/6)) = 1

=> c = 6

(b) To find the mean of Y, we first need to find the transformation function that relates X and Y. We know that Y = X^2, so we can use the transformation formula E(Y) = E(g(X)) = int(-infinity to infinity) (g(x) * f_X(x)dx) to find E(Y).

E(Y) = int(0 to infinity) (x^2 * 6e^(-6x)dx)

Using integration by parts, we can solve this integral to get E(Y) = 1/3.

To find the variance of Y, we use the formula Var(Y) = E(Y^2) - (E(Y))^2. We can use the formula for E(Y) that we just found, and also find E(Y^2) as:

E(Y^2) = int(0 to infinity) (x^4 * 6e^(-6x)dx)

Using integration by parts again, we get E(Y^2) = 1/9. Therefore, Var(Y) = 1/9 - (1/3)^2 = 2/27.

The squared coefficient of variation of X is defined as Var[X]/(E[X])^2. Using the mean and variance of X that we found in part (a), we get (Var[X]/(E[X])^2) = (1/36)/(1/36) = 1. Therefore, the squared coefficient of variation of Y is also 1.

(c) To compute Pr{X > 5}, we can use the p.d.f. that we were given. Since the p.d.f. is zero for x < 0, we only need to compute the integral from 5 to infinity:

Pr{X > 5} = int(5 to infinity) (6e^(-6x)dx)

= e^(-30)

(d) To compute Pr {X >5 | Y> 2}, we can use the formula for conditional probability:

Pr {X >5 | Y> 2} = Pr{X > 5 and Y > 2}/Pr{Y > 2}

Since Y > 2 implies X > sqrt(2), we can write the numerator as:

Pr{X > sqrt(2)} = int(sqrt(2) to infinity) (6e^(-6x)dx)

= e^(-3*sqrt(2))

To find the denominator, we can use the formula for the cumulative distribution function (c.d.f.) of Y:

F_Y(y) = Pr{Y <= y} = Pr{X^2 <= y} = Pr{-sqrt(y) <= X <= sqrt

A random variable is a numerical quantity that can take on different values based on the outcome of a random event. In this context, a probability density function (p.d.f.) describes the probability of observing different values of a random variable.

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Answer:

500

Step-by-step explanation:

Below are some authorial techniques that can be used to create mystery, tension, or surprise in literature.

Order of events: The order in which events are presented can create a sense of mystery or suspense.

Pacing: The pace of a story can also be used to create suspense. A slow-paced story can build tension by allowing the reader to dwell on the details of a situation, while a fast-paced story can create excitement and surprise by keeping the reader guessing what will happen next.

Structure: The structure of a story can also be used to create mystery, tension, or surprise. For example, a story that is told in flashback can create a sense of mystery by revealing information about the past that is relevant to the present.

Time manipulation: The manipulation of time can also be used to create suspense.

Language: The language that an author uses can also be used to create mystery, tension, or surprise. For example, an author might use vague or ambiguous language to create a sense of mystery, or use strong language to create a sense of tension or surprise.

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Answer:

10

Step-by-step explanation:

30 boys

1/2 play football

30/2 = 15

15 boys left

2/3 play rugby

15 x 2/3 = 10

Answer:

The equation of the line is;

y + 4 = 3(x + 4)

Step-by-step explanation:

The general equation of a line is;

y = mx + b

where m is the slope and b is the y-intercept

To get the equation, let us look at the given intercepts

We have the intercepts at the point (0,5) and (-2,-1)

We have the slope of the line as follows;

m = (y2-y1)/(x2-x1) = (-1-5)/(-2-0) = -6/-2 = 3

So we have the equation as;

y = 3x + b

recall, we have the y-intercept as 5

so the complete equation is;

y = 3x + 5

Now, we can rewrite this as;

y+ 4 = 3(x + 3)

Here's a more detailed explanation: To determine if a graph is a function, you can use the vertical line test. The vertical line test states that if you can draw a vertical line that intersects the graph in more than one place, then the graph is not a function.

Determining whether a graph represents a function is an important concept in mathematics, especially in algebra and calculus. A function is a set of ordered pairs where each input is associated with exactly one output.

So, if you take a ruler or a straight edge and place it vertically on the graph, and it intersects the graph in two or more points, then the graph is not a function. This is because if two points in the graph have the same x-value, they must have different y-values, since functions can only have one output for each input.

On the other hand, if you place a vertical line anywhere on the graph and it intersects the graph in only one point, then the graph is a function.

It's also important to remember that a function must also pass the horizontal line test, which means that no horizontal line can intersect the graph in more than one place.

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The numerical value "62" is a statistic because it is based on the sample of passengers aboard the Hindenburg airship.

In the given scenario, the numerical value is "62." We are told that there were 97 passengers aboard the Hindenburg airship and that 62 of them survived its explosion.

Since the numerical value is based on the sample (i.e., the passengers aboard the Hindenburg airship), it is a statistic. It describes the proportion of passengers who survived the explosion in the sample.

If we wanted to know the proportion of passengers who survived the explosion in the entire population (i.e., all passengers who have ever traveled on the Hindenburg airship), we would need to determine the parameter.

However, since we do not have data on the entire population, we cannot determine the parameter.

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Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

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\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\(2 {x}^{2} + 12x + 18\)

Taking 2 as common factor, we have

\( = 2 \: ( {x}^{2} + 6x + 9) \\ = 2 \: ( {x}^{2} + 3x + 3x + 9)\)

Next, we take \(x\) as common from first two terms and 3 from last two terms,

\( = 2 \: [x(x + 3) + 3(x + 3)]\)

Taking the factor \((x+3)\) as common,

\( = 2 \: ( x + 3)(x + 3)\)

\(\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}\)

The slope intercept form has the next form

We have

we need to isolate the y

ANSWER

y=3x-3

Answer:20 questions I believe

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

17 divided by 85%

Answer:

$91

Step-by-step explanation:

20% of 120= 96

96-5=91

Answer:

41.1 feet of ribbon was leftover

(fraction form: 41 1/10)

Step-by-step explanation:

122 1/2 = 122.5

32 2/5 = 32 4/10 = 32.4

122.5 x 0.4 = 49

122.5 - 49 = 73.5

73.52 - 32.4 = 41.1

41.1

Answer:

Step-by-step explanation:

40% of 122.5 \((122\frac{1}{2})\) is 49.

Equation: y=p%·x

p=40% x=122.5

Solve the equation for y.

y=p%·x

y=40%·122.5'

Converting percent to decimal.

p = 40%/100 = 0.4

y=0.4·122.5

y=49

\(49-32\frac{2}{5}\)

\(49-\frac{162}{5}\)

\(\frac{83}{5}\)

\(16\frac{3}{5}\)

Answer:

Exactly \(16\frac{3}{5}\) feet of ribbon remains.

Therefore, the correct statistical decision is (b) reject the null hypothesis with either α = .05 or α = .01.

To determine the correct statistical decision, we need to compare the calculated F-ratio to the critical F-value based on the degrees of freedom and the chosen alpha level (α).

The degrees of freedom for the numerator (df between) is k - 1, where k is the number of conditions (k = 4 in this case). The degrees of freedom for the denominator (df within) is N - k, where N is the total sample size (N = 8 * 4 = 32).

Using a significance level of α = .05, we can consult an F-table or use statistical software to find the critical F-value with (k-1) and (N-k) degrees of freedom. For this case, the critical F-value is 3.10.

Since the calculated F-ratio (F = 4.60) is greater than the critical F-value (3.10) at α = .05, we can reject the null hypothesis and conclude that there are statistically significant mean differences among the four conditions.

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The number of solutions of the algebraic equations are listed below:

In this question we find five cases of algebraic equations whose solutions have to be found by means of algebra properties. Now we proceed to determine the number of solutions:

Case 1

3 · x - 5 = 4 · x + 2

3 · x = 4 · x + 7

- x = 7

x = - 7 (One solution)

Case 2

3 · x - 5 = 3 · x + 2

- 5 = 2 (No solution)

Case 3

3 · (x - 5) = 3 · x - 15

3 · x - 15 = 3 · x - 15

0 = 0 (Infinite solutions)

Case 4

3 · x² = 27

x² = 9

x = ± 3 (Two solutions)

Case 5

3 · x³ = - 24

x³ = - 8

x = - 2 (Three solutions)

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Answer:

X = 5

Y = 7

Step-by-step explanation:

First we will find x

4x + 2 = 3x + 7

x + 2 = + 7

x = 5

Next we will find y

2y + 9 = 4y - 5

-2y + 9 = -5

-2y = -14

y = 7

Answer:

This sequence is a geometric sequence.

The common ratio of the sequence is

3/9 = 1/3

Hope this helps

Step-by-step explanation:

there is no common method, as there are things in various forms that can be multiplied to each other.

you need to assemble experience in multiplying various forms of terms and expressions to remember, what you can aim for.

there are some basic principles like

(a² - b²) = (a + b)(a - b)

(a³ - b³) = (a - b)(a² + ab + b²)

a² + 2ab + b² = (a + b)² = (a + b)(a + b)

and, and, and

also, often you need to try to add or remove some terms to make an expression a perfect multiplication result.

like

x + xy + y = 0

x(1 + y) + y = 0

x(1 + y) + y + 1 = 0 + 1

x(1 + y) + (1 + y) = 1

(1 + y)(x + 1) = 1

or you need to split some things up to create perfect multiplications.

like

x³ + x² = 12

x³ + x² - 12 = 0

x³ + x² - 8 - 4 = 0

x³ + x² - 2³ - 2² = 0

(x³ - 2³) + (x² - 2²) = 0

remember, what we just listed above :

(x - 2)(x² + 2x + 4) + (x - 2)(x + 2) = 0

(x - 2)(x² + 2x + 4 + x + 2) = 0

(x - 2)(x² + 3x + 6) = 0

and so on.

there are many functions like trigonometric functions (sine, cosine, ...), logarithms, ...

there are not just multiplications and exponents.

sure, it is more standardized, when we are only dealing with a squared function like

4x² - 12x + 9

which is easy to see is the same as

(2x - 3)²

or more interesting

6x² - 23x + 20

which would be

(2x - 5)(3x - 4)

and we can get such things only by starting in general by saying this is

(ax + b)(cx + d)

multiply this out and find the factors of in this case 6, 23 and 20 and try the combinations.

so, long story short, there is no general method, formula or something like this. you need to get a feeling what approach could work in a given situation.

Rounded to two decimal places, the variance is 33.25.

The mean of a discrete uniform distribution is given by the formula:

mean = (a + b) / 2

where a and b are the minimum and maximum values of the distribution. In this case, a = 1 and b = 20, so:

mean = (1 + 20) / 2 = 10.5

The variance of a discrete uniform distribution is given by the formula:

variance = (b - a + 1)^2 / 12

where a and b are the minimum and maximum values of the distribution. In this case, a = 1 and b = 20, so:

variance = (20 - 1 + 1)^2 / 12 = 399 / 12 = 33.25

Rounded to two decimal places, the variance is 33.25.

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Applying combination, the number of playlist is: 75,435.

A combination is a way of selecting a certain number of items from a larger set, without regard to the order of the items.

The number of possible playlists would be the number of ways to select 7 songs out of 20 without regard to order, which is commonly known as a combination.

The formula for combination is nCr, where n is the total number of items and r is the number of items being chosen at a time. So in this case, the number of possible playlists would be 20C7.

This can also be written as 20!/(7!*13!)

The answer is 75,435

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Answer:

16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Divide by 2

32/2 = 16

Therefore-

16 books per box

1. The variable in the solution is the population every year

2. The model can be presented as

y= 1175-20x

3. The value of slope is -20 which says that the population decreases by 20 members for every one year increase from 2010

Let y be the population after x years from 2010

So, the model can be presented as

y= 1175-20x

Now for example, in year 2011

x= 2011-2010= 1

The population is y = 1175-20(1) = 1155

The population in year 2012 is

x= 2012-2010= 2

Population is y= 1175-20(2) = 1135

The result obtained is satisfactory and hence ok

The population follows a linear trend with slope of -20 and intercept of 1175.

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Answer:

The last one.

Step-by-step explanation:

The reason we get this answer is because when you are converting from exponential form, to radical form you always place the numerator as our constant's exponent in the radical (  is called the radicand because it is located in the radical) and the denominator in front of the radical, where it would be called the index.

Answer: 10 Weeks

Step-by-step explanation:

24 - 3

divide both by 3

8 - 1

multiply both by 10

80 - 10

Answer:

Step-by-step explanation:

that a huge prob but yah

We may build up a proportion and solve for the scale model radius of Neptune using the ratio between the radii of the two planets and the known scale model radius of the Earth. The scale model of Neptune that is produced has a radius of around 9.7 cm.

We may take advantage of the fact that the ratio between the two planets' radii and the ratio between their respective scale model radii is the same. Let's name the Neptune scale model radius "r" Then, we may set up the ratio shown below:

Neptune's radius is equal to the product of Earth's radius and its scale model.

With the provided values, we may simplify and obtain:

24620 km / 6370 km equals 2.5 cm / r

We obtain the following when solving for "r":

r = (24620 km * 2.5 cm) / (6370 km)

r ≈ 9.7 cm

Therefore, a scale model of Neptune would have to be drawn with a radius of approximately 9.7 cm.

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Answer:

1/4, 0.5, -4/6, 4.5, 1/3, 7/8

explanation: it is the ratio of two integers

a/b where b is not = to 0

Research that provides data which can be expressed with numbers is called quantitative research.

Quantitative research is a type of research that focuses on gathering and analyzing numerical data. It involves collecting information or data that can be measured and quantified, such as numerical values, statistics, or counts. This research method aims to objectively study and understand phenomena by using mathematical and statistical techniques to analyze the data.

Quantitative research typically involves the use of structured surveys, experiments, observations, or existing data sources to gather information. Researchers often employ statistical methods to analyze the data and draw conclusions or make predictions based on the numerical findings.

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Answer:

D

Step-by-step explanation:

as you can see its decreasing