if and are independent exponential random variables with pdf find (round off to third decimal place

Carol has approximately 0.82 seconds to react before the volleyball hits the ground.

To calculate the time Carol has to react, we can use the equation of motion for the vertical direction, considering that the initial velocity is 20f(t)/s and the initial height is 4.5 feet. The equation is given by:

h(t) = h0 + v0*t - 0.5*g*t^2,

where:

- h(t) is the height of the ball at time t,

- h0 is the initial height (4.5 feet),

- v0 is the initial velocity (20f(t)/s),

- g is the acceleration due to gravity (32.2 ft/s^2),

- t is the time.

In this case, we want to find the time when the height of the ball (h(t)) is equal to zero (when it hits the ground). So we can set h(t) = 0 and solve for t:

0 = 4.5 + (20f(t)/s)*t - 0.5*32.2*ft/s^2*t^2.

Simplifying the equation, we get:

16.1t^2 - 20f(t)t - 4.5 = 0.

To find the positive value of t, we can use the quadratic formula:

t = (-b + √(b^2 - 4ac))/(2a),

where a = 16.1, b = -20f(t), and c = -4.5.

Substituting the values into the formula, we have:

t = (-(-20f(t)) + √((-20f(t))^2 - 4*16.1*(-4.5)))/(2*16.1).

Simplifying further, we get:

t ≈ 0.82 seconds.

Therefore, Carol has approximately 0.82 seconds to react before the volleyball hits the ground.

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Answer:

1) (x, y) = (1, 8)

2) (x, y) =(-2, -4)

3) (x, y) = (3, -1)

Step-by-step explanation:

1) Given the equations;

7x+2y =23  .... 1

6x+y= 14  .... 2

From 2; y = 14-6x

Substitute into 1;

From 1; 7x+2y =23

7x + 2(14-6x) = 23

7x + 28 - 12x = 23

-5x = 23 - 28

-5x = -5

x = 5/5

x = 1

Substitute x = 1 into y = 14-6x

y = 14 - 6 (1)

y - 14 - 6

y = 8

Hence (x, y) = (1, 8)

2) Given

y=-4

y=-3x-10

We will simply equate bith expression and get x;

-3x - 10 = -4

-3x = -4 + 10

-3x = 6

x = 6/-3

x = -2

Hence the solution is (-2, -4)

3) Given the equation

y=-3x+8

y=5x-16

Equate both expressions;

-3x + 8 = 5x - 16

-3x - 5x = -16 - 8

-8x = -24

x = 24/8

x = 3

Substitute x = 3 into y=-3x+8

y = -3(3) + 8

y = -9 + 8

y = -1

Hence the solution (x, y) = (3, -1)

Bayesian statistics models parameters with prior distributions, representing uncertainty in beliefs. Consider a fair coin with p ranging from 0 to 1, and flip once, resulting in x.

In this example, we are using Bayesian statistics to model parameters with prior distributions, which represent our uncertainty in beliefs.

Let's suppose we have a coin that may not be fair. The parameter p, which represents the chance of landing heads, can range from 0 to 1.

We flip this coin once and let x represent the outcome of the flip.

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It is difficult to determine the best way to visualize the data without knowing more about the specific data and the goals of the visualization. Here is a brief overview of each of the options you listed:

(a) A histogram is a graphical representation of the distribution of a continuous or discrete variable. It shows the frequency of different values or ranges of values in the data.

(b) Segmented bar charts are bar charts that are divided into segments to show the breakdown of different categories within each bar.

(c) Side-by-side boxplots are boxplots that are placed next to each other to compare the distribution of multiple sets of data.

(d) A pie chart is a circular graph that shows the proportions of different categories or parts of a whole.

(e) A scatterplot is a graph that shows the relationship between two continuous variables by plotting individual data points on a coordinate grid.

To determine the best visualization for your data, consider the type of data you have (e.g. continuous, discrete, categorical), the number of variables you want to compare, and the message you want to convey with the visualization. You may also want to consider any specific guidelines or standards that apply to the context in which the visualization will be used.

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Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

840  ways can we form a subcommittee with 3 republicans and 2 democrats

Given that

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical. (It is not important how each set's members are arranged.) If there are n elements in the set, then C kn is the number of k-combinations.

a senate committee has 8 republicans and 6 democrats.

now, we need to find how many ways can we form a subcommittee with 3 republicans and 2 democrats

= 8\(C_{3}\) × 6\(C_{2}\)

=\(\frac{8!}{5!3!}\) × \(\frac{6!}{4!2!}\)

=56 × 15

=840

840  ways can we form a subcommittee with 3 republicans and 2 democrats

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Therefore , the solution of the given problem of circumference statement is proved by the following below explanation.

Any great circle's circumference, or the distance between the center of the sphere and any plane running through it, is measured in meters. Any large circle that passes through a pole-designated location is referred to as a meridian.

Here,

An arc PQ of a circle that subtends angles POQ at its center O and PAQ at one of its points A on the circumference.

To prove : <POQ = 2<PAQ

To prove this theorem we consider the arc AB in three different situations, minor arc AB, major arc AB and semi-circle AB.

Construction:

Join the line AO extended to B.

Proof :

<BOQ = ZOAQ + ZAQO .....(1)

Also, in A OAQ,

OA = OQ

Therefore,

[Radii of a circle]

ZOAQ = ZOQA

[Angles opposite to equal sides are equal]

<BOQ = 2ZOAQ

.......(2)

Similarly, BOP = 220AP

.(3)

Adding 2 & 3, we get,

<BOP + <BOQ = 2(ZOAP + ZOAQ)

<POQ = 2<PAQ

.......(4)

For the case 3, where PQ is the major arc, equation 4 is replaced by

Reflex angle, <POQ = 2ZPAQ

Therefore , the solution of the given problem of circumference statement is proved by the following below explanation.

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Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π

sec(π4) – trigonometry value

The exact value of trigonometry - sec(π4) is 2√2.

Multiply 2√2 by √2.

2⋅√2⋅2

Combine and simplify the denominator.

2√2

Cancel the common factor of 2.

√2

There are various ways to display the outcome.

Exact Form:

√2

Decimal Form:

1.41421356…

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Answer:

2 hours + 14

Step-by-step explanation:

Since 1 hour = 60 min

Divide by 60 maximum it goes in 134, 2 times the excess is your minutes.

The solution of the recurrence relation is \(a_n=3.2^n\)

For given question,

We have been given a recurrence relation \(a_n = 2a_{n-1}\) for n ≥ 1

and an initial condition \(a_0=3\)

Let \(a_n\) = m², \(a_{n-1}\) = m and \(a_{n-2}\) = 1

So from given recurrence relation we get an characteristic equation,

⇒ m² = 2m

⇒ m² - 2m = 0                     .........( Subtract 2m from each side)

⇒ m(m - 2) = 0                     .........(Factorize)

⇒ m = 0    or  m - 2 = 0

⇒ m = 0   or   m = 2

We know that the solution of the recurrence relation is then of the form

\(a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n\)  where \(m_1,m_2\) are the roots of the characteristic equation.

Let, \(m_1\) = 0   and \(m_2\) = 2

From above roots,

\(\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n\)

For n = 0,

\(\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2\)

But  \(a_0=3\)

This means \(\alpha_2=3\)

so, the solution of the recurrence relation would be \(a_n=3.2^n\)

Therefore, the solution of the recurrence relation is \(a_n=3.2^n\)

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Answer:

x2 + x = 42

Step-by-step explanation:

x = nhmber

x² = its square

then:

The sum of a number and its square is 42 is:

x² + x = 42

Answer:

D.-1.4,-1/2, 3

#CARRY ON LEARNING

The solution of the inequality is x>2 and the graph is attached below.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. When two values are compared, an inequality shows whether one is higher, lower, or simply not equal to the other.

The given inequality is 2x - (3-x) > x + 1,

Now, solving the inequality by opening the bracket,

2x - (3-x) > x + 1

\(2x - 3 + x > x + 1\)

3x - 3 > x + 1

Subtracting x from both sides and  adding 3 on both sides,

2x > 4

x > 2

So, the graph is attached below and Option D is correct.

Therefore, after solving the given inequality, we get x > 2 and the graph is attached below.

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Answer:

58

Step-by-step explanation:

We are given the arithmetic sequence:-

-12,-7,-2,3,...

First, find the common difference which we can obtain by:-

\( \displaystyle \large{d = a_{n + 1} - a_n}\)

Check:-

-7-(-12) = -7+12 = 5

-2+7 = 5

3+2 = 5

Therefore, our common difference is 5.

General Arithmetic Term

\( \displaystyle \large{a_n = a_1 + (n - 1)d}\)

Since we want to find the 15th term, substitute a1 = -12, n = 15 and d = 5.

\( \displaystyle \large{a_{15}= - 12 + (15 - 1)5} \\ \displaystyle \large{a_{15}= - 12 + (14)5} \\ \displaystyle \large{a_{15}= - 12 + 70} \\ \displaystyle \large{a_{15}= 58} \\ \)

Answer: 24

Step-by-step explanation:

Factors of 96:  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 , 120

Highest number between the two sets of factors which is common is 24

Answer:

There's not really a FORMULA

Step-by-step explanation:

I don't understand what you mean, but I can tell you that 10x13 is 130.

Answer: its rational!

Step-by-step explanation:

15p square - 7q square

square(15p-7q)

hope it helps

Answer:

  (c)  (p/6 +7) +8

Step-by-step explanation:

You want an expression equivalent to p/6 +(7 +8).

The associative property of addition lets you move the parentheses in a sum. This means ...

  \(\dfrac{p}{6}+(7+8)\equiv\boxed{\left(\dfrac{p}{6}+7\right)+8}\)

__

Additional comment

The sum (7+8) is not 1, so the first answer option doesn't apply.

8 is not a factor in the expression, so the second answer option doesn't apply.

p/6 is not the same as 6p, so the last answer option doesn't apply.

Answer:

Step-by-step explanation:

Answer:

They're parallel.

Step-by-step explanation:

The reason is that any equation only with a y coordinate is a horizontal line. As they're both horizontal, they'd be parallel.

Answer:

One person represents 360 degrees / (204 + 84 + 36 + 204 + 12) = 360 degrees / 540 = 4/6 = 2/3 degrees.

Answer:

Its answer d

Step-by-step explanation:

I took the quiz  

A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, negative 28.

A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, and 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, and negative 28.

The answer is option D.

Slope measures the rate of change in the dependent variable as the independent variable changes. The greater the slope the steeper the line. Consider the linear function: y = a + bx. b is the slope of the line.

A steeper slope in a graph means that the rate of change is faster.

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The equation of the line in the graph passing through the points (-3, 1) and (6, 5) is  \(y = \frac{4}{9} x + \frac{7}{3}\).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line passes through the points (-3,1) and (6,5).

First, we determine the slope of the line:

\(m=\frac{y_2 - y_1}{x_2 - x_1} \\\\m=\frac{5-1}{6-(-3)} \\\\m=\frac{4}{9}\)

Next, plug the slope m = 4/9 and point (-3,1) into the point-slope form and solve for y:

\(y - y_1 = m( x - x_1 )\\\\y - 1 = \frac{4}{9}( x - (-3)) \\\\y - 1 = \frac{4}{9}( x + 3) \\\\y - 1 = \frac{4}{9} x + \frac{4}{3} \\\\y = \frac{4}{9} x + \frac{4}{3} + 1\\\\y = \frac{4}{9} x + \frac{7}{3}\)

Therefore, the equation of line is \(y = \frac{4}{9} x + \frac{7}{3}\).

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The given triangles are congruent due to the congruent postulate AAS.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

As per the given figure,

In ΔCDE and ΔABF has :

m∠C = m∠A

m∠D = m∠B

side DC = side AB

According to AAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Hence, ΔCDE ≅ ΔABF

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The equation of best fit is y = (-22/5)x + 10.

What is an equation of a line?

The equation of a line is given by:

y = mx + c where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The following coordinates are given:

Pick two coordinates.

(0, 10) and (25, -100)

The equation of best fit.

y = mx + c

Now,

m = (-100 - 10) / (25 - 0)

m = -110 / 25

m = -22/5

Now,

(0, 10) = (x, y)

10 = (-22/5) x 0 + c

c = 10

Now,

y = mx + c

y = (-22/5)x + 10

Thus,

Using the coordinates the equation of best fit is y = (-22/5)x + 10.

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The area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

To find the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ), we need to determine the limits of integration for θ.

First, let's find the values of θ where the circle and the vertical line intersect:

r = 4cos(θ)

sec(θ) = 4cos(θ)

To simplify the equation, let's convert sec(θ) to its reciprocal form:

1/cos(θ) = 4cos(θ)

Multiplying both sides by cos(θ), we get:

1 = 4\(cos^2\)(θ)

Rearranging the equation, we have:

4\(cos^2\)(θ) - 1 = 0

Using the identity \(cos^2\)(θ) - \(sin^2\)(θ) = 1, we can rewrite the equation as:

\(cos^2\)(θ) - \(sin^2\)(θ) = 1/4

Applying the double-angle formula for cosine, we get:

cos(2θ) = 1/4

Taking the inverse cosine of both sides, we have:

2θ = ± \(\cos^{-1}\left(\frac{1}{4}\right)\)

Solving for θ, we get two values:

θ = ± (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Since we are interested in the region to the right of the vertical line, we'll consider the positive value of θ:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Now, we can find the area by evaluating the integral:

A = ∫[θ, π/2] 1/2 (\(r^2\)) dθ

Substituting the equations for r, we have:

\(A = \int_{\theta}^{\frac{\pi}{2}} \frac{1}{2} (4\cos^2(\theta)) \, d\theta\)

Simplifying further:

\(A = \int_{\theta}^{\frac{\pi}{2}} 8\cos^2(\theta) \, d\theta\)

Using the double-angle formula for cosine, we have:

A = ∫[θ, π/2] 4(1 + cos(2θ)) dθ

Integrating term by term, we get:

A = [4θ + 2sin(2θ)] evaluated from θ to π/2

Now, Substituting the limits of integration, we get:

A = [4(π/2) + 2sin(2(π/2))] - [4θ + 2sin(2θ)] evaluated from θ to π/2

Simplifying:

A = 2π + 2sin(π) - (4θ + 2sin(2θ))

Since sin(π) = 0, we can simplify further:

A = 2π - (4θ + 2sin(2θ))

Now, we need to substitute the value of θ, which we found earlier:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Substituting this value, we have:

A = 2π - (4(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(2(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)))

Simplifying:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(\(\cos^{-1}\left(\frac{1}{4}\right)\)))

Since cos(\(\cos^{-1}\left(x\right)\)) = x, we have:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(1 - (1/4)^2)))

Simplifying further:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(15/16)))

A = 2π - 2 \(\cos^{-1}\left(\frac{1}{4}\right)\) - √15

So, the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

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Area of this figure = Area of square + area of triangle

A(square) = 7^2 = 49ft2
A(triangle) = (7x3) : 2 = 10.5ft2

So, the area of this doghouse is : 49 + 10.5 = 59.5ft2.

Data that are accurate, consistent, and available in a timely fashion are considered C) high-quality.

High-quality data is characterized as being reliable, consistent, and timely. High-quality data offers a strong foundation for analysis and decision-making because it is accurate, error-free, and consistent.

It is a valuable asset for organizations because it promotes accurate reporting and analysis, increases operational efficiency, and allows for informed decision-making. Although database management systems like Oracle and Microsoft SQL Server can assist with managing and storing data, the quality of the data is unrelated to the particular technology or program employed.

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Answer:

C) increase by 0.25

Step-by-step explanation:

5 - 4.75 = +0.25

Answer:

The answer is C

Step-by-step explanation:

If you add 7 to the list then the number/mean will increase by 0.25

I might be wrong so im sorry if i am.