Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
F(x) = 0 ; x < 0
x^2/25 ; 0 < x < 5
1 ; 5 < x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places)
a) P(x < 3) (lessthan/equal)
b) P(2.5 < x < 3) (All less than equal to)
c) P(x > 3.5)
d) The median checkout duration [solve 0.5 = F(u)]
e) F'(x) to obtain the density function f(x)
f(x0 = F'(x) =
f) E(X)
g) V(X) and standard deviation_x

The root of the equation sin(x) = 2 - 3 is x = 0, determined using the false position method.

To find the root of the equation sin(x) = 2 - 3 using the false position method, we need to perform iterations by updating the bounds of the interval based on the function values.

Let's define the function f(x) = sin(x) - (2 - 3).

First, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs. Since sin(x) has a range of [-1, 1], we can choose an initial interval such as [0, π].

Let's perform the iterations:

Iteration 1:

Calculate the value of f(a) and f(b) using the initial interval [0, π]:

f(a) = sin(0) - (2 - 3) = -1 - (-1) = 0

f(b) = sin(π) - (2 - 3) = 0 - (-1) = 1

Calculate the new estimate, x_new, using the false position formula:

x_new = b - (f(b) * (b - a)) / (f(b) - f(a))

= π - (1 * (π - 0)) / (1 - 0)

= π - π = 0

Calculate the value of f(x_new):

f(x_new) = sin(0) - (2 - 3) = -1 - (-1) = 0

Since f(x_new) is zero, we have found the root of the equation.

The root of the equation sin(x) = 2 - 3 is x = 0.

The root of the equation sin(x) = 2 - 3 is x = 0, determined using the false position method.

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A standard normal distribution table, or a calculator with a built-in CDF function for the standard normal distribution to calculate this probability.

To calculate the probability of an event occurring between two independent normally distributed variables, we can use the standard normal distribution and the properties of linear combinations of normal variables.

Suppose we have two independent random variables X and Y that are normally distributed with means μX and μY, and standard deviations σX and σY, respectively. Let Z be a linear combination of X and Y given by Z = aX + bY, where a and b are constants.

Then, Z is also normally distributed with mean μZ = aμX + bμY and standard deviation σZ = sqrt(a^2 * σX^2 + b^2 * σY^2).

To calculate the probability of an event occurring between two values, say a and b, for the variable Z, we first standardize Z to a standard normal variable Z* using the formula:

Z* = (Z - μZ) / σZ

Then, we can use the cumulative distribution function (CDF) of the standard normal distribution to calculate the probability of the event occurring between a and b as:

P(a < Z < b) = P[(a - μZ) / σZ < Z* < (b - μZ) / σZ]

We can use statistical software, a standard normal distribution table, or a calculator with a built-in CDF function for the standard normal distribution to calculate this probability.

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The equation which represent total amount of income he earns from selling book is,  \(A=50000+\frac{109}{100}bn\)

Since, Selling price of one novel is n dollars

So, selling price of b books is,  \(n*b=nb\)

Since, he receives 9% commission on each book sale.

So, total commission he receives on selling of b books is,

                                      \(nb*\frac{9}{100}=\frac{9}{100}nb\)

And  also he received a bonus of $50,000 to sign the  contract to write the book,

So, total amount of income he earns is represented by A,

                  \(A=50000+bn+\frac{9}{100}bn\\\\A=50000+\frac{109}{100}bn\)

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Answer: 1024 inches

Step-by-step explanation:

New Murals,

Length= 245+33 =278 inches

Width = 234 inches

Perimeter= 2*(278+234) = 1024 inches

The rate column will be:

A= 30

B= 20

C= x miles

D= x miles

It should be noted that rate simply means the measure, quantity, or frequency that one measure against another quantity or measure.

In this case, Jorden drives to the store at 30 miles per hour and on her way home she averages only 20 miles per hour.

Therefore, the rate column will be:

A= 30

B= 20

C= x miles

D= x miles

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Fill out the Rate column in the table below. Jorden drives to the store at 30 miles per hour. On her way home she averages only 20 miles per hour. If the total driving time takes half an hour, how far does she live from the store? Fill out the Rate column in the table below. a = b =

The median of the sides of the triangle and the distance between the parts of the ellipse, indicates;

33. Median length ≈ 6.02 units

34. Median length ≈ 8.86 units

39. e' = 1 1/3

40. Distance between directrices, d ≈ 8.33

An ellipse is a geometric figure that has the shape of a flattened circle. An ellipse is the set of points such that the sum of the distances from the foci is a constant.

The midpoint of the side AB = ((-3 + (-1))/2, (-2 + 5)/2) = (-2, 1.5)

The median from the vertex C to the side AB = The line segment from C to the midpoint of AB, which indicates that the length of the median can be found as follows;

Coordinates of the point C = (4, 2)

Length of the median = √((4 - (-2))² + (2 - 1.5)²) ≈ 6.02

33. The midpoint of BC = ((3 + 0)/2, (4 + 0)/2, (7 + 0)/2) = (1.5, 2, 3.5)

The length of the median from A to BC is therefore;

Median length = √((3 - 1.5)² + (4 - 2)² + (-5 - 3.5)²) ≈ 8.86

39. The relationship between the distance between the foci and the distance between the vertices can be used to find the second eccentricity as follows;

The distance from the the focus to a vertex = 4 cm

Distance from the focus to the other vertex = 16 cm

Therefore; The distance between the foci 16 cm - 4 cm = 12 cm

Let c represent half the distance between the foci, therefore;

c = 12cm/2 = 6 cm

Let a represent half the distance between the vertices, therefore;

a = (16 cm + 4 cm)/2 = 10 cm

The second eccentricity of an ellipse, e' = √(a² - c²)/a

Therefore; e' = √(10² - 6²)/10 = 8/6 = 4/3 = 1 1/3

40. The eccentricity and the distance between the vertices can be used to find the distance between the vertices as follows;

The distance between the vertices = 10

The distance between the foci = 6

Eccentricity = 6/10 = 0.6

Half the distance between vertices, a = 10/2 = 5

The distance between the directrices, d = (Distance between vertices)/(Eccentricity×2)

d = 10/(0.6 × 2) ≈ 8.33

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Thus, the distance between the directrices is given as: 2b2/a = 2 sqrt (231)/25 units.

For the given vertices of the triangle ABC, the coordinates of the median from C to AB are:

(1.5, 3.5)Therefore, the length of the median is given as:

= AB = sqrt [(1.5 + 3)2 + (3.5 - 1)2] = sqrt (19)33. For the given vertices of the triangle ABC, the coordinates of the median from A to BC are: (1.5, 2, 1)

Therefore, the length of the median is given as:

= BC = sqrt [(1.5 - 0)2 + (2 - 0)2 + (1 - 0)2] = sqrt (10.25) = 2.53.6. A focus of the ellipse is 4 cm from one vertex and 16 cm from the other vertex. The first eccentricity is:

(1) 4cm and the second eccentricity e2 is calculated as: e2 = sqrt [(16)2 - (4)2]/a = sqrt (240)/a = (4 sqrt 15)/3cm39. The distance between the foci of the ellipse is 5. The distance between the directrices is given as:

2a e = 5Therefore, the distance between the directrices is 2a e = 10/3 units.40.

Given, the distance between the vertices of the ellipse is 10 and the distance between the foci is 6. We know that the relation between the distance between the foci and vertices of the ellipse is given as: (2ae)2 = (2a)2 - (2b)2 where, a = distance between center and vertex, b = distance between center and co-vertex

Thus, we have:

(2ae)2 = (2a)2 - (2b)2 (6)2 = (5)2 - (2b)2Solving the above equation, we get b = sqrt (231)/10

Thus, the distance between the directrices is given as: 2b2/a = 2 sqrt (231)/25 units.

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Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

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Notice that

We say that a vertical stretch occurs when a base graph is multiplied by a certain factor greater than 1.

As 1.1>1, f_2(x) is a vertical stretch of f_1(x)

Thus, the answer is The graphs have different vertical stretches, option A.

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Answer:

Is that the whole question or....

We have the following:

What we must do is evaluate in each function and check the values

The answer is the option F

Answer:

(-1,4)

Step-by-step explanation:

Because you look at the (Y,X) line first and then you see the Y is -1 and the X line is 4 and that will give you an answer as (-1,4)

Answer:

right

Step-by-step explanation:

The box in the lower corner means that the angle is equal to 90 degrees, which means the angle is a right angle

The  triangle is a right triangle

Answer:

Right

Step-by-step explanation:

Types of triangle classifications

Acute: a triangle with all angle measures less than 90 degrees

Obtuse: a triangle with an angle of more than 90 degrees

Right: a triangle with a right angle.

Equilateral: a triangle with all equal angles ( more specifically all 60 degree angles )

Now let's look back at the question

Classify the type of triangle

Well looking at the triangle the triangle has a right angle ( indicated by the little square at the bottom left of the triangle)

A triangle with a right angle is known as a right triangle

The system defined by the impulse response h(n) = 28(n+3) + 28n + 28(n-3) can be represented as h(n) = 28δ(n+3) + 28δ(n) + 28δ(n-3), where δ(n) denotes the unit impulse function.

In terms of causality, we can determine whether the system is causal by examining the impulse response. If the impulse response h(n) is non-zero only for n ≥ 0, then the system is causal. In this case, since the impulse response h(n) is non-zero for n = -3, 0, and 3, the system is not causal.

To determine the stability of the system, we need to examine the summation of the absolute values of the impulse response. If the summation is finite, the system is stable. In this case, we can calculate the summation as ∑|h(n)| = 28 + 28 + 28 = 84, which is finite. Therefore, the system is stable.

However, since the impulse response is given in the time domain and not in a closed-form expression, it is not possible to directly determine the frequency response without further manipulation or additional information.

Given the absence of specific frequency domain information or a closed-form expression for the frequency response, it is not possible to accurately represent the module and phase of the system H(e^ω) without further calculations or additional details about the system.

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Answer: 50

Step-by-step explanation: add DBC and ABD to get 50 ABC is 50

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Central Idea of the Poem; In the poem ‘Animals’, the poet Walt Whitman praises animals for being better than human beings and for possessing all such qualities that humans lack or have forgotten.

The poem Animals' central theme is that humans might get wisdom and virtues from the animals they formerly owned but have since lost.

The poet claims that animals possess many admirable traits like self-control, impartiality, and tranquility.

The comparison of people to animals in order to emphasize the shortcomings in human nature is the poem's main focus rather than praising how wonderful animals are.

The poet thinks that possibly people once possessed all of the virtues listed above, but that they have since lost them.

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Answer:

The answer would be -9 and -3 which would be B and D

Step-by-step explanation:

Answer:

Step-by-step explanation:

∠EMC  = ∠EMD + ∠DMC

∠EMC = 90

∠EMD + ∠DMC = 90

∠EMD + 20 =90

∠EMD  = 90 - 20

∠EMD  = 70

∠FMD + ∠DMB = 180  {Linear pair}

90 + ∠DMB = 180

        ∠DMB = 180 - 90

       ∠DMB = 90

Answer:

The answer should be, 28x36.

The partygoer would need to consume 33 g of ethanol to have a 50% chance of getting a buzz. This is a high dose and could lead to alcohol poisoning. It is not recommended to consume such high levels of alcohol.

The ed50 of a recreational drug is defined as the amount required for 50% of a test group to feel high or get a buzz. If the ed50 value of ethanol is 470 mg/kg body mass, what dose would a 70 kg partygoer need to quickly consume to have a 50% chance of getting a buzz?Solution:The ed50 value for ethanol is 470 mg/kg body mass.This means that 50% of the test group feels high or gets a buzz at this level.To calculate the required dose for a 70 kg partygoer, the formula is as follows:Dose required

= (ed50 value) × (body mass)Dose required

= (470 mg/kg) × (70 kg)Dose required

= 32900 mgOr, the dose required for a 70 kg partygoer to quickly consume to have a 50% chance of getting a buzz is 32.9 g or 33 g (approx.) since 1 g

= 1000 mg.The partygoer would need to consume 33 g of ethanol to have a 50% chance of getting a buzz. This is a high dose and could lead to alcohol poisoning. It is not recommended to consume such high levels of alcohol.

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Answer:

1/3

Because 1/3 if divide into two, it'll be 0.5/3 but if the question says that the answer have to be in whole number, that means it must be 1/6.

Answer:12

Step-by-step explanation:

because it will take 2 to make a cup

Answer:

Step-by-step explanation:

To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is a point on the line.

Substituting the given values, we get:

y - (-5) = 3(x - 1)

Simplifying the equation, we get:

y + 5 = 3x - 3

Subtracting 5 from both sides, we get:

y = 3x - 8

Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.

To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.

Answer:

greater than

Step-by-step explanation:

positive is higher than negative

The correct answer is 2 (C) - 2 days is the total slack for activity F. To determine the total slack for activity F, we need to calculate the slack for each activity in the network. Slack refers to the amount of time an activity can be delayed without affecting the project completion time.

1. First, let's draw the network using the information provided:
  - A is the start node and G is the stop node.
  - Activity A has a duration of 5 days and has no predecessor.
  - Activities B, C, and D have durations of 8, 7, and 6 days respectively, and their predecessors are A.
  - Activity E has a duration of 9 days and its predecessors are B, C, and D.
  - Activity F has a duration of 10 days and its predecessors are B, C, and D.
  - Activity G has a duration of 5 days and its predecessors are E and F.

                 A
                /|\
               / | \
              /  |  \
             B   C   D
              \  |  /
               \ | /
                \|/
                 E
                 |
                 F
                 |
                 G

2. Now, let's calculate the slack for each activity:
  - Slack is calculated by subtracting the earliest start time of an activity from the latest start time without delaying the project completion time.
  - The earliest start time for activity F is 17 days.
  - The latest start time for activity F is 19 days (project completion time is 22 days).
  - Total slack for activity F = latest start time - earliest start time = 19 - 17 = 2 days.

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