a) Suppose that X is a uniform continuous random variable where 0 < x < 5. Find the pdf f(x) and use it to find P(2 < x < 3.5). b) Suppose that Y has an exponential distribution with mean 20. Find the pdf fly) and use it to compute P(18

Answer:75.708L

Step-by-step explanation:

there are 33 pleasing ordered triples.

We are given a set {1, 2, 3, 4, 5, 6}. We need to count the number of pleasing ordered triples (a, b, c), where a < b < c, and a, b, c are elements of the set.

Condition (b) requires that both b and c be greater than a. Since a can take any value from 1 to 4, the number of possibilities for (a, b, c) is:

For a = 1, there are 4 choices for b (2, 3, 4, 5) and 5 choices for c (3, 4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 4 × 4 - 1 = 15 pleasing triples with a = 1.

For a = 2, there are 3 choices for b (3, 4, 5) and 4 choices for c (4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 3 × 4 - 1 = 11 pleasing triples with a = 2.

For a = 3, there are 2 choices for b (4, 5) and 3 choices for c (5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 2 × 3 - 1 = 5 pleasing triples with a = 3.

For a = 4, there is only 1 choice for b (5) and 2 choices for c (6, 5). Therefore, there is only 1 × 2 = 2 pleasing triples with a = 4.

The total number of pleasing ordered triples is:

15 + 11 + 5 + 2 = 33

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The toll collector collected money from 38 sedans and 16 trucks during the 4-hour period.

To determine the number of sedans and trucks that passed through the toll booth, we can set up a system of equations based on the given information. Let's assume the number of sedans is represented by 'S' and the number of trucks is represented by 'T'.

From the information provided, we know that the toll for sedans is $8 and the toll for trucks is $9. We also know that the total amount collected over the 4-hour period is $376.

Based on this, we can set up the following equations:

8S + 9T = 376       (equation 1)

S + T = 4           (equation 2)

Equation 1 represents the total amount collected, and equation 2 represents the total number of vehicles passing through the toll booth during the 4-hour period.

To solve this system of equations, we can use various methods such as substitution or elimination. Let's use the substitution method:

From equation 2, we can rearrange it to get S = 4 - T.

Substituting this value of S into equation 1:

8(4 - T) + 9T = 376

32 - 8T + 9T = 376

T = 16

Substituting the value of T back into equation 2:

S + 16 = 4

S = 4 - 16

S = -12

Since the number of vehicles cannot be negative, we discard the negative solution. Therefore, the number of sedans (S) is 0, and the number of trucks (T) is 16.

Hence, during the 4-hour period, the toll collector collected money from 38 sedans and 16 trucks.

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Solve this problem using the golden ratio. Given the golden ratio (1 + √5) : 2 and the width of the door, we will find the height of the door.

Step 1: Write the ratio as a fraction.
The golden ratio can be written as a fraction: (1 + √5) / 2.

Step 2: Set up a proportion.
Let the height of the door be h. Then we can write the proportion:

height : width = (1 + √5) / 2
h / 36 = (1 + √5) / 2

Step 3: Solve for h.
To find the height of the door, we'll cross-multiply and solve for h:

h = 36 * (1 + √5) / 2

Step 4: Simplify the expression.
First, we'll distribute the 36:

h = (36 + 36√5) / 2

Next, we'll divide each term by 2:

h = (18 + 18√5)

So, the height of the door is 18 + 18√5 inches, which is in simplest radical form.

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The value of the side a is 12. 8 . Option C

From the diagram shown, we have that;

m<A = 45 degrees

c = 17

m<B = 25

Note that the sum of the angles in a triangle is 180, then, we have;

<A + <B + < C = 180

substitute the values

45 + 25 + < C = 180

collect the like terms

<C = 110

Using the sine rule, we have;

sin A/a = sin B/b = sin C/c

Substitute the values, we get;

sin 45/a = sin 110/17

cross multiply the values, we have;

a = 12. 02/0. 9396

a = 12. 79

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Answer:

The area is 8

Step-by-step explanation:

If the perimeter is 12, we can just start guessing and checking. in this case, if 4 is the length, that means 2 is its width, since 4-2=2. then you find the area(basexhight) 4x2=8!

Answer:

Step-by-step explanation:

Let's look at the options

A. Equal side lengths and equal diagonal lengths.

B. Impossible without angle measure.

C. Equal side lengths and diagonals bisect each other.

D. Equal side lengths and diagonals.

Answer:

C

Step-by-step explanation:

Let's replace cohordinates on the system

A:

-5 < -6 + 12 --> -5 < 6 TRUE

-5 >= -10 +7 --> -5 >= -3 FALSE

B:

2 < 3 + 12 TRUE

2 >= 5 +7 FALSE

C:

17 < 6+12. TRUE

17 >= 10 + 7. TRUE

D

-1 < 0 +12 TRUE

-1 >= 0 + 7  FALSE

This lab report examines neutralization reactions in an acidic lake and investigates the effects of lime treatment. The objective is to understand the ecological implications of neutralization reactions and explore potential solutions for acidic lake environments.

The experiment involves collecting water samples from the lake and conducting neutralization reactions using lime as the neutralizing agent. Data is gathered and analyzed to determine the effectiveness of the treatment. The results are then interpreted and discussed, highlighting any trends or patterns observed. The report concludes with a summary of the findings and suggestions for further research or improvements to the experimental methodology.

The lab report focuses on studying neutralization reactions in an acidic lake to gain insights into their ecological impact and address potential remediation strategies. Acidic lakes pose significant challenges to aquatic ecosystems, and understanding the neutralization process is crucial for developing effective solutions. The experiment involves collecting water samples from the acidic lake and subjecting them to neutralization reactions using lime as a common neutralizing agent. The experimental procedure is carefully described, including details on materials, measurements, and observations made during the experiment. The obtained data is then presented in a clear and organized manner, utilizing tables, graphs, or charts. The results are interpreted and discussed, taking into account any observed trends, patterns, or deviations. The report compares the findings with existing literature or prior studies on similar topics to provide context and support the conclusions drawn. Limitations and sources of error in the experiment are also addressed. The report concludes by summarizing the key findings and their implications for acidic lake environments, as well as suggesting areas for further research or improvements to the experimental approach.

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a) the inverse function is:

f-1(y) = (y-b)/a

b) f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

First, let's answer the first part of the question:

To determine whether the function f(x) = ar+b is one-to-one, we need to check if different inputs produce different outputs. Let's suppose that f(x1) = f(x2), where x1 and x2 are distinct inputs. Then, we have:

ar+b = f(x1) = f(x2) = ar+b

Subtracting ar+b from both sides, we get:

ar-ar+b-b = 0

Simplifying, we get:

a(x1 - x2) = 0

Since a is nonzero, this equation implies that x1 = x2, which contradicts our assumption that x1 and x2 are distinct. Therefore, the function f(x) = ar+b is one-to-one.

To find the inverse function of f(x) = ar+b, we can solve for x in terms of y:

y = ar+b

y-b = ar

r = (y-b)/a

x = (y-b)/a

Therefore, the inverse function is:

f-1(y) = (y-b)/a

Now, let's answer the second part of the question:

To find (F-1)(a) for f(x) = x2 + 2x - 1 and a = -4, we set y = -4 and solve for x:

y = x2 + 2x - 1

-4 = x2 + 2x - 1

x2 + 2x - 3 = 0

(x + 3)(x - 1) = 0

x = -3 or x = 1

Since f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

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Answer:

16. 53 = 14.50 + p  The answer is 38.50. 17a. Your final bowling score is 105-14, which is equal to 91.

Step-by-step explanation:

53 = 14.50 + p

53-14.50=p

38.50=p

For b... I don't know what a "10nth frame" is. Or a spare. Sorry...

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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The shaded area between the two hexagons is 128√3 square feet.

A regular polygon is a two-dimensional shape with straight sides, where all sides are of equal length and all angles between the sides are of equal measure.

The center-to-vertex distance of the small hexagon is given as 4 ft. This means that the side length of the small hexagon is 4 ft/√3 or (4√3)/3 ft.

The distance between the small and larger hexagons is also given as 4 ft. This means that the radius of the circle circumscribing the larger hexagon is (4√3)/3 + 4 ft.

The formula for the area of a regular hexagon is:

Area = (3√3 / 2) × (side length)²

For the smaller hexagon, the side length is (4√3)/3 ft, so its area is:

Area of smaller hexagon = (3√3 / 2) × [(4√3)/3]²= 16√3 ft²

For the larger hexagon, the side length is the distance from the center to a vertex, which is the radius of the circle circumscribing the hexagon. So the area of the larger hexagon is:

Area of larger hexagon = (3√3 / 2) × [(4√3)/3 + 4]² = 144√3 ft²

Therefore, the area between the two hexagons is:

Area = Area of larger hexagon - Area of smaller hexagon

Area = 144√3 - 16√3

Area = 128√3 square feet

So the area between the two hexagons is 128√3 square feet.

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The Owen's long-term assets amount to $44,000. This is calculated by subtracting his annual expenses of $48,000 from his total assets, which are determined to be $92,000 based on a debt-to-asset ratio of 0.5 and total liabilities of $46,000. Therefore, the correct option is d) $44,000.


Owen's long-term assets can be calculated using the given information. Let's break down the problem step by step:

1. Debt-to-asset ratio: Owen's debt-to-asset ratio is 0.5. This ratio is calculated by dividing total liabilities by total assets. Since we know the ratio, we can express it as a fraction: Debt-to-asset ratio = Liabilities / Assets.

2. Liabilities: Owen's liabilities total $46,000, which means Liabilities = $46,000.

3. Total assets: To find Owen's total assets, we can use the debt-to-asset ratio. We know that Debt-to-asset ratio = Liabilities / Assets. Rearranging the equation, we have Assets = Liabilities / Debt-to-asset ratio.

  Plugging in the given values, we can calculate Owen's total assets:

  Assets = $46,000 / 0.5 = $92,000.

4. Emergency fund: Since Owen needs to maintain the minimum emergency fund, we need to subtract the annual expenses from the total assets. Owen's annual expenses are $48,000. So, his long-term assets would be:

  Long-term assets = Total assets - Annual expenses = $92,000 - $48,000 = $44,000.

Therefore, Owen's long-term assets amount to $44,000. The correct answer option would be d) $44,000.

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9514 1404 393

Answer:

  126°

Step-by-step explanation:

To find the exterior angle, we need to know one of the acute angles. Those are found using the fact that they are complementary.

  (5x -6) +(3x) = 90

  8x = 96 . . . . . . . . . . . add 6, collect terms

  x = 12 . . . . . . . . . . . . . divide by 8

  3x° = 3·12° = 36° . . . . . . find the "remote" acute angle

  exterior angle = 90° +36°

  exterior angle = 126°

__

The exterior angle is the supplement of the one marked (5x-6)°. It is also the sum of the two remote interior angles, 90° and 3x°. Being lazy, we figure that 90 +3·12 is easier to compute than 180 - (5·12 -6). Either way, the exterior angle is 126°.

An equal-interval line graph and a ratio scale are similar in that they both involve the representation of data using a linear scale.

In both cases, the horizontal axis represents the independent variable, while the vertical axis represents the dependent variable. Both methods allow for the visualization of the relationship between variables and enable data comparison. The main difference between an equal-interval line graph and a ratio scale lies in the nature of the scales used. In an equal-interval line graph, the scale on both axes is divided into equal intervals or increments.

This means that the distance between any two points on the graph represents an equal change in the variables being measured. The values on the axes are not necessarily based on a specific mathematical relationship or proportionality. On the other hand, a ratio scale is based on a specific mathematical relationship where the values have a meaningful zero point and are proportionate to each other. In a ratio scale, the intervals between values represent equal ratios or proportions.

This allows for more precise and meaningful comparisons between data points. Examples of ratio scales include measurements of weight, distance, or time.While both an equal-interval line graph and a ratio scale involve the representatioof data using linear scales, the key difference lies in the nature of the scales themselves. An equal-interval line graph uses equal intervals on the axes without necessarily having a specific mathematical relationship, while a ratio scale has a meaningful zero point and represents proportional values.

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Answer:

6 wholes

Step-by-step explanation:

\( \frac{19}{3} = 6 \frac{1}{3} \)

So there are 6 wholes in 19/3.

Readers of the Young Professional blog might find the arcticles on personal development, world news, and self-improvement interesting.

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Answer:

square the vertical starting from bisect angle !

Answer:

A

Step-by-step explanation:

if h(x)=(x/2)-6, find h(10)

What this means is that wherever there is an x on the right hand side, replace it with a 10

h(10) = (10/2) - 6

h(10) = 5 - 6

h(10) = -1

The given initial value problem's exact solution: y(t) = 1, and thus y(1) = 1. The Euler approximation of y(1) using a step-size h = 0.5 i: y(1) ≈ 1. Given the initial value problem:

y' = ty ' (0)

 = 0

We are to determine the exact solution y(t) and compute y(1), and also find the Euler approximation of y on the interval [0, 1] using a step-size h = 0.5 (half step size).

(a) The given initial value problem is a first-order linear differential equation, whose standard form is:

y' + P(t)y = Q(t), where P(t) = 0 and Q(t) = 0. Thus, the integrating factor is:

I(t) = e^∫ P(t)dt

      = e^∫ 0 dt

      = 1.

The exact solution y(t) is obtained by multiplying both sides of the differential equation by the integrating factor,

I(t) = 1, and integrating:

y' + P(t)y = Q(t) becomes

y' + 0y = 0, which implies

y' = 0.

Hence, y(t) = Ce^0 = C, where C is a constant determined using the initial condition y(0) = 1. Therefore, we have:

C = y(0) = 1.

Hence, the initial value problem's exact solution is y(t) = 1, and thus y(1) = 1.

(b) Euler Approximation of y using step-size h = 0.5We have h = Δt = 0.5, t0 = 0, tn = 1. The number of steps, n, is given by:

n = (tn - t0)/h

n = (1 - 0)/0.5

n = 2.

Therefore, we have two grid points:

t0 = 0, and

t1 = 0 + 0.5

  = 0.5

For the Euler approximation of y on [0, 1], we use the formula:

yi+1 = yi + h * f(ti, yi), for i = 0, 1, 2, ..., n - 1, where

f(ti, yi) = tiyi

= (0)(yi)

= 0, for i = 0, 1, 2, ..., n - 1.

Hence, we have:

y0 = y(0) = 1, and

y1 = y0 + h * f(t0, y0)

= y0 + h * 0

= 1 + 0

= 1

Therefore, the Euler approximation of y(1) using a step-size h = 0.5 is: y(1) ≈ y1 = 1. Therefore, y(1) ≈ 1. The exact solution of the given initial value problem is: y(t) = 1, and thus y(1) = 1. The Euler approximation of y(1) using a step-size h = 0.5 is: y(1) ≈ 1.

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Answer:

\(p=\frac{1}{8}\)

Step-by-step explanation:

\(-3p+\frac{1}{8}=-\frac{1}{4}\)

Subtract \(\frac{1}{8}\) from both sides:

\(-3p=-\frac{1}{4}-\frac{1}{8}\)

Multiply \(\frac{1}{4}\) by \(\frac{2}{2}\) and simplify:

\(-3p=-\frac{3}{8}\)

Divide both sides by -3:

\(p=\frac{3}{24}\)

Simplify:

\(p=\frac{1}{8}\)

Answer: x=4

Step-by-step explanation:

firstly you solve the barracks first by multipy 2 into ( x+8) after that you collect like terms on one side of the equation or make x become the subject of the equation and solve for x

Answer:

  D. It decreases by $108.49

Step-by-step explanation:

You want to know the effect on the value of 18,000 yuan in NZ$ if the exchange rate changes from 4.75 yuan per NZ$ to 4.89 yuan per NZ$.

Sampson's account has an initial value in NZ$ of ...

  (18,000 yuan) × (1 NZ$)/(4.75 yuan) ≈ NZ$ 3789.47

After the change in exchange rate, the account value is ...

  (18,000 yuan) × (1 NZ$)/(4.89 yuan) ≈ NZ$ 3680.98

The change in value is the difference between the new value and the old value:

  NZ$ 3680.98 -3789.47 = NZ$ -108.49

The value of Sampson's bank account decreases by $108.49, choice D.

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The height is changing at the rate of 1/20in per minute in the given right cylindrical tank.

So, the changing the rate of the height:

Calculate height as follows:

Therefore, the height is changing at the rate of 1/20in per minute in the given right cylindrical tank.

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The number of sundaes sold is 20 and the number of frozen yogurts sold is 28.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, the local ice cream show sold sundaes for $3.25 and frozen yogurt for $4 and made a total of $177.

Let the number of sundaes be s, and frozen yogurts be f.

The shop sold 8 fewer sundaes than frozen yogurts.

So, s=f-8 -------(I)

Here, the equation is 3.25s+4f=177-------(II)

Substitute s=f-8 in equation (II)

⇒ 3.25(f-8)+4f=177

⇒ 3.25f-26+4f=177

⇒ 7.25f=203

⇒ f=203/7.25

⇒ f=28

So, s=f-8=20

Therefore, 20 sundaes and 28 frozen yogurts were sold on that day.

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Answer:

Dilation

Step-by-step explanation:

A rotation followed by a dilation is a similarity transformation. Therefore, the two triangles are similar.

. . .

Hope this helped! Goodluck on what you're doing and stay safe! ♥♥♥

Answer:

35.m3

160.cm3

1,584.cm3

56.m3

1,344 cm3

Step-by-step explanation:

Multiply l x w x h

Hope it helps

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