The dimensions of a pool: height = x - 2 meters, length = 2x + 5 meters, and width = 2x - 1 meters. If the volume of the pool is 182 cubic meters, what is the value of x?​

(a) The probability that a starter motor fails within 4 years is approximately 0.6321.

(b) The probability that a motor fails in less than 4 years given that it has lasted more than two years is approximately 0.4866.

(c) The probability that a motor fails in less than two years is

approximately 0.1813.

(d) The motor with δ = 4000 and β = 3.4 has a longer lifetime based on the time exceeded by 99% of the motors.

(a) To find the probability that a starter motor fails within 4 years, we can use the cumulative distribution function (CDF) of the Weibull distribution. Given δ = 3000 and β = 2.0, we can substitute these values into the formula:

P(T ≤ 4 years) = 1 - e^(-((4/3000)^2.0))

This calculates the probability that the time to failure, denoted as T, is less than or equal to 4 years.

(b) To find the probability that a motor fails in less than 4 years given that it has lasted more than two years, we need to calculate the conditional probability P(B|A), where A is the event that the motor lasts more than two years, and B is the event that the motor fails in less than four years. We can use the formula:

P(B|A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) represents the probability that both events A and B occur, and P(A) represents the probability of event A occurring.

(c) To compare the probability from part (b) to the probability that a motor fails in less than two years, we can calculate P(T ≤ 2 years) using the CDF of the Weibull distribution:

P(T ≤ 2 years) = 1 - e^(-((2/3000)^2.0))

By comparing the calculated probability from part (b) to P(T ≤ 2 years), we can analyze whether the lack of memory property applies to this distribution. The lack of memory property implies that the probability of failure within a specific time period does not depend on how long the motor has already been in operation.

(d) To determine which motor has a longer lifetime, we can find the times exceeded by 99% of the motors for each distribution. This can be done by using the inverse CDF at a probability level of 0.01 for each distribution.

For the first motor, with δ = 3000 and β = 2.0, we find the time exceeded by 99% of the motors using the inverse CDF.

For the second motor, with δ = 4000 and β = 3.4, we find the time exceeded by 99% of the motors using the inverse CDF.

By comparing the two times, we can determine which motor has a longer lifetime based on the time exceeded by 99% of the motors.

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The dependent variable in this experiment is the level of anxiety as measured by a standardized measure of anxiety before and after the interventions or waitlist period.

The dependent variable in this experiment is the standardized measure of anxiety that was administered to participants before and after the interventions or waitlist period.

The dependent variable is what is being measured or observed to determine the effectiveness of the two interventions (cognitive-behavioral therapy and mindfulness-based stress reduction program) for anxiety.

Therefore,  The researchers are trying to find out how the interventions affect anxiety, so anxiety levels are the outcome or result of the intervention and therefore the dependent variable.

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Answer:

$ 100

Step-by-step explanation:

$ 200 = 200 %

x$ = 100%

The Rule of Three

x = (100%) ($200) / 200%

x = $ 100

Answer:

5 dollars per week

Step-by-step explanation:

20 ÷ 4 = 5

30 ÷ 6 = 5

I believe that is your question.

The postulate that can be used to prove the two triangles are congruent is the HL this is the last option

HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.

The theorem says that, two angles of a right angle triangle that have equal

then two triangles are congruent

The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal

Therefore, this theorem says that the two triangle are congruent

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Answer:

6(x) + 8 \(\geq\) 32

x = 4, 3, 2, 1, 0

Step-by-step explanation:

This is the answer because:

1) 8 more than 6 times a number is 6 times x + 8

6(x) + 8

2) "is at least 32" means 6(x) + 8 \(\geq\) 32

3) x = 4, 5, 6, 7, 8 and etc. because -8 from +8 and 32

6(x) = 24

4) 6(4) = 24

5) x can equal anything less than 4

Therefore, the inequality is 6(x) + 8 \(\geq\) 32 and x = 4, 3, 2, 1, 0

Hope this helps! :D

Answer:

A

Step-by-step explanation:

the other options have a common difference

Answer:

A is not arithmetic series

Step-by-step explanation:

In B,C and D there is arithmetic series as a2-a1=a3-a2

In A. there is no such series.....

Answer: 3 = b (maybe, usually unsure)

Step-by-step explanation: bing

y = mx + b, this is the formula.

b = y-intercept
m = slope

1. We know that (-1,6) is our pair.

2. The formula when written with the info is y = -3x + b

3. We know that -1 is the x and the y is 6, so subbing the x and y in the formula, it is 6 = -3(-1) + b.

4. When multiplied, it becomes 6 = 3 + b

5. Then we combine like terms, by subtracting 3 into 6, making 3 = b

6. So, it is 3 = b

Answer:

Step-by-step explanation:

Each term in the sequence is 4 less than the previous term.  That indicates an arithmetic sequence, which has the form a(n) = a(1) + d(n -1), where d is the common difference.  Here the common difference is -4, and so the appropriate sequence is

a(n) = 14 - 4(n - 1)

Answer:

All systems have 2 real solutions.

Step-by-step explanation:

there are X and Y unknowns.

Answer:

a₃₀ = 201

Step-by-step explanation:

there is a common difference between consecutive terms , that is

453 - 462 = 444 - 453 = - 9

this indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 462 and d = - 9 , then

a₃₀ = 462 + (29 × - 9 ) = 462 - 261 = 201

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:

False

Step-by-step explanation:

\(2x_1+6x_2\leq 30\\2(4)+6(5)\stackrel{?}{\leq}30\\8+30\stackrel{?}{\leq}30\\38\nleq30\)

Therefore, (4,5) is not a feasible point for the constraint

a 65%

b 91

c 231

now im typing so it will let me answer

ssssssssssssssssssssssssssss

The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 3 ,multiply the bottom equation by -2 then add the equation and is denoted as option B.

This is a mathematical term which is made up of two expressions and is connected by an equal sign.

In the example given below:

2x + 8y = -3

3x + 6y = -4

We can multiply the top by 3 and the bottom by -2 which will result in:

6x + 24y = -9

-6x - 12y = 8

They are then added to each other to give:

6x - 6x + 24y - 12y = -9+8

12y = -1

y = -1/12

From this we can notice that the variable x was eliminated which is why option B is the correct choice.

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Answer:

A rectangle is bounded by the x-axis and the semicircle y = √(25 - x²). What length and width should the rectangle have so that its area is a maximum?

Step-by-step explanation:

X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.

To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.

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Answer:

\(3ft^2\)

Step-by-step explanation:

SA = \(6a^{2}\)        

SA = \(6(3)^2\)      Solve for the exponent first

SA = 6(9)       Multiply

SA = 54 square feet  

Answer:

h = - 105

Step-by-step explanation:

Given

\(\frac{h}{14}\) = - 7.5 ( multiply both sides by 14 to clear the fraction )

h = - 105

Answer:1.86

Step-by-step explanation:

Step-by-step explanation:

I can't read Spanish or read Spanish I'm sorry

To find the general solution for the given ordinary differential equation (ODE):

xdy - [y + xy^(2)(1 + ln(x))]dx = 0

We can rearrange the terms and separate the variables:

xdy = [y + xy^(2)(1 + ln(x))]dx

Dividing both sides by x and rearranging the terms:

dy/y + y(ln(x) + 1)dx = dx

Now, let's integrate both sides:

∫(dy/y) + ∫[y(ln(x) + 1)]dx = ∫dx

Integrating the left-hand side with respect to y and the right-hand side with respect to x:

ln|y| + y(ln(x) + 1) = x + C

where C is the constant of integration.

We can simplify the equation further:

ln|y| + yln(x) + y = x + C

Combining the logarithmic terms:

ln|y| + yln(x) = x + C - y

To eliminate the logarithm, we can take the exponential of both sides:

e^(ln|y| + yln(x)) = e^(x + C - y)

Using the properties of exponents:

|y| * x^y = e^(x + C - y)

We can rewrite the absolute value expression as a piecewise function:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

So, the general solution to the given ODE is the combination of these two equations:

y * x^y = e^(x + C - y) if y > 0 -y * x^(-y) = e^(x + C - y) if y < 0

These equations represent the family of solutions to the given ordinary differential equation (ODE).

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Answer:

Step-by-step explanation:

There are 7+4+1=12 marbles in the bag.  The chances of drawing a green one on the first draw is 7/12.  The chance of drawing a green marble on the second draw is 6/11 (since you didn't replace the first marble you drew).

To find the probability, you just multiply these fractions: 7/12*6/11= 7/22 (reduced fraction).

Answer:

2556

Step-by-step explanation:

Answer:

ccghuiuujkll vhijkhjjjkjjjjjjjj

Since the area is zero, the coordinates of the centroid are undefined. This means that the centroid does not exist for this region.

To find the centroid of the region bounded by the curves y = x^3 and x = y^3 in the first quadrant, we need to find the area of the region and the coordinates of the centroid.

First, we can find the area of the region by integrating with respect to x:

A = ∫[0, 1] x^3 dx - ∫[0, 1] y^3 dy

= 1/4 - 1/4

= 0

This means that the area of the region is zero, which is not possible. Therefore, we must have made an error in our integration. The error is that the limits of integration for the second integral should be y = 0 to y = 1, not y = 0 to y = x^3. So, let's correct that:

A = ∫[0, 1] x^3 dx - ∫[0, 1] y^3 dy

= 1/4 - 1/4

= 0

Now, the area is zero because the region is symmetric with respect to the line y = x, and the areas on either side of this line cancel each other out.

To find the coordinates of the centroid, we need to integrate with respect to x and y:

x-bar = (1/A) * ∫∫[R] x dA

= (1/0) * ∫[0,1] ∫[y^3, y^(1/3)] x dx dy

= undefined

y-bar = (1/A) * ∫∫[R] y dA

= (1/0) * ∫[0,1] ∫[0, x^3] y dy dx

= undefined

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Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x)=2(x-2)²-5

f(x)=2(x²-4x+4)-5

f(x)=2x²-8x+3

The data item corresponding to a given z-score, we need the mean and standard deviation of the Distribution. Without this information, it is not possible to determine the specific data item.

To find the data item in a distribution that corresponds to a given z-score, we need to know the mean and standard deviation of the distribution. The formula to convert a z-score to a data value is:

data value = (z-score * standard deviation) + mean

Using this formula, we can find the data item corresponding to the given z-score.

It's important to note that without the mean and standard deviation of the distribution, it is not possible to determine the specific data item corresponding to the z-score.

The z-score represents the number of standard deviations a particular data point is from the mean. A positive z-score indicates a data point above the mean, while a negative z-score indicates a data point below the mean.

To find the specific data item, we would substitute the z-score, mean, and standard deviation into the formula and calculate the corresponding data value. However, since the z-score and the necessary information about the distribution are not provided in your question, it is not possible to provide a specific data item.

In summary, to find the data item corresponding to a given z-score, we need the mean and standard deviation of the distribution. Without this information, it is not possible to determine the specific data item.

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