I need help answering this

Answer:

Step-by-step explanation:

1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

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Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

Which triangle is ​△abc​ similar to and why? responses △abc is similar to △ghi by ​aa similarity postulate. triangle a b c, is similar to , triangle g h i, by , ​, a a similarity postulate, ., △abc is similar to △jkl by ​aa similarity postulate​. triangle a b c, is similar to , triangle j k l, by , ​, a a similarity postulate, ​, . △abc is similar to △def by ​aa similarity postulate​. triangle a b c, is similar to , triangle d e f, by , ​, a a similarity postulate, ​, . ​△abc​ is not similar to any of the triangles given.

Step-by-step explanation:

(x-2)^2 + (y-9)^2   = r^2

this is of the form fora circle with center  h,k and radius r

(x-h)^2 + (y-k)^2 = r^2

for the equation given   center =   2, 9    and radius = r

Answer:

Each leg is 13√2 cm long

Step-by-step explanation:

The hyotenuse of a right  triangle is calculated by the formula

c² = a² + b²

where c is the hypotenuse and a, b the other sides

and then finding the square root of the above

For a right isosceles triangle the two sides a = b

So c² = a² + a² = 2a²

In the given problem the equal sides are given as x

So c² = 2x²

c = √2x

We are given c = 26

26 = √2x

x = 26/√2

Rationalizing the denominator we get

x = 26 · √2 /2

= 13√2

Answer: 53.67 in

Step-by-step explanation:

Answer:

Step-by-step explanation:

Direction: Opens Up

Vertex:

(

0.784

¯¯¯¯

09

,

551.69488

¯¯¯¯

63

)

Focus:

(

0.784

¯¯¯¯

09

,

551.75170

¯¯¯¯

45

)

Axis of Symmetry:

x

=

0.784

¯¯¯¯

09

Directrix:

y

=

551.63806

¯¯¯¯

81

Select a few

x values, and plug them into the equation to find the corresponding

y values. The

x values should be selected around the vertex.

Replace the variable

x

with

0

in the expression.

f

(

0

)

=

4.4

(

0

)

2

−

6.9

⋅

0

+

554.4

Simplify the result.

Tap for more steps...

554.4

The

y

value at

x

=

0

is

554.4

.

y

=

554.4

Replace the variable

x

with

−

1

in the expression.

f

(

−

1

)

=

4.4

(

−

1

)

2

−

6.9

⋅

−

1

+

554.4

Simplify the result.

The best line that fits the data that is represented in the graph above would be diagram A.

A straight line graph is defined as the type of graph that is shows that there is a linear relationship between the two variables that are being plotted.

From graphs given above, they are a typical example of a straight line graph but the line that best fits the data is line if diagram A.

This is because most of the plotted data passed through the straight line from origin(0,0).

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hello

the answer to the question is:

u × v + u × w = u(w + v) = (5i - j)((i + 7j) + (6i + j)) =

(5i - j)(7i + 7j) = 35i + 35ij - 7ij - 7j²

= - 7j² + 28ij + 35i

The function that models the growth of this account is [tex]P(t) = 500 e^{0.025t[/tex]

From the question, we have the following parameters that can be used in our computation:

Principal, P = 500

Rate of interest, r = 2.5%

The function that models the growth of this account is represented as

[tex]P(t) = P_oe^{rt[/tex]

substitute the known values in the above equation, so, we have the following representation

[tex]P(t) = 500 e^{0.025t[/tex]

Hence, the function that models the growth of this account is [tex]P(t) = 500 e^{0.025t[/tex]

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Answer: The median is 7

To find the expected value of the absolute difference between a random variable x and a constant 4, given that the expected value of x is 4, we can use the linearity property of expectation.

Let's break down the absolute difference expression E(|x - 4|):

E(|x - 4|) = E(x - 4) for x ≥ 4

           = -(E(4 - x)) for x < 4

Since the expected value of x is given as E(x) = 4, we can substitute this into the equation:

E(|x - 4|) = E(x - 4) for x ≥ 4

           = -(E(4 - x)) for x < 4

           = E(x) - E(4) for x ≥ 4

           = -(E(4) - E(x)) for x < 4

           = 4 - 4 for x ≥ 4

           = -(4 - 4) for x < 4

           = 0

Therefore, the expected value of |x - 4| is 0 when the expected value of x is 4.

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Answer:

a = 2 , b = 2 , c = - 12

Step-by-step explanation:

given the zeros of f(x) are say x = a and x = b , then the corresponding factors are (x - a) and (x - b)

the function is then the product of the factors , that is

f(x) = p(x - a)(x - b) ← p is a multiplier

from the graph the zeros are x = - 3 and x = 2 , then factors are

(x - (- 3) ) and (x - 2) , that is (x + 3) and (x - 2) , then

f(x) = p(x + 3)(x - 2)

to find p substitute any other point lying on the graph into f(x)

using the point (1, - 8 )

- 8 = p(1 + 3)(1 - 2)

- 8 = p(4)(- 1) = - 4p ( divide both sides by - 4 )

2 = p

f(x) = 2(x + 3)(x - 2) ← expand factors using FOIL

     = 2(x² + x - 6) ← distribute parenthesis by 2

f(x) = 2x² + 2x - 12 ← in the form ax² + bx + c , and by comparison

a = 2 , b = 2 , c = - 12

Option (d) is the correct answer

Given, the sequence is -9, 0, 9, 18, 27, ……We can observe that the common difference is 9 i.e.9 – 0 = 9, 18 – 9 = 9, 27 – 18 = 9, …….To find the 24th term of the sequence, we can use the following formula:an = a1 + (n – 1)d, wherean = nth term of the sequencea1 = first term of the sequencen = the number of terms in the sequence.d = common difference of the sequenceUsing the above formula, we can get the value of the 24th term as follows:a24 = a1 + (24 – 1)dSince the first term of the sequence is -9 and the common difference is 9, we can substitute the values in the above formula and get:a24 = -9 + (24 – 1) × 9a24 = -9 + 23 × 9a24 = -9 + 207a24 = 198Therefore, the 24th term of the sequence is 198.

Hence, option (d) is the correct answer.

NOTE: It is important to observe the pattern of the sequence and identify the common difference to solve problems like these. The formula for finding the nth term of an arithmetic sequence is very useful in such cases.

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The simplified expression for log(9) - log(8) - log(√(75)) + log(√(25/27)) is

log((9/8) × (5/3[tex])^{(1/2)[/tex] - (1/2)log(75).

To rewrite the expression as a single term using the properties of logarithms, we can apply the following rules:

log(a) - log(b) = log(a/b)

log(a) + log(b) = log(ab)

log(√(x)) = (1/2)log(x)

Using these rules, let's simplify the given expression:

log(9) - log(8) - log(√(75)) + log(√(25/27))

= log(9/8) - log(√(75)) + log(√(25/27))

= log(9/8) + log(√(25/27)) - log(√(75))

Now, applying the rule log(a) + log(b) = log(ab):

= log((9/8) × √(25/27)) - log(√(75))

= log((9/8) × (25/27[tex])^{(1/2))[/tex] - log(√(75))

= log((9/8) × (5/3[tex])^{(1/2)[/tex]) - log(√(75))

Finally, applying the rule log(√(x)) = (1/2)log(x):

= log((9/8) × (5/3[tex])^{(1/2)[/tex] - (1/2)log(75)

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The calculated values of x in the figures are x = 70, x = 48 and x = 55

Figure (a)

In this figure, we have

Angles = 55 and 70 degrees

Also, we have

Two isosceles triangles

So, we have

PRQ = (180 - 70)/2

PRQ = 55

The sum of angles on a line is 180

So, we have

x + 55 + 55 = 180

Evaluate

x = 70

Figure (b)

In this figure, we have

Angle = 98 degrees

Also, we have

One isosceles triangle and One parallelogram

So, we have

MNR = 180 - 2x

The sum of angles on a line is 180

So, we have

180 - 2x + 98 = 180

Evaluate

x = 48

Figure (c)

The value of x is calculated as

2x = 180 - 70

So, we have

2x = 110

Evaluate

x = 55

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in essence it boils down to, when investing, you take risks all the time, the money is going to be invested on some expenditure that may work or not work, if it doesn't work, your money is Kaput, and if it works, how much are you getting back?  2%, 17%? or whatever.

If a company would like you to invest and provides you with 2% return, is kinda low but the issue is that whatever they're going to use it for and the health of their finances is such that you'll get 2%, or the probability of you getting that much is pretty good.

Now, if the same company instead offers 35% return on investment, hell that's high, the hell is going on?  Why are they so generous?

Well, they're not really being generous, the issue is the probability that you'll get that much is not really that good, there's a good chance your money will go Kaput, so the risk is really much higher, before you invest you're told of those chances, hmmmm should you do it knowing there's a good chance of being left just holding an empty bag?  So you'd hesitate and possibly say forget it, unless  the returns make it tilt that balance.  So the investors get attracted by the higher percent of return, but is always counter-balanced with the risk associated with it.

Check the picture below.

The measure of angle labelled 4 as required to get determined in the task content is; 90°.

It follows from the task content in that the measure of the angle labelled 8 is to be determined

Recall, when a diameter of a circle intersects with the tangent of a circle at the point if tengency, a right angle is formed at the point .

Consequently, the measure of angle 4 is; 90°.

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Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 [tex]a_5[/tex] =  26- 6( 5)  

[tex]a_5[/tex] =  26- 30

[tex]a_5[/tex] = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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The residual for the point (21, 7.1) is given as follows:

1.3 hours.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

The points in the data-set are given as follows:

(19, 5.4), (21, 7.1), (27, 5.6), (27, 5.4), (46, 3.9), (59, 3.4), (62, 2.1), (67, 3.3), (69, 3.8), (76, 4.1).

Inserting these points into a linear regression calculator, the line of best fit is given as follows:

y = -0.05331x + 6.9317

For x = 21 hours, the predicted value is given as follows:

y = -0.05331(21) + 6.9317

y = 5.8 hours.

Hence the residual is given as follows:

7.1 - 5.8 = 1.3 hours.

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Answer:

4×(3-2)/4+18

=4×1/4+18

=4/4+18

=1+18

=19

Answer: 30%

Step-by-step explanation:
12/40 = 3/10 = 0.30

0.30*100 = 30%

[tex]\sin( x )=\cfrac{\stackrel{opposite}{p}}{\underset{hypotenuse}{a}} \implies a\sin(x)=p ~~ \leftarrow \textit{pole's height}[/tex]

The direction of rotation used to create the image is 90°  counterclockwise rotation. To determine the direction and degree of rotation used to create the image, we can compare the positions of the vertices of the original triangle ABC with the corresponding vertices of the image triangle A' B' C'.

Let's analyze the changes in the coordinates of the vertices.

Original Triangle ABC:

A(-4, -4)

B(3, -3)

C(0, -10)

Image Triangle A' B' C':

A'(4, -4)

B'(3, 3)

C'(10, 0)

By comparing the coordinates, we can observe that the image triangle has undergone a 90° counterclockwise rotation.

To determine this, we can focus on a single vertex, such as A. The original point A(-4, -4) has been rotated counterclockwise by 90° to its new position A'(4, -4). This rotation is evident in the change of sign for the y-coordinate (-4 to -4) and the swapping of the x-coordinate (-4 to 4). This pattern is consistent across all three vertices.

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Answer:

Counterclockwise rotation of 90° about the origin

The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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The median of the set {79, 70, 85, 77.5} is 78.25. The median is a statistical measure that refers to the center value in an ordered data set.

The median of a set of numbers is the number that lies in the middle of that set when the numbers are arranged in numerical order.

The following is an example of how to find the median of a set of numbers:What is the median of 79, 70, 85, and 77.5? Arrange the data in numerical order first:70, 77.5, 79, 85.

Since there are an even number of values in this set, the median is the average of the two middle numbers. The two middle numbers in this set are 77.5 and 79. So, to find the median, we need to add them up and divide by two:77.5 + 79 = 156.5156.5 ÷ 2 = 78.25.

Therefore, the median of the set {79, 70, 85, 77.5} is 78.25.

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Step-by-step explanation:

12  4/5 ft    *   1/4 in / ft = 3.2 inches