perform the indicated operation. Be sure the answer is reduced.
2a+1/3a + 5/4 - 2a-3/6a^2
A 23a^2 + 6/12a^2
B -23a^2 + 6/12a^2
C 23a^2 - 6/12a^2

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Step-by-step explanation:

in a geometric sequence every new term is created by multiplying the previous term by a constant factor. this factor is constant (= the same) for the whole sequence.

a1 = a1

a2 = a1 × f

a3 = a2 × f = a1 × f × f = a1 × f²

...

an = a1 × f^(n-1)

so, we have here

a1 = -2

a2 = a1 × f = -2 × f = 10

f = 10/-2 = -5

an = -2 × -5^(n-1)

in any case, the next 2 terms are

-50 × -5 = 250

250 × -5 = -1250

Answer:

Step-by-step explanation:

its (x+1,y+-3)

Answer:

C

Step-by-step explanation:

Because if you plug those numbers into the graph, only C and D fit. Now we have to look at the unit price. If LaMar buys 2 lbs and pays 3.00 dollars, we know that the unit price is 3/2=1.5 dollars per pound. You could also check with the other peoples. $7.5/5lbs=1.5 dollars. $4.5/3lbs=$1.5

The relationship between the data and the line and the unit price of oranges of $1.50 per pound is best represented by option C.

The slope of a line is the tangent of the angle that the line makes with the positive direction of the x-axis.

It signifies the rise in the y-variable for a unit change in the x-variable.

If the line passes through the points (x, y) and (x, y), then the slope of the line, m = (y - y)/(x - x).

In the question, we are asked to identify the graph and mention the unit price of the orange from the available data.

Taking the quantity of oranges bought in pounds and the cost of oranges in dollars on the x and y axes respectively, we can say that the line must pass through the points:

(2, 3) representing the purchase by LaMar,

(5, 7.5) representing the purchase by Enrico,

(3, 4.5) representing the purchase by Anna.

The unit price can be calculated by calculating the slope of the line,

m = (7.5 - 4.5)/(5 - 3) = 3/2 = 1.5.

These points and the required unit rate is satisfied by option C, thus it is the best choice.

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Answer:

change f(x) to 0 than 7*2x=14x

0=14x-28x+21

0=-14x+21

-21=-14x

x=3/2

Answer: its (4f 5) ^3

Step-by-step explanation:

Answer:

5:6

Step-by-step explanation:

The height of the painting in the scale drawing is approximately 5.8 centimeters (rounded to the nearest tenth).

To find the height of the painting in the scale drawing, we can set up a proportion using the given scale.

Given:

Scale: 2 centimeters represent 9 inches

Real height of the painting: 26 inches

Height in the scale drawing: ?

Let's set up the proportion:

2 centimeters / 9 inches = x centimeters / 26 inches

To solve for x (the height in the scale drawing), we can cross-multiply and then divide:

2 centimeters * 26 inches = 9 inches * x centimeters

52 centimeters = 9x

Dividing both sides by 9:

x = 52 centimeters / 9

x ≈ 5.8 centimeters

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Answer:

21.038 ft

Step-by-step explanation:

6.7x3.14=21.038

hope this helps

plz can  i get brainliest:)

Answer:

if your looking for radius it would be 3.35 if your looking for surface area its 3.14(3.35)^2  

Step-by-step explanation:

Answer:

(n-2) x 180 degrees where n is the number of sides

Step-by-step explanation:

From one vertex of the polygon you draw triangles inside the polygon.  Multiply the number of triangles by 180 since all triangles interior angles add up to 180 degrees.

example

Pentagon has 5 sides.  (5-2) x 180 = 540 degrees

This is the same as 180n-360

===================================================

Explanation:

Draw any polygon you want. Let's say we draw a hexagon. Split the hexagon into 6 triangles. Check out the diagram below.

The goal is to find what the red angles sum to. Recall that any triangle always has its three angles add to 180 degrees. We have 6 triangles, so all of the angles (red+blue) add to 6*180 = 1080 degrees. However, we don't want to include the blue inner angles. So we'll subtract off 360 since the blue angles add up to this amount (they form a full rotation).

So we have 6*180 - 360 as the expression that represents the sum of the interior angles for this hexagon. The hexagon doesn't have to be a regular polygon.

We can generalize to any polygon and not just hexagons. Simply replace that "6" with n and we get n*180 - 360 which is the same as 180n-360 = 180(n-2)

The length of radius of the circle having center at (2-i) and point on circle at (8+7i) is 10 units .

To find the length of the radius of a circle with a center at (2-i) and a point on the circle at (8+7i), we can use the distance formula , which is

The formula to find distance between 2 points (x₁, y₁) and (x₂, y₂) is given by:

⇒ d = √[(x₂ - x₁)² + (y₂ - y₁)²] ,

In this case, the center of the circle is (2-i), which means that the x-coordinate of the center is 2 and the y-coordinate is -1.

The point on the circle is (8+7i), which means that the x-coordinate of the point is 8 and the y-coordinate is 7.

By using distance formula, we can find distance between the center and the point on circle ,

⇒ d = √[(8 - 2)² + (7 - (-1))²]

⇒ d = √[6² + 8²]

⇒ d = √[36 + 64]

⇒ d = √100

⇒ d = 10

Therefore, the length of the radius of the circle is 10 units.

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The given question is incomplete , the complete question is

What is the length of the radius of a circle with a center at (2-i) and a point on the circle at (8+7i)?

Answer:

C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A linear function is a straight line when graphed so is not B.

For confirmation of A note how for each increase of 3 in x we get the same increase of 5 in y.

The Bayesian odds of QA to QS given that a bug was found is 0.22:1.

Let P(Ar) and P(St) be the proportions of biomes sent to Arstotzka and Stardew respectively, which is 0.32 and 0.68 respectively.

Let P(bug|QA) and P(bug|QS) be the probabilities of finding a bug given that a biome was sent to QA and QS respectively, which is 0.13 and 0.55 respectively.

The probability of finding a bug is given by:P(bug) = P(bug|QA) × P(QA) + P(bug|QS) × P(QS)

Substituting the values, we get:P(bug) = 0.13 × 0.32 + 0.55 × 0.68= 0.4164

Let A be the event that a biome was sent to Arstotzka, and B be the event that a bug was found.

Then, we need to find the Bayesian odds of QA to QS given that a bug was found, which is given by:

Bayesian odds = (P(A|B) / P(St|B)) × (1 - P(A) / P(St))

Substituting the values, we get:

Bayesian odds = (P(B|A) × P(A) / P(B|St) × P(St)) × (1 - P(A) / P(St))P(B|A) = P(A ∩ B) / P(A) = P(B|A) × P(A) / P(bug) = (0.13 × 0.32) / 0.4164 = 0.0998

P(B|St) = P(St ∩ B) / P(St) = P(B|St) × P(St) / P(bug) = (0.55 × 0.68) / 0.4164 = 0.9022

P(A|B) = P(B|A) × P(A) / P(B) = (0.13 × 0.32) / 0.4164 = 0.0998 / 0.4164 = 0.2398

P(St|B) = P(B|St) × P(St) / P(B) = (0.55 × 0.68) / 0.4164 = 0.9022 / 0.4164 = 2.1688

Bayesian odds = (P(A|B) / P(St|B)) × (1 - P(A) / P(St))= (0.2398 / 2.1688) × (1 - 0.32 / 0.68)= 0.22:1

Therefore, the Bayesian odds of QA to QS given that a bug was found is 0.22:1.

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Answer:

3ft

Step-by-step explanation:

because 9 times 3 equal 27

To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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Answer:

1

The answer is 1

One

Un

Uno

Aight nvm

By adding 5 to both side we will just get x2= -4+5

-4+5=1

The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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Answer:

Option B: $20x + $30 < $170 is the correct answer.

Step-by-step explanation:

Given that:

Service fee of Tina's business = $30

Per day charges = $20

Number of days =  x

Customer's budget = less than $170

According to given statement;

20x + 30 < 170

Hence,

Option B: $20x + $30 < $170 is the correct answer.

Answer:

8.9%

Step-by-step explanation:

Probability of picking a red marble first: \(\frac{2}{10}=\frac{1}{5}\)

Probability of picking a blue marble (no replacement): \(\frac{4}{9}\)

\(\frac{4}{9} *\frac{1}{5} =\frac{4}{45} = 8.8888888888...%\) % ≈ 8.9%

(2,9)

this needs 20 characters

A matrix A with three eigenvalues, one-dimensional eigenspace, and two-dimensional eigenspace is diagonalizable because it has a complete set of linearly independent eigenvectors.

To show that matrix A is diagonalizable, we need to prove that it has a complete set of linearly independent eigenvectors.

1. Given that A is a 4x4 matrix with three eigenvalues, one of which has a multiplicity of 2, it means that A has a total of 4 eigenvectors.
2. The fact that one eigenspace is one-dimensional implies that one eigenvalue has a multiplicity of 1, and therefore, it has a corresponding eigenvector.
3. Additionally, we are told that one of the other eigenspaces is two-dimensional, which means that the corresponding eigenvalue has a multiplicity of 2, and there are two linearly independent eigenvectors associated with it.
4. Since A has a total of 4 linearly independent eigenvectors (one from the one-dimensional eigenspace and two from the two-dimensional eigenspace), we can conclude that A is diagonalizable.

Therefore, a matrix A with three eigenvalues, one-dimensional eigenspace, and two-dimensional eigenspace is diagonalizable because it has a complete set of linearly independent eigenvectors.

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In a triangle, the sum of any two sides is greater than the third side. Hence, by applying the same rule in this case: 4.72 + 1.67 > 6.31, 1.67 + 6.31 > 4.72, 4.72 + 6.31 > 1.67Thus.

The expression w^10 z^4 / w^10 z^-4 can be simplified by applying the rules of exponentiation. When dividing two expressions with the same base, we subtract the exponents. Therefore, the simplified expression is:

w^(10-10) z^(4-(-4)) = w^0 z^8.

Since any non-zero number raised to the power of zero is equal to 1, we have:

w^0 z^8 = 1 * z^8 = z^8.

Therefore, the equivalent expression is z^8.

Hence, the correct answer is:

B. z^8.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The following probability which  is true: P(1.5 - .02 < X < 1.5 + .02) = 0.68 for the distribution of log-cell counts of red blood cells for women.

Given that the distribution of log-cell counts of red blood cells for women age 25-30 is approximately normally distributed with µ = 1.5 cells/microliter and σ = 0.1 cells/microliter.

In this, the probability of the Z score for a range is asked.

The value of Z is given by:

Z = (X - µ)/σZ

= (1.5 - 1.5)/0.1

= 0

In the Z table, the value of 0 is 0.5.

So, the following probability will be found:

P(1.5 - .02 < X < 1.5 + .02) = P(-0.2 < Z < 0.2)

We know that 0.2 value is in between 0 and 0.25 in the Z table.

P(1.5 - .02 < X < 1.5 + .02) = P(-0.2 < Z < 0.2)

= P(Z < 0.2) - P(Z < -0.2)

= 0.5793 - 0.4207

= 0.1586

≈ 0.16

Therefore, the option which is true is: P(1.5 - .02 < X < 1.5 + .02) = .68.

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The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

The realization of the stochastic process implies that the values of the stochastic process are observed at particular points in time. It is denoted by x(t) and takes the form of a function of time t.

If the process is discrete, then the function is a sequence of values at discrete points in time.

A stochastic process is one that evolves over time and the outcomes are uncertain.

The given expression P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1) gives the probability of X5 being equal to 3 given that X4 is equal to 3, X3 is equal to 3, X2 is equal to 1, X1 is equal to 4, and X0 is equal to 1.

To understand the above expression, suppose we have a stochastic process with values X0, X1, X2, X3, X4, and X5.

The given expression provides the conditional probability of the value of X5 being equal to 3 given that X0, X1, X2, X3, and X4 take specific values.

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

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Tom earns $32,660.

A z-score of 0.9 means that Tom's salary is 0.9 standard deviations above the mean. The mean salary is $27,800 and the standard deviation is $5400, so Tom's salary is $27,800 + 0.9 * $5400 = $32,660.

Here is a more detailed explanation of how to calculate Tom's salary:

The mean salary is $27,800.

The standard deviation is $5400.

A z-score of 0.9 means that Tom's salary is 0.9 standard deviations above the mean.

To calculate Tom's salary, we can use the following formula:

Salary = Mean + (Z-score * Standard deviation)

Substituting the known values into the formula, we get:

Salary = $27,800 + (0.9 * $5400)

Salary = $32,660

Therefore, Tom earns $32,660.

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Based on the given data, the professors' grading procedures have different variances. To determine if the difference is statistically significant at the 2% level of significance, we can use a two-sample F-test. The F-statistic is calculated by dividing the larger variance by the smaller variance. In this case, the F-statistic is 2.97. Using a critical value of 5.05, we can reject the null hypothesis that the variances are equal. Thus, the decision is that there is a statistically significant difference in the variance of the professors' grading procedures.

In statistics, variance is a measure of the spread of a distribution. When comparing two variances, we can use a two-sample F-test to determine if they are statistically different. The F-statistic is calculated by dividing the larger variance by the smaller variance. If the calculated F-value is greater than the critical value, we reject the null hypothesis that the variances are equal.

In this case, the professors' grading procedures have different variances, with Professor 1 having a larger variance than Professor 2. Using a two-sample F-test, we determined that the difference in variances is statistically significant at the 2% level of significance. This means that there is strong evidence to suggest that the professors' grading procedures differ in their spread of grades.

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30 dollars each member

Step-by-step explanation:

1,300 minus the 550 that they already raised, divided by 25 (for the number of team members = 30 dollars each member .

The tables that represent a linear function are:

A straight line on the coordinate plane is represented by a linear function.

For instance, y = 4x - 3 indicates a straight line on a coo.rdinate plane and hence a linear function.

This function may be expressed as function of x = 4x - 3 since y can be substituted with function of x.

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