Problem 1 (Exercise 8.3.1) Each character in a password is either a digit [0-9], lowercase letter [a-z] or special characters
{ ∗ , &​ ,​ $,#}. Compute the number of passwords that satisfy the given constraints. a) Strings of length 6 . Characters can be special characters, digits, or letters, with no repeated characters. b) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. The first character cannot be a special character.

An invertible matrix is a square matrix that has a multiplicative inverse. Suppose λ is an eigenvalue of an invertible matrix A; then, 1/λ is an eigenvalue of the inverse of A, denoted by A⁻¹.

If A is an invertible matrix, the inverse of A is denoted by A⁻¹. If λ is an eigenvalue of A, then we need to show that λ is an eigenvalue of A⁻¹.

Let x be the corresponding eigenvector of A for the eigenvalue λ.

i.e., Ax = λx.

Now, we want to show that λ is an eigenvalue of A⁻¹.

For that, we need to find a non-zero vector y such that A⁻¹y = λy.

If we multiply both sides of Ax = λx by A⁻¹, we get

A⁻¹Ax = λA⁻¹x.

But A⁻¹A = I (the identity matrix) since A is invertible.

Therefore, we have Ix = λA⁻¹x.

Rearranging, we get

A⁻¹x = (1/λ)x. This implies that x = λA⁻¹x.

Multiplying both sides of this equation by A^-1, we get

λy = A⁻¹x, where y = A⁻¹x is a non-zero vector.

Hence, λ is an eigenvalue of A⁻¹.

Therefore, we have shown that if λ is an eigenvalue of an invertible matrix A, then 1/λ is an eigenvalue of A⁻¹.

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Answer:

m=4

Step-by-step explanation:

6.33 × 10^9 / 1.79 × 10^5=3.54 × 10^m

Find m

6.33 × 10^9 / 1.79 × 10^5 =3.54 × 10^m

Divide the multipliers

6.33/1.79

=3.54

Divide the other multipliers

10^9/10^5

Division in scientific notation with superscript with the SAME base requires subtraction of the superscript using one of the bases

10^9/10^5

= 10^9-5

=10^4

Therefore,

6.33 × 10^9 / 1.79 × 10^5 = 3.54 × 10^4

m = 4

Answer:

4 :)

Step-by-step explanation:

The surface area of the rectangular gift box is 1070 square inches.

To find the surface area of a rectangular gift box, we need to calculate the areas of each of its six faces and then add them together.

The rectangular gift box has three pairs of equal faces:

1. Top and bottom faces: Each face has dimensions of length × width = 25 inches × 15 inches = 375 square inches.

2. Front and back faces: Each face has dimensions of width × height = 15 inches × 4 inches = 60 square inches.

3. Side faces: Each face has dimensions of length × height = 25 inches × 4 inches = 100 square inches.

To find the total surface area, we add up the areas of all six faces:

2 × (375 square inches) + 2 × (60 square inches) + 2 × (100 square inches) = 750 square inches + 120 square inches + 200 square inches = 1070 square inches.

Therefore, the surface area of the rectangular gift box is 1070 square inches.

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Answer:

aaaaaa

Step-by-step explanation:

did it on edge

Answer:

-17+4a=0

-17= -4a(-,-=+)

a=17/4

Answer:

i think it is 4a - 17 but i might be wrong or it is 3a - 17 try either one of those and if i am wrong i am sorry

Step-by-step explanation:

Answer: C

Step-by-step explanation: The slope of Function A is 6 and the slope of Function B is 5.

Step-by-step explanation:

Let's solve for c.

5c=d

Step 1: Divide both sides by 5.

5c

5

=

d

5

c=

1

5

d

Answer:

Step-by-step explanation:

circumference of a circle = 2 π r = 56.52

                                                   r = 56.52

                                                         2 * π

                                                   r = 9 cm

Answer:

r = 9 cm.

Step-by-step explanation:

Circumference = 2πr = 56.52

r = 56.52 / 2π

r = 9 cm.

x=28

2.8×X=11.2×7

2.8x=78.4

2.8x÷2.8=78.4÷2.8

x=28

Answer:

It should be 1/2 sorry if i"m wrong

The value of x to make A║B is 8 degrees.

In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of the given angles are supplementary angles because they are same side interior angles:

A + B = 180°

8x + 8x + 52 = 180°

16x = 180° - 52°

x = 128/16

x = 8°

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The expanded expression is 2log₂(a) - log₂(11/7)

The given expression is:
\(log_{2}((a^2) / (1 + 4/7))\), with a > 2

To expand this expression, we can apply the following logarithm properties:
1. logₐ(x y) = logₐ(x) + logₐ(y)
2. logₐ(x / y) = logₐ(x) - logₐ(y)
3. logₐ(\(x^y\)) = ylogₐ(x)

Now, apply property 2 to the given expression to get:
log₂(a²) - log₂(1 + 4/7)

Next, apply property 3 to the first term to get:
2 log₂(a) - log₂(1 + 4/7)

Finally, simplify the second term to get:
2 log₂(a) - log₂(7/7 + 4/7) = 2 log₂(a) - log₂(11/7)

So, the expanded expression is:
2log₂(a) - log₂(11/7)

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Here since the ratios are not all equal, we can conclude that x and y are not in a proportional relationship.

What is meant by ratios?

Ratios are a mathematical tool used to compare the sizes of two or more quantities, expressed as a ratio of their values. Ratios can be simplified, converted to fractions or decimals, and used to solve problems in various fields.

What is meant by proportional?

Proportional refers to the constant relationship between two or more quantities where their ratio remains the same. Scaling one quantity by a certain factor requires scaling the other quantity by the same factor to maintain the proportion.

According to the given information

To determine if x and y are in a proportional relationship, we need to check if the ratio of y to x is constant.

Let's calculate the ratio of y to x for each pair of corresponding values:

y/x for (1, 2.5) = 2.5/1 = 2.5

y/x for (2, 5) = 5/2 = 2.5

y/x for (3, 7.5) = 7.5/3 = 2.5

y/x for (6, 12) = 12/6 = 2

Since the ratios are not all equal, we can conclude that x and y are not in a proportional relationship.

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Answer:

F(p) = 500 + 0.5p

Step-by-step explanation:

Given that :

Bonus point on first purchase = 500

Number of points earned for every 2 dollar spent = 1

Points earned as a function of amount spent :

Bonus point + points earned per dollar

Number of points earned per dollar = 1 / 2

Let p = amount spent

F(p) = function representing the points earned

Hence,

F(p) = 500 + 0.5p

The value of such that the matrix is the augmented matrix of a linear system with The system has an infinite number of solutions if $k=-1$.

To find out the value of $k$ that results in the matrix being the augmented matrix of a linear system with infinitely many solutions, you need to reduce the matrix to row echelon form and check the conditions. If you get a row of all zeroes but the last entry in that row is not zero, then there is no solution. If you get a row of all zeroes including the last entry in that row, then there are infinitely many solutions. Therefore, the value of $k$ that leads to the augmented matrix of a linear system with infinitely many solutions is $k=-1$.

A system of linear equations has an infinite number of solutions if and only if its augmented matrix, after being transformed to row-echelon form, has at least one free variable column.

The matrix in question is given as:

\($$\begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix}$$\)

To find the value of $k$, we need to convert it to a row-echelon form.

\($$ \begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix} \overset{R2\rightarrow R2+\frac{3}{2}R1}{\longrightarrow} \begin{bmatrix}2 & -2 & 4 \\ 0 & 0 & 0 \\ 1 & -1 & k\end{bmatrix} $$\)

Notice that the second row of the matrix is all zeros, so the system either has no solution or has an infinite number of solutions. Therefore, we need to determine the value of $k$ to figure out which of the two cases apply. Since the third row is independent, we can choose to work with it only.

\($$1a - 1b = c \rightarrow c = a - b$$\)

We can also write it as a linear combination of $a$ and $b$:

\($$\begin{aligned} c &= a - b \\ &= a(1) + b(-1) \end{aligned}$$\)

Therefore, it follows that if $k$ equals -1, we can rewrite the last row as a linear combination of the first two rows.

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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The required solution to the given inequality is x > - 5.5 which means x is greater than -5.5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The statement is given as "twice x is greater than -11"

This can be in the algebraic form written as :

2x > - 11

Divided both sides of the above inequality, we get

x > - 11/2

x > - 5.5

Thus, the required solution to the given inequality is x > - 5.5.

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The question seems incomplete, the complete question would be as:

What is the solution to the inequality that represents twice x is greater than -11?

x>-1

Step-by-step explanation:

I don't see any number lines but it would be one with an open circle going right from -1.

Solution:

Given the parallelogram below:

According to the properties of a parallelogram, the opposite sides are parallel and equal in dimensions.

Thus,

A) Height of the parallelogram:

The length BE is the height of the parallelogram, which is evaluated using the Pythagorean theorem.

According to the Pythagorean theorem,

Where

To evaluate h, we need to determine the value of EC.

Recall that

Thus, we have

We can now determine the value of h.

From the Pythagorean theorem,

The price of each ounce of shampoo for the 20-oz bottle is:

And the price of each ounce of shampoo for the 12-oz bottle is:

Answer: The 12-oz bottle is the best buy.

To find the equation of the directrix of a parabola. The parabola has a focus at (-8, 10), passes through the point (-24, 73), has a horizontal directrix, and opens upward the equation of the directrix is y = 41..

To find the equation of the directrix, we need to determine the vertex of the parabola. Since the directrix is horizontal, the vertex lies on the vertical line passing through the midpoint of the segment joining the focus and the given point on the parabola.

Using the midpoint formula, we find the vertex at (-16, 41). Since the parabola opens upward, the equation of the directrix is of the form y = k, where k is the y-coordinate of the vertex.

Therefore, the equation of the directrix is y = 41.

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The x-component of vector A: 25 m. The y-component of vector A: 43.3 m. The x-component of vector B: -9.9 m. The y-component of vector B: 15.5 m.Vector C: (131.6 i + 206.2 j)Magnitude of vector C: 243.1 m. Direction of vector C: 57.3° north of the east.

Given information: Vector A:(50.0m, 30°

East of North)Vector B:(20.0m, 40° North of West)

Vector C = 5A - (2/3)B

Represent both vectors in an x-y coordinate system and find the components of vectors A and B: The angle between vector A and the positive x-axis: (90 - 30) = 60 degrees.

The magnitude of vector A: 50.0 m.

The x-component of vector A: Acosθ = 50cos60° = 25 m.

The y-component of vector A: Asinθ = 50sin60° = 43.3 m.

The angle between vector B and the positive x-axis: (90 + 40) = 130 degrees.

The magnitude of vector B: 20.0 m.The x-component of vector B: Bcosθ = 20cos130° = -9.9 m.

The y-component of vector B: Bsinθ = 20sin130° = 15.5 m.

Express vector C = 5A - (2/3)B as a linear combination of the unit vectors:

                               Vector C = 5A - (2/3)

                            B=5(25 i + 43.3 j) - (2/3)(-9.9 i + 15.5 j)= (125 i + 216.5 j) + (6.6 i - 10.3 j)= 131.6 i + 206.2

jMagnitude of vector C:|C|=√((131.6)² + (206.2)²)= 243.1 m

Direction of vector C:θ= tan⁻¹((206.2)/(131.6))= 57.3° north of the east.

Therefore, The x-component of vector A: 25 m.

The y-component of vector A: 43.3 m. The x-component of vector B: -9.9 m.

The y-component of vector B: 15.5 m.

Vector C: (131.6 i + 206.2 j)

Magnitude of vector C: 243.1 m. Direction of vector C: 57.3° north of the east.

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Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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If demand or annual usage increases by 10 percent, the Economic Order Quantity (EOQ) will increase. The EOQ model is used in inventory management to determine the optimal order quantity that minimizes total inventory costs.

The Economic Order Quantity (EOQ) is a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. It takes into account factors such as demand, holding costs, and ordering costs. When demand or annual usage increases by 10 percent, it means that more units are being consumed or sold within a given time period.

With an increase in demand, the EOQ will also increase. This is because the EOQ formula takes into consideration the trade-off between holding costs and ordering costs. Holding costs are the costs associated with holding inventory, such as warehousing and insurance, while ordering costs are the costs incurred when placing an order, such as administrative and transportation costs.

When demand increases, more units need to be ordered to meet the higher demand. This results in an increase in ordering costs, as more frequent orders will need to be placed. Consequently, the EOQ will increase to find the new optimal order quantity that balances the increased ordering costs with the holding costs.

In summary, if demand or annual usage increases by 10 percent, the EOQ will increase due to the need to order more frequently to meet the higher demand, resulting in increased ordering costs. This adjustment ensures that the inventory management system remains efficient and cost-effective.

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Answer:

no outlier

Step-by-step explanation:

An outlier is basically a number that "different" or "outcast" in a group of numbers.

If we look at this data set, there are no particular outliers that are "different" or an "outcast."

Therefore, the answer is no outliers.

Answer:

6 bags of flavored Chips .

Step-by-step explanation:

The statements second, Third and Fifth are correct statement related probabilities. which represent the 0.25 indicates an unlikely event and

0.75 indicates a likely event and 0.5 indicates equally likely to occur or not occur.

According to the statement

we have given that the some points related the probability and we ahve to express the correct statement and explain them.

So, We know that the

Probability is a the chance that a given event will occur.

And we know that the

You might split the likelihood in some notorious outcomes:

0: impossible (the event will never happen)

Close to zero (about 0 - 0.3): unlikely (the chances are small)

0.5: even (equal chances of happening and not happening)

Close to 1 (about 0.7 - 1): likely (the changes are large)

1: certain (it is 100% sure that the event will happen)

This means that:

first statement, 0 indicates a certain event, is incorrect.

0.25 indicates an unlikely event (second statement is correct)

0.75 indicates a likely event (third statement is correct)

fourth statement is incorrect (1 does not indicate an impossible event, but a certain event)

0.5 indicates equally likely to occur or not occur (fith statement is correct).

So, The statements second, Third and Fifth are correct statement related probabilities. which represent the 0.25 indicates an unlikely event and

0.75 indicates a likely event and 0.5 indicates equally likely to occur or not occur.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Given that the Probability of a chance event is a number between zero and one that expresses the likelihood of the event occurring, choose all that are correct.

•0 indicates a certain event

•0.25 indicates an unlikely event

•0.75 indicates a likely event

•1 indicates an impossible event

•0.5 indicates equally likely to occur or not occur.

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Answer:

Solution given:

volume

V=s³

if s=1/3 of units

new volume will be

V new=(1/3)³=1/27 or 0.037unit³ is your answer