Which best describes the range of possible values for the third side of the triangle?x < 12.5, x > 18.912.5 < x < 18.9x < 6, x > 266 < x < 26

Answer: 243

Step-by-step explanation:

To find f(g(9)), we need to first substitute g(9) into the function f(x), and then evaluate the resulting expression.

Given that g(x) = 3√x, we can replace x with 9 (since we're looking for g(9)) in the expression for g(x):

g(9) = 3√9

Simplifying the square root of 9, we get:

g(9) = 3 * 3

g(9) = 9

Now, we can substitute g(9) into the function f(x) = x^3/3, replacing x with 9:

f(g(9)) = (9)^3/3

Using the exponent rule for cube, we get:

f(g(9)) = 729/3

Simplifying the division, we get:

f(g(9)) = 243

So, the value of f(g(9)) is 243.

The percent probability that a person likes blue​ pens is 30%, Black​ pens are liked by 44.8%, and Pencils are liked by 301 people.

Part 1:

To find the percent probability that a person likes blue pens, we need to divide the number of people who like blue pens by the total number of people surveyed and multiply by 100:

P(blue pens) = (75/250) x 100%

= 30%

Therefore, the percent probability that a person likes blue pens is 30%.

Part 2:

To find the percent probability that a person likes black pens, we use the same formula:

P(black pens) = (112/250) x 100%

= 44.8%

Therefore, the percent probability that a person likes black pens is approximately 44.8%.

Estimating the number of people who like pencils or black pens in a survey of 400 people:

To estimate the number of people who like pencils or black pens in a survey of 400 people, we can assume that the proportion of people who like pencils or black pens in the larger sample of 250 people is the same as in the smaller sample of 400 people.

The estimated number of people who like pencils or black pens in a survey of 400 people is:

(63 + 112)/250 x 400 = 300.8

Therefore, we can estimate that about 301 people in a survey of 400 people would say they like pencils or black pens.

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It takes 7/5 hours to paint one room.

To find the time it takes to paint one room, we need to determine the reciprocal of the fraction representing the number of rooms painted per hour.

If it takes 3/7 hours to paint 3/5 of a room, then the fraction representing the rate of painting is (3/5) / (3/7). To divide fractions, we multiply by the reciprocal of the second fraction. Therefore:

(3/5) / (3/7) = (3/5) * (7/3) = (3 * 7) / (5 * 3) = 21/15

So, it takes 21/15 hours to paint one room. This can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

21/15 = (21/3) / (15/3) = 7/5

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Answer:

False

Step-by-step explanation:

A line is a simple geometric shape that extends in both the directions, but a line segment has two defined endpoints. So, the answer is false. My mistake.

Answer:

line segment have 2 end points and a line has no end pionts so it just keeps going so False

Step-by-step explanation:

false

The only value of k that makes Ax=0 have non-trivial solutions is k=0. Option (C) is the correct answer.

To determine the values of k such that Ax=0 has non-trivial solutions, we need to find the values of k that make the determinant of the matrix A equal to zero.

This is because the determinant of A is equal to the product of its eigenvalues, and a non-trivial solution exists when at least one of these eigenvalues is zero.
Using the formula for the determinant of a 3x3 matrix, we have:
det(A) = 1 x (-20k) - 0 x (-8k) + 4 x (-2)(-2k) = -20k + 16k = -4k
Setting det(A) equal to zero, we get:
-4k = 0
Solving for k, we get:
k = 0
To find the values of k, if any, such that Ax=0 has non-trivial solutions, we need to find the values of k that make the matrix A singular, i.e., that make the determinant of A equal to 0.

If the determinant of A is not 0, then the only solution to Ax=0 is the trivial solution (x=0).

Using the formula for a 3x3 determinant, we have:

det(A) = 1 x  (1 x (-10k) - 4 x (-2k)) - 0 x (0 x (-10k) - 4 x (-2))) + 4 x  (0 x (-2k) - 1 x (-2)))

det(A) = 10k - 8k

det(A) = 2k

So, the determinant of A is equal to 2k.

If 2k = 0, then det(A) = 0 and the matrix A is singular.

This occurs when k = 0.
Therefore, the only value of k that makes Ax = 0 have non-trivial solutions is k=0. Option (C) is the correct answer.

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(A ∩ D) ∩ B' can be rewritten as (tax returns with itemized deductions AND selected for audit) AND (tax returns NOT showing business income).

In words, (A ∩ D) ∩ B' refers to the set of tax returns that meet the following criteria: they have itemized deductions and were selected for audit, but they do not show business income.

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The probability that Hannah's number is an even palindrome is 1/45.

There are 45 even palindrome numbers between 1000 and 9999, out of a total of 4500 possible 4-digit numbers.

So, the probability of Hannah writing an even palindrome number is 1/45.

A palindrome number is the same when read from left to right or right to left. There are 90 possible 2-digit palindrome numbers (11, 22, 33, etc.), and 9 possible 1-digit palindrome numbers (1, 2, 3, etc.), making a total of 99 palindrome numbers from 1 to 999. In a 4-digit number, the first and last digits must be the same for it to be a palindrome.

Therefore, the first digit has 9 choices (1-9), and the last digit also has 9 choices. The second digit can be any of the 10 digits (0-9), and the third digit can be any of the 5 remaining even digits (0, 2, 4, 6, 8).

Thus, there are 45 even palindrome numbers between 1000 and 9999.

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One way to summarize hotel costs versus quality ranking in New York City is by using a scatter plot graph. The x-axis represents the cost per night, and the y-axis represents the quality ranking. This graph allows for easy visual comparison between the two variables.

A scatter plot graph is an effective way to summarize the relationship between hotel costs and quality rankings in New York City.

By plotting the cost per night on the x-axis and the quality ranking on the y-axis, viewers can easily see the relationship between the two variables. Hotels with higher quality rankings and lower costs per night will appear in the upper left-hand corner of the graph, while hotels with lower quality rankings and higher costs per night will appear in the lower right-hand corner.

By using a scatter plot graph, the travel website can provide valuable information to users who are looking to compare hotel costs and quality rankings in New York City.

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The area of the sector FGH of the given circle with center G is 120.93 to the nearest hundredth.

Given a circle G.

Two radius are joined at G to form FGH.

Here,

FG and GH are radius.

Length of FG = Length of GH = 13

Measure of ∠FGH = 82°

The formula to find the area of the sector is,

Area of sector = (x / 360°) πr²

x = 82°

r = 13

Area of sector FGH = (82/360) π (13)²

                                 = 120.93

Hence the area of the sector is 120.93.

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In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.

The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.

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We have shown both implications, and we can conclude that tu is self-adjoint if and only if tu = ut.

To prove that tu is self-adjoint if and only if tu = ut, we need to show two implications:

If tu is self-adjoint, then tu = ut.

If tu = ut, then tu is self-adjoint.

Let's prove each implication separately:

If tu is self-adjoint, then tu = ut:

To show this, we need to consider the definition of a self-adjoint operator. An operator T is self-adjoint if it satisfies the property ⟨Tv, u⟩ = ⟨v, Tu⟩ for all vectors v and u in the inner product space.

Now, let's apply this definition to tu:

⟨tu v, u⟩ = ⟨v, tu u⟩

Since tu is self-adjoint, we have:

⟨tu v, u⟩ = ⟨v, ut u⟩

Now, since this holds for all vectors v and u, we can conclude that tu = ut.

If tu = ut, then tu is self-adjoint:

To show this, we need to verify that ⟨tu v, u⟩ = ⟨v, tu u⟩ for all vectors v and u.

Using the assumption tu = ut, we have:

⟨tu v, u⟩ = ⟨ut v, u⟩

Since u and v are vectors, we can swap their order inside the inner product:

⟨tu v, u⟩ = ⟨v, ut u⟩

Again, since this holds for all vectors v and u, we can conclude that tu is self-adjoint.

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The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.

We have,

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]

Simplify the expression, then we have

⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]

⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]

⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]

⇒ (x² + 2x - 1) / 7(x + 5)

The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.

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- Span{v1, v2, v3, 0} is equal to the span of {v1, v2, v3}.
- Span{v1, v1-v2, v3} is equal to the span of {v1, v2, v3}.
- Span{v1, v2} is NOT equal to the span of {v1, v2, v3}.

Let's analyze each of the sets of vectors to determine if they are equal to the span of {v1, v2, v3}:
1. Span{v1, v2, v3, 0}:
This set is equal to the span of {v1, v2, v3} because adding the zero vector (0) does not affect the linear independence or the span of the other vectors.

A span is the set of all possible linear combinations of the vectors, and since the zero vector does not change the linear combinations, the span remains the same.
2. Span{v1, v1-v2, v3}:
This set is also equal to the span of {v1, v2, v3}.

The reason is that the vector (v1-v2) can be written as a linear combination of v1 and v2: (v1-v2) = 1*v1 + (-1)*v2.

Since all vectors in this set can be expressed as linear combinations of {v1, v2, v3}, the span remains the same.
3. Span{v1, v2}:
This set is NOT equal to the span of {v1, v2, v3} because it is missing the vector v3.

Since v1, v2, and v3 are linearly independent, removing one of them (v3 in this case) means that the set cannot span the same space as {v1, v2, v3}.

It has a lower dimension, and therefore, the span is different.

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By using PEMDAS, the value of solution is,

⇒ 12 /5

We have to given that;

Expression is,

⇒ (6 (3 - 5 + 4) / (4 + (3 - 4)²)

Now, By using PEMDAS, the value of solution is,

⇒ (6 (3 - 5 + 4) / (4 + (3 - 4)²)

⇒ (6 (3 - 5 + 4) / (4 + (- 1)²)

⇒ (6 (7 - 5)) / (4 + 1))

⇒ (6 × 2) / 5

⇒ 12 / 5

Thus, By using PEMDAS, the value of solution is,

⇒ 12 /5

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The electric field pierces the cylinder at the points where the field lines intersect the surface of the cylinder. The location of these intersections depends on the geometry of the cylinder and the distribution of charges.

For example, if the cylinder has a uniform charge distribution, the electric field lines will be perpendicular to the surface of the cylinder and will intersect it at every point. If the cylinder has a non-uniform charge distribution, the electric field lines may be curved and the intersections may occur at different angles.It is also possible for the electric field to pass through the center of the cylinder, which is known as the axial field.

This occurs when the charges are distributed symmetrically around the cylinder.Overall, the location of the electric field piercing the cylinder depends on the specific conditions of the system and can be determined using mathematical equations and physical principles such as Coulomb's Law and Gauss's Law.

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The farmer is selling 2.656 kg of apples and 5.644 kg of pears at the farmers market.

Let's start by figuring out how many kilograms of apples are being sold. We're told that 2/5 of the weight is apples, so we can set up an equation:

2/5 * 8.3 kg = x

Simplifying the left side, we get:

16/50 * 8.3 kg = x

Multiplying 16/50 by 8.3, we get:

2.656 kg = x

So the farmer is selling 2.656 kg of apples. To find the weight of the pears, we can subtract this amount from the total weight:

8.3 kg - 2.656 kg = 5.644 kg

So the farmer is selling 2.656 kg of apples and 5.644 kg of pears at the farmers market.

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Answer: The term "unit square" refers to a square with sides that have a length of one unit. By convention, the unit used is often determined by the context of the problem or measurement being made. For example, if we are measuring the area of a rectangular field in feet, we might use a unit square that is one foot by one foot, or 1 square foot. If we are measuring the area of a room in meters, we might use a unit square that is one meter by one meter, or 1 square meter.

The term "square unit" is used to refer to the units used to measure area. So, when we say that the area of a field is 120 square feet, we mean that the area can be divided into 120 unit squares, each with an area of 1 square foot.

Using unit squares to measure area allows us to easily compare the sizes of different areas and to perform calculations involving area. For example, if we want to find the area of a triangle, we can divide the triangle into smaller shapes (such as rectangles or triangles) and then count the number of unit squares needed to fill those shapes. We can then add up the areas of the smaller shapes to find the total area of the triangle, all in square units.

P(A) / P(A|B) can be expressed as P(A and B) / P(B).

The expression P(A) / P(A|B) represents the ratio of the probability of event A occurring to the conditional probability of A given that event B has occurred.

Using Bayes' theorem, we can express P(A|B) in terms of P(A and B) and P(B) as:

P(A|B) = P(A and B) / P(B)

Rearranging this equation, we get:

P(A and B) = P(A|B) * P(B)

Substituting this expression for P(A and B) in the original ratio, we get:

P(A) / P(A|B) = P(A) / (P(A and B) / P(B))

= P(A) * P(B) / P(A and B)

Therefore, we can express P(A) / P(A|B) as P(A and B) / P(B).

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If the slope of line m is 1/25, the slope of line p include the following; A. 1/25.

In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Mathematics and Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of these two lines are equal and the same, and as such, we have the following:

Slope of line m = Slope of line p

1/25 = 1/25

In conclusion, we can reasonably infer and logically deduce that the slope of line p is equal to 1/25.

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It will cost £768 to paint the outside of the box.

To calculate the cost of painting the outside of the box, we need to find the surface area of the box and then multiply it by the cost per square centimeter of paint.

The surface area of a rectangular box can be calculated by adding the areas of all its faces.

The box has six faces:

Top and bottom face: Length x Width

Two side faces: Length x Height

Front and back faces: Width x Height

Let's calculate the surface area of the box:

Top and bottom face: 80cm x 10cm = 800cm²

Two side faces: 80cm x 20cm = 1600cm²

Front and back faces: 10cm x 20cm = 200cm²

Total surface area of the box: 2(800cm²) + 2(1600cm²) + 2(200cm²) = 4800cm²

Now, we can calculate the cost of painting the outside of the box by multiplying the surface area by the cost per square centimeter of paint:

Cost = Surface Area x Cost per cm²

Cost = 4800cm² x £0.16/cm²

Calculating the cost:

Cost = 4800cm² x £0.16/cm²

Cost = £768

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A relationship where the minimum and maximum cardinality are both one is a one-to-one relationship. This type of relationship means that each entity in one entity set is associated with only one entity in the other entity set, and vice versa.

One-to-one relationships are often used in database design to enforce uniqueness and prevent data redundancy. They are commonly used when one entity has a unique identifier that can only be associated with one other entity. For example, in a database for a hospital, each patient may have only one unique medical record, and each medical record may be associated with only one patient.

In contrast, a one-to-many relationship allows each entity in one entity set to be associated with multiple entities in the other entity set, but each entity in the other entity set can only be associated with one entity in the first entity set. A many-to-many relationship allows each entity in both entity sets to be associated with multiple entities in the other entity set.

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A relationship where the minimum and maximum cardinality are both one is a one-to-one relationship. This type of relationship means that each entity in one entity set is associated with only one entity in the other entity set, and vice versa.

One-to-one relationships are often used in database design to enforce uniqueness and prevent data redundancy. They are commonly used when one entity has a unique identifier that can only be associated with one other entity. For example, in a database for a hospital, each patient may have only one unique medical record, and each medical record may be associated with only one patient.

In contrast, a one-to-many relationship allows each entity in one entity set to be associated with multiple entities in the other entity set, but each entity in the other entity set can only be associated with one entity in the first entity set. A many-to-many relationship allows each entity in both entity sets to be associated with multiple entities in the other entity set.

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Military or computer time, also known as the 24-hour clock, is a method of timekeeping that represents the hour of the day using a single continuous count of 24 hours. This system avoids the ambiguity that can arise from using the 12-hour clock, which uses AM and PM notations. In the 24-hour clock, hours are numbered from 00 to 23, and minutes are numbered from 00 to 59.

To convert 6:20 AM to military time, you can simply represent the hour "6" with "06" and keep the minutes "20" unchanged, as morning hours are the same in both systems. Therefore, 6:20 AM in military time is 06:20.

For converting 2:30 PM, you need to add 12 hours to the hour part of the time, as military time counts hours continuously from 0 to 23. In this case, 2 + 12 = 14, so the hour becomes "14". The minutes "30" remain unchanged. Thus, 2:30 PM in military time is 14:30.

In summary, 6:20 AM and 2:30 PM in military/computer time are 06:20 and 14:30, respectively.

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It would take approximately 723.1 minutes to lay 500 bricks.

We can use the formula for direct variation which is:

y = kx

where y is the dependent variable, x is the independent variable, and k is the constant of variation.

In this case, the number of bricks laid is the dependent variable and the amount of time spent is the independent variable.

To find k, we can use the given information that 45 bricks are laid in 65 minutes:

45 = k * 65

Solving for k, we get:

k = 45/65 = 0.6923

Now we can use k to find how many minutes it would take to lay 500 bricks:

500 = 0.6923x

Solving for x, we get:

x = 723.1 minutes

Therefore, it would take approximately 723.1 minutes to lay 500 bricks.

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Answer:

C = 2(7π) = 14π = 43.98 ft

Mariah will need at least 44 feet of fence.

The probability that he rolls a sum equal to 4 is 3 / 36 or 1 / 12. Then the correct option is B.

Given that:

Two dice are rolled.

The total number of samples is calculated as,

⇒ 6²

⇒ 6 x 6

⇒ 36

The sample space for two dice is given as,

(1, 1),  (1, 2),  (1, 3),  (1, 4),  (1, 5),  (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

The probability is given as,

P = (Favorable event) / (Total event)

The probability that he rolls a sum equal to 4 is calculated as,

P = 3 / 36

P = 1 / 12

Thus, the correct option is B.

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Answer:

You can use additive inverse to combine like terms that are on the opposite sides of the equation.

Step-by-step explanation:

Example:

3x + 1 = 6x - 12

You can use additive inverse to move -12 to the +1.

Paul can type 16 pages in one hour and 80 pages in five hours.

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Answer: To find the percentage of bad units, we need to divide the number of bad units by the total number of units and then multiply by 100 to get the percentage.

Percentage of bad units = (number of bad units / total number of units) x 100

In this case, the total number of units is 256 and the number of bad units is 29.

Therefore, the percentage of bad units is approximately 11.33%.

Prism B could have a rectangular base with dimensions l and w, where lw = s^2. Alternatively, Prism B could have a base with a different shape, such as a triangle or a circle, as long as the area of the base and the height are chosen such that the volume is equal to that of Prism A.

Since the volume of Prism A and Prism B are the same, the dimensions of Prism B will depend on the dimensions of Prism A. The volume of a prism is calculated by multiplying the area of the base by the height of the prism. Therefore, if we assume that Prism A has a base area of A and a height of h, then the volume of Prism A is given by V = Ah.

To find the dimensions of Prism B, we can start by considering different shapes for its base. For example, if Prism A has a square base with side length s, then its area is A = s^2. If Prism B has a rectangular base with length l and width w, then its area would be A = lw. To ensure that Prism B has the same volume as Prism A, we can set V = Ah = lw*h, which simplifies to lw = s^2.

Therefore, Prism B could have a rectangular base with dimensions l and w, where lw = s^2. Alternatively, Prism B could have a base with a different shape, such as a triangle or a circle, as long as the area of the base and the height are chosen such that the volume is equal to that of Prism A.

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If Prism A and Prism B have the same volume, what could be the dimensions of Prism B?