The median of an odd data set is the value in the________of the ordered list. If the number of values is even, then the median is the ________ of the two middle values.

(f/g)(x) including the restrictions on the domain is: C. [tex](\frac{f}{g} )(x)=\frac{\sqrt[3]{4x} }{2x\;+\;3}[/tex], x ≠ -3/2.

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(f/g)(x) = (∛4x)/(2x + 3)

[tex](\frac{f}{g} )(x)=\frac{\sqrt[3]{4x} }{2x\;+\;3}[/tex]

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

2x + 3 ≠ 0

2x ≠ -3

x ≠ -3/2

In conclusion, we can reasonably infer and logically deduce that x must not be equal to -3/2.

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Answer:

C.   10

Step-by-step explanation:

The length of any side of a triangle must be between the difference and the sum of the lengths of the other two sides.

Difference of the lengths of the 2 given sides: 13 - 5 = 8

Sum of the lengths of the 2 given sides: 5 + 13 = 18

The third side of the triangle has a length between 8 and 18.

Answer: 10

Answer:

4 × 5 × 0 = 0, so 450 = 0.

Step-by-step explanation:

6 × 5 × 2 = 60

5 × 3 × 5 = 75

4 × 8 × 2 = 64

The relations should be classified according to whether or not they are functions as follows;

In Mathematics and Geometry, a function defines and represents the relationship that exists between two or more variables in a relation, table, ordered pair, or graph.

Part 1.

Based on the given relation -3x = 15, we can logically deduce that it does not represent a function because the input value is not related to an output value.

Part b.

Based on the given equation 2y = 10, we can logically deduce that it represents a function because it takes an input value.

Part c.

Based on the given equation 3x − 0.25y = 3, we can logically deduce that it represents a function because it takes all input values (domain).

Part d.

Based on the mapping diagram, we can logically deduce that it does not represent a function because the input value (d) has more than one output values (123 and 126).

Part e.

Based on the graph, we can logically deduce that it represents a function because it maps all input values or real numbers (domain) to y.

Part f.

Based on the given relation {(2, 3), (1, 3), (5, 3), (2, 6)}, we can logically deduce that it does not represent a function because the input value (x = 2) has more than one output values (y = 3 and y = 6).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

A woman invests $6,998.66 at 8% and about $24,001.34 at 9.5% .Let's assume that the amount invested at 8% is x dollars. Then the amount invested at 9.5% is (31,000 − x) dollars.The annual income from the investment at 8% would be 0.08x dollars.

Similarly, the annual income from the investment at 9.5% would be 0.095(31,000 − x) dollars.

As per the question, the investment at 9.5% provides $407.50 more income than the investment at 8%, so we can write this in equation form:0.095(31,000 − x) − 0.08x = 407.50.

Solve for x:

0.095(31,000 − x) − 0.08x = 407.50.2945(31,000 − x) − .08x = 407.503,027.50 − .2945x − .08x = 407.50.

Combine like terms :3,027.50 − .3745x = 407.50

Subtract 3,027.50 from both sides:− .3745x = − 2,620

Divide both sides by − .3745:x ≈ 6,998.66

We invested about $6,998.66 at 8% and (31,000 − 6,998.66) ≈ $24,001.34 at 9.5%.

Therefore, a woman invests $6,998.66 at 8% and about $24,001.34 at 9.5%.

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With the given information, the class intervals are 12-21, 22-31, 32-41 and 42-51. The frequency table has been attached.

To create a frequency table, you must first determine the class intervals.

In this case, it is already given as 10

The range of the data is from 12 to 50, and the difference is 38.

These are the class intervals

12-21

22-31

32-41

42-51

Now count the number of values that fall into each interval and create a table with the intervals and their corresponding frequencies

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Answer:

  (A, B, C, D) = (0, 1, -3, 1)

Step-by-step explanation:

You want the result of the first operation when using the Gauss-Jordan elimination method to find the inverse of the given 2×2 matrix.

As given in the question, you want to find -3R1 +R2 ⇒ R2. The result of this is shown in the first attachment. You can see there that ...

  (A, B, C, D) = (0, 1, -3, 1)

__

Additional comment

Similarly, the process is finished up by -2R2 +R1 ⇒ R1. The result of this is shown in the second attachment. The inverse matrix is the right half of the augmented matrix result.

<95141404393>

The inverse of the matrix [1 2] [3 7] is [7 -2] [-3 1].

To find the inverse of a 2 by 2 matrix, we can follow the method of augmenting the matrix with the identity matrix and performing Gauss-Jordan elimination. Let's use the matrix [1 2] and [3 7] as an example.

We start by augmenting the matrix with the 2 by 2 identity matrix:

[1 2 | 1 0]

[3 7 | 0 1]

Next, we perform Gauss-Jordan elimination to transform the left side of the augmented matrix into the identity matrix. We achieve this by applying elementary row operations while keeping the right side of the augmented matrix in sync.

By performing the necessary row operations, we can simplify the augmented matrix as follows:

[1 2 | 1 0] (Row 2 - 3 * Row 1)

[0 1 | -3 1] (Row 1 - 2 * Row 2)

Now, we have the left side of the augmented matrix as the identity matrix, while the right side gives us the inverse matrix:

[1 0 | 7 -2]

[0 1 | -3 1]

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Answer:

0.0138

Step-by-step explanation:

The probability of getting exactly 4 questions right by guessing can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials (17 questions), k is the number of successes (4 correct answers), p is the probability of success on a single trial (1/5 for guessing), and (n choose k) is the binomial coefficient.

Plugging in the values, we get:

P(X = 4) = (17 choose 4) * (1/5)^4 * (4/5)^13

P(X = 4) ≈ 0.0138 (rounded to four decimal places)

Therefore, the probability that the student will get exactly 4 questions right by guessing is approximately 0.0138.

The graph that represents a function among the options given is the last option. See image below.

To determine if a graph represents a function, check if any vertical line intersects the graph in more than one point. If every vertical line intersects the graph at most once, then the graph represents a function.

Considering the options given, the last option shown in the image given will have only one point intersected on the graph if we run a vertical line on it. The rest will have at more than one point.

Therefore, the graph that is a function is the last option.

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Answer:

357.08 in²

Step-by-step explanation:

In the problem, we are given two figures (a semicircle and a triangle). To find the area of the entire figure, we find the area of each figure and add them together.

Given information:

Area of a semi circle: 1/2 × r² × π

                                     1/2 × (10)² × π

                                     1/2 × 100 × π

                                     50π ≈ 157.08 in²

Area of a triangle: 1/2 × base × height

                               1/2 × 20 × 20

                               1/2 × 400

                               200 in²

As 10 is the radius of the semicircle, and the diameter of a semicircle is twice the radius, the height of the triangle is 2 × 10, or 20 inches.

Total area: Area of the semicircle + Area of the triangle

                  157.08 + 200

                  357.08 in²

Answer:

357.08 in²

Step-by-step explanation:

In the problem, we are given two figures (a semicircle and a triangle). To find the area of the entire figure, we find the area of each figure and add them together.

Given information:

   The radius of the semicircle: 10 in.

   The base and height of the triangle: 20in. (base) and 20 in. (height).

Area of a semi circle: 1/2 × r² × π

                                    1/2 × (10)² × π

                                    1/2 × 100 × π

                                    50π ≈ 157.08 in²

Area of a triangle: 1/2 × base × height

                              1/2 × 20 × 20

                              1/2 × 400

                              200 in²

As 10 is the radius of the semicircle, and the diameter of a semicircle is twice the radius, the height of the triangle is 2 × 10, or 20 inches.

Total area: Area of the semicircle + Area of the triangle

                 157.08 + 200

                 357.08 in²

Answer:

42 feet

Step-by-step explanation:

We are looking for the perimeter of a rectangle.

8 ft 4 in. + 8 ft 4 in = 16 feet 8 inches

12 ft + 8 in. + 12 ft 8 in = 24 ft 16 inches

16 ft  8 in + 24 ft 16 in = 40 feet 24 inches

24 inches is 2 feet

40 feet + 2 feet = 42 feet

To find the amount of fencing needed, calculate the perimeter of the garden. Given that the garden is 8 feet 4 inches wide and 12 feet 8 inches long, the total fencing required is 41 feet 4 inches.

To find out the amount of fencing needed to enclose the garden, we need to calculate the perimeter of the garden. The perimeter of a rectangle (which is our garden in this case) is calculated by adding together the lengths of all its sides. In this case, it is 8 feet 4 inches wide and 12 feet 8 inches long. Hence, the perimeter would be 2*(Length + Width). So, the total fencing required would be 2*((8 feet 4 inches) + (12 feet 8 inches)) = 2*(20 feet 12 inches) = 41 feet 4 inches. Therefore, you will need a fencing of 41 feet 4 inches to completely enclose the garden.

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The answer choices provided (A, B, C, D) accurately describes the effect on the area of the rhombus when it is dilated by a scale factor of 3.

When a rhombus is dilated by a scale factor of 3, the effect on the area can be determined by considering the relationship between the side lengths and the area of a rhombus.
In a rhombus, the area is given by the formula: Area = (diagonal1 * diagonal2) / 2.
Since the side lengths of the original rhombus are 5 units, we can find the length of the diagonals using the Pythagorean theorem.

The length of each diagonal is equal to the hypotenuse of a right triangle with legs of length 5/2 and 5/2.
Using the Pythagorean theorem, we can calculate the length of each diagonal to be approximately 5.59 units.
Now, when the rhombus is dilated by a scale factor of 3, the side lengths will be multiplied by 3, resulting in a new rhombus with side lengths of 15 units.
To find the length of the diagonals in the new rhombus, we multiply the length of the original diagonals (5.59 units) by the scale factor of 3, resulting in new diagonal lengths of approximately 16.77 units.
Substituting the new diagonal lengths into the formula for the area of a rhombus, we get:
Area = (16.77 * 16.77) / 2
= 140.95 square units.
Comparing the areas of the original rhombus and the dilated rhombus, we can conclude that the new rhombus has an area approximately 28.19 times as big as the original rhombus.
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The dot product between the vectors is:

<5, 3>.<12, 4> =72

To find the dot product, just multiply the correspondent components between the two vectors and then add them, here the two vectors are u= <5,3>, w= <12,4>​

For the dot product we will get:

<5, 3>.<12, 4> = 5*12 + 3*4 = 60 + 12 = 72

The dot product between the vectors U and W is 72.

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From the table with positive integers in row D and move to the right, writing each consecutive integer until we reach row G, the number 1998 is in column E.

To see this, start by counting the number of integers that are written in row D. There are 4 integers in row D, so the first integer in row E is 5.

The next 4 integers are written in row A, so the first integer in row F is 9.

The next 4 integers are written in row G, so the first integer in row B is 13.

Can continue in this way to see that the first integer in row C is 17, the first integer in row D is 21, and the first integer in row E is 25.

Therefore, the number 1998 must be in column E.

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There are approximately 1.0875 milligrams of iron in 87 grams of food that contains 0.00125% iron.

To find the amount of iron in 87 grams of food, we first need to convert the percentage into a decimal. The food contains 0.00125% iron, which is equivalent to 0.0000125 as a decimal.

Next, we multiply the decimal by the weight of the food to determine the amount of iron in grams. So, 0.0000125 x 87 = 0.0010875 grams of iron.

Since we want the answer in milligrams, we need to convert grams to milligrams. There are 1,000 milligrams in one gram. Therefore, 0.0010875 grams is equal to 1.0875 milligrams.

It's worth noting that this calculation assumes a homogeneous distribution of iron throughout the food sample. In reality, the iron content may vary within different parts of the food or across different food items.

Additionally, the accuracy of the iron content measurement and the precision of the percentage value provided can also impact the final result.

Therefore, it's always advisable to consult reliable sources or conduct laboratory tests for precise and accurate nutrient information.

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Answer:

Step-by-step explanation:

There is only one different way to start with the letter $A$ and move from letter to letter to spell the word "ARCH".

In the given array, we need to find the number of different ways we can start with the letter $A$ and move from letter to letter (horizontally, vertically, or diagonally) to spell the word "ARCH". Let's break down the problem step by step.
Step 1: Locate the letter $A$ in the array. In this case, the letter $A$ is located at position (0,0).
Step 2: From the letter $A$, we can move to any adjacent letter (horizontally, vertically, or diagonally). In this case, we can move to the letters $C$ and $H$, which are adjacent to $A$.
Step 3: From the letter $C$, we can move to the letter $H$, which is adjacent to $C$.
Step 4: From the letter $H$, we can move to the letter $R$, which is adjacent to $H$.
Step 5: From the letter $R$, we cannot move to any letter adjacent to $R$ that would help us spell the word "ARCH". Therefore, this path is a dead end.
Step 6: Now, let's go back to the letter $H$ and explore other possible paths. From the letter $H$, we can move to the letter $C$.
Step 7: From the letter $C$, we can move to the letter $H$, which is adjacent to $C$. This creates a loop and we will end up repeating the same path as before.
Step 8: Since we have exhausted all possible paths, we have found that there is only one way to start with the letter $A$ and move from letter to letter to spell the word "ARCH" in the given array.

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Step-by-step explanation:

To DIVIDE by a fraction, flip the fraction and MULTIPLY

7 / (3/8)  = 7 * 8/3  = 56 / 3 = 18  2/3

COS 2/3 ≠ cos 5/3. The reason for this is because the angles themselves are different, resulting in different cosine values when evaluated using the unit circle.

To start, let's first understand what COS represents. COS is an abbreviation for cosine, which is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse in a right triangle.
Now, let's examine the given values, 2/3 and 5/3. These values represent the angles in radians. In trigonometry, an angle is typically measured in radians, not degrees.
In the case of COS 2/3, it means we are considering an angle of 2/3 radians. Similarly, COS 5/3 represents an angle of 5/3 radians.
To determine if COS 2/3 is equal to cos 5/3, we need to evaluate the cosine of each angle.
By using the unit circle, we can find the cosine values for each angle. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane.
When we evaluate the cosine of 2/3 radians on the unit circle, we find a specific point on the circle that corresponds to the cosine value. Similarly, for 5/3 radians, we find another point on the unit circle that corresponds to the cosine value.
Since these two points are different on the unit circle, it means that the cosine values for 2/3 and 5/3 radians are not equal.

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I. The m∠ABC to one half of the mAC.

II. The measure of mAC is 80°.

III. The measure of mABC is 280°.

In Mathematics and Geometry, the inscribed angle of a circle is equal to half of the central angle of a circle. In this context, we can logically deduce that the angle subtended by major arc ABC is equal to one half of the minor arc AC;

m∠ABC = 1/2(mAC)

Part II.

Based on the relationship that we established in Part I above, the measure of minor arc AC can be calculated as follows;

m∠ABC = 1/2(mAC)

mAC = 2m∠ABC

mAC = 2(40)

mAC = 80°.

Part III.

Based on the relationship that we established in Part II above, the measure of major arc ABC can be calculated as follows;

mABC + mAC = 360°

mABC = 360° - mAC

mABC = 360° - 80

mABC = 280°.

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Complete Question:

An arc is a smooth piece of a circle. A major arc of a circle is an arc that is longer than half the circumference of the circle. Find the measure of the major arc ABC.

Part I: The m∠ABC is equal to/one half of the mAC. (Circle one) (1 point)

Part II: Using the relationship you established in Part I, find the mAC. Show your work and explain

your answer. (2 points)

Part III: Using your answer from Part II, find the mABC. Show your work. (2 points)

The no-par value stock does not have a designated par value, so the entry only reflects the issuance of the shares and the corresponding cash received.

When Hip-Hop Architecture issues 1,000 shares of its $1 par value common stock at $21 per share, the entry to record the issuance of the stock would be as follows:

Date: [Date of issuance]

Common Stock (1,000 shares x $1 par value)

Cash (1,000 shares x $21 per share)

[To record the issuance of 1,000 shares of $1 par value common stock at $21 per share]

If Hip-Hop issued no-par value stock, the entry would differ as follows:

Date: [Date of issuance]

Common Stock (1,000 shares)

Cash (1,000 shares x $21 per share)

[To record the issuance of 1,000 shares of no-par value common stock at $21 per share]

In this case, the no-par value stock does not have a designated par value, so the entry only reflects the issuance of the shares and the corresponding cash received.

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The zeros and the multiplicities are

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

f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³

The power of each factor are the multiplicities

So, we have

Zero(s) of multiplicity one:

x - 6 = 0

Zero(s) of multiplicity two:

x - 11 = 0

Zero(s) of multiplicity three:

x + 6 = 0 and x + 5 = 0

When evaluated, we have

Zero(s) of multiplicity one:

x = 6

Zero(s) of multiplicity two:

x = 11

Zero(s) of multiplicity three:

x = -6 and x = -5

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The possible numbers of pounds Keisha will buy are p < 7, where p represents the number of pounds. In interval notation, it can be written as (0, 7).

Let p be the number of pounds Keisha will buy. Since the candy costs $8 per pound, the total cost will be 8p dollars.

According to the given information, Keisha will spend less than $56 on candy. We can express this as an inequality:

8p < 56

To solve for p, we divide both sides of the inequality by 8:

p < 7

Therefore, the possible numbers of pounds Keisha will buy are any value of p that is less than 7. In interval notation, this can be written as (0, 7).

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The correct statement regarding the exponential function in this problem is given as follows:

D. Decay, (0,3).

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The function for this problem is given as follows:

[tex]f(x) = 3\left(\frac{1}{2}\right)^x[/tex]

Then the parameter values are given as follows:

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The largest absolute value is |29,400|, and the smallest absolute value is |667|.

The given expression |3 × 10^4 - 6 × 10^2| equals |30000 - 600|, which simplifies to |29,400|. This represents the largest possible absolute value using the digits 1 to 9. It is the largest because it maximizes the value by using the highest digits (9 and 8) in the tens of thousands and hundreds places, respectively.

To find the smallest possible answer, we need to arrange the remaining digits (1, 2, 3, 4, 5, 6, and 7) to minimize the value. Since we want to subtract the largest possible number from the smallest, we arrange the digits in ascending order, resulting in |1,234 - 567|.

Calculating this expression gives us |667|, which represents the smallest possible absolute value using the remaining digits. It is the smallest because it minimizes the value by using the lowest digits (1, 2, 3, 4, 5, 6, and 7) in their respective places.

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The difference between simple and compound interest is given as follows:

Simple interest is paid on the principal, while compound interest is paid on the principal and interest accrued.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

Hence the interest amount is given as follows:

I(t) = Prt.

Which is paid over the principal.

For compound interest, the equation is given as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

As the function is exponential, it is also paid over the amount earned.

The options are given as follows:

O Simple interest is paid on small, short-term loans, while compound interest is paid on large, long-term loans.

O Simple interest is paid on the principal, while compound interest is paid on the principal and interest accrued.

Simple interest is paid on large, long-term loans, while compound interest is paid on small, short-term loans.

O Simple interest is paid on the principal and interest accrued, while compound interest is paid only on the principal.

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Answer:

4 1/4

Step-by-step explanation:

additive inverse of -4 1/4 would be 4 1/4

as additive inverse is the number which when added to the original number results in zero so in this case the additive inverse would be 4 1/4 which when added to -4 1/4 will result in zero

Answer: [tex]4 \frac{1}{4}[/tex]

Step-by-step explanation:

The additive inverse of a number is defined as a pair number that, when both added together, result in a sum of zero.

[tex]-4\frac{1}{4} + 4\frac{1}{4} = 0[/tex]

Answer:

B.  10

Step-by-step explanation:

A:

cost = 20 + 3x

B:

cost: 30 + 2x

20 + 3x = 30 + 2x

x = 10