If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours

The formula for v(x) is v(x) = 2x - 3, and its domain is all real numbers. The formula for w(x) is w(x) = 5x + 4, and its domain is also all real numbers.

To find the formulas and domains for v(x) = s(x) / t(x) and w(x) = t(x) / s(x), we will substitute the given expressions for s(x) and t(x) into the respective formulas.

Let's start with v(x) = s(x) / t(x):

v(x) = (2x - 3) / (5x + 4)

To simplify the expression, we need to find a common denominator for the numerator and denominator:

v(x) = (2x - 3) / (5x + 4) * (1 / 1)

Now, we can multiply the numerator and denominator by the conjugate of the denominator, which is (5x + 4):

v(x) = (2x - 3) * (1 / (5x + 4)) * ((5x + 4) / (5x + 4))

Expanding the expression, we have:

v(x) = (2x - 3) * (5x + 4) / (5x + 4)

Canceling out the common factor of (5x + 4), we get:

v(x) = (2x - 3)

Therefore, the formula for v(x) is v(x) = 2x - 3.

To determine the domain of v(x), we need to consider any values of x that would make the denominator (5x + 4) equal to zero. However, in this case, there is no such value since the denominator is a linear function that never equals zero. Therefore, the domain of v(x) is all real numbers.

Now, let's find w(x) = t(x) / s(x):

w(x) = (5x + 4) / (2x - 3)

Following a similar process, we can simplify the expression:

w(x) = (5x + 4) / (2x - 3) * (1 / 1)

Multiplying the numerator and denominator by the conjugate of the denominator, which is (2x - 3):

w(x) = (5x + 4) * (1 / (2x - 3)) * ((2x - 3) / (2x - 3))

Expanding the expression, we have:

w(x) = (5x + 4) * (2x - 3) / (2x - 3)

Canceling out the common factor of (2x - 3), we get:

w(x) = 5x + 4

Therefore, the formula for w(x) is w(x) = 5x + 4.

Similar to v(x), the domain of w(x) is all real numbers since there are no values of x that would make the denominator (2x - 3) equal to zero.

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. When the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.

Average and rms values for the function y(t)=25+10sin6πt over the time periods (a) 0 to 0.1 s, (b) 0.4 to 0.5 s, (c) 0 to 1/3 s, and (d) 0 to 20 s are as follows:

a) For t=0 to t=0.1s:

Average value, y_avg = 25

RMS value, y_RMS = 25.1987

Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.

b) For t=0.4 to t=0.5s:

Average value, y_avg = 25

RMS value, y_RMS = 28.2843

Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.

c) For t=0 to t=1/3 s:

Average value, y_avg = 25

RMS value, y_RMS = 23.7176

Comment: RMS value is less than the average value. This means that the signal has a lesser amount of high-frequency content. It can be inferred that the function y(t) oscillates slowly.

d) For t=0 to t=20 s:

Average value, y_avg = 25

RMS value, y_RMS = 25

Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. Comment on the nature and meaning of the results in terms of analysis of dynamic signals.The results indicate that the function y(t) oscillates rapidly at the start and end of the time period and slowly in the middle. When the RMS value is greater than the average value, it means that the signal has a considerable amount of high-frequency content.

On the other hand, when the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.

Furthermore, if the RMS value is equal to the average value, it means that the signal does not have any high-frequency content.

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The function of the town's population is an exponential growth

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

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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Answer:

x = √11

Step-by-step explanation:

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

=> x² - 3x + 3x - 9 = 2

=> x² - 9 = 2

=> x² = 11

=> x = √11

Hoped this helped.

Answer:

Solutions below.

Step-by-step explanation:

This question tests on the concept of Composite Functions

Composite functions are functions that is derived from another new and separate function.

Example: f(x) = 5x, g(x) = 9x , (f • g)(x) = f(g(x)) = f(9x) = 5(9x) = 45x

Given to us are 2 functions:

f(x) =

\( {x}^{2} - 7x + 4\)

g(x) =

\( - 2x\)

We are asked to find (f • g)(4). We first find (f • g)(x).

(f • g)(x) = f(g(x)) = f(-2x) =

\( {( - 2x)}^{2} - 7( - 2x) + 4 \\ = 4 {x}^{2} + 14x + 4 \\ = 2(2 {x}^{2} + 7x + 2)\)

Now, we will find the value of (f • g)(4) by substituting x = 4 into (f • g)(x).

(f • g)(4) =

\(2(2 {(4)}^{2} + 7(4) + 2) \\ = 2(2(16) + 28 + 2) \\ = 2(32 + 28 + 2) \\ = 2(62) \\ = 124\)

Answer:

20 counters.

Step-by-step explanation:

50/200 or 1/4 of the counters have white paint on them.

That means you can expect 1/4 of the 80 counters pulled out to have white paint on them or 20 counters.

Answer:

The distance between two points

d = \(\sqrt{289}\)  = 17

Step-by-step explanation:

Explanation:-

Given points are ( 7,-1) and (-8,-9)

The distance between the two points

d =  \(\sqrt{(x_{2}-x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

d = \(\sqrt{(( (-8- 7 )^{2}+(-9-(-1))^{2} ) }\)

\(d = \sqrt{(( (-15 )^{2}+(-8)^{2} ) }\\d = \sqrt{225+64}\)

d = \(\sqrt{289}\)

d = 17

The distance between two points

d = 17

Answer:

Step-by-step explanation:

45.6

Answer:

width = 15 inches

length = 30 inches

Step-by-step explanation:

\(\sf \boxed{\text{\bf Perimeter of rectangle =2*length + 2*width}}\)

  Let width = x inches

     Length =  2*x = 2x inches

                 Perimeter = 90 inches

2 *length  + 2* width = 90

            2*2x  + 2*x     = 90

                   4x + 2x    = 90

Combine like terms,

                             6x = 90

Divide both sides by 6,

                                x = 90/6

                                x = 15

Dimensions:

Width = 15 inches

Length = 2*15 = 30 inches.

To prove the statement by contrapositive, we assume the negation of the consequent and prove the negation of the antecedent.

Statement: For every pair of real numbers x and y, if x + y is irrational, then x or y is irrational.

Contrapositive: For every pair of real numbers x and y, if x and y are rational, then x + y is rational.

Proof:

Assume x and y are rational numbers. By definition, a rational number can be expressed as a ratio of two integers, say x = a/b and y = c/d, where a, b, c, and d are integers and b ≠ 0, d ≠ 0.

Now consider the sum x + y:

x + y = (a/b) + (c/d) = (ad + bc)/(bd)

Since ad + bc is an integer (as the sum of integers), and bd is a nonzero integer (as the product of nonzero integers), we can conclude that x + y is a rational number.

Therefore, we have proven the contrapositive of the statement.

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To prove the statement by contrapositive, we assume the negation of the consequent and prove the negation of the antecedent.

Statement: For every pair of real numbers x and y, if x + y is irrational, then x or y is irrational.

Contrapositive: For every pair of real numbers x and y, if x and y are rational, then x + y is rational.

Proof:

Assume x and y are rational numbers. By definition, a rational number can be expressed as a ratio of two integers, say x = a/b and y = c/d, where a, b, c, and d are integers and b ≠ 0, d ≠ 0.

Now consider the sum x + y:

x + y = (a/b) + (c/d) = (ad + bc)/(bd)

Since ad + bc is an integer (as the sum of integers), and bd is a nonzero integer (as the product of nonzero integers), we can conclude that x + y is a rational number.

Therefore, we have proven the contrapositive of the statement.

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Moving the vertices does not affect the relationship between the diagonals. They bisect each other in all cases.

Answer:

Despite changing the vertices, the opposite sides and opposite interior angles of the parallelogram remain equal.

Step-by-step explanation:

PLATO AWNSER

Answer:

3 gallons of water

Step-by-step explanation:

1 gallon = 8 pints

24 pints of water (bottles) divided by 8 would be 3

therefore 24 pints of water is equivelant to 3 gallons of water.

Answer:

9

Step-by-step explanation:

in order to find the range of a given set of numbers, you find the difference between the biggest and smallest numbers. So here, it would be -9 and 0. The range is 9.

Answer:

First find slope. m = (y2 - y1)/(x2 - x1) = (6 -1)/(-6 --3) = 5/-3. then. use. y - y1 =. m (x - x1). which gives. y - 1 = -5/3(x - 3)

Step-by-step explanation:

Given:

The pyramid has base sides measurements 6 cm and slant height 8 cm.

Required:

What is the surface area of the pyramid?

Explanation:

The surface afrea formula fo pyramid:

We have base sides equal 6 cm and slant height equals 8 cm.

So,

Answer:

Surface area of pyramid equals 132 cm square.

The expression for the sequence of operations described would be:

(10 x (u + 6))

We have,

(u + 6):

This part of the expression adds 6 to the variable "u".

It represents the addition operation between "u" and 6.

10 x (u + 6):

This part multiplies the result of the previous step by 10.

It represents the multiplication operation between 10 and the result of

(u + 6).

By combining these operations, the overall expression calculates the result of adding 6 to "u" and then multiplying the sum by 10.

In this expression,

"u" represents a variable or a value.

The sequence first adds 6 to "u" and then multiplies the result by 10.

Thus,

The expression for the sequence of operations described would be:

(10 x (u + 6))

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The solution to the line diagram are:

1) AB

2) Point B

3) A, B and C are the three collinear points

4) ABD

1) A line can be defined by two points that are connected by the given line.

We can see that the line r connects the points A and B, then we can call this line as:

AB (the notation usually uses a double arrow in top of the letters)

2) In the image we can see that lines r and s intersect at the point B, then another name for that intersection is: B.

3) 3 collinear points are 3 points that are connected by a single line, an example of this can be the points A, B and C.

4) A plane can be defined by a line and a point outside the line.

For example, we can choose the line AB and the point D, that does not belong to the line.

Then we can call the plane as ABD.

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Answer:

Difference = 62.5 micrometer

Step-by-step explanation:

Given that:

Diameter of red blood cell = 7.5 micrometer

Diameter of coarse grain of sand = 70 micrometers

For calculating the difference between two diameters, we will subtract the diameter of red blood cell from diameter of grain of sand.

Difference = 70 - 7.5

Difference = 62.5 micrometer

Hence,

Difference = 62.5 micrometer

Answer:

39% of 198 = 77.22

Have a nice day.

1: Calculate the percentage of a number.

For example: 39% of 198 = 77.22

2: Calculate a percentage based on 2 numbers.

For example: 77.22/198 = 39%

hope this help!

The Cronbach’s alpha is an indicator of the reliability in which the researcher calculates the correlation of each item with every other item.

In order to get a reliable and trustworthy measure, a number of essential requirements must be met. Firstly, the scale should be reliable. This indicates that the scale is internally reliable and that each item's score is closely linked to the other items' scores. The Cronbach’s alpha measures the internal consistency of the items on a scale, indicating how well the items are related to one another, and is an indicator of the scale's reliability.

The closer the alpha is to 1.0, the more reliable the scale is, whereas an alpha of 0.7 or greater is required for the measure to be reliable. Therefore, the Cronbach’s alpha is an indicator of the reliability in which the researcher calculates the correlation of each item with every other item.

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Answer:

4

Step-by-step explanation:

If they spent 36 dollars

and the shoes were 4 dollars,

36-4=32 dollars left for the games

32/8=4 games

Answer:

A. a rotation 90° counterclockwise about the origin, then a translation 3 units up and 7 units right

The sequence of transformation is "a rotation 90° counterclockwise about the origin, then a translation 3 units up and 7 units right" option (A) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The missing figure is attached to the picture, please refer to the picture.

From the figure we can see the transformation applied on the pentagon is a 90° counterclockwise rotation around the origin, followed by a translation of Three units up and seven right

Thus, the sequence of transformation is "a rotation 90° counterclockwise about the origin, then a translation 3 units up and 7 units right" option (A) is correct.

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Answer:

A

Step-by-step explanation:

It’s the opposite

Answer:

4

Step-by-step explanation:

There are 4 numbers to the right of decimals in question.

Pls mark Brainiest :)

(a) Therefore, the range of possible values for "x" is 1 to 5. (b) Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.  Therefore, there are 31 different ways this can happen

To find the number of different ways this can happen, we can consider the number of internet friends each person can have. Since each person has the same number of internet friends, let's denote that number as "x". We can then create equations based on the given information:

1. Some, but not all, of them are internet friends with each other: This means that at least two people are internet friends with each other, but not everyone is friends with each other. This implies that the minimum number of internet friends any person can have is 1, and the maximum number is 5 (since there are 6 people in total).

Therefore, the range of possible values for "x" is 1 to 5.

2. None of them has an internet friend outside this group: This means that each person's internet friends must be within this group of 6 people. So, the number of internet friends each person can have is limited to the remaining 5 people.

To find the number of different ways this can happen, we need to sum up the possible values of "x" and calculate the corresponding combinations. For "x = 1", we choose 1 person out of 5 remaining people, giving us C(5, 1) = 5. For "x = 2", we choose 2 people out of 5 remaining people, giving us C(5, 2) = 10.

Similarly, for "x = 3", "x = 4", and "x = 5", we have C(5, 3) = 10, C(5, 4) = 5, and C(5, 5) = 1 respectively. Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.

Therefore, there are 31 different ways this can happen

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