Determine the independent and dependent variable from the following situation. Flora was given 10 pencils at the beginning of the school year. Every week she receives 2 more pencils.
what is the independent variable and what is the independent variable.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

What is weight ?

Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.

The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

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dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.

The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

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The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25.

The sample space is the set of all possible outcomes, which in this case is 36. The number of desired outcomes is 9, as the question specifies.

The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25. You calculate this by taking the number of desired outcomes (9) and dividing it by the total number of possible outcomes (36).

The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25. This is calculated by taking the number of desired outcomes (9) and dividing it by the total number of possible outcomes (36).

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When rolling two number cubes, the likelihood of first getting an even number and then an unusual one is 1/4, or 0.25. You can determine this by dividing the total number of possible outcomes by the number of intended outcomes (9). (36).

When rolling two number cubes, the likelihood of first getting an even number and then an unusual one is 1/4, or 0.25. This is calculated by dividing the total number of possible outcomes (which is 36) by the number of intended outcomes (9). (36).

The first derivative will give the slope of the function.

The second derivative will give you the point at which the function is increasing or decreasing the most rapidly.

If the 3rd derivative is negative, the rate of increase at the 2nd derivative point will be maximum; if positive, it will be a minimum.

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable).

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The sketch field of given differential  equation is attached in image .

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The equation  y′=f(x,y) gives you a slope at each point in the  (x,y)-plane. And this is the slope a solution y(x) would have at x  if its value was y. In other words,  f(x,y) is the slope of a solution whose graph runs through the point  (x,y). At a point  (x,y), we plot a short line with the slope f(x,y).

We have y'=y2

we can write it,

[tex]\frac{dy}{dx}=y^2[/tex]

[tex]\int y^{-2}dy=dx\\\\\frac{-1}{y}=x+c\\[/tex]

The sketch field of the given differential equation is attached in image.

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The option D. See what x is when y = -5 is not a possible way to evaluate the value of f(-5).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

The given function is f(x) = 3x² - 2x + 5.

f(-5) is actually the value of y or f(x) when x = -5.

By substituting -5 in place of x of the function, we will get f(-5).

Also we can find the value of f(-5) by graphing the function and finding the y value corresponding to the x value of -5.

Hence the way that is not possible is option D.

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Answer: 14 eggs

Step-by-step explanation: Hello!

You know that there are 10 chickens that lay eggs every day.  There are 7 neighbors that she needs to give eggs to so that they each get the same amount otherwise there is one egg left over.  We know that each chicken must produce at least one egg per day, meaning that the bare minimum amount of eggs per day is 10.  Let's try 10.

10/7 = 1 and 3/7.  This means that there would be 3 eggs remaining.  This is not possible.  Let's try 11.

11/7 = 1 and 4/7.  This means there would be 4 eggs remaining.  Let's try 14.

14/7 = 2.  This is the smallest number of eggs for each neighbor to get the same amount of eggs each per day (2).  The smallest number of eggs she needs in total is 14.

It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

Now, According to the question:

"Information available from the question"

A physicist measures the remaining radioactivity in a sample.

She finds that it reduces by 18% each year.

If there was 1.52 g of radioactive material left after 4 years.

In order to find the initial quality of radioactive material, we will use the formula:

Initial Quality = Final Quantity * (1 - Reduction Rate)^Years

We know that -

The final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.

Initial Quantity = 1.52 g × [tex](1-0.18)^4[/tex]

Initial Quantity = 1.52 g × 0.452

Initial Quantity = 0.68 g

Hence, the initial quantity of the radioactive material is 0.68 g.

b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:

Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)

We know that -

the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).

Years = log(0.2 / 0.0.68) / log(1 - 0.18)

Years = 7.15

Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

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Answer:

To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the answer.

3 * 17 = 51

The square root of 51 is: 7.141

7.141 is the geometric mean of 3 and 17.

Step-by-step explanation:

Hope it helps! =D

The statement "The results of the experiment do not agree with the theory, there's something wrong with the experiment" is wrong as it does not indulge any other reasons for the results of the experiment not agreeing with the theory.

This statement assumes that the experiment is always at fault and neglects the possibility that the theory may be incorrect or incomplete.

The outcome of an experiment can be influenced by various factors, such as measurement errors, incorrect experimental design, or limitations of the equipment used.

Thus, it is always important to consider multiple explanations before concluding that there is a problem with the experiment.

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Chuck and Wendy's investment assets is to use their gross assets as a base and then add in any net assets.

For example, if Chuck and Wendy have $100,000 in gross assets and $50,000 in net assets, their investment assets would be $120,000.

Chuck and Wendy's fixed assets and total wealth depend on many factors, including the level of risk they are willing to take, expected return, and overall financial stability.

For example, Chuck and Wendy's may have higher risk if they have a higher return on investment but still have $100,000 in total assets if their expected return is 5%.

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The equation formed will be - cost × number of hiking boots + cost × number of canteens and the cost of canteens will be 15.

The equation that will be formed is -

Total cost of purchase = cost of hiking boots × number of hiking boots + cost of canteens × number of canteens

Keep the values in formula to find number of canteens, as it is the only value not provided in the question.

98 = 2×34 + 2× cost of canteens

Performing multiplication on Right Hand Side of the equation

98 = 68 + 2×cost of canteens

Rewriting the formula -

2× cost of canteens = 98 - 68

Performing subtraction on Right Hand Side of the equation

2× cost of canteens = 30

Cost of canteens = 30/2

Performing division on Right Hand Side of the equation

Cost of canteens = 15 each

Thus, the cost of canteens is 15 each.

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If DE = 4x + 5 and GJ = 3x + 25, and the value of both the expressions is same, then value of DE is, 85

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

Two expressions,

DE = 4x + 5 and GJ = 3x + 25,

If DE = 4x + 5 and GJ = 3x + 25, and they have the same value, then we can set the two expressions equal to each other:

4x + 5 = 3x + 25

Solving for x, we get:

x = 20

So, when x = 10,

DE = 4 x20 + 5

      = 85

and GJ = 3 x 20 + 25

            = 85

Therefore, the value of DE is 85.

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Lukes's age is 47

Gibson's age is 26

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Lukes's age = x

Gibson's age = y

Now,

x + y = 73 ______(1)

x = 2y - 5

Substituting in (1)

2y - 5 + y = 73

3y = 78

y = 26

Now,

x = 2 x 26 - 5

x = 52 - 5

x = 47

Thus,

Lukes's age = 47

Gibson's age = 26

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The coterminal angle with -210° is -570°. This is because subtracting 360° from -210° gives us -570° which is between -720° and -360°.

To find an angle coterminal with -210° that is between -720° and -360°, we need to subtract 360° from -210°. By doing this, we end up with -570° which is the coterminal angle with -210° that lies between -720° and -360°. This is because angles on the circle can 'wrap around' infinitely, and when we subtract 360° from -210°, we end up with an angle that is still equivalent to -210°, but between the two values we are looking for. Therefore, the angle we were looking for is -570°.

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Answer: A) 16.425 in^2.

Step-by-step explanation: The figure is broken down, so let's find the area of the rectangle first. We are given 4 in and 2.3 in, which can be multiplied to get 9.2 in. Now, we need to find the area of the two triangles, but let's start with the one to the left. The area of a triangle is b x h x 1/2. 2.3 in x 2.5 in is 5.75 in, but we need to multiply that by 1/2 which is 2.875 in. Finally, we can find the area of the bottom triangle by using the same formula. 3 in x 2.9 in is 8.7 in, but we need to multiply it by 1/2, which is 4.35 in. Now, all we need to do is add all the areas we found together to get the total area of the figure. 9.2 in + 2.875 in + 4.35 in is 16.425 in^2, which means that option A is your answer.

Let me know if this is right! :)

Answer:

16.425 in²

Step-by-step explanation:

total area of the figure= area of (left triangle+ rectangle+ down triangle)

=1/2*base*height+length*breath+ 1/2*base*height

=1/2*2.5*2.3+4*2.3+1/2*3*(5.2-2.3)

=16.425 in²

Gauss-Jordan Elimination is a technique for solving systems of linear equations and for determining the inverse of any invertible matrix.

Gauss-Jordan Elimination is a method for finding the inverse of any invertible matrix and for solving systems of linear equations. It is based on the three simplest row operations one may do on a matrix: Place two of the rows in opposite positions. A nonzero scalar multiplied by one of the rows

Since a similar version was described by Wilhelm Jordan in 1888 in his book "Handbuch der Vermessungskunde" independently of B. I. Clasen, who published something similar in the same year, the procedure known as Gauss-Jordan elimination for converting a matrix into reduced echelon form also includes the name Jordan.

This method, which is also known as row reduction, has two steps: forward elimination and back substitution. These two Gaussian elimination method steps differ from one another not by the operations that can be performed through them but rather by the outcome that is obtained.

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Answer:

z = -3

Step-by-step explanation:

-7(z - 3) = 42

Distribute -7 to both numbers inside the parenthesis:

(-7(z) - -7(3)) = 42

-7z + 21 = 42

Subtract 21 from both sides:

-7z = 21

Divide both sides by -7:

[z = -3]

Answer:

y = -4 + 1.4

Step-by-step explanation:

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

y + 3/5 = -4x + 2

y + 0.6 = -4x + 2

y = -4 + 1.4

The equation representing the total amount Emma earns at the event is y = $10x.

If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:

y = kx

where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:

y = $10 * x

Therefore, the equation representing the total amount Emma earns at the event is y = $10x.

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The equation representing the total amount Emma earns at the event is y = $10x.

If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:

y = kx

where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:

y = $10 * x

Therefore, the equation representing the total amount Emma earns at the event is y = $10x.

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The correct statement regarding the sign of the absolute value function is given as follows:

B. The function is never negative.

A function is classified as positive in the intervals that it's graph is positioned above the x-axis.

A function is classified as negative in the intervals that it's graph is positioned below the x-axis.

When the graph of the function is exactly at the x-axis, it is said that the function assumes a value of zero.

For this problem, the lowest value assumed by the function is at the x-axis, hence it is of zero and the function is never negative, meaning that option B is correct.

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The coordinates of point T' is (2, -2)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point T (3, -3) is transformed under a dilation of 2/3 with respect to the origin.

So the image point is (kx, ky) = (3 * 2/3, -3 * 2/3) = (2, -2)

So the image point of T under a dilation of 2/3 with respect to the origin is (2, -2)

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A triangular land has area 336 q meter, perimeter 84 meter and length of an edge 26 meter. The lenght of the remaining two sides are both 29 meters long.

Let's call the length of the remaining two sides x.

Since the perimeter of the triangle is 84, then the sum of all three sides is 84, so:

x + x + 26 = 84

Therefore, the sum of the remaining two sides is:

2x = 84 - 26 = 58

And the length of each remaining side is:

x = 58 / 2 = 29 meters required lenght of the remaining two sides.

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Answer:

Let x be Jenny's hourly rate. Then Mary's hourly rate is x + 0.2x = 1.2x.

The total amount of money they earned for the hours they worked is the same, so we can set up the equation:

30x + 25(1.2x) = 610

Expanding the second term and solving for x:

30x + 30x = 610

60x = 610

x = 10.17

So Jenny's hourly rate is $10.17 and Mary's hourly rate is $12.20.

Answer:

Step-by-step explanation:

Add, Added to, the sum of, more than, increased by, the total of, plus. +. Add x to y x + y y added to 7.

The composite function which expresses the given correspondence correctly is f of g of x

Composite functions are when the output of one function is used as the input of another. If we have a function f and another function g, the function f g ( x ) fg(x) fg(x), said as “ f of g of x”, or “ f g fg fg of x”, is the composition of the two functions.

The composite function rule shows us a quicker way. If f(x) = h(g(x)) then f (x) = h (g(x)) × g (x). In words: differentiate the 'outside' function, and then multiply by the derivative of the 'inside' function.

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(a) The expressions (x + x + x + x) and (4x) are equivalent.

(b) The expressions (5x) and (x + 5) are not equivalent.

Equivalent expressions are expressions that perform the same function notwithstanding their appearance. If two algebraic expressions are equivalent, they have the same value when the variable is set to the same value.

a) True

The expressions (x + x + x + x) and (4x) are equivalent.

Both expressions represent the same mathematical operation, which is adding x four times.

b) False

The expressions (5x) and (x + 5) are not equivalent. They represent different mathematical operations.

The expression (5x) is multiplying x by 5, while the expression (x + 5) is adding x and 5.

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The car travel before stopping is 400 meters

The car's initial speed was 80 m/s.

Acceleration/Deferral = 8 m/s2.

The following is the equation of motion for time t and distance s:

v = u + at

s = ut + 1/2 * a * t ^2

v = final velocity = 0 where

Thus, s = 80 * 10 - 1/2 * 8 * 10 *10

= 800 - 400

= 400 meters were covered before stopping, giving us 0 = 80 - 8 * t t

= 80/8

= 10 seconds.

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The full question:

A car moving a straight highway with a speed of 80 m/s is forced to slow down at a rate of 8 m/s^2. How far does a car travel before stopping?

"The customer yields $780 per year in profits for this retailer."

Customer lifetime value (CLV) is a prediction of the total value a customer will bring to a business over their entire relationship with the company. Retailer profits refer to the financial gain a retailer makes after subtracting all costs, including the cost of goods sold, operating expenses, and taxes, from the revenue generated by their retail sales.

The customer spends $250 a week, so the retailer profits:

If the shopper visits the store every week for a year, the retailer profits:

If this shopper remains loyal for a 10-year lifespan, the retailer profits:

This is the CLV  without considering inflation or any other factors. To consider inflation, we can apply the 8% annual interest rate to calculate the present value of the future profits. The present value of $7,800 over 10 years with an 8% interest rate is approximately $5,100 (the exact value will depend on the method used to calculate the present value).

This question should be provided as:

Assume that a customer shops at a local grocery store spending an average of ​$250 a​ week, resulting in a retailer profit of ​$15 each week from this customer. Assuming the shopper visits the store all 52 weeks of the​ year, calculate the customer lifetime value if this shopper remains loyal over a​ 10-year life span. Also assume a 8 percent annual interest rate and no initial cost to acquire the customer.

The customer yields ​$_____ per year in profits for this retailer.

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The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

Explanation:

We will identify the given three events that are mutually exclusive.

From example 2.10

A = {Chevrolet, Pontiac, Buick }

B = {Ford, Mercedes }

C = {Lincoln, Chrysler }

Step 1 of 1

If A∩B=∅ where A and B

are two events then we can say that they are mutually exclusive.

And if there are three or more events then they are mutually exclusive if no two events have an element in common.

Now, events from example 2.10

are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

We can see that all the name card are car brand and their intersection is empty.

Hence, they are mutually exclusive.

Then,

A∩B=∅ and A∩C =∅ and B∩C=∅

Final answer

The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

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The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}



We will identify the given three events that are mutually exclusive.

From example 2.10

A = {Chevrolet, Pontiac, Buick }

B = {Ford, Mercedes }

C = {Lincoln, Chrysler }

Step 1 of 1

If A∩B=∅ where A and B

are two events then we can say that they are mutually exclusive.

And if there are three or more events then they are mutually exclusive if no two events have an element in common.

Now, events from example 2.10

are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

We can see that all the name cards are car brands and their intersection is empty.

Hence, they are mutually exclusive.

Then,

A∩B=∅ and A∩C =∅ and B∩C=∅

Final answer

The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

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