Let k be a real number and (M) be the following system.
(M): {x + y = 0
(2x + y = k – 1}
Using Cramer's Rule, the solution of (M) is
A. x=1-k,y=2-2k
B. x=k-1,y=1-k
C. x=1-k,y=2k-2
D. None of the mentioned

Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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calculate the same thing as a result of the same thing as a

Answer:

System of equations:

5x + 20y = 425

x + y = 25

5 skates

20 bicycles

Step-by-step explanation:

Let x represent the number of skates and let y represent the number of bikes.

So each pair of skates costs $5 to rent and each bike costs $20 to rent. This means we can multiply the price of each time the amount of each we want to rent.

So, for the skates we would multiply 5 * x to get the total amount spent on skates.

Similarly for the bikes, we would multiply 20 * y to get the total amount spent on bikes.

We know that a total of $425 was spent on skates and bikes that day.

So, we can add the total amount spent on skates and the total amount spent on bikes to get the total amount spent that day (which we are told is $425).

Therefore, we have 5x + 20y = 425.

Since we've established that x represents the number of skates and y represents the number of bikes we can add x and y to find the total number of rentals that day (which we are told is 25).

Therefore we have x+ y = 25.

Finally we solve for x and y. I will be using the elimination method.

Step 1 - write down system of equations

(1) 5x + 20y = 425

(2) x + y = 25

Step 2 - multiply the second equation (2)  by -5 to eliminate x

-5(x+y=25)

which results in

(2) -5x - 5y = -125

Step 3 - rewrite system of equations using your new 2nd equation (2)

(1) 5x + 20y = 425

(2) -5x - 5y = -125

Step 4 - Add like-terms

Left hand side of equals symbol

5x + (-5x) = 0 (we have now eliminated x)

20y + (-5y) = 15y

Right hand side of equals symbol

425 + (-125) = 300

Since y was on the left side of the 2 equations we now have

15y = 300

Step 5 - Solve for y

15y = 300

We can divide both sides by 15 to isolate y, so

15y/15 = 300/15

which results in

y = 20

Since y represents the total number of bikes, we now know that 20 bikes were rented out that day.

Step 6 - Solve for x

Since we already have y, we can simply plug it into one of our original equations from our system of equations.

To make it simple, we can use our 2nd equation (2).

(2) x + y = 25

y = 20

x + 20 = 25

subtract 20 from both sides to isolate x.

so

x + 20 - 20 = 25 - 20

x = 5

Since x represents the total number of skates, we now know that 5 skates were rented out that day.

I'm sorry for the long explanation, but I wanted to make sure you understood the basics of creating and solving a system of equations. I used the elimination method, but I encourage you to check out the substitution method or ask your teacher about it if you haven't learned it in class yet.

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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The the distance between the school and Nokesville be on the map is 0.7 inches.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that :

The distance between the school and Target is 4.2 miles and on a map the ratio is 0.5 inches is equal to 3 miles that is :

3 miles = 0.5 inches on map

Now to find the distance between the school and Nokesville be on the map we first find for 1 miles on the map and then multiply it by 4.2 miles :

3 miles = 0.5 inches on map

1  miles = 0.5/3 inches on map

4.2 miles = (0.5/3) x 4.2 inches on map

4.2 miles = 0.7 inches inches on map

Therefore, the the distance between the school and Nokesville be on the map is 0.7 inches.

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Answer:

the 10 pound bag by $0.10 per pound

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

Ask every tenth customer over the period of a week.

Step-by-step explanation:

Required

Select which of the options is true

(a) Every 5th male customer

This method will not produce a correct representative sample because only the male customers are surveyed. The opinion of the female customers will not be represented in the sample

(b) Every customer after 5:00pm

This method will not produce a correct representative sample because only the customers who come to the bakery before 5:00pm will not be represented. The opinion of these customers will not be represented in the sample

(c) Every 10th customer over the week

This method will produce a correct representative sample because the opinions of the customers are taken, irrespective of the gender or the time the customer walks into the bakery.

Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

Answer:

"General Formulas" in mathematics is the general equation you can use for certain things, by just adding the numbers given to the equation so that you can solve the problem.

Form example:

The general formula to find the y-intercept: y=mx+b

Hope this helped!

Have a nice day:)

Answer:

"General Formulas" in mathematics is the general equation you can use for certain things, by just adding the numbers given to the equation so that you can solve the problem.

Step-by-step explanation:

The quadratic equation \(b^2 - 4b + 4 = 0\) can be solved using the quadratic formula. The two solutions are b = 2.

To solve the equation \(b^2 - 4b + 4 = 0\) using the quadratic formula, we first identify the coefficients a, b, and c. In this case, a = 1, b = -4, and c = 4. Substituting these values into the quadratic formula:

\(\[b = \frac{{-(-4) \pm \sqrt{((-4)^2 - 4(1)(4))}}}{{2(1)}}\]\)

Simplifying the equation gives:

\(\[b = \frac{{4 \pm \sqrt{{16 - 16}}}}{2}\]\)

Since the discriminant (the term under the square root) is zero, we have:

b = (4 ± √0) / 2

The square root of zero is zero, so we can simplify further:

b = (4 ± 0) / 2

This yields two identical solutions:

b = 4 / 2 = 2

Hence, the quadratic equation \(b^2 - 4b + 4 = 0\) has a single solution, which is b = 2.

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Profit function in terms of x = 33x + 390.

What is a profit in business?

Given that revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial

\(2x^{3} + 30x - 130\)

The cost, in dollars, of producing the skateboards can be modeled by

\(2x^{3} -3x - 520\)

Profit function = Revenue - cost

                         = \(2x^{3} + 30x - 130 - ( 2x^{3} - 3x - 520)\)

                          = 33x + 390

Therefore, profit function in terms of x = 33x + 390

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Answer:

for 1 it is 76,4

Step-by-step explanation:

5X6X8 divided by 3,14 = 76,4

Answer:

Step-by-step explanation:

I have attached a written explanation to help :).

Let's say each side of the square =\(x\)

If we put 7 squares in a row to make the rectangle,

length of the rectangle = \(7x\)

Area of a rectangle = length multiplied by width

Area of rectangle =  \(7x\) multiplied by \(x\) = \(7x^2\)

We are also told that the total area = 567

So \(7x^2 = 567\)

Now solve for \(x\).

Divide both sides by 7.

\(\frac{7x^2}{7} = \frac{567}{7}\)

\(x^2 = 81\)

Then square root both sides to find \(x\)

\(x = \sqrt{81}\) = 9

Finally, the question asks to find the length of the collage which we said was \(7x\) and we know \(x = 9\)

Length of collage = \(7x = 7\) multiplied by \(9\) = ?

Answer:

6

Step-by-step explanation:

The correct answer is option D. Because the residuals do not form a pattern, there is a linear relationship between the amount of time and the count of bacteria as demonstrated by y= -143+51x.

Residuals are the differences between the observed values and the predicted values of a variable, and they are used to assess the fit of a statistical model. If the residuals form a random, non-patterned distribution, this suggests that the model is a good fit for the data and that there is a linear relationship between the variables being modeled. On the other hand, if the residuals form a pattern, this suggests that the model is not a good fit for the data and that there may be other factors influencing the relationship between the variables being modeled.

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On solving the provided question, we can say that the equation is 4x+2 x%2B8=4x%2B2 => 3x=6 => x=2

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation

4x+2

x%2B8=4x%2B2

3x=6

x=2--------two weeks

They each will pass 10 scales.

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To answer the questions related to the ANOVA table, we need to use the provided information. Here are the calculations:

a-1. The standard error of estimate (SE) can be calculated using the mean square error (MSE) from the ANOVA table. It is the square root of MSE.

SE = √(MSE) = √(52.80) ≈ 7.27

a-2. About 95% of the residuals will be within ±2 standard errors of estimate.

The range of residuals will be between ±2 * SE, which is ±2 * 7.27 = ±14.54.

b-1. The coefficient of multiple determination (R-squared) can be found by dividing the regression sum of squares (SSR) by the total sum of squares (SST).

R-squared = SSR / SST = 3,918.73 / 6,664.41 ≈ 0.588

b-2. The percentage variation for the independent variables is calculated by multiplying R-squared by 100.

Percentage variation = R-squared * 100 ≈ 0.588 * 100 ≈ 58.8%

c. The coefficient of multiple determination, adjusted for the degrees of freedom, can be calculated using the formula:

Adjusted R-squared = 1 - [(1 - R-squared) * (n - 1) / (n - p - 1)]

where n is the total number of observations and p is the number of independent variables (regressors).

Since the degrees of freedom are not provided in the ANOVA table, we cannot calculate the adjusted R-squared without that information.

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Therefore , the solution of the given problem of median comes out to be  R students still present (maximum) =35

The number that precisely falls in the center of a sorted collection is the median value. An average or maximum probability metric is the difference between the initial and final 50% of the data. Different algorithms are employed to compute the average and mode depending on if you do have an unusual or perhaps even number of data points.

Here,

Median is 55

P :Q: R :S :average of 45 :50: 55 :65

The number of pupils within every section needs to be as low as possible 

R is a mean

P differs by 1: 10 from the mean.

Q is 1.5 away from the mean.

Then S will just have three students, or three times five, to keep the population's mean constant.

R students still present (maximum):

=> 40 - 1- 1-3

=> 35

Therefore , the solution of the given problem of average comes out to be  R students still present (maximum) =35

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The boolean expressions that evaluate to false are b) 1 == 0 and e) false.

a) 8 <= 4: This expression compares the values of 8 and 4. Since 8 is not less than or equal to 4, this expression evaluates to false.

b) 1 == 0: This expression checks whether 1 is equal to 0. Since 1 is not equal to 0, this expression evaluates to false.

c) (5 - 2) == (10 - 7): This expression compares the result of subtracting 2 from 5 with the result of subtracting 7 from 10. Since both subtractions yield 3, the expression evaluates to true.

d) (true and true) or: This expression combines the logical AND operation between two true values and then performs the logical OR operation with an unspecified value. Without the second operand, the expression is incomplete and cannot be evaluated.

e) false: This expression directly evaluates to false since false is a boolean literal.

Therefore, the boolean expressions that evaluate to false are b) 1 == 0 and e) false.

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The discrete probability distribution you are referring to in order to calculate the coefficient of variation. The coefficient of variation is a statistical measure that describes the amount of variation or dispersion relative to the mean of a probability distribution.

Assuming you provide me with the necessary information, I can calculate the coefficient of variation by dividing the standard deviation by the mean, and then multiplying the result by 100 to express it as a percentage. A higher coefficient of variation indicates that the data has more variability relative to the mean, while a lower coefficient of variation indicates that the data has less variability relative to the mean.

The coefficient of variation is most useful when comparing the variability of two or more distributions with different means. If two distributions have similar means, then comparing their standard deviations alone may be more informative. Additionally, the coefficient of variation may not be appropriate for all types of data, such as data that contains negative values or data that has a highly skewed distribution.

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The term that describes a group of statements that executes as a single unit is a "block". A block of code is a program that is grouped together and treated as a single unit. So, the correct option is D.

In computer programming, a block is a group of statements or declarations that are enclosed within a set of curly braces ({ }). The block serves as a single unit that is executed together. Blocks are used to organize code and to apply control structures, such as loops and conditional statements, to multiple statements.

A block can contain any number of statements, which can include variable declarations, function calls, loops, conditional statements, and other constructs. The statements within a block are executed in sequence, one after another, unless a control statement is encountered that alters the normal sequence of execution.

For example, a while loop in Java consists of a block of code that is executed repeatedly while a certain condition is true:

while (condition) {

   // block of code to be executed while condition is true

}

In this example, the block of code inside the curly braces will be executed repeatedly while the condition specified in the while statement is true. The block can contain any number of statements, and these statements will be executed each time the loop iterates.

Another common use of blocks is to define functions or methods. A function or method is a block of code that can be called from other parts of the program, and can take inputs (arguments) and return outputs. For example, in Python, a function can be defined as follows:

def function(argument1, argument2):

   # block of code to be executed in the function

   return result

In this example, the block of code enclosed within the function definition is executed when the function is called. The function can take inputs (argument1 and argument2), which can be used within the function, and it can return a result using the return statement.

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Answer:

C) 1/2

Step-by-step explanation:

We know that 3/8 cup of brown sugar and 1/3 cup of white sugar are mixed together to make the sugar mixture.

From this sugar mixture, 1/4 cup is set aside for the crumb topping.

To find out how much sugar mixture is used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.

We can start by converting the mixed unit of measurement (brown sugar in cups and white sugar in cups) to a single unit of measurement (cups)

3/8 cup of brown sugar + 1/3 cup of white sugar = (3/8)+(1/3) = 5/12 cup + 4/12 cup = 9/12 cup.

1/4 cup is set aside for the crumb topping.

So, the remaining sugar mixture used to make the cake is 9/12 cup - 1/4 cup = (9/12) - (1/4) = (9-3)/12 = 6/12 cup = 0.5 cup

Answer:

its B

Step-by-step explanation:

The correct option is A 25-foot ladder is propped against a wall forming an 18-degree angle.  

Trigonometric ratio is used to show the relationship between the sides and angles of a right-angled triangle.

A right-angled triangle is a triangle in which one of the angle is 90 degrees.

Given a 25-foot-long ladder is propped against a wall at an angle of 18° with the wall.

Here, the right-angled triangle ABC with side AB as the hypotenuse

The diagram of the scenario is attached below.

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Answer:

His claim is false.

Step-by-step explanation:

People put nasty fake answers, so I will answer your question here. 16h15 minus 45 minutes is 15h30. If he was gone 48 minutes, he left at 15h27m

Answer:

x = \(\frac{11}{c}\)

Step-by-step explanation:

Given

cx - 4 = 7 ( add 4 to both sides )

cx = 11 ( isolate x by dividing both sides by c )

x = \(\frac{11}{c}\)

Answer:

y = 60x + 20

y = 65x

0 = 5x - 20

5x = 20

x = 4  ---> 4 hours

Substitute x as 4:

y = 65 x 4

y = 260 ---> 260 miles

So the answer is A

Answer:

x=0,−10

Step-by-step explanation:

1) Factor out the common term x.

x(x+10)=0

2) Solve for x.

x=0,−10

Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

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Smaller of the triangle’s two acute angles is 34°.

A triangle is said to have a right angle if one of the angles is 90 degrees. Right triangles are those with angles at 90 degrees, which are referred to as right angles.

As per the given data:

cos(7x) = sin(4x + 2)

The triangle is right-angled.

As it is a right angle triangle:

cosθ = sin(90 - θ)

∴ 7x + 4x + 2 = 90

11x + 2 = 90

11x = 88

x = 8

The two angles now are:

7x = 7 × 8 = 56°

4x + 2 = 4 × 8 + 2 = 34°

Now 34° < 56°

Hence, the smaller of the triangle’s two acute angles is 34°.

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Answer:

y = -\(\frac{5}{3}\)x - -\(\frac{23}{3}\)

Step-by-step explanation:

First, let's divide both sides by 5 to get the first equation into the form y = mx + b. We get y = \(\frac{3}{5}\)x + 5. The m value, \(\frac{3}{5}\), is the slope and the b value, 5, is the y-intercept of this line.

When a line is perpendicular to another line, the slopes must multiply to get -1. In other words, the slopes must be a negative reciprocal of each other. Since the slope of the original line is \(\frac{3}{5}\), we know that the slope of the line perpendicular to that is -\(\frac{5}{3}\).

Then, since we know x, y, and m of the second equation, we can substitute those three values into the equation, y = mx + b, to find the y-intercept (b).

-1 = (-\(\frac{5}{3}\))(-4) + b

-1 = \(\frac{20}{3}\) + b

b = -\(\frac{23}{3}\)

After plugging in the values of m and b we calculated, we get the equation for the line perpendicular to the original line: y = -\(\frac{5}{3}\)x -\(\frac{23}{3}\).