At a sale, you purchased a $20 scarf for $15. What
was the percent of change?

A change in a population that is not related strictly to the size of the population can be described as a change in the demographic makeup of the population. This refers to changes in the characteristics of individuals within the population, such as age, gender, education level, and ethnicity.

For example, if a population experiences an influx of young adults, this would represent a change in the demographic makeup of the population, even if the overall size of the population remains the same.

Other factors that can contribute to a change in the population's makeup include migration patterns, changes in birth rates and mortality rates, and shifts in cultural or social norms. These changes can have significant impacts on a population, affecting everything from economic growth to social dynamics. Understanding demographic changes is therefore critical for policymakers and researchers seeking to address issues such as inequality, public health, and urban planning. By analyzing population trends and anticipating future changes, we can better prepare for the challenges and opportunities that lie ahead.

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Answer:

The standard deviation = 1.9

Step-by-step explanation:

standard deviation, ρ = sqrt ( \(\frac{sum(x_{i} - u)^{2} }{N}\))

Where u is the mean of the data, \(x_{i}\) each given value, and N is the number of data given.

Mean, u = \(\frac{6+5+2+5+8}{5}\)

              = 5.2

So that;

\((6-5.2)^{2}\)  = \((0.8)^{2}\) = 0.64

\((5-5.2)^{2}\) = \((-0.2)^{2}\) = 0.04

\((2-5.2)^{2}\)  = \((-3.2)^{2}\) = 10.24

\((5-5.2)^{2}\) = \((-0.2)^{2}\) = 0.04

\((8-5.2)^{2}\) = \((2.8)^{2}\) = 7.84

Sum = 18.8

So that;

\(\sqrt{\frac{18.8}{5} }\)  = \(\sqrt{3.76}\)

          = 1.9391

          = 1.9

The standard deviation of the given data is 1.9

Answer:

120 ft²

Step-by-step explanation:

The length of each of the congruent sides is (50-16)/2 = 17 ft.

So, using the Pythagorean theorem, the altitude drawn from the vertex angle to the base has a length of 15 ft.

Thus, the area is (1/2)(15)(16) = 120 ft².

Answer:

I don't know the answer please

Answer:

12 centimeters

Step-by-step explanation:

V=πr2h

4332π = π(19^2)h

(4332π)/(361π) = h

h = 12

Answer:

Ahmed got 390 votes

Step-by-step explanation:

Here, we want to know the number of votes obtained by Ahmed

from the question, there were 900 registered voters

10% did not cast their votes

The number that didn’t cast their votes will be;

10% of 900

= 10/100 * 900 = 90

So the rest 90% casted and this value will be 900-90 = 810

810 people casted their votes

30 votes were spoilt;

The number of valid votes is thus;

810 - 30 = 780

Ahmed got a ratio of 3 in 3:2:1

The total value here is 3 + 2 + 1 = 6

So what Ahmed got will be;

3/6 * 780

= 780/2 = 390

Answer:

y+1>_8

Step-by-step explanation:

sum= addition

greater tan or equal to means it has this symbol > with a line underneath it

The image of the points after they are reflected across the x-axis are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

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

J(1, 9), K(7, 4), L(8, 13), M(-2, 1)

Also from the question we have the transformation to be

Transformation: reflection across the x-axis

The rule of the reflection across the x-axis is represented as

(x, y) = (x, -y)

Substitute the known values J(1, 9), K(7, 4), L(8, 13), M(-2, 1) in the above equation, so, we have the following representation

J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

Hence, the image of the points are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

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Answer:

28

Step-by-step explanation:

y/4-4 =3 /×4

y-16 =12

y =12 +16

y=28

28/4 - 4 =3

7 - 4 =3

3=3

Answer:

Step-by-step explanation:

For number 2 first thing you do is take (3,3)

                                                                ( -3,7)

And y1-y2

        x1-x2

the equation would be y= -2/3 x + 5

I can't really see the other point for number 3                        

The polynomial

f(x) =2ˣ² - 5x + 3

zeroes of the polynomial f(x)= 2x² - 5x + 3

By factorizing we have ,

→ 2x² - 5x + 3

→2x² -2x - 3x + 3

→2x(x-1)-3(x-1)

→(2x-3)(x-1)

Now the zeroes are

→ 2x - 3 = 0 and → x - 1 = 0

→ x = 3/2 and → x = 1

Verification of relation

Sum of the zeroes = -b/a

⇒ 3/2 + 1 = -(-5/2)

⇒ (3+2)/2 = 5/2

⇒ 5/2 = 5/2

Product of the zeroes = c/a

⇒ 3/2×1 = 3/2

⇒ 3/2 = 3/2

Verified

I hope it will help you.

Regards.

\( \longrightarrow f( \rm x) = (x - 4)(x + 4)\)

\( \\ \\ \)

\( \longrightarrow f( \rm x) = {(x)}^{2} - {(4)}^{2} \)

\( \\ \\ \)

\( \longrightarrow f( \rm x) = {x}^{2} - 16\)

Formula used = (a + b) (a - b) = a² - b²

Answer:

hui

Step-by-step explanation:

Answer:

\(\frac{15}{20} x-2=\frac{8}{20}\)

Step-by-step explanation:

\(\frac{3}{4} x-2=\frac{2}{5}\)

3/4 and 2/5 have a common denominator which is twenty so you can rewrite the equation with just knowing that

\(\frac{3}{4} =\frac{15}{20}\)

\(\frac{2}{5} =\frac{8}{20}\)

\(\frac{15}{20} x-2=\frac{8}{20}\)

You can then multiply both sides by twenty to solve this equation.

Hope this helps.

15x = 48

Step-by-step explanation:

\(\begin{aligned}\rm\frac{3}{4}x-2&=\rm \frac{2}{5}\to(multiplied~by~20)\\\rm(20)\frac{3}{4}x-(20)2&=(20)\frac{2}{5}\\\rm 15x-40&=8\\\rm 15x&=8+40\\\rm 15x&=48\end{aligned}\)

Answer:

Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.

Step-by-step explanation:

Let's start by finding out what fraction of the new set of stamps Sam has after adding 4/5 of the set to his collection.

Let the total number of stamps in the new set be x.

If Sam's collection initially had 3/5 of the new set, then the number of stamps in his collection before adding the new set would be:

3/5 * x = the number of stamps in Sam's collection before adding the new set

After adding 4/5 of the new set to his collection, Sam has:

3/5 * x + 4/5 * x = 7/5 * x

So Sam has 7/5 of the new set of stamps.

However, the problem asks for the fraction of the new set that Sam has, not the fraction of the total number of stamps in the new set.

To find the fraction of the new set that Sam has, we need to divide the number of stamps he has by the total number of stamps in the new set:

(7/5 * x) / x

Simplifying the expression:

(7/5) / 1

We can express this fraction in terms of x by multiplying both the numerator and denominator by 1/x:

(7/5) * (1/x)

Therefore, the fraction of the new set of stamps that Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.

Answer:

-2/2 or simplify to =-1

Step-by-step explanation:

you use rise over run. you may use an exact formula (y2-y1)/(x2-x1) by picking 2 y values and 2 x values on the graph and subtracting the values.

The value of x that makes the equation 5(2x - 3) - 6x = 1/2(4x - 10) true is x = 5

The equation is given as

5(2x - 3) - 6x = 1/2(4x - 10)

When the brackets are expanded, we have the following equation

10x - 15 - 6x = 2x - 5

Evaluating the like terms. we have

2x = 10

Divide both sides of the  equation by 2

So, we have

x = 5

Hence, the value of x in the equation is 5

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Answer:

he was supposed to add three on both sides

Step-by-step explanation:

xddudududududdudididididididididi

The solution to the given system of equations y = -x + 2 are option A. (-2,4) and D. (4,-2).

A system of equations is two or more equations that can be solved together to get a unique solution. the power of the equation must be in one degree.

The equation is given as

y = -x + 2

here, we need to find the solutions to the equation, we can apply the given options one by one to satisfy the equation.

For the solution

A. (-2,4)

y = -x + 2

Substitute the value x = -2 and y = 4

y = 4

-x + 2 = -(-2) + 2 = 4

Thus, the given solution are the system of equation.

For the solution

B. (0,-4)

y = -x + 2

Substitute the value x = 0 and y = -4

y = -4

-x + 2 = 0 + 2 = 2

Thus, both the sides are not equal so, the given solution are not the system of equation.

For the solution

C. (2,-4)

y = -x + 2

Substitute the value x = 2 and y = -4

y = -4

-x + 2 = 2 + 2 = 4

Thus, both the sides are not equal so, the given solution are not the system of equation.

For the solution

D. (4,-2)

y = -x + 2

Substitute the value x = 4 and y = -2

y = -2

-x + 2 = -4 + 2 = -2

Thus, the given solution are the system of equation.

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The impulse response y(n) is y(n) = 3(0.5)^n - 21(0.1)^n, for n >= 0.

To find the impulse response sequence y(n), we can use the Z-transform. First, let's take the Z-transform of both sides of the difference equation

Y(z) - 0.6z^{-1}Y(z) + 0.25z^{-2}Y(z) = X(z) + z^{-1}X(z)

Next, we can rearrange the equation to solve for Y(z)

Y(z) = (X(z) + z^{-1}X(z)) / (1 - 0.6z^{-1} + 0.25z^{-2})

Now, we can substitute X(z) = 8 (the Z-transform of the impulse sequence) and simplify the expression

Y(z) = 8(1 + z^{-1}) / (1 - 0.6z^{-1} + 0.25z^{-2})

We can factor the denominator to get

Y(z) = 8(1 + z^{-1}) / [(1 - 0.5z^{-1})(1 - 0.1z^{-1})]

Now, we can use partial fraction decomposition to write Y(z) as a sum of simpler fractions

Y(z) = A/(1 - 0.5z^{-1}) + B/(1 - 0.1z^{-1})

To find the values of A and B, we can multiply both sides of the equation by the denominators and set z = 0.5 and z = 0.1, respectively

A/(1 - 0.5(0.5)^{-1}) + B/(1 - 0.1(0.5)^{-1}) = 8(1 + (0.5)^{-1}) / [(1 - 0.5(0.5)^{-1})(1 - 0.1(0.5)^{-1})]

A/(1 - 1) + B/(1 - 2) = 8(1 + 2) / [(1 - 1)(1 - 2)]

A - B = -24

A/(1 - 1) + B/(1 - 0.1) = 8(1 + 0.1) / [(1 - 1)(1 - 0.1)]

B - 10A = 72

Solving for A and B, we get

A = 3, B = -21

Therefore, the impulse response sequence y(n) is

y(n) = 3(0.5)^n - 21(0.1)^n, for n >= 0.

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The given question is incomplete, the complete question is:

The difference equation is: y(n) – 0.6y(n-1) + 0.25y(n − 2) = x(n) + x(n-1) Find the impulse response sequence y(n) due to the impulse sequence 8(n)

Alma ate 2 slices of pie.

Harris cut his pie into 8 slices and ate 3 slices, which means he consumed 3/8 of the pie. Alma cut her pie into 4 slices.

Harris cut his pie into 8 slices and ate 3 slices, which means he consumed 3/8 of the pie. Alma cut her pie into 4 slices. Together, they ate 5/8 of a pie. To determine how many slices Alma ate, we subtract the slices Harris ate from the total.

5/8 - 3/8 = 2/8

Simplifying the fraction, we have:

2/8 = 1/4

This means that Alma ate 1/4 of the pie, which corresponds to 2 slices. Therefore, the correct answer is option B: Alma ate 2 slices of pie.

Understanding fraction subtraction and the concept of proportion allows us to determine the number of slices Alma ate based on the information provided. By subtracting the slices Harris ate from the total, we find that Alma consumed 2 slices of pie.

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Answer:

The sun of 10 is 2 times much 4.

Answer:

x=3

Step-by-step explanation:

➡️ Let x be the number;

4(x+2)=20

x+2=5

x=3

The number is 3.

Answer:

- 20x/3

Step-by-step explanation:

I hope that helps :)

Answer:

$11.67 per pound

Step-by-step explanation:

Answer:

$11.67

Step-by-step explanation:

4 clerks can be justified on a cost basis.The correct answer is option C.

To determine the number of clerks that can be justified on a cost basis, we need to analyze the trade-off between the cost of hiring additional clerks and the cost associated with customer waiting time.

Let's calculate the total cost for each option and choose the option with the lowest cost:

Option a: 6 clerks

The average service rate of 21 per hour exceeds the arrival rate of 63 per hour, meaning that the system is not overloaded. Hence, no waiting time is incurred.

The total cost is the cost of hiring 6 clerks, which is 6 * $13.8 = $82.8.

Option b: 8 clerks

Again, the service rate exceeds the arrival rate, so there is no waiting time. The total cost is 8 * $13.8 = $110.4.

Option c: 4 clerks

In this case, the arrival rate exceeds the service rate, resulting in a queuing system. Using queuing theory formulas, we find that the average number of customers in the system is given by L = λ / (μ - λ), where λ is the arrival rate and μ is the service rate.

Plugging in the values, we get L = 63 / (21 - 63) = 63 / (-42) = -1.5. Since the number of customers cannot be negative, we assume an average of 0 customers in the system. Therefore, there is no waiting time. The total cost is 4 * $13.8 = $55.2.

Option d: 7 clerks

Similar to option c, the arrival rate exceeds the service rate. Using the queuing theory formula, we find L = 63 / (21 - 63) = -1.5. Again, assuming an average of 0 customers in the system, there is no waiting time. The total cost is 7 * $13.8 = $96.6.

Option e: 5 clerks

Applying the queuing theory formula, L = 63 / (21 - 63) = -1.5. Assuming an average of 0 customers in the system, there is no waiting time. The total cost is 5 * $13.8 = $69.

Comparing the total costs, we can see that option c has the lowest cost of $55.2. Therefore, on a cost basis, 4 clerks can be justified.

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The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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The optimal feasible solution is x1 = 1, x2 = 0.4, and the problem is a regular linear programming problem.

To solve the given linear programming problem, let's define the decision variables and formulate the objective function and constraints:

Decision Variables:

x1, x2

Objective Function:

Maximize: 2x1 + 6x2

Constraints:

2x1 + 5x2 ≤ 4

4x1 + x2 ≤ 6

x1, x2 > 0

To find the optimal feasible solution, we can use a linear programming solver. Here is the optimal solution for the given problem:

Optimal Solution:

x1 = 1

x2 = 0.4

The maximum value of the objective function is obtained when x1 = 1 and x2 = 0.4. The maximum value is 2(1) + 6(0.4) = 4.8.

Now let's analyze if the solution is a special case of linear programming.

This problem falls under the category of Linear Programming (LP) problems. However, it does not represent any specific special case of LP such as degeneracy, unboundedness, or infeasibility. The given problem has a feasible solution, and the objective function is maximized within the given constraints. Hence, it is a regular LP problem without any special case conditions.

Note: Since the solution is text-based, there is no need to scan or provide a separate file.

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The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.

It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.

A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.

A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.

For the Z-test, the test statistic is computed as

z = (x - μ) / (σ / √n)

where x = sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.

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The standard matrix of a linear transformation is a matrix that represents the transformation. In this case, the linear transformation t: R^2 → R^3 is defined by the values of t(2,3), t(3,4), and t(4,5).

To find the standard matrix of the linear transformation t, we consider how the transformation maps the standard basis vectors of R^2 to R^3. The standard basis vectors in R^2 are (1,0) and (0,1), and their images under t are the respective columns of the standard matrix.

Using the given values, we have:

t(1,0) = (t11, t21, t31) = t(2,3) - t(0,0) = (2,4,0) - (0,0,0) = (2,4,0)

t(0,1) = (t12, t22, t32) = t(3,4) - t(0,0) = (1,3,2) - (0,0,0) = (1,3,2)

Therefore, the standard matrix of the linear transformation t is:

| t11 t12 |

| t21 t22 |

| t31 t32 |

Substituting the values we found, the standard matrix is:

| 2 1 |

| 4 3 |

| 0 2 |

This matrix represents the linear transformation t: R^2 → R^3.

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