a unit rate is a rate in which the unit in the denominater is?

This piecewise function allows us to understand the behavior of f(t) for different ranges of t, where it takes different constant values based on the conditions defined in each interval.

The Heaviside function, denoted as H(t), is a mathematical function commonly used in piecewise functions to represent step functions. Given the expression f(t) = H(t - 1) - H(t - 2), we can express it as a piecewise function as follows:

f(t) =

{

 0,                  if t < 1,

 1,                  if 1 ≤ t < 2,

 0,                  if t ≥ 2

}

Let's break down the piecewise function into its different cases:

For t < 1: In this case, the expression H(t - 1) evaluates to 0 since t - 1 is negative. Similarly, H(t - 2) also evaluates to 0. Therefore, f(t) equals 0 for t less than 1.

For 1 ≤ t < 2: In this interval, the expression H(t - 1) evaluates to 1 since t - 1 is non-negative. On the other hand, H(t - 2) evaluates to 0. Hence, f(t) equals 1 for t between 1 (inclusive) and 2 (exclusive).

For t ≥ 2: In this case, both H(t - 1) and H(t - 2) evaluate to 1 since t - 1 and t - 2 are non-negative. Therefore, f(t) equals 0 for t greater than or equal to 2.

By combining these cases, we obtain the piecewise function representation of f(t) = H(t - 1) - H(t - 2) as shown above. This piecewise function allows us to understand the behavior of f(t) for different ranges of t, where it takes different constant values based on the conditions defined in each interval.

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hi

(x+3)^2 -4 = ( (x+3) +2) ( (x+3)-2 )

= ( x+5) (x +1)

so

solutions are : x+5=0 so x=-5

x+1= 0. so x= -1

solution are -5 +and -1

The equation of the fitted regression line for the given data {(1, 2), (2, 4), (3, 5), (4, 7)} is y = 1.5x + 0.5, calculated using least-squares method.

To find the equation of the regression line, we can use the least-squares method. This method aims to minimize the sum of the squared differences between the actual data points and the predicted values on the line. In this case, we want to find a line of the form y = mx + b, where m represents the slope and b represents the y-intercept.

To calculate the slope (m) and y-intercept (b), we can use the following formulas:

m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

b = (Σy - mΣx) / n

where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x values, Σy is the sum of y values, and Σ(x^2) is the sum of squared x values.

Using these formulas and the given data, we can calculate the slope and y-intercept as follows:

Σx = 1 + 2 + 3 + 4 = 10

Σy = 2 + 4 + 5 + 7 = 18

Σxy = (1 * 2) + (2 * 4) + (3 * 5) + (4 * 7) = 2 + 8 + 15 + 28 = 53

Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) = 1 + 4 + 9 + 16 = 30

n = 4

Now, let's substitute these values into the slope formula:

m = (4 * 53 - 10 * 18) / (4 * 30 - 10^2)

m = (212 - 180) / (120 - 100)

m = 32 / 20

m = 1.6

Next, we can substitute the calculated slope and the sum values into the y-intercept formula:

b = (18 - 1.6 * 10) / 4

b = (18 - 16) / 4

b = 2 / 4

b = 0.5

Therefore, the equation of the fitted regression line is y = 1.5x + 0.5.

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The nine fundamental solutions to the differential equation are:

\(e^{(-3+i)t}, e^{(-3-i)t}, e^t, te^t,\) 1, t, t²/2!, t³/3!, \(t^4\)/4!, \(e^{(-5+i)t}, ~and ~e^{(-5-i)t}\)

We have,

The characteristic equation of the given differential equation is:

\((r^2 + 6r + 10)^2 \times r^2 (r - 1)^3 = 0\)

We can find the fundamental solutions by looking at the roots of the characteristic equation.

The roots can be categorized as follows:

Roots of multiplicity 2 = -3 + i and -3 - i

Roots of multiplicity 2 =  1

Root of multiplicity 1 =  0

Root of multiplicity 2 = -5 + i and -5 - i

For each of these roots, we need to find the corresponding fundamental solution.

For the roots (-3 + i) and (-3 - i), the corresponding fundamental solutions are:

\(e^{(-3+i)t}~ and~ e^{(-3-i)t}\)

For root 1, the corresponding fundamental solutions are:

\(e^t~and~te^t\)

For the root 0, the corresponding fundamental solutions are:

1, t, t²/2!, t³/3!, ..., \(t^8\)/8!

For the roots (-5 + i) and (-5 - i), the corresponding fundamental solutions are:

\(e^{(-5+i)t} ~and~e^{(-5-i)t}\)

Therefore,

The nine fundamental solutions to the differential equation are:

\(e^{(-3+i)t}, e^{(-3-i)t}, e^t, te^t,\) 1, t, t²/2!, t³/3!, \(t^4\)/4!, \(e^{(-5+i)t}, ~and ~e^{(-5-i)t}\)

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Answer:

The square root of 4489 is:

Step-by-step explanation:

To find the square root by división method you must do the next:

1. you write the square root:

\(\sqrt{4489}\)

2. You separe the number inside the square root in groups of two digits, begining by the right (in this case doesn't matter, because we have 4 digits, but remember this when the number has an odd number of digits):

√44 89

3. You must find a whole number which squaring gives us a number equal to or less than our first pair of digits (44), in this case is 6, because 6*6 = 36 and, if we take 7, 7*7 = 49 (we would pass):

√44 89 ║6

4. Now, we subtract the squaring of the number obtained to our first pair of digits:

√44 89 ║6

-36

= 8

5. We duplicate the root obtained (6) and we lower the next pair of digits next to the result of the previous subtraction, but this time we make pairs of digits from the left:

√44 89 ║6

-36       ║12

= 88 9

6. We divide 88 (our pair of digits) in 12 (the double of the obtained root):

88 ÷ 12 = 7.3333333 (we approximate to 7)

7. We put the number obtained in the division (7) to the right side of the double of the obtained root (12) and we multiply by this too:

√44 89 ║6

-36       ║127 * 7 = 889

= 88 9

8. we subtract the number obtained in the multiplication to the digits we order in pairs (889):

√44 89 ║6

-36       ║127 * 7 = 889

= 88 9

- 889

= 0

9. We raise the number that we multiply by twice the previous root found, as another digit of the root:

√44 89 ║67

-36       ║127 * 7 = 889

= 88 9

- 889

= 0

As you can see, the square root of 4489 with this method gave us the result 67.

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

No, when finding the upper and lower quartiles, the median is not included in the calculations.

When finding the upper and lower quartiles of a data set, the median (or second quartile) is not included in the calculations. The quartiles divide the data set into four equal parts, with the median representing the second quartile.

To find the lower quartile (Q1), one needs to determine the median of the lower half of the data set, excluding the median itself. This includes the data points below the median.

Similarly, to find the upper quartile (Q3), the median of the upper half of the data set is determined, excluding the median. This includes the data points above the median.

The inclusion of the median in the calculation of quartiles can cause confusion, but it is important to note that the median is separate and distinct from the quartiles.

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Answer:

An integer 0

Step-by-step explanation:

Answer:

(-1,1)

Step-by-step explanation:

the answer is where the two lines intersect.

Answer:

r= 5.71%

Step-by-step explanation

Just did it

Answer:

5.71%

Step-by-step explanation:

Using Trigonometric Identities, The value of y equals 20.36.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.

These identities are in use when trigonometric function-based expressions need to be made simpler. The integration of non-trigonometric functions is a crucial application; a typical method is employing the substitution rule with a trigonometric function first, and then simplifying the resulting integral with a trigonometric identity.

Using Trigonometric ratios,

Sin θ = perpendicular / hypotenuse

Sin 69 = 19 / y

0.933 = 19 / y

y = 19 / 0.933

y = 20.36

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Answer:

$110

Step-by-step explanation:

The computation is shown below:

Provided that

Number of desk purchased    Fund Left $

           0                                   700

           1                                    590

           2                                   480

           3                                   370

           4                                   260

           5                                   150

           6                                    40

Now the Fund decreased while purchasing is

= 5 desks - 2 desks

= 3 desks

i.e

= $480 - $150

= $330

Now the amount of money left for decreased the desk fund is

\(= \frac{Fund\ decreased }{number\ of\ desk\ decreased}\)

\(= \frac{\$330}{3\ desk}\)

= $110

Answer:

A)$110

Step-by-step explanation:

This value will represent the range within which the middle 50% of Emilia's daily miles are distributed

Hi! The box plot represents the miles Emilia ran after school for 21 days. To find the IQR (Interquartile Range), you can use the box plot by identifying the values of the first quartile (Q1) and the third quartile (Q3).

The IQR is calculated by subtracting Q1 from Q3 (IQR = Q3 - Q1). By examining the box plot, locate Q1 and Q3 on the plot, and perform the subtraction to find the IQR.

This value will represent the range within which the middle 50% of Emilia's daily miles are distributed.

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Answer: 2 one

Step-by-step explanation:

Answer:

last one

Step-by-step explanation:

Sinkholes are cavities in the ground that form when water erodes an underlying rock layer.

The solution to the system of linear equations using the Gauss-Jordan elimination method is (x, y, z) = (1, -2, 3).

To solve the system of linear equations using the Gauss-Jordan elimination method, we write the augmented matrix:

[3 2 -2 | 11]

[3 -2 2 | -5]

[4 -1 3 | -8]

Applying row operations, we aim to transform the augmented matrix into reduced row-echelon form. After performing the necessary row operations, we obtain the following matrix:

[1 0 0 | 1]

[0 1 0 | -2]

[0 0 1 | 3]

The matrix represents the system of equations:

x = 1

y = -2

z = 3

Therefore, the solution to the system of linear equations is (x, y, z) = (1, -2, 3). The Gauss-Jordan elimination method was used to obtain the reduced row-echelon form, and the augmented matrix played a crucial role in performing the row operations.

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The first and third linear systems are possible and the second and the fourth have no solution.

(a) A linear system of 3 equations and 3 unknowns can have infinitely many solutions if the equations are linearly dependent or if the system represents a plane intersecting a line or three planes intersecting at a single point. An example of an augmented row-reduced echelon matrix that satisfies this description could be:

[ 1  0  0 |  3 ]

[ 0  1  0 | -2 ]

[ 0  0  0 |  0 ]

(b) A linear system of 3 equations and 4 unknowns cannot have exactly one solution. This is because there are more unknowns than equations, which leads to an underdetermined system. Therefore, there will be infinitely many solutions or no solutions at all.

(c) A linear system of 3 equations and 2 unknowns can have exactly one solution if the equations represent three lines that intersect at a single point. An example of an augmented row-reduced echelon matrix that satisfies this description could be:

[ 1  0 |  2 ]

[ 0  1 | -3 ]

[ 0  0 |  0 ]

(d) A linear system of 3 equations and 2 unknowns cannot have a unique solution. This is because there are more equations than unknowns, resulting in an overdetermined system. Therefore, there will be either infinitely many solutions or no solutions at all.

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Answer:

y = -1/3x - 7/3

Step-by-step explanation:

To find the slope, you have to plug the values into the slope formula.

y2 - y1/ x2 - x1

-4 - (-2) / 5 - (-1)

-1/3

Now to find the y-intercept, plug in one of the coordinates into the equation.

y = -1/3x + b

-2 = -1/3(-1) +b

-2 = 1/3 + b

-7/3 = b

The equation is y = -1/3x - 7/3.  

The Solution is Y = - ( 1 / 3 )X - 7 / 3 where points are ( 5 , - 4) and ( - 1 , - 2) that passes through a straight line. Y = MX + C is the Formula for Straight line equation.

As per given problem, M is Slope

M = (Y2 - Y1) / (X2 - X1)

M = (- 4 - (- 2)) / ( 5 - (- 1))

M = - (1 / 3)

Now, Line becomes

- 2 = - ( 1 / 3) x (- 1)+ C

- 2 = 1 / 3 + C

C = - (7 / 3)

So, Solution:  Y = - (1 / 3)X - (7 / 3)

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Answer:

so y represents her age right now so if we go back we are subtracting so he age would be y-5

a

Hope This Helps!!!

The rules and the sequence are aₙ = aₙ₋₁ - 2, aₙ = -aₙ₋₁ and -3, -5 and -7 & 1, -1 and 1

The sequence is given as

1, -1

Assume the sequence is an arithmetic sequence, then we have

Common difference, d = -1 - 1

Evaluate

d = -2

So, we have the sequence to be

aₙ = aₙ₋₁ - 2

This means that the next three terms are -3, -5 and -7

Here, we have

1, -1

Assume the sequence is a geometric sequence, then we have

Common ratio, r = -1/1

Evaluate

r = -1

So, we have the sequence to be

aₙ = -aₙ₋₁

This means that the next three terms are 1, -1 and 1

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Answer:

16

Step-by-step explanation:

Answer:

n= -9

Step-by-step explanation:

The calculator is correct haha, You're welcome.

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Answer:

w = \(\frac{p -2l}{2}\)

Step-by-step explanation:

p = 2l + 2w  Subtract 2l from both sides of the equation

p - 2l = 2p  Divide both sides by 2

\(\frac{p -2l}{2}\) = w

The mark-up (percent increase) of the price of the shoe from the manufacturing company to the store is 100%.

Given the following data:

To determine the mark-up (percent increase) of the price of the shoe from the manufacturing company to the store:

First of all, we would determine the increase in price of this shoe:

\(Increase = selling\;price -cost\;price\\\\Increase = 150-75\)

Increase = $75

For mark-up (percent increase):

\(Mark\;up = \frac{Increase}{Cost\;price} \times 100\\\\Mark\;up = \frac{75}{75} \times 100\)

Mark-up = 100%

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Answer:

Positive factors of 76 are 1, 2, 4, 19, 38, and 76. Thus, it has 6 positive factors.

Step-by-step explanation:

Answer:

about 6 positive factors, including 1, 2, 4, 19, 38, and 76

Step-by-step explanation:

Answer:

\( \frac{7}{8} = 0.875\)

Step-by-step explanation:

\( \frac{3}{4} \div \frac{6}{7} \)

\( \frac{3}{4} \times \frac{7}{6} = \frac{1}{4} \times \frac{7}{2} \)

\( \frac{1 \times 7}{4 \times 2} = \frac{7}{4 \times 2} \)

\(\boxed{\green{ = \frac{7}{8} = 0.875}}\)

Answer:

115

Step-by-step explanation:

Given :

Mean of intelligence score = 100

Standard deviation of intelligence score = 15

Since both are perfectly correlated,

The Zscore ON SAT = +1.0

Using the standard normal interpretation, Xcore on SAT of +1.0 means 1 standard deviation to the right

This means :

Mean + 1 standard deviation

100 + 1*15

= 115

We could use the Zscore formula directly too:

Zscore = (x - mean) / standard deviation

Zscore = +1 ; x = score

Hence, we have

1 = (x - 100) / 15

1 * 15 = x - 100

15 = x- 100

x = 15 + 100

x = 115

The f-value having an area of 0.975 to its left is the critical value of the F-distribution with degrees of freedom (df1 = 1, df2 = infinity) or (df1 = infinity, df2 = 1). This value is approximately 3.84.

The F-distribution is a probability distribution that arises in the analysis of variance (ANOVA) and other statistical tests. It is a continuous distribution that takes values greater than or equal to zero. The distribution has two parameters, the degrees of freedom (df1 and df2), which depend on the sample sizes and the number of groups in the ANOVA.The critical value of the F-distribution is the value that separates the rejection region (where the null hypothesis is rejected) from the non-rejection region (where the null hypothesis is not rejected). The critical value depends on the level of significance (alpha), which is usually set at 0.05 or 0.01, and the degrees of freedom.

In this case, we want to find the critical value of the F-distribution with an area of 0.975 to its left. This means that the area to the right of the critical value is 0.025. Using a table of the F-distribution or a statistical software, we can find that the critical value with (df1 = 1, df2 = infinity) or (df1 = infinity, df2 = 1) is approximately 3.84. Therefore, if the calculated F-value is greater than 3.84, we can reject the null hypothesis with a significance level of 0.05 and conclude that there is a significant difference between the groups in the ANOVA.

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