A system of two linear equations is graphed on a coordinate plane.If the system has infinitely many solutions, which statement must be true

For all positive integers n and r with 0 ≤ r ≤ n, the following statements are true regarding combinations (denoted as c(a, b)):

1. c(n, 0) = 1

2. c(n, n) = 1

3. c(n, r) = c(n, n - r)

4. c(n, r) + c(n, r + 1) = c(n + 1, r + 1)

1. c(n, 0) = 1: When selecting 0 elements from a set of n elements, there is only one way to do so, which is to choose no elements. Therefore, c(n, 0) = 1.

2. c(n, n) = 1: When selecting n elements from a set of n elements, there is only one way to do so, which is to choose all the elements. Therefore, c(n, n) = 1.

3. c(n, r) = c(n, n - r): The number of combinations of r elements from a set of n elements is equal to the number of combinations of (n - r) elements. This is because choosing r elements is equivalent to choosing the remaining (n - r) elements.

4. c(n, r) + c(n, r + 1) = c(n + 1, r + 1): The sum of the number of combinations of r elements and (r + 1) elements from a set of n elements is equal to the number of combinations of (r + 1) elements from a set of (n + 1) elements. This can be understood by considering that when a new element is added to the set, the number of combinations increases based on including or excluding that element in the selection.

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For all positive integers n and r with 0 ≤ r ≤ n, the following statements are true:

c(n, r) = c(n, n - r) (symmetry property)

c(n, 0) = c(n, n) = 1 (boundary cases)

c(n, 1) = c(n, n - 1) = n (selection of one element)

c(n, r) = c(n - 1, r - 1) + c(n - 1, r) (Pascal's identity)

The symmetry property states that the number of combinations of choosing r elements from a set of size n is equal to the number of combinations of choosing n - r elements. This property arises from the fact that choosing r elements is equivalent to choosing the remaining n - r elements.

When selecting 0 elements or all n elements from a set of size n, there is only one possible combination, which is the entire set itself. Hence, c(n, 0) = c(n, n) = 1.

When selecting one element from a set of size n, there are n possible choices. Thus, c(n, 1) = c(n, n - 1) = n.

Pascal's identity states that the number of combinations of choosing r elements from a set of size n is equal to the sum of the number of combinations of choosing r - 1 elements and the number of combinations of choosing r elements from a set of size n - 1. This identity can be derived from the concept of counting combinations recursively.

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The relationship between the ratios of sin x° and cos yº is that they are reciprocals. The correct answer is option c. The ratios of sin x° and cos yº are reciprocals of each other.

In trigonometry, sin x° represents the ratio of the length of the side opposite the angle x° to the length of the hypotenuse in a right triangle. Similarly, cos yº represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Since the hypotenuse is the same in both cases, the ratios sin x° and cos yº are related as reciprocals. This means that if sin x° is equal to 12/13, then cos yº will be equal to 13/12. The reciprocals of the ratios have an inverse relationship, where the numerator of one ratio becomes the denominator of the other and vice versa.

It's important to note that the signs of the ratios can vary depending on the quadrant in which the angles x° and yº are located. However, the reciprocal relationship remains the same regardless of the signs.

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The number of employees that must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean is 107 employees.

To estimate the mean number of hours worked by all grocery store employees in the county with 95% confidence and a margin of error of 1.5 hours, we can use the sample size formula:

n = (Z * σ / E)²

where:
- n is the required sample size
- Z is the critical value (1.96 for a 95% level of confidence)
- σ is the population standard deviation (7.9 from the previous study)
- E is the margin of error (1.5 hours)

Plugging in the given values:

n = (1.96 * 7.9 / 1.5)²

n ≈ 106.56

Since you cannot have a fraction of an employee, you need to round up to the nearest whole number. Therefore, the researcher must include 107 employees in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean.

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Answer:

A

Step-by-step explanation: When she got to 14-4+3*4 she added 4+3 first instead of multiplying 3*4.

Explanation: I would do this problem by setting up a chart.

For the equation x = 3, if we set up a chart for x and y,

since x must be equal to 3, the random values we

choose in this problem are not for x, they are for y.

If we had an equation like y = 2x + 3, then we would pick values for x

and plug them into the equation to get y, but here, x is our only value.

So let's choose the values 1, 0, and -1 for y.

For each of these values, x must be equal to 3.

So we have the points (3, 1), (3,0), and (3, -1).

Notice that our graph is a vertical line, as I showed this below.

Answer:

8

Step-by-step explanation:

Answer: y = (n - 7)/x.

Step-by-step explanation: xy + 7 = n  The rule is you can do any valid operation on both sides of an equation and it will still be equal. Subtract 7.

xy = n - 7  Divide by x.

y = n/x - 7/x = (n - 7)/x

The complementary angles will be 65.6° and 24.4°.

What exactly are complementary angles?

Supplementary and complementary angles are defined by the sum of two angles. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined. If the total of two angles is 180 degrees, they are considered to be supplementary angles since they produce a linear angle when combined.

Now,

Let x be a angle then its complementary angle will be 90°-x as sum of complementary angles is equal to 90°.

as given

90°-x-x=18.8°

9--2x=18.8

2x=71.2

x=65.6° and 90-x°=24.4°

hence,

                The complementary angles will be 65.6° and 24.4°.

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Because you want to set aside three months' worth of fixed expenses for an emergency fund, the sum saved each month comes to \($416.70.\)  

In mathematics, interest is the fee or payment made for using borrowed funds; it is typically stated as a percentage of the principal sum. Interest can be divided into two categories.

Simple Interest is computed solely using the principal of the debt or investment. I = PRT, where P is the capital, R is the interest rate per period, and T is the time period, is the formula for simple interest.

Given,

The monthly wage is  \($2,415.64\) dollars.

After expenses, discretionary funds equal 54% of monthly revenue.

Fixed monthly expenses equal \((100–54%)%\) of overall monthly income.

\(= 46%\)  of monthly gross revenue

\(= 0.46 × 2,415.64\)

\(= $ 1,111.1944\)

Thus, the fixed expenditures for three months equal three times the fixed expenses for one month.

\(= 3 × 1,110.5544 = $ 3331.6632\)

This money will be conserved in 8 months, so

As a result, the monthly savings equal 1/8 of \($ 3331.6632\) .

\(= $ 416.6979 ≈ $ 416.70\)

Therefore, Because you want to set aside three months' worth of fixed expenses for an emergency fund, the sum saved each month comes to \($416.70\)  .

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The above question is incomplete, the complete question is given below:

Your realized income is $2,415.64/month, and 54% are discretionary monies. If you want to save 3 months of fixed expenses for an emergency fund, how much must you save each month to fund it in 8 months

(a)  u(x,y) = -8x'y + 8xy` is harmonic. (b) The value of the integral is `(-3/2) + i(1/6)`.

Given function is `u(x,y) = -8x'y + 8xy`.

a) To show that given function is harmonic, we need to show that `u_xx + u_yy = 0`.

Let's find `u_xx` and `u_yy`.We have `u(x,y) = -8x'y + 8xy`

Differentiating w.r.t `x` we get, `u_x = -8y + 8y = 0`

Again differentiating `u_x` w.r.t `x` we get, `u_{xx} = 0`

Differentiating `u(x,y)` w.r.t `y` we get, `u_y = -8x + 8x = 0`

Again differentiating `u_y` w.r.t `y` we get, `u_{yy} = 0`

Hence, `u_{xx} + u_{yy} = 0` Hence, `u(x,y) = -8x'y + 8xy` is harmonic.

b) To find the conjugate harmonic function, we need to find `v(x,y)` such that `f(x + iy) = u(x,y) + iv(x,y)` is analytic.

We have, `u(x,y) = -8x'y + 8xy`So, `v_x = 8xy` and `v_y = -8x'y`

Now, we can use `v_x = -u_y` and `v_y = u_x` to get `v(x,y)`

Let's differentiate `v_x` w.r.t `y` and `v_y` w.r.t `x`.

We have, `v_{xy} = 8x` and `v_{yx} = -8x`

Since, the functions are continuous and `v_{xy} = v_{yx}`.

So, `v(x,y)` is a harmonic function.

Now, `v_x = 8xy` implies `v = 4x^2y + g(x)`

Differentiating `v` w.r.t `x`, we get `v_y = 4x^2 + g'(x)`

Comparing with `v_y = -8x'y`, we get `g'(x) = -8x^2`

So, `g(x) = -8(x^3)/3

Thus, `v(x,y) = 4x^2y - 8(x^3)/3`

So, `f(x + iy) = -8x'y + 8xy + i(4x^2y - 8(x^3)/3)`

Now, let's evaluate the integral `I = \oint_C (y + x - 4ix")dz`where `C` is represented by:`G:`

The straight line from `Z = 0` to `Z = 1 + i``C_2:`

Along the imaginary axis from `Z = 0` to `Z = i`

So, `I = \int_0^1 (1 - 4t) dt + i \int_0^1 (t - 4t^2) dt`

Evaluating the integral, we get, `I = (-3/2) + i(1/6)`

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Answer:

(3x - 4) (2x + 15)

Step-by-step explanation:

6x² + 37x - 60

Using "splitting the middle term" method,

we get;

6x² + 45x - 8x - 60

= 3x (2x + 15) - 4 (2x + 15)

= (3x -4) (2x + 15)

Answer:

sorry I am very sorry to say your question is incomplete. best of luck

The missing term in the equation is n = -2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the missing term be represented as n

-2x + 18 = nx + 18

Subtracting 18 on both sides of the equation , we get

-2x = nx

Divide by x on both sides of the equation , we get

n = -2

Therefore , the missing term is n = -2

Hence , the equation is n = -2

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Answer:

b

Step-by-step explanation:

The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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Jimmy’s total income is $91838.61

You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period

The given parameters that will help us to determine the income are

wages from accounting job,             $75,937.84;

interest,                                                   $839.40

wages from museum job,                  $14,937.92;

dividends,                                                $123.45.

Therefore Jimmy's total income is the sum of all the incomes

$(75,937.84 + 839.40 + 14,937.92 + 123.45)

Total income = $91838.61

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JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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(a) Condition 2: Constant variance: The variance of the series is constant for all t, i.e., Var(Yt) = σ², where σ² is a constant for all t. Condition 3: Autocovariance is independent of time: Cov(Yt, Yt-h) = Cov(Yt+k, Yt+h+k) for all values of h and k for all t. (b) The test statistics for the Dickey-Fuller test is DFE = p - ρ / SE(p).

(a) If we let t=1, we have Y1= E1+A E0

Now let t=2, then Y2=Y1+ E2+A E1

On applying recursive substitution up to time t, we get Yt= E(Yt-1)+A Σ i=0 t-1 Ei

From the above equation, we observe that if A≠-1, the process {Yt} will be non-stationary since its mean is non-constant. There are three conditions that ensure a covariance stationary process: Condition 1: Constant mean: The expected value of the series is constant, i.e., E(Yt) = µ, where µ is a constant for all t. If the expected value is a function of t, the series is non-stationary.

(b) The problem of applying the Dickey-Fuller test when testing for a unit root when the model of a time series is given by t = pxt-1+u, where the error term ut exhibits autocorrelation is that if the error terms are autocorrelated, the null distribution of the test statistics will be non-standard, so using the standard critical values from the Dickey-Fuller table can lead to invalid inference.

The null hypothesis for the Dickey-Fuller test is that the time series has a unit root, i.e., it is non-stationary, and the alternative hypothesis is that the time series is stationary. In DFE = p- ρ / SE(p), p is the estimated coefficient, ρ is the hypothesized value of the coefficient under the null hypothesis (usually 0), and SE(p) is the standard error of the estimated coefficient.

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Answer:

domain expansion

Step-by-step explanation:

jujutsu kaisen brúh

The given statement "the estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line." is True. The estimated simple linear regression equation is obtained by minimizing the sum of the squared deviations between each value of y and the line.

This is known as the method of least squares. The line that minimizes the sum of the squared deviations is called the regression line. It is the line that best fits the data, in the sense that it minimizes the difference between the observed values of y and the values predicted by the equation of the line.

The least squares method is a widely used technique in statistics and data analysis, and is used to fit linear models to data in many different fields, including finance, economics, and engineering.

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Answer:

1.) 22+(33+44)

2.) (5+3)+(1+9)

3.) (-a+d)+(-c+b)

Step-by-step explanation:

Associative property of addition: Changing the grouping of addends does not change the sum. For example,

(2+3)+4= 2+(3+4)

No matter how you rearrange the numbers, they will always add to the same amount.

Answer: 1.) 22+(33+44)

2.) (5+3)+(1+9)

3.) (-a+d)+(-c+b)

Answer:

the answer is 9

Step-by-step explanation:

I just did the test