Irene made a mistake when she solved this inequality:

Step 1: -6(x + 3) + 10 < -2
Step 2: -6x − 18 + 10 < -2
Step 3: -6x − 8 < -2
Step 4: -6x < 6
Step 5: x < -1

Between which two consecutive steps did Irene make a mistake?

Answer: 8.5x+25y−9

Step-by-step explanation:

To find the polar coordinates (r, θ) corresponding to the Cartesian coordinates (-6, 6), we can use the following formulas:

r = √(x² + y²)

θ = arctan(y / x)

(a) For the given point (-6, 6):

x = -6

y = 6

First, let's find the value of r:

r = √((-6)² + 6²) = √(36 + 36) = √72 = 6√2

Next, let's find the value of θ:

θ = arctan(6 / -6) = arctan(-1) = -π/4 (since the point lies in the third quadrant)

Therefore, the polar coordinates of the point (-6, 6) are (6√2, -π/4).

(b) For r > 0 and 0 ≤ θ < 2:

In this case, the polar coordinates will remain the same: (6√2, -π/4).

(c) For r < 0 and 0 ≤ θ < 2:

Since r cannot be negative in polar coordinates, there are no valid polar coordinates for r < 0 and 0 ≤ θ < 2.

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The solution to the system of equations is:
x ≈ 0.48, y ≈ 1.86, z ≈ -2.83

To solve the given system of equations by elimination, we can follow these steps:
1. Multiply the first equation by 5 and the second equation by -1 to make the coefficients of x in both equations opposite to each other.
The equations become:
  5x + 5y - 10z = 40
 -5x + 3y - z = 6
2. Add the modified equations together to eliminate the x variable:
   (5x + 5y - 10z) + (-5x + 3y - z) = 40 + 6
   Simplifying, we get:
   8y - 11z = 46

3. Multiply the first equation by -2 and the third equation by 5 to make the coefficients of x in both equations opposite to each other.
The equations become:
 -2x - 2y + 4z = -16
 5x - 5y + 20z = -65
4. Add the modified equations together to eliminate the x variable:
  (-2x - 2y + 4z) + (5x - 5y + 20z) = -16 + (-65)
  Simplifying, we get:
 -7y + 24z = -81
5. We now have a system of two equations with two variables:
   8y - 11z = 46

  -7y + 24z = -81
6. Multiply the second equation by 8 and the first equation by 7 to make the coefficients of y in both equations        opposite to each other
The equations become:
 56y - 77z = 322
-56y + 192z = -648
7. Add the modified equations together to eliminate the y variable:
  (56y - 77z) + (-56y + 192z) = 322 + (-648)
 Simplifying, we get:
  115z = -326
8. Solve for z by dividing both sides of the equation by 115:
  z = -326 / 115
 Simplifying, we get:
  z = -2.83 (approximately)
9. Substitute the value of z back into one of the original equations to solve for y. Let's use the equation 8y - 11z = 46:
    8y - 11(-2.83) = 46
 Simplifying, we get:
  8y + 31.13 = 46
 Subtracting 31.13 from both sides of the equation, we get:
  8y = 14.87
  Dividing both sides of the equation by 8, we get:
  y = 1.86 (approximately)

10. Substitute the values of y and z back into one of the original equations to solve for x. Let's use the equation x + y -  2z = 8:
x + 1.86 - 2(-2.83) = 8
 Simplifying, we get:
  x + 1.86 + 5.66 = 8
 Subtracting 1.86 + 5.66 from both sides of the equation, we get:
   x = 0.48 (approximately)

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The exponential equation that represents the number of followers y the Miami Marlin’s had x years after they joined the site in 2009 is:

\(y = 3205(1.85252343783)^x\)

An exponential function is modeled by:

\(A(t) = A(0)(b)^t\)

In which:

In this problem:

Given two points, the rate of change is given by:

\(b^{7 - 2} = \frac{240000}{11000}\)

\(b^5 = 21.818181\)

\(b = \sqrt[5]{21.818181}\)

\(b = 1.85252343783\)

Then, the equation is:

\(y = a(1.85252343783)^x\)

Point (2, 11000) means that when \(x = 2, y = 11000\), hence this is used to find a.

\(11000 = a(1.85252343783)^2\)

\(a = \frac{11000}{(1.85252343783)^2}\)

\(a = 3205\)

Hence, the exponential equation is:

\(y = 3205(1.85252343783)^x\)

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Step-by-step explanation:

Paul behavior is not unethical is that the information is firsthand hand factual and

Answer: 67m + 16

Step-by-step explanation:

       We can use the difference between an algebraic equation and an algebraic expression. Here, an algebraic equation will have an equal sign (=) while an algebraic expression will not.

        This leads us to the answer of;

             67m + 16

The statement " to find the leading coefficent we have to write our polynomial so that the order of the degree goes from least to greatest" is false.

To find the leading coefficient of a polynomial, we need to write the polynomial in standard form, where the terms are arranged in descending order of degree, from highest to lowest. The leading coefficient is the coefficient of the term with the highest degree.

In order to determine the leading coefficient, we need to write the polynomial in standard form, where the terms are arranged in descending order of degree.

For example, consider the polynomial 3x^2 + 2x - 1. In this case, the highest degree term is 3x^2, and the leading coefficient is 3. By arranging the polynomial in standard form, with the terms in descending order of degree, we can easily identify the leading coefficient.

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Answer:

30 gallons.

Step-by-step explanation:

If you multiply 6 x 5

(6 being the gallons)

(5 being the minutes)

I believe that the answer is 30 gallons.

The relationship between y and x is y = 5x + 15.

A linear equation is in the form:

y = mx + b

where y, x are the variables, m is the rate of change (slope) and b is the initial value of y (y intercept).

From the table, using point (5, 40) and (25, 140):

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-40=\frac{140-40}{25-5} (x-5)\\\\y=5x+15\)

The relationship between y and x is y = 5x + 15.

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Therefore, the expected annual profit of Ruby Company is 2.703 billion dollars using probability.

Let X be the annual profit of the company. We know that X follows a normal distribution with variance equal to the cube of its mean, i.e., Var(X) = (E[X])^3.

To find the expected annual profit, we need to find the mean of X, denoted as E[X].

We are given that the probability of an annual loss is 5%. This means that the probability of making a profit is 1 - 0.05 = 0.95.

Let Z be a standard normal random variable, then we have:

P(X < 0) = P((X - E[X]) / sqrt(Var(X)) < (0 - E[X]) / sqrt(Var(X)))

= P(Z < -E[X] / (E[X])^(3/2))

Since P(X < 0) = 0.05, we have:

0.05 = P(Z < -E[X] / (E[X])^(3/2))

Using a standard normal table or calculator, we can find that P(Z < -1.645) = 0.05, where -1.645 is the 5th percentile of the standard normal distribution.

Thus, we have:

-E[X] / (E[X])^(3/2) = -1.645

this equation, we get:

E[X]^(1/2) = 1.645

Taking the square of both sides, we get:

E[X] = 2.703

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To prove that the triangles are similar by the SSS similarity theorem, we use MN corresponds to QR, also ∠S ≅ ∠O

Two triangles are comparable if the measurements of their corresponding sides are proportionate. Additionally, if the measurements of two sides in one triangle are proportional to the measurements of the corresponding sides in another triangle and the included angles are congruent, the triangles are similar.

Similar figures

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides is in the same proportion.

From the image, MN corresponds to QR, also ∠S ≅ ∠O

To prove that the triangles are similar by the SSS similarity theorem, we use MN corresponds to QR, also ∠S ≅ ∠O

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EXPLANATION.

The whole numbers are the same natural numbers that start from zero to infinity, they are positive and negative, for example in the number line we can see them from zero to positive infinity, and from zero to negative infinity.

Whole numbers express a complete unit, this means that they do not have an integer part and a decimal part.

Now according to what has already been mentioned, we can see in the exercise that the integers are 9 and 1.00000, which we must enclose in a circle.

By adding all the money she spend we get $0.69

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that Dee spends $0.25, $0.30, $0.10 and $0.04.

We need to find the money she spend in all.

Therefore, we have to add all the expenditure

0.25 + 0.30 + 0.10 + 0.04 = 0.69

The total money she spend could be 0.69.

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The coefficient of determination is the percentage of variance in one variable that can be predicted or explained by another.

Therefore, the coefficient of determination is the percentage of variance in one variable that can be predicted or explained by another.

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The orthorhombic unit cell illustrating the (1 2 1) direction will have a straight line connecting the starting corner with the point reached after moving 1 unit along the x-axis, 2 units along the y-axis, and 1 unit along the z-axis

1. Orthorhombic unit cell have lattice parameters a, b, and c and have all angles equal to 90 degrees (α = β = γ = 90°).

2. The (1 2 1) direction refers to the vector direction that moves 1 unit in the x direction (a), 2 units in the y direction (b), and 1 unit in the z direction (c).

3. In an orthorhombic unit cell, you can visualize the (1 2 1) direction by starting at a corner of the unit cell and moving 1 unit along the x-axis, 2 units along the y-axis, and 1 unit along the z-axis.

4. Since all angles in the orthorhombic unit cell are 90 degrees, the (1 2 1) direction will be a straight line connecting the starting point and the final point after moving along the x, y, and z directions.

So, the orthorhombic unit cell illustrating the (1 2 1) direction will have a straight line connecting the starting corner with the point reached after moving 1 unit along the x-axis, 2 units along the y-axis, and 1 unit along the z-axis.

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The z score on his first quiz was 1.29 and the z score on his second quiz was 1.73.

Alvin feels he did better on the second quiz than the first because he received a higher z score. A z score is a measure of how many standard deviations an individual score is from the mean. The higher the z score, the more standard deviations away from the mean the individual score is.

In this case, Alvin's score of 15 on his second quiz was 1.73 standard deviations away from the mean of 12.2, which is higher than his score of 16 on his first quiz which was 1.29 standard deviations away from the mean of 14.3.

This indicates that Alvin's second quiz score was further away from the mean than his first quiz score, which is why he feels he did better on the second quiz than the first.

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Answer:

The answer is B

Answer:

external conflict

Step-by-step explanation:

The probability that the first person picked will be female is 2/5.

Two quantities are compared to form a ratio. Discover how to calculate the ratio of two items, such as apples to oranges.

Total audience = 120

Ratio of males to females; 3:2

Total males : 3*120/ 5 = 72

Total females: 2*120/5 = 48

Probability that the first person picked will be female = total females / total audience

Probability = 48 / 120

Probability = 2/5

Thus, the probability that the first person picked will be female is 2/5.

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The magnetic field in tesla at a point midway between the wires is (e) 20 x 10^(-4).

To find the magnetic field at a point midway between two parallel wires carrying currents, we can use Ampere's Law.

Ampere's Law states that the magnetic field around a closed loop is directly proportional to the current passing through the loop. In the case of two parallel wires, the magnetic field at a point between them is the sum of the magnetic fields generated by each wire.

The formula for the magnetic field due to a straight wire is given by:

B = (μ₀ * I) / (2π * r)

Where:

B is the magnetic field,

μ₀ is the permeability of free space (4π × 10^(-7) T*m/A),

I is the current, and

r is the distance from the wire.

For the wire carrying a current of 8.0A, the magnetic field at the midpoint between the wires is:

B₁ = (4π × 10^(-7) * 8.0) / (2π * 0.002)

  = 2 × 10^(-4) T

For the wire carrying a current of 12A, the magnetic field at the midpoint between the wires is:

B₂ = (4π × 10^(-7) * 12) / (2π * 0.002)

  = 3 × 10^(-4) T

To find the total magnetic field at the midpoint, we sum the magnetic fields due to each wire:

B_total = B₁ + B₂

        = 2 × 10^(-4) T + 3 × 10^(-4) T

        = 5 × 10^(-4) T

Therefore, the magnetic field at a point midway between the wires is 5 × 10^(-4) T.

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Answer:

Area of Floor= (12*30)+ (20*10)

=360+ 200= 560

Ans C

The intervals at which the function is increasing is x ≥ 4, which can also be written as (4, ∞).

The intervals at which the function is increasing or decreasing is calculated as follows;

f(x) = 2x² - 16x  + 2

The derivative of the function is calculated as;

f'(x) = 4x - 16

The critical points are calculated as follows;

4x - 16 = 0

4x = 16

x = 16/4

x = 4

We will determine if the function is increasing or decreasing as follows;

let x = 0

4(0) - 16 = -16

let x = 2

4(2) - 16 = -8

let x = 4

4(4) - 16 = 0

let x = 5

4(5) - 16 = 4

Thus, the function is increasing at x ≥ 4.

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When estimating a confidence interval for variance, the statistical table that we use is option (E) The chi square table

When estimating a confidence interval for variance, we are trying to determine a range of values that we are confident the true population variance falls within. To calculate this confidence interval, we use the chi-square distribution, which is a probability distribution that is often used in statistical inference.

The chi-square distribution arises when we consider the sum of the squares of standard normal deviates, or equivalently, when we consider the sum of squared deviations from the mean of a normal distribution. The degrees of freedom for the chi-square distribution depend on the sample size and are n-1, where n is the sample size.

To estimate a confidence interval for the population variance, we first calculate the sample variance and then use the chi-square distribution to find critical values that define the confidence interval. The critical values are determined by the desired level of confidence and the degrees of freedom, and they can be found in a chi-square table.

Therefore, the correct option is (E) The chi square table

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If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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The domain of the function is R - {m} and the range of the function is (-∞, ∞).

We are given a function f: R−{n}→R defined by f(x) = (x-n)/(x-m), where m ≠ n.

To find the domain of the function, we need to consider the values of x for which the denominator (x-m) is zero. Since m ≠ n, we have m - n ≠ 0, and therefore the function is defined for all x except x = m.

Therefore, the domain of the function is R - {m}.

To find the range of the function, we can consider the behavior of the function as x approaches infinity and negative infinity. As x approaches infinity, the numerator (x-n) grows without bound, while the denominator (x-m) also grows without bound, but at a slower rate. Therefore, the function approaches positive infinity.

Similarly, as x approaches negative infinity, the numerator (x-n) becomes very negative, while the denominator (x-m) also becomes very negative, but at a slower rate. Therefore, the function approaches negative infinity.

Thus, we can conclude that the range of the function is (-∞, ∞).

In summary, the domain of the function is R - {m} and the range of the function is (-∞, ∞).

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Answer:

8 ''A''-students out of 40 is bigger

Step-by-step explanation:

8 "A"-students out of 40:

\(\frac{8}{40}\) = \(\frac{1}{5}\) = 20%

9 "A"-students out of 50:

\(\frac{9}{50}\) = 18%

20% > 15%

8 ''A''-students out of 40 is bigger

The percentage of 8 ''A'' students out of 40 is more than 9 ''A''-students out of 50.

Given that, to determine which percent is bigger: 8 ''A''-students out of 40 or 9 ''A''-students out of 50.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
According to the question,
8 ''A''-students out of 40 = 8 / 40 × 100%
                                         = 20%

9 ''A''-students out of 50 = 9 / 50 × 100%
                                         = 18%

Thus, the percentage of 8 ''A'' students out of 40 is more than 9 ''A''-students out of 50.

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Answer:

D

Step-by-step explanation:

Answer:  30 in²

Step-by-step explanation:

Area = base x height

A = 6 in x 5 in

A = 30 in²

Answer:

D. None of the above.

Step-by-step explanation:

Supplementary angles must add up to 180 degrees.

Complementary angles must add up to 90 degrees.

Vertical angles are opposite of each other.

Hope this helps!

If not, I am sorry.