A phone company charges a base fee of $15 per month plus an additional charge per minute. the monthly phone cost p can be represented by this equation: p = 15 + am, where a is the additional charge per minute, and m is the number of minutes used.

The solutions of the given system of equations y-(1/2)² = 1+3x and

y+ (1/2)x² = x are x=-0.775 and x=-3.224

To solve the system of equations by substitution, we need to isolate one variable in one equation and substitute it into the other equation.

Let's start by isolating y in the first equation:
y - (1/2)² = 1 + 3x
y - 1/4 = 1 + 3x
y = 1 + 3x + 1/4
y = 3x + 5/4

Now, we substitute this value of y into the second equation:
y + (1/2)x² = x
(3x + 5/4) + (1/2)x² = x
3x + 5/4 + (1/2)x² = x

To solve this equation, we need to multiply everything by 4 to get rid of the fractions:
12x + 5 + 2x² = 4x

Now, let's solve this quadratic equation. We move all terms to one side to get:
2x² + 8x + 5 = 0

Unfortunately, this equation does not factor nicely. So we can solve it using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 2, b = 8, and c = 5. Plugging these values into the quadratic formula, we get:
x = (-8 ± √(8² - 4(2)(5))) / (2(2))

Simplifying further:
x = (-8 ± √(64 - 40)) / 4
x = (-8 ± √(24)) / 4

The solutions of the system of equations are x=-0.775 and x=-3.224

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The range of Abby's data is 6.The correct option is (b) 6.

Range can be defined as the difference between the maximum and minimum values in a data set. Abby has recorded the number of students who like playing different sports.

The range can be determined by finding the difference between the maximum and minimum number of students who like a particular sport.

We can create a table like this:

Number of students Favorite sport 3 Volleyball 8 Basketball, Swimming 5 Soccer 2 Track and Field

The range of Abby’s data can be found by subtracting the smallest value from the largest value.

In this case, the smallest value is 2, and the largest value is 8. Therefore, the range of Abby's data is 6.The correct option is (b) 6.

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The function g(x) to represent the price after the $200 rebate is g(x) = x - $200.

The function g(x) represents the final price after applying the $200 rebate. To calculate the final price, we subtract the rebate amount from the original price.

The original price is denoted by x. Since the manufacturer offers a $200 rebate for each purchase of a computer, we subtract $200 from the original price to obtain the final price.

Therefore, the function g(x) = x - $200 represents the price after the $200 rebate is applied.

This function can be used to calculate the final price for any given original price x. For example, if the original price is $1000, we can substitute x = $1000 into the function to find g($1000) = $1000 - $200 = $800, indicating that the final price after the rebate would be $800.

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Answer:

Half of 1 and a half inches is 0.5 and 0.75 inches.

Step-by-step explanation:

The cobweb model can be extended to incorporate more complex dynamics, such as an AR(2) (autoregressive of order 2) model, where the current value depends on the two previous values.

It is worth noting that the cobweb model can be extended to incorporate more complex dynamics, such as an AR(2) (autoregressive of order 2) model, where the current value depends on the two previous values.

The dynamics produced by the cobweb model are generally consistent with an AR(1) (autoregressive of order 1) model. The cobweb model is a simple economic model that illustrates the dynamic behavior of a market where producers and consumers adjust their behavior based on past conditions.

In the cobweb model, producers make decisions based on their expectations of future prices, which are influenced by past prices. This type of behavior can be captured by an autoregressive model, where the current value of a variable depends on its past values.

On the other hand, the cobweb model is not directly consistent with an MA(infinity) (moving average of infinite order) model. MA models capture the dependence of the current value of a variable on past error terms, rather than past values of the variable itself. The cobweb model does not involve error terms in the same way as an MA model.

It is worth noting that the cobweb model can be extended to incorporate more complex dynamics, such as an AR(2) (autoregressive of order 2) model, where the current value depends on the two previous values. However, the basic cobweb model itself is typically described by an AR(1) model.

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The z-score for a data value of 144 is 0.2.

To find the z-score for a data value of 144 in a normal distribution with a mean of 143 and a standard deviation of 5, we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (144 - 143) / 5

z = 1 / 5

z = 0.2

The z-score measures how many standard deviations a data point is away from the mean. In this case, since the z-score is positive, it means that the data value of 144 is 0.2 standard deviations above the mean.

The z-score helps us determine the relative position of a data point within a distribution, providing a standardized way of comparing values across different normal distributions.

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The expression 14√x + 3√y is simplified.

To simplify the expression, we need to determine if there are any like terms. In this case, we have two terms: 14√x and 3√y.

Although they have different radical parts (x and y), they can still be considered like terms because they both involve square roots.

To combine these like terms, we add their coefficients (the numbers outside the square roots) while keeping the same radical part. Therefore, the simplified form of the expression is:

14√x + 3√y

No further simplification is possible because there are no other like terms in the expression.

So, in summary, the expression: 14√x + 3√y is simplified and cannot be further simplified as there are no other like terms to combine.

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The test statistic is approximately 0.8314 (rounded to 4 decimal places).

To determine if U.S. residents with a high school diploma make significantly more than those with a GED, we can conduct a two-sample t-test.
The null hypothesis (H0) assumes that there is no significant difference in the average yearly income between the two groups.

The alternative hypothesis (Ha) assumes that there is a significant difference.

Using the formula for the test statistic, we calculate it as follows:
Test statistic = (x₁ - x₂) / √((s₁² / n₁) + (s₂² / n₂))
Where:
x₁ = average yearly income of group 1 ($35,621)
x₂ = average yearly income of group 2 ($34,598)
s₁ = standard deviation of group 1 ($3,510)
s₂ = standard deviation of group 2 ($3,510)
n₁ = number of observations in group 1 (100)
n₂ = number of observations in group 2 (120)
Substituting the values, we get:
Test statistic = (35621 - 34598) / √((3510² / 100) + (3510² / 120))
Calculating this, the test statistic is approximately 0.8314 (rounded to 4 decimal places).

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Based on these scenarios, we see that if Gina walks 3 additional laps, each lap will take her 10 minutes. Therefore, on the days that she walks until 3:40, Gina walks 3 extra laps.

From 2:00 to 3:10 (1 hour and 10 minutes), Gina warms up, plays soccer, and walks two laps.

This means that Gina has 1 hour and 10 minutes - the time it takes to warm up, play soccer, and walk two laps - to walk additional laps until 3:40. We need to find out how many laps she can walk in this remaining time.

The remaining time from 3:10 to 3:40 is 30 minutes (3:40 - 3:10 = 0:30).

Since Gina takes the same amount of time to walk each lap, we need to determine the duration of time she spends on each lap. To do this, we divide the remaining time by the number of additional laps:

30 minutes ÷ Number of additional laps = Time per lap

Now, we can check different scenarios by assuming a number of additional laps and calculating the time per lap:

1 additional lap:

30 minutes ÷ 1 additional lap = 30 minutes per lap

2 additional laps:

30 minutes ÷ 2 additional laps = 15 minutes per lap

3 additional laps:

30 minutes ÷ 3 additional laps = 10 minutes per lap

Based on these scenarios, we see that if Gina walks 3 additional laps, each lap will take her 10 minutes. Therefore, on the days that she walks until 3:40, Gina walks 3 extra laps.

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This random assignment of participants and comparison of outcomes helps to establish a cause-and-effect relationship between the medication and the reduction in symptoms.

The experimental units in this study are the adult volunteers who suffer from allergies.

These volunteers were randomly assigned to two groups: the treatment group, which received the new experimental medication, and the control group, which received an existing medication.

The researchers then measured the percentage of participants in each group who reported a significant reduction in their allergy symptoms without experiencing drowsiness. The results showed that 44% of those in the treatment group and 28% of those in the control group experienced this improvement.

By comparing the outcomes between the two groups, the researchers can determine if the new medication effectively reduces allergy symptoms without causing drowsiness compared to the existing medication.

This random assignment of participants and comparison of outcomes helps to establish a cause-and-effect relationship between the medication and the reduction in symptoms.

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Diego travelled x miles in the cab. To find out how far Diego travelled in the cab, we need to use the information given. We know that City Cabs charges a pickup fee of $ and $ per mile travelled.

Let's assume that Diego traveled x miles in the cab. The fare for the ride would be the pickup fee plus the cost per mile multiplied by the number of miles traveled. This can be represented as follows:

Fare = Pickup fee + (Cost per mile * Miles traveled)

Since we know that Diego's fare for the ride is $, we can set up the equation as:

$ = $ + ($ * x)

To solve for x, we can simplify the equation:

$ = $ + $x

$ - $ = $x

Divide both sides of the equation by $ to isolate x:

x = ($ - $) / $

Now, we can substitute the values given in the question to find the distance travelled:

x = ($ - $) / $

x = ($ - $) / $

x = ($ - $) / $

x = ($ - $) / $

Therefore, Diego travelled x miles in the cab.

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The number of eigenvalues possible for the covariance matrix of a data matrix X with n rows and p columns is equal to the smaller of n and p.

1. Start with a data matrix X with n rows and p columns.

2. Compute the covariance matrix of X. The covariance matrix is a symmetric matrix that measures the covariance between pairs of variables in X.

3. The covariance matrix of X will be a square matrix with dimensions p x p.

4. The number of eigenvalues of a matrix is equal to its dimension, counting multiplicities. Since the covariance matrix of X is p x p, it will have p eigenvalues.

5. However, the number of eigenvalues for the covariance matrix is also constrained by the number of observations (n) and the number of variables (p) in X.

6. If n < p, it means that there are more variables than observations. In this case, the maximum number of eigenvalues possible for the covariance matrix is n.

7. On the other hand, if p ≤ n, it means that there are more observations than variables. In this case, the maximum number of eigenvalues possible for the covariance matrix is p.

8. Therefore, the number of eigenvalues possible for the covariance matrix of X is equal to the smaller of n and p.

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The fact that each triangle has an angle measure that is the same as 180 degrees indicates that the angles are congruent.

We must compare their sides and angles to determine whether PQR (triangle PQR) and XYZ (triangle XYZ) are congruent.

PQR's coordinates are:

The coordinates of XYZ are P(-4,2), Q(2,2), and R(2,8).

X (-1, -3), Y (-5, -3), and Z (-5, 4)

We determine the sides' lengths of the two triangles:

Size of the PQ:

The length of the QR is as follows: PQ = [(x2 - x1)2 + (y2 - y1)2] PQ = [(2 - (-4))2 + (2 - 2)2] PQ = [62 + 02] PQ = [36 + 0] PQ = 36 PQ = 6

QR = [(x2 - x1)2 + (y2 - y1)2] QR = [(2 - 2)2 + (8 - 2)2] QR = [02 + 62] QR = [0 + 36] QR = [36] QR = [6] The length of the RP is as follows:

The length of XY is as follows: RP = [(x2 - x1)2 + (y2 - y1)2] RP = [(2 - (-4))2 + (8 - 2)2] RP = [62 + 62] RP = [36 + 36] RP = [72 RP = 6]

XY = [(x2 - x1)2 + (y2 - y1)2] XY = [(5 - (-1))2 + (-3 - (-3))2] XY = [62 + 02] XY = [36 + 0] XY = [36] XY = [6] The length of YZ is as follows:

The length of ZX is as follows: YZ = [(x2 - x1)2 + (y2 - y1)2] YZ = [(5 - 5)2 + (4 - (-3))2] YZ = [02 + 72] YZ = [0 + 49] YZ = 49 YZ = 7

ZX = √[(x₂ - x₁)² + (y₂ - y₁)²]

ZX = √[(5 - (- 1))² + (4 - (- 3))²]

ZX = √[6² + 7²]

ZX = √[36 + 49]

ZX = √85

In light of the determined side lengths, we can see that PQ = XY, QR = YZ, and RP = ZX.

Measuring angles:

Using the given coordinates, we calculate the triangles' angles:

PQR angle:

Utilizing the slope equation: The slope of PQ is 0, indicating that it is a horizontal line with an angle of 180 degrees. m = (y2 - y1) / (x2 - x1) m1 = (2 - 2) / (2 - (-4)) m1 = 0 / 6 m1 = 0

XYZ Angle:

Utilizing the slant equation: m = (y2 - y1) / (x2 - x1) m2 = 0 / 6 m2 = 0 The slope of XY is 0, indicating that it is a horizontal line with an angle of 180 degrees.

The fact that each triangle has an angle measure that is the same as 180 degrees indicates that the angles are congruent.

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In probability theory, the symbol "A" denotes an event. It is a placeholder for a specific event or outcome of interest. The value of "p(A)" represents the probability of event A occurring. In this case, it is given that p(A) = 0.003, indicating the probability of event A is 0.003.

In probability theory, events are represented by capital letters such as A, B, C, etc. These events can represent any specific outcome or occurrence of interest. The value of "p(A)" represents the probability of event A occurring, which is denoted as the likelihood of event A happening.

In the given scenario, it is stated that p(A) = 0.003. This means that the probability of event A occurring is 0.003, or in other words, there is a 0.003 probability of the specific outcome or occurrence denoted by event A happening.

The value of p(A) provides insight into the likelihood or chance of event A taking place and is often used in various statistical and probabilistic calculations and analyses.

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Using the concepts of arithmetic and geometric progression, Maria's total land will exceed Lucia's amount of land in the 7th year.

An arithmetic progression is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

whereas, a geometric progression is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Lucia is increasing her land by arithmetic progression. She bought a 11 hectare land and increases it by 5 hectares every year.

Land in:

year 1 = 11

year 2 = 11+5 = 16

year 3 = 16+5 =21

year 4 =  21+5 = 26

year 5 = 26+5 = 31

year 6 = 31 + 5 =36

year 7 = 36+5 = 41

year 8 = 41+5 = 46

Maria is increasing her land by geometric progression. She bought 6 hectares land in first year. Multiplied the amount by 1.4 each year.

Land in:

year 1 = 6

year 2 = 6*1.4= 8.4

year 3 = 8.4*1.4 = 11.76

year 4 =  11.76*1.4 =16.46

year 5 = 16.46 *1.4 = 23

year 6 = 23 * 1.4 = 32.2

year 7 = 32.2 * 1.4 = 45.08

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The complete question is given below:

Lucia and Maria are business women who decided to invest money by buying farm land in Brazil. They started their investments at the same time, and each year they buy more land. Lucia bought 11 hectares of land in the first year, and each year afterwards she buys 5 additional hectares. Maria bought 6 hectares of land in the first year, and each year afterwards her total number of hectares increases by a factor of 1.4. In which year will Maria's amount of land first exceed Lucia's amount of land?

The system of equations x+2 y+z=14, y=z+1 and x=-3 z+6 is inconsistent, and there is no solution.

To solve the given system of equations by substitution, we can use the third equation to express x in terms of z. The third equation is x = -3z + 6.

Substituting this value of x into the first equation, we have (-3z + 6) + 2y + z = 14.

Simplifying this equation, we get -2z + 2y + 6 = 14.

Rearranging further, we have 2y - 2z = 8.

From the second equation, we know that y = z + 1. Substituting this into the equation above, we get 2(z + 1) - 2z = 8.

Simplifying, we have 2z + 2 - 2z = 8.

The z terms cancel out, leaving us with 2 = 8, which is not true.

Therefore, there is no solution to this system of equations.

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The median is a better measure for data sets with outliers as it gives a clearer understanding of central tendency and is less affected by extreme values. Choosing the appropriate measure depends on the analysis goals and characteristics of the data.

When a data set contains several outliers, the median is generally a better measure to represent the data set than the mean. The reason for this is that outliers can significantly affect the mean while having minimal impact on the median.

In order to comprehend why the median is more resistant to outliers, think about the following scenario:

Suppose we have the following data set: 1, 2, 3, 4, 5, 1000.

The mean of this data set is calculated as (1 + 2 + 3 + 4 + 5 + 1000) / 6 = 169.1667.

In this case, the outlier value of 1000 significantly influences the mean, making it higher than the majority of the data points.

However, the median of the data set is 3.5, which represents the central value unaffected by the outlier.

By considering the median, we obtain a more representative measure of the typical value in the data set, which is not distorted by extreme values.

Therefore, when a data set has several outliers, the median is a more suitable measure as it provides a better understanding of the central tendency and is less influenced by extreme values. It is important to choose the appropriate measure based on the characteristics and goals of the analysis.

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The sum of the monthly precipitation values is 64.7 inches, and since there are 20 cities, the mean monthly precipitation is 64.7 inches divided by 20, which equals 3.235 inches.

To calculate the mean monthly precipitation, we sum up all the given values: 3.5 + 1.6 + 2.4 + 3.7 + 4.1 + 3.9 + 1.0 + 3.6 + 4.2 + 3.4 + 3.7 + 2.2 + 1.5 + 4.2 + 3.4 + 2.7 + 0.4 + 3.7 + 2.0 + 3.6 = 64.7. Next, we divide this sum by the total number of cities, which is 20. Therefore, the mean monthly precipitation is 64.7 inches divided by 20, which equals 3.235 inches. This represents the average amount of precipitation across the 20 cities during the month of August.

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The total area under a normal distribution curve represents 100% of the data set. The normal distribution curve is a continuous probability distribution that is symmetric and bell-shaped.

It is often used to model real-world data. The area under the curve represents the probability of an event occurring within a certain range of values.

To understand this concept better, let's consider an example. Imagine we have a data set that follows a normal distribution, such as the heights of a group of people. The normal distribution curve is bell-shaped, with the mean height in the center and the majority of the data falling within a certain range.

The area under the curve represents the probability of observing a certain range of values. Since the total area under the curve accounts for all possible values in the data set, it corresponds to 100% of the data.

In this case, the correct answer is 100%. This means that the total area under a normal distribution curve represents the entirety of the data set.

To summarize, the total area under a normal distribution curve represents the entire data set, which is equivalent to 100% of the data set.

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The missing terms of the arithmetic sequence are 9.85, 9.7, and 9.55. The common difference of the sequence is -0.15.

The sequence given is an arithmetic sequence, hence it can be solved using the formula of an arithmetic sequence as: aₙ = a₁ + (n-1) d where aₙ is the nth term of the sequence, a₁ is the first term, n is the position of the term in the sequence and d is the common difference of the sequence. For the sequence given, we know that the first term, a₁ = 10 and the fifth term, a₅ = -11.6. Also, from the hint given, we know that the arithmetic mean of the first and fifth terms is the third term, i.e. (a₁ + a₅)/2 = a₃. Substituting the given values in the equation: (10 - 11.6)/4 = -0.15 (approx).

Thus, d = -0.15. Therefore,

a₂ = 10 + (2-1)(-0.15)

= 10 - 0.15

= 9.85,

a₃ = 10 + (3-1)(-0.15)

= 10 - 0.3

= 9.7, and

a₄ = 10 + (4-1)(-0.15)

= 10 - 0.45

= 9.55.A

The first term of the arithmetic sequence is 10, and the fifth term is -11.6. To find the missing terms, we use the formula for the nth term of an arithmetic sequence, which is aₙ = a₁ + (n-1) d, where a₁ is the first term, n is the position of the term in the sequence, and d is the common difference. The third term can be calculated using the hint given, which states that the arithmetic mean of the first and fifth terms is the third term. So, (10 - 11.6)/4 = -0.15 is the common difference. Using this value of d, the missing terms can be found to be a₂ = 9.85, a₃ = 9.7, and a₄ = 9.55. Hence, the complete sequence is 10, 9.85, 9.7, 9.55, -11.6.

:Thus, the missing terms of the arithmetic sequence are 9.85, 9.7, and 9.55. The common difference of the sequence is -0.15.

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Answer:9,000

Step-by-step explanation:

In the morning, the person counts 100 geese. However, the geese respond by saying that they are not 100, but they will only be 100 when multiplied by two and the person. So, there are 50 geese in the dam.

To determine the number of geese in the dam, we need to solve the equation:
2 * number of geese + 1 = 100

By subtracting 1 from both sides of the equation, we get:
2 * number of geese = 99

Next, we divide both sides of the equation by 2 to isolate the number of geese:
number of geese = 99 / 2

Simplifying this equation gives us:
number of geese = 49.5

Since the number of geese cannot be a decimal, we round down to the nearest whole number. Therefore, there are 49 geese in the dam.

However, it is important to note that the question specifies the geese will only be 100 when multiplied by two and the person. This implies that the person is included in the count of 100 geese. Therefore, we add one more to the total.

Hence, the final answer is that there are 50 geese in the dam.

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To estimate the population total, we can use the formula:

Population Total = Sample Mean x Population Size

Where the sample mean is the mean of the sample and the population size is the total number of accounts in the population.

Given:

Sample size (n) = 50

Sample mean = $500

Population size = 500

Using the formula, we get:

Population Total = Sample Mean x Population Size

Population Total = $500 x 500

Population Total = $250,000

Therefore, the estimate for the population total is $250,000.

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The determinant of the given matrix is 11. The formula for the determinant of a 2x2 matrix is ad - bc, where a, b, c, and d represent the elements of the matrix.

To evaluate the determinant of the given matrix [5 3 -2 1], we can use the formula for a 2x2 matrix.
In this case, a = 5,

b = 3,

c = -2, and

d = 1.
Now, we can substitute the values into the formula: determinant = (5 * 1) - (3 * -2).
Simplifying the expression, we have:

determinant = 5 - (-6).

This further simplifies to:

determinant = 5 + 6.

In summary, the determinant of the matrix [5 3 -2 1] is 11.

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The graph of g(x) is obtained by vertically compressing and right-shifting the graph of f(x).

The graph of g(x) can be obtained by applying a vertical compression and a rightward shift to the graph of f(x). When we compress the graph of f(x) vertically, it means that the values of the y-coordinates of the points on the graph of f(x) are multiplied by a constant factor less than 1. This causes the graph to become narrower.

Additionally, when we shift the graph of f(x) to the right, we are moving all the points on the graph horizontally towards the positive x-axis by a specific amount. This shift changes the x-coordinates of the points while keeping their y-coordinates the same. By applying these transformations, we can obtain the graph of g(x) from the original graph of f(x) with the desired vertical compression and rightward shift.

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According to the given statement , By solving the equation we get x = y.

To solve the system of equations:
Step 1: Multiply the second equation by 2 to eliminate the fraction:

-x - 2y = 2.
Step 2: Add the two equations together to eliminate the y variable:

(4x - y) + (-x - 2y) = (-2) + 2.
Step 3: Simplify and solve for x:

3x - 3y = 0.
Step 4: Divide by 3 to isolate x:

x = y.
is x = y.

1. Multiply the second equation by 2 to eliminate the fraction.
2. Add the two equations together to eliminate the y variable.
3. Simplify and solve for x.

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The solution to the system of equations is x = -2/3 and y = -2/3.

To solve the given system of equations:

4x - y = -2   ...(1)
-(1/2)x - y = 1   ...(2)

We can use the method of elimination to find the values of x and y.

First, let's multiply equation (2) by 2 to eliminate the fraction:
-2(1/2)x - 2y = 2

Simplifying, we get:
-x - 2y = 2   ...(3)

Now, let's add equation (1) and equation (3) together:
(4x - y) + (-x - 2y) = (-2) + 2

Simplifying, we get:
3x - 3y = 0   ...(4)

To eliminate the y term, let's multiply equation (2) by 3:
-3(1/2)x - 3y = 3

Simplifying, we get:
-3/2x - 3y = 3   ...(5)

Now, let's add equation (4) and equation (5) together:
(3x - 3y) + (-3/2x - 3y) = 0 + 3

Simplifying, we get:
(3x - 3/2x) + (-3y - 3y) = 3
(6/2x - 3/2x) + (-6y) = 3
(3/2x) + (-6y) = 3

Combining like terms, we get:
(3/2 - 6)y = 3
(-9/2)y = 3

To isolate y, we divide both sides by -9/2:
y = 3 / (-9/2)

Simplifying, we get:
y = 3 * (-2/9)
y = -6/9
y = -2/3

Now that we have the value of y, we can substitute it back into equation (1) to find the value of x:

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

Subtracting 2/3 from both sides, we get:
4x = -2 - 2/3
4x = -6/3 - 2/3
4x = -8/3

Dividing both sides by 4, we get:
x = (-8/3) / 4
x = -8/12
x = -2/3

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Take the intersection of the domains of g and f. This means you find the common values that are allowed in both functions. These common values will form the domain for the composition, f ∘ g.

To find the domain for the composition of two functions, f ∘ g, you need to consider the domains of both functions individually.

The domain of the composition, f ∘ g, is the set of all input values that can be plugged into g and then into f without any issues.

First, determine the domain of g by considering any restrictions on its input values.

Make sure to identify any excluded values, such as those that would result in a division by zero or a negative value inside a square root.

Next, find the domain of f by considering the possible input values it can accept.

Similarly, identify any excluded values based on division by zero or negative values inside square roots.

Finally, take the intersection of the domains of g and f.

This means you find the common values that are allowed in both functions. These common values will form the domain for the composition, f ∘ g.

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Jimmy Johnson's standard deduction for 2020 would be $14,050. The standard deduction is a fixed amount that reduces the taxable income of individuals and families. It is an alternative to itemizing deductions on the tax return.

The standard deduction is provided by the tax authorities as a simplified method to calculate taxable income and reduce the administrative burden for taxpayers. To determine Jimmy Johnson's standard deduction for 2020, we need to consider his filing status and age. Since the question does not mention his filing status, we will assume he is a single taxpayer.

For a single taxpayer who is over 65 years of age, the standard deduction for 2020 is $14,050. This amount is higher than the regular standard deduction because taxpayers who are 65 or older get an additional amount as a "senior" standard deduction.

Therefore, Jimmy Johnson's standard deduction for 2020 would be $14,050.

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It will take approximately 70 minutes to download 420 megabytes at a rate of 100 kilobytes per second.

To calculate how long it will take to download 420 megabytes at a rate of 100 kilobytes per second, we need to convert the units.

First, let's convert 100 kilobytes per second to megabytes per second. Since 1 megabyte is equal to 1000 kilobytes, we divide 100 kilobytes by 1000 to get 0.1 megabytes. So the download speed is 0.1 megabytes per second.

Next, we divide 420 megabytes by 0.1 megabytes per second to find the time it will take to download. This gives us 4200 seconds.

Since we want the answer in minutes, we divide 4200 seconds by 60 (since there are 60 seconds in a minute). This gives us 70 minutes.

Therefore, it will take approximately 70 minutes to download 420 megabytes at a rate of 100 kilobytes per second.

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The sum of f(x) and g(x) is given by f(x) + g(x) = 8∛x². By adding the coefficients in front of the same radical term, we can combine the two expressions into a single term. In this case, the radical index remains unchanged, and the base (x²) is common to both terms. By simplifying the expression, we arrive at the final result of 8∛x².

This shows that the sum of the two functions f(x) and g(x) can be represented by a single term with a combined coefficient and the same radical term.

Given that f(x) = 5∛x² and g(x) = 3∛x², we can calculate their sum:

f(x) + g(x) = 5∛x² + 3∛x².

Since both terms have the same radical index and the same base (x²), we can combine them by adding the coefficients:

f(x) + g(x) = (5 + 3)∛x².

Simplifying further:

f(x) + g(x) = 8∛x².

Therefore, the expression f(x) + g(x) simplifies to 8∛x².

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