The function of fx has been transformed to give go. Witch of the following functions represent gx?

Answer:

x= negative three over two or -3/2

Step-by-step explanation:

An equation is formed of two equal expressions. The equation of the ellipse is,

⇒ [(x-6)²/49] + [(x-2)²/9] = 1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it can be seen that the centre of the ellipse is at (6,2). Also, the major radius is equal to 7 units, while the minor radius is equal to 3 units. The general equation of the ellipse is given as,

(x - h)²/a² + (y - k)²/b² = 1

(x - 6)²/7² + (y - 2)²/3² = 1

[(x-6)²/49] + [(x-2)²/9] = 1.

Hence, the equation of the ellipse is,

⇒ [(x-6)²/49] + [(x-2)²/9] = 1 .

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Answer:

the answer is A on edge :)

Step-by-step explanation:

good luck <3

Using factorization method to solve the quadratic equation, the number of seed Martha and Miguel donated are 5 and 10 respectively

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants, and x is an unknown variable. The solution to such an equation is a value of x that will make the equation true.

To determine the number of seeds they donated, we have to write two equations and solve.

data;

The product of the seeds is (2x - 3)(4x - 6) = 8x² - 24x + 18

This can be written as

8x² - 24x + 18 = 50

Solving the quadratic equation;

8x² - 24x + 18 - 50 = 0

8x² - 24x - 32 = 0

Using factorization method;

8(x - 4)(x + 1) = 0

x - 4 = 0, x = 4

x + 1 = 0, x = -1

x = 4, x = -1

The number of packs Martha donated is

Martha = 2x - 3 = 2(4) - 3 = 5

The number of packs Miguel donated is

Miguel = 2 * 5 = 10

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The probability of the component failing within the first 6 months is approximately 0.3935 or 39.35%.

For the probability of the component failing within the first 6 months, we need to find the cumulative distribution function (CDF) of the Gamma distribution with parameters α = 2 and λ = 2, and evaluate it at t = 0.5 years (6 months).

Hence, The CDF of a Gamma distribution with parameters α and λ is given by:

F(t) = γ(α, λt) / Γ(α)

where γ is the lower incomplete Gamma function and Γ is the Gamma function.

Plugging in α = 2 and λ = 2, we get:

F(t) = γ(2, 2t) / Γ(2) = (1 - e^(-2t))(2t)

To find the probability of the component failing within the first 6 months (t = 0.5 years), we simply evaluate the CDF at t = 0.5:

F(0.5) = (1 - e^(-2(0.5)))(2(0.5))

= 0.3935

Therefore, the probability of the component failing within the first 6 months is approximately 0.3935 or 39.35%.

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For the regression equation 9 = 7 - 1.2x the predicted value y when x=4 is (b) 2.2√ is the predicted value of y.

The regression equation 9 = 7 - 1.2x is given. The task is to find the predicted value y when x = 4. Let's find out:

Putting x = 4 in the regression equation: 9 = 7 - 1.2x

⇒ y = 7 - 1.2(4)

⇒ y = 7 - 4.8

⇒ y = 2.2

Therefore, when x = 4, the predicted value of y is 2.2. Hence, the option (b) 2.2√ is correct.

Next, the second question is incomplete and the options are not provided. Please provide the complete question and options so that I can assist you better.

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5- For the regression equation 9 = 7 - 1.2x the predicted value y when x=4is? a) 0 b) 2.2√ c) 3.4 $1.6 6- If A and B make a partition of the sample space, (i. e AUB-S). Then the probability that at  least one of the events occur is equal to a) 0 b) 0.25 c) 0.50 7- Let X be a continuous random variable and pdf f(x)=, 0sxs3 then P<X<D) is: a)- b) 8- If X is a discrete random variable with values (2, 3, 4, 5), which of the following functions is the probability mass function of X: C) IS

The predicted value of y when x=4 for the regression equation 9 = 7 - 1.2x is 2.2.

Explanation:

Given the regression equation: 9 = 7 - 1.2x, we need to find the predicted value of y when x=4.

To do this, we substitute x=4 into the equation and solve for y.

Substituting x=4 into the equation, we have:

9 = 7 - 1.2 × 4

9 = 7 - 4.8

9 = 2.2

Therefore, the predicted value of y when x=4 is 2.2.

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Answer:

Step-by-step explanation:

The fourth image because when looking for liner equations if you draw a line through them and it only touches once its linear equation!

sorry if im wrong...  

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is important is called the counting rule for permutations.

What is a counting rule? Counting rule is a mathematical technique that aids in determining the number of ways that certain events or observations can occur. The counting principle is a basic method of calculating the number of feasible events, allowing us to determine the likelihood of different events occurring when several possibilities are available.

What is permutation? Permutations are the ways in which a group of objects or symbols can be ordered or arranged. The order of selection is important in permutations, and each permutation is unique because of this. The formula for computing the permutations of n objects taken r at a time is:

nPr = n! / (n - r)!, where n is the number of objects and r is the number of objects being chosen for the permutation.

This is different from combinations which is used when order of selection is not important, independent events which involves two or more events that are unrelated, and multiple-step random experiments which are experiments that involve two or more random steps.
Therefore, the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is important is called the counting rule for permutations.

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Answer:

$35

Step-by-step explanation:

This is actually pretty simple!

All you have to do is plug 5 in place of x and solve.

Y=5(5)+10

Y=25+10

Y=35

She raises $35 if she walks 5 kilometers.

Using the normal distribution, it is found that there is a 0.0968 = 9.68% probability that this student will receive a grade that is above 90.

-------------------

Normal Probability Distribution  

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{90 - 78.3}{9}\)

\(Z = 1.3\)

\(Z = 1.3\) has a p-value of 0.9032.

1 - 0.9032 = 0.0968.

0.0968 = 9.68% probability that this student will receive a grade that is above 90.

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The probability that the sample mean will be within plus minus 2 of the population mean if the sample size is n = 100 between z-scores of 0 and 2.5 using a z-table.

The standard deviation of the sample distribution, commonly known as the standard error, can be computed using the formula given that the population mean is 100 and the standard deviation is 16:

Standard Error = Standard Deviation / sqrt(sample size)

Let's determine the likelihoods for sample sizes of n = 100 and n = 400:

For n = 100:

Standard Error = 16 / sqrt(100) = 16 / 10 = 1.6

We can determine the z-scores for the upper and lower boundaries to establish the likelihood that the sample mean will be within plus or minus 2 of the population mean:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 1.6

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 1.6

Upper Bound z-score = 4 / 1.6

Upper Bound z-score = 2.5

We can calculate the region under the normal distribution curve between z-scores of 0 and 2.5 using a z-table or statistical software. This shows the likelihood that the sample mean will be within +/- 2 standard deviations of the population mean.

For n = 400:

Standard Error = 16/√400

Standard Error = 16/20

Standard Error = 0.8

We determine the z-scores by following the same procedure as above:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 0.8

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 0.8

Upper Bound z-score = 4 / 0.8

Upper Bound z-score = 5

Once more, we may determine the region under the normal distribution curve between z-scores of 0 and 5 using a z-table or statistical software.

A larger sample size, like n = 400, has the benefit of a lower standard error. The sampling distribution of the sample mean will be more constrained and more closely resemble the population mean if the standard error is less.

As a result, there is a larger likelihood that the sample mean will be within +/- 2 of the population mean. In other words, the estimate of the population mean gets more accurate and dependable as the sample size grows.

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Answer:

it would be 64-81  than answer devide by 6.

(i) State whether the term is a variable name or a variable value.

(ii) State the level of measurement.

A. age

(i) Variable name.

(ii) Ratio.

Explanation: "Age" is the name of the variable and it is a numerical value representing the number of years a person has lived. It is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

B. conservative

(i) Variable name.

(ii) Nominal.

Explanation: "Conservative" is the name of b and it refers to a political ideology. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., conservative, liberal, socialist) and have no meaningful mathematical operations.

C. strongly oppose

(i) Variable value.

(ii) Ordinal.

Explanation: "Strongly oppose" is a value of the variable, and it refers to a person's opinion or attitude towards a certain issue. It is measured on an ordinal scale, meaning it has a rank or order (e.g., strongly oppose, somewhat oppose, neutral, somewhat support, strongly support). However, the difference between two values is not necessarily equal (e.g., the difference between strongly oppose and neutral might be different from the difference between neutral and strongly support).

D. region

(i) Variable name.

(ii) Nominal.

Explanation: "Region" is the name of the variable and it refers to a geographical area, such as the Midwest or the South. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Midwest, South, West, Northeast) and have no meaningful mathematical operations.

E. 57 years

(i) Variable value.

(ii) Ratio.

Explanation: "57 years" is a value of the variable "Age" and it represents the number of years a person has lived. As mentioned above, "Age" is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

F. strictly enforced

(i) Variable value.

(ii) Ordinal.

Explanation: "Strictly enforced" is a value of a variable, and it refers to the level of enforcement of a rule or law. It is measured on an ordinal scale, meaning it has a rank or order (e.g., not enforced, loosely enforced, strictly enforced). However, the difference between two values is not necessarily equal (e.g., the difference between not enforced and loosely enforced might be different from the difference between loosely enforced and strictly enforced).

G. Catholic

(i) Variable name.

(ii) Nominal.

Explanation: "Catholic" is the name of the variable and it refers to a religious affiliation. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Catholic, Protestant, Jewish, Muslim) and have no meaningful mathematical operations.

H. Gender

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Answer:

Step-by-step explanation:

Both of the triangles are isosceles as marked on the diagram.

The right triangle has missing angles of:

The missing angles of the bigger triangle:

Answer:

122

Step-by-step explanation:

21 + x = 133

x= 133- 21

x = 112

hope it helps

Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

Answer:

0 dots = 10

1 dot = 1, 2, 3, 9

2 dots = 0, 4, 5, 7, 8, 11

3 dots = none

4 dots = 6

A person babysits for about 6 hours each week. The graph has one single peak at the center (6) and is a bell shaped distribution. The peak at 6 shows that there is a high number of data points in that area of the graph, meaning it is the typical number of hours for babysitters to babysit.

Answer:

$0.90/kg

Step-by-step explanation:

4.50/5=0.90

The answer is - the singular point of the given differential equation is x = (1/3).

The given differential equation is (3x - 1)' + y - y = 0. The singular point of the differential equation is as follows:

Step-by-step explanation:

We have the following differential equation:

(3x - 1)' + y - y = 0.

The general form of first-order differential equation is:

dy/dx + P(x)y = Q(x)

Here P(x) = 1, Q(x)

= 0.

Hence the differential equation can be written as:

dy/dx + y = 0.

The characteristic equation is:

mr + 1 = 0.

The roots of the characteristic equation are:

r = -1/m

For m = 0, the roots are imaginary, and the solution is non-oscillatory.

Thus , the singular point of the given differential equation is x = (1/3).

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Answer:

a. f(0) = 4

b. f(6) = 8

Step-by-step explanation:

This is a piecewise function, so the actual equation is on the left, and the inequalities are on the right.

If x = 0, this would fall under the first part of the function because x < 5 is the requirement for the first part. Then, evaluating it: f(0) = 0 + 4 = 4.

If x = 6, this would fall under the second part of the function because 5 \(\leq\) x < 7 is the requirement. 6 falls under this category, so that means the second part of the function is used. Because it is a constant, 8, this evaluates to f(6) = 8.

The total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.

In the question, we are given that a package weighs P pounds, P being a whole number. To ship this package by express costs $1.65 for the first five pounds and 12c for each additional pound. The total shipping cost was $3.45.

We are asked for the package weight in pounds.

First, we design a general cost function.

The cost is given to be $1.65 for the first 5 pounds, and 12c for each additional pound.

The weight of the package is given to be P pounds.

We assume the total cost function to be C(P), a function of the weight of the package, P pounds.

Thus, the total cost function can be shown as the sum of $1.65 and 12c or $0.12 multiplied with (P - 5), as it is the cost for additional pounds after 5 pounds.

Thus, the total cost function, C(P) = 1.65 + 0.12(P - 5).

Now, we are given that the total shipping cost was $3.45.

Thus, to find the weight of the package, we equate the total cost function, C(P) to 3.45, to get:

1.65 + 0.12(P - 5) = 3.45,

or, 1.65 + 0.12P - 0.6 = 3.45,

or, 0.12P + 1.05 = 3.45,

or, 0.12P = 3.45 - 1.05,

or, 0.12P = 2.40,

or, P = 2.40/0.12 = 20.

Thus, the total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.

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Answer:

2 ≤ x ≤ 8

Step-by-step explanation:

0 ≤ 3x - 6 ≤ 18

0 ≤ 3x - 6

6 ≤ 3x

2 ≤ x

3x - 6 ≤ 18

3x ≤ 18 + 6

3x ≤ 24

x ≤ 8

Combined:

2 ≤ x ≤ 8

Answer:

2 ≤ x≤ 8

2nd option:)

Step-by-step explanation:

The System Effectiveness is approximately 0.763.

To calculate the System Effectiveness, we need to multiply the values of Operational Readiness, Design Adequacy, Availability, Maintainability, and Mission Reliability.

System Effectiveness = Operational Readiness * Design Adequacy * Availability * Maintainability * Mission Reliability

Plugging in the given values:

System Effectiveness = 0.89 * 0.95 * 0.98 * 0.93 * 0.99

System Effectiveness ≈ 0.763

Therefore, the System Effectiveness is approximately 0.763.

The correct answer is a. 0.763.

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Expressions B) 5 + (-3) and C) -6 + 4 have values that are greater than -3.

B) 5 + (-3) simplifies to 2, which is greater than -3.

C) -6 + 4 simplifies to -2, which is also greater than -3.

A) -8 + 3 simplifies to -5, which is less than -3.

D) 3 + (-4) simplifies to -1, which is also less than -3.

In summary, when evaluating expressions, it's important to remember that the order of operations matters, and we can simplify the expression to determine its value. In this case, expressions B and C have values that are greater than -3, while expressions A and D have values that are less than -3.

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The percentage of Measurements that are 124.4 or higher is approximately 0.99%.

In order to determine the percentage of measurements that are 124.4 or higher in a population of measurements that is approximately normal with a mean of 95 and a standard deviation of 15, we need to use the z-score formula.

The z-score formula is used to standardize a distribution so that it can be compared to a normal distribution with a mean of 0 and a standard deviation of 1.

The formula for calculating the z-score is: z = (x - μ) / σWhere:x is the measurement we want to standardize.μ is the population mean.σ is the population standard deviation.

The first step is to calculate the z-score for the measurement of 124.4:z = (124.4 - 95) / 15z = 2.2933The second step is to find the percentage of measurements that are 124.4 or higher using a standard normal distribution table. We look up the area to the right of the z-score of 2.2933 in the table.

The closest value in the table is 0.9901, which corresponds to a z-score of 2.33. We know that the area to the left of a z-score of 2.33 is 0.9901, so the area to the right of a z-score of 2.33 is:1 - 0.9901 = 0.0099

This means that approximately 0.99% of the measurements are 124.4 or higher.

Therefore, the percentage of measurements that are 124.4 or higher is approximately 0.99%.

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The term "normally distributed error term with mean of zero" refers to the residual errors in a statistical model that follow a normal distribution with an average (mean) value of zero.

In statistics, when we use a model to represent data, there is often some variability or discrepancy between the predicted values of the model and the actual observed values. This discrepancy is captured by the error term, which represents the unexplained variation in the data.

A normally distributed error term with a mean of zero means that, on average, the errors have no bias or systematic tendency to be positive or negative. This means that the model is not consistently overestimating or underestimating the true values.

To illustrate this concept, let's consider a simple example. Suppose we have a linear regression model that predicts the exam scores of students based on the number of hours they studied. The error term in this model represents the difference between the predicted scores and the actual scores.

If the error term is normally distributed with a mean of zero, it implies that, on average, the predicted scores will be equal to the actual scores. However, individual predictions may still deviate from the true values due to random fluctuations.

In practical terms, a normally distributed error term with a mean of zero is desirable because it indicates that the model is unbiased and does not systematically under- or over-predict the outcomes. This assumption is often made in statistical analyses to ensure the validity of the results and to make appropriate inferences.

In summary, a normally distributed error term with a mean of zero implies that the errors in a statistical model have no systematic bias and follow a normal distribution. This assumption is important in many statistical analyses and helps to ensure the accuracy and reliability of the model's predictions.

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To determine the missing value in the inverse variation between the given pairs of points (5.5, 8) and (x, 4), we can apply the inverse variation equation:

y = k/x

where y represents the dependent variable, x represents the independent variable, and k is the constant of variation.

Using the first point (5.5, 8), we can substitute the values into the equation:

8 = k/5.5

To find the value of k, we can multiply both sides of the equation by 5.5:

8 * 5.5 = k

44 = k

Now that we know the value of k is 44, we can substitute it into the equation to find the missing value using the second point (x, 4):

4 = 44/x

To solve for x, we can multiply both sides of the equation by x:

4x = 44

Dividing both sides of the equation by 4:

x = 44/4

x = 11

The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.

From the above given data, the following solution is given below:

Given:

Let f(x,y,z) = x³z - yz²

To find the partial derivatives of f

Here the directional derivative of a function f(x,y,z) is given by:

(df/dx , df/dy, df/dz)

df/dx = 3x²

df/dy = -z²

df/dz = x³ - 2yz

at points(1,3,2)

(df/dx)₍₁,₃,₂₎ = 3(1)² = 3

| (df/dx)₍₁,₃,₂₎ | = 3

(df/dy)₍₁,₃,₂₎ = -2² = 4

| (df/dy)₍₁,₃,₂₎ | = 4

(df/dz)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11

| (df/dz)₍₁,₃,₂₎  | = 11

As we got the maximum modulus of derivative in direction of x. Since, therefore we should move into z direction to maximize the directional derivative.

(df/dz)₍₁,₃,₂₎  = -11

Hence, the instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.

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The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point | (∂f/∂z)₍₁,₃,₂₎  | = 11.

What is instantaneous rate of change?

The derivative value change at a particular point is the same as the instantaneous rate of change, which is the change in rate at a specific instant. The tangent line slope and the instantaneous rate of change at a given point on a graph are the same. That is, the slope is curved.

From the given data, the solution is given below:
Given:
Let f(x, y, z) = x³z - yz²
To find the partial derivatives of f
Here the directional derivative of a function f(x, y, z) is given by:
(∂f/∂x , ∂f/∂y, ∂f/∂z)

∂f/∂x = 3x²

∂f/∂y = -z²

∂f/∂z = x³ - 2yz

at points(1,3,2)

(∂f/∂x)₍₁,₃,₂₎ = 3(1)² = 3

| (∂f/∂x)₍₁,₃,₂₎ | = 3

(∂f/∂y)₍₁,₃,₂₎ = -2² = 4

| (∂f/∂y)₍₁,₃,₂₎ | = 4

(∂f/∂z)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11

| (∂f/∂z)₍₁,₃,₂₎  | = 11

As we got the maximum modulus of derivative in direction of z. Since, therefore we should move into z direction to maximize the directional derivative.
(∂f/∂z)₍₁,₃,₂₎  = -11
Hence, The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.

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Complete question:

Complete question is attached below.

Answer: s = p - 0.25p; $30

Step-by-step explanation:

      First, we need to know that a percent divided by 100 becomes a decimal.

          25% / 100 = 0.25.

      Next, we will use this equation because it takes 25% off of the original price (p) by subtracting 0.25p from p.

          s = p - 0.25p

      Lastly, we will substitute 40 in for 0 and solve.

          s = ($40) - 0.25($40)

          s = $30