Solve for y. Y= -x/3+4 when x is equal to 0

\(\text{Hello! :)}\)

\(\large\boxed{(3x + 4)(x + 8)}\)

\(\text{Factor the polynomial:}\\3x^{2} +28x +32\\\\\text{Find two numbers that multiply into 32 and sum up to 28.}\\\text{Take into account the leading coefficient of 3:}\\\\\text{The numbers 4 and 8 work; arrange them so that they sum up to 28:}\\\\(3x + 4)(x + 8)\)

Answer: B: 7.14 in²

Step-by-step explanation:

Area of the square: 2x2 = 4in²

Area of the circle: πr² = 3.14 x 1² = 3.14

add them both to get the composite area:

4 + 3.14 = 7.14 in²

Answer:

w = -6

Step-by-step explanation:

\(9w=-54~(Given)\\\\\frac{9w}{9}=\frac{-54}{9}~(Divide~9~on~both~sides)\\\\w=-6~(Simplify)\)

The rate of discount for the CD radio cassette is 17.65%.

To calculate the rate of discount, we need to find the difference between the original price and the discounted price, and then divide that difference by the original price.

Original price: $16,999

Discounted price: $13,999

So, the Discount amount

= Original price - Discounted price

= $16,999 - $13,999

= $3,000

Rate of discount = (Discount amount / Original price) * 100%

= ($3,000 / $16,999) x 100%

≈ 17.65%

Therefore, the rate of discount for the CD radio cassette is 17.65%.

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The true equation would be = DE/DF = AB/AC

What does an equivalent ratio look like?

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

Are all proportions an equivalent ratio?

Proportional quantities are represented by a collection of corresponding ratios. We can claim, for instance, that 2:3 and 4:6 are proportionate.

Is proportion a constant?

"X is to Y as A Is to B" is how a proportion is expressed. Cross products are the xb and ay products. A proportion's cross products are consistently equal.

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In general, the energy levels of a system increase as the system gets closer. This is because when objects get closer, the force between them increases, which increases the potential energy of the system.

The potential energy of a system is related to the energy levels of the system, so increasing the potential energy leads to higher energy levels.

To see this mathematically, let's consider a system of two particles with masses m1 and m2, separated by a distance r, and interacting via a potential energy function U(r). The total energy of the system, E, is given by:

E = 1/2 m1 v1^2 + 1/2 m2 v2^2 + U(r)

where v1 and v2 are the velocities of the particles. We can simplify this expression by using the reduced mass μ, defined as:

1/μ = 1/m1 + 1/m2

and the relative distance vector r = r2 - r1. Then, we have:

E = 1/2 μ v^2 + U(r)

where v is the relative velocity of the particles.

If we assume that the particles are moving in a circular orbit with radius r, we can use the centripetal force to relate v to r:

v^2 = F_c/m = U'(r)/μr

where F_c is the centripetal force and U'(r) is the derivative of U with respect to r. Substituting this into the expression for E, we get:

E = U'(r)/2μ + U(r)

The first term on the right-hand side represents the kinetic energy of the system, while the second term represents the potential energy. The total energy E is conserved, so it must be a constant.

Now, suppose we decrease the distance r between the particles. This means that U'(r) is negative (since the force is attractive), so the first term on the right-hand side decreases, while the second term increases. Thus, the total energy E must increase to stay constant.

Therefore, we can conclude that when objects get closer, their energy levels get higher.

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To solve the differential equation y" - 3y + 2y = x + 1 using the method of variation of parameters, we will first find the complementary solution by solving the associated homogeneous equation. Then, we will find the particular solution using the method of variation of parameters.

The associated homogeneous equation for the given differential equation is y" - 3y + 2y = 0. To solve this equation, we assume a solution of the form y_h = e^(rt), where r is a constant.

Plugging this into the homogeneous equation, we get the characteristic equation r^2 - 3r + 2 = 0. Factoring the equation, we find the roots r1 = 1 and r2 = 2. Therefore, the complementary solution is y_c = C1e^t + C2e^(2t), where C1 and C2 are constants.

Next, we need to find the particular solution using the method of variation of parameters. We assume the particular solution to be of the form y_p = u1(t)e^t + u2(t)e^(2t), where u1(t) and u2(t) are functions to be determined.

We substitute this form into the original differential equation and solve for u1'(t) and u2'(t) by equating the coefficients of the terms e^t and e^(2t) to the right-hand side of the equation.

After finding u1'(t) and u2'(t), we integrate them to obtain u1(t) and u2(t). Then, the particular solution is given by y_p = u1(t)e^t + u2(t)e^(2t).

Finally, the general solution is obtained by combining the complementary solution and the particular solution: y = y_c + y_p = C1e^t + C2e^(2t) + u1(t)e^t + u2(t)e^(2t), where C1, C2, u1(t), and u2(t) are determined based on the initial conditions or additional constraints given in the problem.

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Test the hypothesis step of the scientific method is he performing.

Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

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This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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The equation for Garage A can be expressed as A = 12 + 4t, and the equation for Garage B as B = 7 + 5t.

A = 12 + 4t

B = 7 + 5t

12 + 4t = 7 + 5t

4t - 5t = 7 - 12

-t = -5

t = 5 hours

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Answer:

ΔWUV⁓ΔSRT

Step-by-step explanation:

∠W⁓∠S

∠U⁓∠R

Since LMNO is a parallelogram, opposite angles are congruent, which means that angle L is congruent to angle N and angle M is congruent to angle O.

Since angles L and M are adjacent angles in a parallelogram, they are supplementary, which means that their sum is 180 degrees. Therefore, the sum of the measures of angles L and M is:

L + M = 180 degrees.

Answer: 180 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

So and L and M add up to 180 degrees.

Answer:

Step-by-step explanation: A= π r²

π=3.14

4x4 = 16

so 3.14 x 16 =50.24

The probability that a pregnancy will last 307 days or longer is nothing. The length that separates premature babies from those who are not premature is approximately 236.25 days.

Mean (μ) = 267 days, Standard deviation (σ) = 15 days

(a) Probability of a pregnancy lasting 307 days or longer: We need to find the probability of a pregnancy lasting 307 days or longer. Using the Z-score formula: z = (X - μ)/σHere, X = 307 days, μ = 267 days, and σ = 15 days.

Substituting the values in the above formula we get: z = (307 - 267)/15z = 2.667

The probability that a pregnancy will last 307 days or longer is nothing. (Round to four decimal places as needed.) Hence, the answer is 0.0038 (approx). (Rounded to four decimal places)

(b) Length that separates premature babies from those who are not premature: If the length of pregnancy is in the lowest 2%, then the baby is premature. We need to find the length that separates premature babies from those who are not premature. Using the Z-score formula: z = (X - μ)/σHere, X is the required length, μ = 267 days, and σ = 15 days.

To find the Z-score, we can use the Z-table. The Z-table provides the area (or probability) under the normal distribution curve to the left of the Z-score. Since the length of pregnancy is in the lowest 2%, the area to the left of the Z-score will be 0.02. Hence, we need to find the Z-score corresponding to 0.02 area in the Z-table. Using the Z-table, we get the Z-score as -2.05. Now, substituting the Z-score value in the Z-score formula we get: Z-score = (X - μ)/σ-2.05 = (X - 267)/15X - 267 = -2.05 × 15X - 267 = -30.75X = 267 - 30.75X = 236.25

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Answer:

➢ 0.9

➢ -95

➢ -79

\(BlackSparkles...\)

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Answer:

Total cost of all fruits = $17

Step-by-step explanation:

Given:

Number of mangoes Peter bought = 6

Cost of each mango = x

Cost of papaya = $5

Find:

Total cost of all fruits if x = 2

Computation:

If x = 2

So,

Cost of each mango = x

Cost of each mango = $2

Cost of 6 mangoes = 6 × Cost of each mango

Cost of 6 mangoes = 6 × 2

Cost of 6 mangoes = $12

Total cost of all fruits = Cost of 6 mangoes + Cost of papaya

Total cost of all fruits = 12 + 5

Total cost of all fruits = $17

The area of the rectangle changing at the instant when the other side is cm and increasing at cm per minute is k²/min

Let's start by defining the variables:

Let x be the length of the rectangle (in cm).

Let y be the width of the rectangle (in cm).

Let A be the area of the rectangle (in cm²).

We know that one side of the rectangle (y) is constant, so its derivative with respect to time is zero:

dy/dt = 0

We also know that the other side of the rectangle (x) is increasing at a rate of dx/dt = cm/min.

We can use the formula for the area of a rectangle to express A in terms of x and y:

A = x×y

To find how fast the area of the rectangle is changing with respect to time, we can take the derivative of both sides with respect to time:

dA/dt = d/dt (x×y)

Using the product rule of differentiation, we get:

dA/dt = x × dy/dt + y × dx/dt

Since dy/dt = 0 (as we established earlier), we can simplify the equation to:

dA/dt = x × 0 + y × dx/dt

Plugging in the given values for y and dx/dt, we get:

dA/dt = (cm) × (cm/min) = k²/min

Therefore, the area of the rectangle is increasing at a rate of k²/min at the instant when one side is cm and increasing at cm per minute.

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The complete question is :

A rectangle has one side of "k" cm. how fast is the area of the rectangle changing at the instant when the other side is cm and increasing at cm per minute?

For any given value of n, you can substitute it into (-1)^(n+1) / 3^(n-1) to find the corresponding term in the sequence.

To find the nth term of the pattern, we need to identify the pattern's rule. Let's examine the given terms:

1/3, -1/9, 1/27, -1/81

We can observe that each term alternates between positive and negative signs. Additionally, the denominator of each term is a power of 3 (3^1, 3^2, 3^3, 3^4). Therefore, we can conclude that the pattern follows the rule of alternating signs with a denominator that increases as a power of 3.

To find the nth term, we can express this pattern using a general formula. Let's denote n as the position of the term in the sequence. If n is odd, the term will be positive, and if n is even, the term will be negative.

The denominator of each term can be represented as 3^(n-1) since the sequence starts with 3^1 (denominator of 1/3). To account for the alternating signs, we can include (-1)^(n+1) in the formula.

Putting it all together, the formula for the nth term of the pattern is:

(-1)^(n+1) / 3^(n-1)

So, for any given value of n, you can substitute it into this formula to find the corresponding term in the sequence.

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Answer:

A

Step-by-step explanation:

Using the given differential equation with the solution \(x^4\) and reduction order, we can substitute \(y^2 = ux^4\) to obtain the new equation \(2x^2u'' + 12xu' - 16u = 0\).

Given the differential equation \(x^2(d^2y/dx^2) - 7x(dy/dx) + 16y = 0\), with \(x^4\) as a solution, we can apply reduction order to obtain a simpler differential equation.

Reduction order involves substituting \(y^n = ux^i\), where i is the lowest positive integer for which the equation becomes simpler.

We can substitute \(y^n = ux^4\) into the given equation, which yields:

\(y^2 = ux^4\)

⇒\(2y(dy/dx) = 4x^3u + x^4u'\)

⇒\((d/dx)(y^2) = (d/dx)(x^4u)\)

⇒\(2y(dy/dx) + y^2(d^2y/dx^2) = 4x^3u' + 4x^4u''\)

Substituting this into the original equation and simplifying gives:

\(2x^2u'' + 12xu' - 16u = 0\), which is a second-order linear homogeneous differential equation that can be solved by substitution or other methods.

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we remove the parenthesis and add the number that have the same exponent

Answer:

3

Step-by-step explanation:

The interquartile range is where the 2nd and 5th dots are, on the opposite ends of the square, from 15-18.

Answer:

3

Step-by-step explanation:

The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁).

In a box plot:

From inspection of the given box plot:

Therefore:

IQR = Q₃ - Q₁

      = 18 - 15

      = 3

So the interquartile range of the given box plot is 3.

Answer:

D

Step-by-step explanation:

Randomly surveying sixth grade students would give the most accurate result, as randomly surveying students in middle school wouldn't just be limited to 6th graders, sixth grade teachers would not be relevant as Carmen wants to know the favorite lunch menu amount 6th grade students, sixth grade boys would only include a certain gender, which is not the focus of the study. Therefore, D would be the best choice

Answer/ Step-by-step explanation: The answer is definitely D.) Randomly surveys sixth grade students

The  recursive formula of g(n)  g(1) = -50 and g(n) = g(n-1) - 15

g(n) = g(n-1) - 15

Start with the given formula: G(n) = -50 - 15n

To find the recursive formula, we need to find the value of g(n) in terms of g(n-1).

To do this, we can subtract 15 from both sides of the equation:

G(n) - 15 = -50 - 15n - 15

Simplifying the equation, we get:

G(n) - 15 = -65 - 15n

Rearranging the equation, we get:

G(n) = -65 - 15n + 15

Now, we can substitute g(n-1) for -65 - 15n:

G(n) = g(n-1) - 15

Finally, we can find the value of g(1) by substituting n = 1 into the original equation:

G(1) = -50 - 15(1)

G(1) = -50 - 15

G(1) = -65

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Complete question is also attached below:/

G(n)=−50−15n  complete the recursive formula of g(n)

g(1)=

g(n)=g(n−1) +=

The ordered pair that is a solution of the system of equations shown in the graph is (-3, 5). The correct option is (2) (-3, 5)

From the question, we are to determine the ordered pair that is a solution of the system of equations shown in the graph.

The solutions of the system of equations are the coordinates of the points where the quadratic curve and the straight line cut each other.

From the graph,

The quadratic curve and the straight line intersect at the point (-3, 5)

Also,

The quadratic curve and the straight line intersect at the point (1, -3)

Hence, the ordered pair is (-3, 5)

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Given statement solution is :- The value of the number is -1/9.

Let's solve the problem step by step.

Let's assume the number we're looking for is represented by the variable "x".

The problem states that the sum of 9 times the number (9x) and 7 is equal to 6. We can write this as an equation:

9x + 7 = 6

To isolate the variable "x," we need to move the constant term (7) to the other side of the equation. We can do this by subtracting 7 from both sides:

9x + 7 - 7 = 6 - 7

This simplifies to:

9x = -1

Finally, to solve for "x," we divide both sides of the equation by 9:

9x/9 = -1/9

This simplifies to:

x = -1/9

So, the value of the number is -1/9.

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Answer:

y=-0.5ˣ

Step-by-step explanation:

each time the x-value is increased by one, the y-value is cut in half compared to the previous point

Answer:

y=-0.5ˣ

Step-by-step explanation:

each time the x-value is increased by one, the y-value is cut in half compared to the previous

There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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Statistical quality control (SQC) can be applied in various industries such as manufacturing, healthcare, finance, and services to monitor and improve the quality of products or services.

SQC involves the use of statistical tools and techniques to analyze and interpret data to identify and address any issues related to quality control. Some of the common applications of SQC include process control, acceptance sampling, and control charts.

In manufacturing, SQC can be used to monitor the production process and ensure that products meet the desired quality standards. For example, control charts can be used to track the performance of a particular machine or process and identify any deviations from the expected values.

In healthcare, SQC can be applied to monitor patient outcomes and ensure that the quality of care is consistent across different healthcare providers. For example, statistical analysis can be used to identify any trends or patterns in patient data and improve the effectiveness of treatments.

Overall, SQC can be applied in any industry where there is a need to ensure that products or services meet the desired quality standards. It is a valuable tool for identifying and addressing any issues related to quality control and improving overall efficiency and effectiveness.

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