Determining if a function is linear which table represent a linear function?

Answer:

\(y = 2\)

Step-by-step explanation:

1) Simplify 5y/9 - y/9 to 4y/9.

\( \frac{4y}{9} = \frac{8}{9} \)

2) Multiply both sides by 9.

\(4y = \frac{8}{9} \times 9\)

3) Cancle 9.

\(4y = 8\)

4) Divide both sides by 4.

\(y = \frac{8}{4} \)

4) Simplify 8/4 to 2.

\(y = 2\)

Hence, the answer is y = 2.

Answer:

5/12

Step-by-step explanation:

5x - 12y = 24

~Subtract 5x to both sides

-12y = 24 - 5x

~Divide -12 to everything

y = -2 + 5/12x

~Reorder

y = 5/12x - 2

Slope is represent by "m" in slope intercept form [ y = mx + b ]. As we can see m = 5/12 from the given information.

Best of Luck!

(a) the required monthly loan payment on the car is approximately $528.23, (b)your friend still owes approximately $17,833.86 on the car loan after the 24th monthly payment, (c)it will take your friend approximately 23 months (rounded up to the nearest month) to pay off the remaining loan she owes after the 24th payment, given the increased monthly payment of $100.

(a) The required monthly loan payment on the car can be calculated using the formula for the monthly payment on a loan. Given a car loan of $28,000, financed at an interest rate of 0.50% per month for 60 months, the monthly payment can be determined using the following formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Plugging in the values, we have:

Monthly Payment = (28000 * 0.005) / (1 - (1 + 0.005)^(-60))

Calculating this, the required monthly loan payment on the car is approximately $528.23.

(b) After making the 24th monthly payment, your friend still owes a remaining balance on the car loan. To calculate this, we need to determine the remaining balance based on the number of payments made and the original loan amount. We can use the formula:

Remaining Balance = Loan Amount * (1 + Monthly Interest Rate)^Number of Payments - (Monthly Payment * ((1 + Monthly Interest Rate)^Number of Payments - 1) / Monthly Interest Rate)

Plugging in the values, we have:

Remaining Balance = 28000 * (1 + 0.005)^24 - (528.23 * ((1 + 0.005)^24 - 1) / 0.005)

Calculating this, your friend still owes approximately $17,833.86 on the car loan after the 24th monthly payment.

(c) If your friend decides to pay $100 more each month after the 24th payment, we can calculate the number of months it will take her to pay off the remaining loan balance. Using the increased monthly payment, we can calculate the new remaining balance and divide it by the increased monthly payment to determine the number of months needed to pay off the loan.

New Remaining Balance = Remaining Balance - (Monthly Payment + Additional Monthly Payment) * ((1 + Monthly Interest Rate)^Number of Payments - 1) / Monthly Interest Rate

Number of Months = New Remaining Balance / (Monthly Payment + Additional Monthly Payment)

Plugging in the values, we have:

New Remaining Balance = 17,833.86 - (528.23 + 100) * ((1 + 0.005)^x - 1) / 0.005

Number of Months = New Remaining Balance / (528.23 + 100)

By solving the equation, it will take your friend approximately 23 months (rounded up to the nearest month) to pay off the remaining loan she owes after the 24th payment, given the increased monthly payment of $100.

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The length of leaves from a tree. The correct option D.

Measurement units are standardized systems used to quantify and express the magnitude or size of physical quantities. They provide a common language for scientists, engineers, and other professionals to communicate about the physical world.

Measurement units are typically classified into two main categories: base units and derived units. Base units are the fundamental building blocks of measurement and are used to define other units. Derived units are created by combining base units and are used to measure quantities that are derived from the fundamental ones.

Examples of base units include the meter for length, the kilogram for mass, the second for time, the ampere for electric current, the Kelvin for temperature, the mole for amount of substance, and the candela for luminous intensity. These units are defined based on natural phenomena and are universally recognized.

Derived units are created by combining base units using mathematical operations such as multiplication, division, and exponentiation. For example, the unit for speed is meters per second (m/s), which is derived from the base units of length and time. Other examples of derived units include the newton for force, the joule for energy, the watt for power, and the volt for electric potential.

Measurement units play a crucial role in science, engineering, and many other fields. They allow us to express physical quantities with precision and accuracy, making it possible to analyze, compare, and communicate complex data effectively.

The measurements which are given in question are most suitable for length of leaves.

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Answer:

Vertices = 8

Edges = 12

Faces = 6

Step-by-step explanation:

A cuboid ( or a rectangular solid ) has 8 vertices , 12 edges & 6 faces.

Answer:

24

Step-by-step explanation:

The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

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Step-by-step explanation:

To solve for inverse, utilize the following steps.

Step 1: let f(x)=y so we get

\(y = \sqrt{x - 6} + 5\)

Step 2: Swap y and x

\(x = \sqrt{y - 6} + 5\)

Solve for y.

\(x - 5 = \sqrt{y - 6} \)

\((x - 5) { }^{2} + 6 = y\)

Step 4: Let y =f^-1(x)

\((x - 5) {}^{2} + 6 = f {}^{ - 1} (x)\)

Answer: \(f^{-1}(x) =\) x²-10x+19

Step-by-step explanation:

Let's replace f(x) for y for now.

\(y=\sqrt{x-6}+5\)

To find inverse.  make your y into x, and your x into y

\(x=\sqrt{y-6}+5\)        >Now you solve for y.  subtract 5 from both sides

\(x-5=\sqrt{y-6}\)        >Square both sides to get rid of root

\((x-5)^{2} =(\sqrt{y-6})^{2}\)     >drop root and square (x-5)

(x-5)(x-5) = y-6              >FOIL

x²-5x-5x+25 = y-6        > combine like terms

x²-10x+25 = y-6            >add 6 to both sides

x²-10x+19=y            > this is your inverse now put the y into inverse form

\(f^{-1}(x) =\) x²-10x+19

To find the expected value of the question, we need to find the probability of having a card with a value less or equal to 5, and the probabilities greater than 5. We are told that the aces are considered the highest card in the deck. So, this card is not part of the group less or equal to 5.

Then, we have in a standard deck of cards 52 cards.

• Those cards that are equal or less than 5 are 16 cards.

• Those cards that are greater than 5 are 36 cards.

The probability of having a card equal to or less than 5 is equal to:

The probability of having a card greater than 5 is equal to:

When we pay someone, we have a "loss" in a game. Then, if we pay $22, we need to write this value as -$22.

Therefore, the expected value of the proposition is as follows:

If we round the result to two decimal places, we have that the expected value is equal to E(V) = $ -3.23.

Step-by-step explanation:

Give me the answer each one please.

The 99.5% confidence interval for the mean weight of all one-year-old baby boys in the United States is (24.8, 26.2) pounds.

We are given a sample of 360 one-year-old baby boys in the United States with a mean weight of 25.5 pounds and a population standard deviation of σ=5.1 pounds. We need to construct a 99.5% confidence interval for the mean weight of all one-year-old baby boys in the United States.

To construct the confidence interval, we can use the formula:

Confidence interval = sample mean ± (z-score)(standard error)

where the z-score is based on the confidence level and the standard error is calculated as:

standard error = σ/√n

Plugging in the given values, we get:

standard error = 5.1/√360 = 0.27 pounds

Since we want a 99.5% confidence interval, the corresponding z-score is 2.807. Therefore, the confidence interval is:

Confidence interval = 25.5 ± (2.807)(0.27) = (24.8, 26.2) pounds

We can be 99.5% confident that the mean weight of all one-year-old baby boys in the United States falls within the range of 24.8 to 26.2 pounds.

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#Relation 1 is a function, for each value of x, there is a corresponding value of Y. Also there's no element in the x, without corresponding values in Y.So this is a Function

1) The easiest way to make it, is by sketching it a diagram.

Let's do this

For the 1st Relation:

As we can see, for each value of x, there is a corresponding value of Y. Also there's no element in the x, without corresponding values in Y.So this is a Function

#2 Relation

Since for 5 there are 2 corresponding values this can't be a function. Because in a function one value in the domain can only relate to another only one value in the Range.

Answer: We can simplify 27 as 3^3 and 9 as 3^2. Then, we have:

27^2/9^4 = (3^3)^2/(3^2)^4

Using the power of a power rule, we can simplify:

= 3^(3x2)/(3^2x4)

= 3^6/3^8

Using the quotient rule, we can subtract the exponents:

= 3^(6-8)

= 3^-2

Therefore, 27^2/9^4 can be expressed as 3^-2 in terms of a power of 3.

brainliest???? (:

Answer:

j=15

Step-by-step explanation:

Let's set up an equation:

2j+7=37

Subtract both sides by 7

2j=30

Divide both sides by 2

j=15

Answer:

15

Step-by-step explanation:

37=2j+7

so subract 7 from both sides

30=2j

then divide by 2 on each side

j=15

For the given statement, we have to correctly rejecting the null hypothesis.

According to the statement

we have to find the outcome when hypothesis test evaluating a treatment that has a very large and robust effect.

For this purpose, we know that the

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

And according to the given statement it is clear that the by this we have to rejected this hypothesis.

because this treatment and the large effects are not possible for the independent values of the hypothesis.

In other words, we can say that the we have to correctly rejecting the null hypothesis.

So, For the given statement, we have to correctly rejecting the null hypothesis.

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the answer is b. y-5=1/2(x+3)^2

9514 1404 393

Answer:

  B.  y -5 = (1/2)(x +3)^2

Step-by-step explanation:

The parent function f(x) = x^2 has been shifted left 3 and up 5, and scaled vertically. The translation of the vertex to (h, k) can be modeled by ...

  y -k = a(x -h)^2

For (h, k) = (-3, 5), the form of the answer will be ...

  y -5 = a(x +3)^2

Only one answer choice has that form.

_____

Additional comment

The coefficient 'a' will be positive when the parabola opens upward. This eliminates choices A and C. Choice D represents a translation of 3 units right and 5 units down—directions opposite of those shown on this graph.

Substituting these values in the given function, we get:

h(-2) = 4 + 8 + 2

Simplifying the expression further, we get:

h(-2) = 14

So, h(-2) is equal to 14.

The function h(t) = ť – 4t + 2 represents a quadratic equation in t, where t is the independent variable and h(t) is the dependent variable.

To find h(-2), we need to substitute -2 in place of t in the given function as follows:

h(-2) = (-2)^2 - 4(-2) + 2

Here, (-2)^2 means -2 multiplied by itself, which equals 4.

Also, -4(-2) means the product of -4 and -2, which equals 8.

Therefore, substituting these values in the given function, we get:

h(-2) = 4 + 8 + 2

Simplifying the expression further, we get:

h(-2) = 14

So, h(-2) is equal to 14.

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Answer:

From left to right it's square square rectangle.

Answer:

B. 9

Step-by-step explanation:

the trapezoids are the same size so the length of AB is the same length of RS

The points of discontinuity for a rational function occur when the denominator is equal to zero.

In a rational function, the denominator represents the values where the function is undefined. To find the points of discontinuity, we need to identify the values that make the denominator zero. These values are the zeros of the denominator.

When the denominator is zero, the rational function is undefined because division by zero is not possible. Thus, the points of discontinuity are the values that make the denominator zero, but are not canceled out by factors in the numerator. These points can be vertical asymptotes or removable discontinuities, depending on the factors present in the numerator. It is important to check for these points and understand their nature when analyzing rational functions.

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What are the points of discontinuity for the given rational function?

6th terms of given geometric progression whose common ratio is 3/2 and first term is 4  is 243/8 using the farmula ar^(n-1).

What is a geometric sequence?

A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.

Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).

a = First term where

The common Ratio is r.

nth term = ar^(n-1)

6th terms ar^(6-1) = ar^5.

given is that r =3/2. a = 4.

6th term = 4 * (3/2)^5

= 4 * 3^5/2^5

=4*243/4*8

=243/8.

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The general solution to the given differential equation y" - 10y' + 29y = 0, where the auxiliary equation has complex roots, is given by y(x) = e^(5x)(C1cos(2x) + C2sin(2x)), where C1 and C2 are arbitrary constants.

To find the general solution of the given differential equation, we first solve the auxiliary equation, which is obtained by substituting y(x) = e^(rx) into the homogeneous equation. The auxiliary equation for the given differential equation is r^2 - 10r + 29 = 0.

Solving this quadratic equation, we find that the roots are complex: r = 5 ± 2i. Since the roots are complex, we can express them as r = 5 ± 2i.

Using Euler's formula, e^(ix) = cos(x) + isin(x), we can rewrite e^(2ix) as cos(2x) + i sin(2x). Therefore, the general solution can be written as y(x) = e^(5x)(C1cos(2x) + C2sin(2x)), where C1 and C2 are arbitrary constants.

This general solution represents a linear combination of the exponential function e^(5x) and the trigonometric functions cosine and sine with a double frequency of 2x.

Hence, the general solution to the given differential equation is y(x) = e^(5x)(C1cos(2x) + C2sin(2x)), where C1 and C2 are arbitrary constants.

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The limit of (f(x) + 1) / sin(x) as x approaches 0 is 0, the approximation for f(1/2) using Euler's method with two steps is 19/32 and the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1.

(a) To find the limit of (f(x) + 1) / sin(x) as x approaches 0, we can first rewrite the given differential equation as:

dy / dx = y²  (2x + 2)

Separating variables, we get:

dy / y²  = (2x + 2) dx

Integrating both sides, we have:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side gives:

-1 / y = x²  + 2x + C1

where C1 is the constant of integration.

Since we have the initial condition f(0) = -1, we substitute x = 0 and y = -1 into the above equation:

-1 / (-1) = 0²  + 2(0) + C1

1 = C1

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Now, to find the limit (f(x) + 1) / sin(x) as x approaches 0, we substitute x = 0 into the particular solution equation:

f(0)(0²  + 2(0) + 1) + 1 = 0

-1(0) + 1 = 0

1 = 0

Therefore, the limit of (f(x) + 1) / sin(x) as x approaches 0 is 0.

(b) Using Euler's method, we approximate the value of f(1/2) starting at x = 0 with two steps of equal size. Let's choose the step size h = 1/4.

First step:

x0 = 0, y0 = f(0) = -1

Using the differential equation, we have:

dy / dx = y²  (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (-1)²  (2(0) + 2) (1/4)

Δy ≈ 1/2

Next, we update the values:

x1 = x0 + Δx = 0 + 1/4 = 1/4

y1 = y0 + Δy = -1 + 1/2 = 1/2

Second step:

x0 = 1/4, y0 = 1/2

Using the differential equation again:

dy / dx = y^2 (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (1/2)²  (2(1/4) + 2) (1/4)

Δy ≈ 3/32

Updating the values:

x2 = x1 + Δx = 1/4 + 1/4 = 1/2

y2 = y1 + Δy = 1/2 + 3/32 = 19/32

Therefore, the approximation for f(1/2) using Euler's method with two steps is 19/32.

c)To find the particular solution to the differential equation dy/dx = y^2 (2x + 2) with the initial condition f(0) = -1, we can solve the separable differential equation.

Separating variables, we have:

dy / y² = (2x + 2) dx

Integrating both sides:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side:

-1 / y = x²  + 2x + C

where C is the constant of integration.

To find the particular solution, we substitute the initial condition f(0) = -1:

-1 / (-1) = 0²  + 2(0) + C

1 = C

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Therefore, the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1

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Answer:

nonliner and linear c.

Step-by-step explanation:

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Answer:

The answer is the equation for the function describing the movement of the buoy:

f(x) = 5 * sin(2 * pi * x / 16) + 8

Step-by-step explanation:

To graph the function, we need to find an equation that describes the buoy's movement. Since the buoy bobs up and down 5 meters from the ocean's depth, we can use the sine function. The amplitude of the function is 5, since the buoy moves 5 meters from the normal ocean depth. The period of the function is 16 seconds, since it takes 16 seconds for the buoy to go from its highest point to its lowest point.

Using this information, we can write the equation for the function as:

f(x) = 5 * sin(2 * pi * x / 16) + 8

where x is the time in seconds.

The first point on the graph would be (0, 8), since at x = 0 the buoy is at normal ocean depth. The second point would be either a maximum or minimum value on the graph closest to x = 0, which can be found by finding the derivative of the function and setting it equal to zero.

The graph of the function would look like a wave that oscillates up and down, with a maximum value of 5 meters above the normal ocean depth and a minimum value of 3 meters below the normal ocean depth.

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Answer:

x-2y+5=0

Step-by-step explanation:

y+1= \(\frac{x+7}{2}\)

y=\(\frac{x+7}{2}\) -1

y=\(\frac{x+7-2}{2}\)

y=\(\frac{x+5}{2}\)

2y=x+5

x-2y+5=0

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-1)=\dfrac{1}{2} (x-(-7)}\)

Simplify

\(\rm{y+1=\dfrac{1}{2}(x+7)}\)