help meeee

6x-3=3x+12

The system of first-order equations that is equivalent to the given second-order differential equation is dy/dt = z, dz/dt = w, and dw/dt = (-3z - 2w - 6y)/t².

To write the given second-order differential equation as a system of first-order equations, we need to introduce new variables.

Let z = dy/dt. Then, we can rewrite the given equation as

d³y/dt³ = dz/dt

d²y/dt² = dz/dt = z

Substituting these expressions into the original equation, we get

(t²) (d³y/dt³) + 3(d²y/dt²) + 2(dy/dt) + 6y = t² (dz/dt) + 3z + 2(dy/dt) + 6y

Simplifying and grouping the terms, we obtain

d/dt [y, z, w] = [z, w, (-3z - 2w - 6y)/t²]

where w = dt/dt = 1.

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The expression that represents the difference between (7x - 9) and (8x - 5) in Simplest terms is -x - 4.

The difference between (7x - 9) and (8x - 5), we need to subtract the second expression from the first.

(7x - 9) - (8x - 5)

To simplify this expression, we distribute the negative sign to the terms inside the parentheses:

7x - 9 - 8x + 5

Next, we can combine like terms by adding or subtracting coefficients of similar variables:

(7x - 8x) + (-9 + 5)

Simplifying further:

-x + (-4)

Finally, we can combine the two negative terms:

-x - 4

Therefore, the expression that represents the difference between (7x - 9) and (8x - 5) in simplest terms is -x - 4.

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In this case, the mean is 5.5 cm and the standard deviation is 0.1 cm. So, one standard deviation below the mean is 5.4 cm and one standard deviation above the mean is 5.6 cm. Therefore, about 68% of the data falls between 5.4 cm and 5.6 cm, which includes the range of 5.3 cm to 5.7 cm.

Your question involves a normal distribution with a mean (µ) of 5.5 cm and a standard deviation (σ) of 0.1 cm. You want to find the percentage of data between 5.3 cm and 5.7 cm.

First, we need to standardize the scores using the z-score formula: z = (x - µ) / σ

For 5.3 cm: z1 = (5.3 - 5.5) / 0.1 = -2
For 5.7 cm: z2 = (5.7 - 5.5) / 0.1 = 2

Now, referring to a standard normal distribution table or using a calculator, we find the area between these z-scores:

This can be determined using the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean
- About 95% of the data falls within two standard deviations of the mean
- About 99.7% of the data falls within three standard deviations of the mean

P(-2 < z < 2) = P(z < 2) - P(z < -2) = 0.9772 - 0.0228 = 0.9544

Converting it to a percentage, we get 95.44%, which is approximately 95%.

So, the answer is A. 95%.

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Step-by-step explanation:

he ran 75 of 100 m, that means he ran the fraction of 100m 75/100 × 100 = 0.75×100 = 75%

The Length of the rectangle is 18 unit.

Perimeter of rectangle = 2(length + width)

Given the following:

Let x represent the width of the rectangle

Width of the rectangle = x

Length of the rectangle = 4x + 6

Perimeter of rectangle = 42 units

Therefore, we would write the following equation to find x based on the formula for finding the perimeter of a rectangle:

2(4x + 6 + x) = 42

2(5x + 6) = 42

10x + 12 = 42

10x = 42 - 12

10x = 30

10x/10 = 30/10

x = 3

The width (x) = 3.

Length of the rectangle = 4(3) + 6

Length of the rectangle = 18 unit.

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Answer: 5/96

Step-by-step explanation:

The given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

The errors of a slope and an intercept will be connected if you fit them simultaneously.

By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept.

Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.

Therefore, the given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

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Drops = 27

First, we need to find the volume of the given tank using the following equation

\(Volume = Length*Width*Height\\Volume =14*9*10\\Volume =1260\\\)

Now that we know the volume, we need to find out how many drops that we need to use. We can find that out using the following equation

\(Drops = 3\frac{Volume}{140} \\Drops = 3\frac{1260}{140} \\Drops = 3(9) \\Drops = 27\)

Answer:

1:12

Step-by-step explanation:

To simplify 3 yards :

3 yd.* 36 in. = 108 inches

9:108 simplified :

9/9 = 1

108/9 = 12

So, the ratio for the scale factor is 1:12 :)

Answer:

11

Step-by-step explanation:

6+(2x+28)=x+23=-11 -> Answer can't be negative -> 11

Given:

ABCD is a parallelogram.

To prove:

Proof:

Hence proved.

Step-by-step explanation:

77 ft

Answer:

 101.5 ft^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h where b1 and b2 are the lengths of the bases and h is the height

A = 1/2 ( 11+18) * 7

   = 1/2 (29) *7

     101.5 ft^2

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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First subtract 4 from both sides to isolate the 3x.

That leaves us with 3x = -9.

Since x is being multiplied by 3, to get x by itself,

we need to divide both sides of the equation by 3.

So our final answer is x = -3.

Answer:

x = -3

Step-by-step explanation:

3x + 4= -5

Subtract 4 from both sides.

3x = -9

Divide both sides by 3.

x = -3

Answer:

y=-8/3x+31/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-3))/(2-5)

m=(5+3)/-3

m=8/-3

y-y1=m(x-x1)

y-(-3)=-8/3(x-5)

y+3=-8/3(x-5)

y=-8/3x+40/3-3

y=-8/3x+40/3-9/3

y=-8/3x+31/3

Average price is the mean price of an asset or security observed over some period of time.

Define average price in gas?

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Answer:

I am assuming the 8:15 was a typo and was actually supposed to be a 8:14. Anyways, they are equivalent because they all make 4:7 when simplified.

Step-by-step explanation:

4:7 = itself at this point, as they don't have numbers that can simplify each other on both sides, unless you are looking for a decimal answer.

8:14 = 4:7 <- You can divide the 8 and 14 by two. 8 divided by 2 is four, and 14 divided by 2 is 7.

16:28 = 4:7 <- You can divide the 16 and the 28 by four. 16 divided by 4 is 4, and 28 divided by 4 is 7.

20:35 = 4:7 <- You can divide both sides by 5. 20 divided by 5 is 4, and 35 divided by 5 is 7.

Answer:

1.1. 3(2a-7)

1.2. 3x(2x+3)

Step-by-step explanation:

Put the common factor on the outside of the parentheses.

1.1. 6a-21

The lowest common factor for 6a and -21 is 3.

     3(2a-7)

1.2. \(6x^{2} +9x\)

The lowest common factor for \(6x^{2}\) and 9x is 3x.

      3x(2x+3)

The sum of interior Angles of Hexagon is always 720°

Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:

720°÷6 = 120°

In a regular hexagon, each inside angle is 120°.

An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.

Therefore, the interior angles of a hexagon are always added up to 720°.

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The cube's surface area inaccuracy can go up to a maximum of Δs=9 in²

What is a surface area?

The surface area is the sum of the areas of an object's face.  Surface is mainly used in real-life.

The surface area can be of two types in geometry:

1. Lateral surface area (It is also known as curved surface area)

2. Total surface area

Surface area is mainly used in chemical kinetics. Here is the question, the concept of the surface area is used.

The surface area of a cube=6a²

Let the surface area is s

s(x)= 6a²

Here, given x=6 feet

Δx=1.5/1.2

=0.125

Differentiating with respect to a,

ds=12a da

Δs=12(6)(0.125)

Δs=9  in²

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Answer:

A=2035.75

V=4033.81

Step-by-step explanation:

Depending on which formula you need you will need to solve for the separate shapes then add the answers together.

Cone: A=pi×r(r+hSquared +rSquared)

V=pi×rSquared×h/3

Cylinder: A=2pi×rh+2pi×rSquared

V=pi×rSquared ×h

Answer:

The answer is 91

Step-by-step explanation:

~Hoped this helped~

Answer:

41 cartons will be needed

Step-by-step explanation:

here, we need to know the number of cartons the farmer needs to hold all the eggs

To calculate this, we simply make a division of the number of eggs by the number of eggs in a carton

That would be 1957/48 = 40.77

The closest number of cartons here is 41

The amount to be paid after 3 years is  $23,329.97.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.

Given:

P= 20,000

r= 5.2%

t= 3 years

r = R/100

r = 5.2/100

r = 0.052 rate per year,

Now, solve for A

A = P\((1 + r/n)^{nt\)

A = 20,000.00\((1 + 0.052/2)^{(2)(3)\)

A = 20,000.00\((1 + 0.026)^(6)\)

A = $23,329.97

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Answer:

-14 meters below sea level

Step-by-step explanation:

I am not completely sure if what you are asking is for an integer for this word problem but if it is then I hope this helps you.

The dimensions of the original painting using the scale of th copy are 3200 cm x 2400 cm.

To find the dimensions of the original painting, we need to use the scale of the copy, which is 1 in 40 cm. This means that for every 1 inch on the copy, there are 40 centimeters on the original painting.

First, we need to convert the dimensions of the copy from inches to centimeters.

2 inches x 40 cm/inch = 80 cm

1.5 inches x 40 cm/inch = 60 cm

So, the dimensions of the copy in centimeters are 80 cm x 60 cm.

Next, we can use these dimensions and the scale to find the dimensions of the original painting.

Original painting width = copy width x scale

Original painting width = 80 cm x 40

Original painting width = 3200 cm

Original painting height = copy height x scale

Original painting height = 60 cm x 40

Original painting height = 2400 cm

Therefore, the dimensions of the original painting are 3200 cm x 2400 cm.

Note: The question is incomplete. The complete question probably is: Marie has a small copy of Rene Magritte's famous painting The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inch. The scale of the copy is 1 in 40 cm. How do you find the dimensions of the original painting?

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Answer:

X = 13

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Lane 3 turtle.

Step-by-step explanation:

The slope for the lane 3 turtle is steeper than that of the lane 1 turtle. We know slope of a position vs time graph is velocity, so whichever turtle has the steeper/greater slope that turtle is fastest.

If a  bacteria colony triples every 4 days the population is p0 bacteria then  the population of the bacteria  pt is t days later will be P=Po\(3^{t/4}\)

Exponential function:

An exponential function is a Mathematical function in form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

In this question, it is said that the bacteria triples in every 4 days and the original amount of bacteria is Po.

P(bacteria in t days)= Po(\(number of multipier^{t/days}\))

                               =Po(\(3^{t/4}\))

So when a bacteria triples in every 4 days then the population of bacteria in t days will be Po(\(3^{t/4}\))

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Answer:

a

Step-by-step explanation:

trust

Answer:

A

Step-by-step explanation: