Suppose that in modeling a solar panel system which measures the energy output through two output points modeled as yi (t) and y2 (t) is described mathematically by the system of differential equation

Answer:

Ashley=1450

Ben= 1080

Mischa= 1210

Step-by-step explanation:

M= Mischa

B= Ben

A= Ashley

M+B=2290

A+B=2530

M+A=2660

M-A= -240

so 2M = 2420, and M= 1210

Then

1210 + B = 2290

B= 1080

Then

1210 + A= 2660

A= 1450

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

Answer: the answer is 20

Step-by-step explanation:

I had the same question and did my math and got it right

The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.

It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.

The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.

The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.

A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.

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Answer:

I think it's right

but plz let me know if im wrong

Step-by-step explanation:

The function has an equation of f(x) = (x + 4)(x - 2)

The given parameters in the question are

Roots = -4 and 2

Point = (1, -5)

The above parameters can be rewritten as

Roots: x = -4 and x = 2

Point: (x, y) = (1, -5)

A quadratic equation can be represented as

f(x) = a * (x - Roots)

Where Roots: x = -4 and x = 2

The above parameters imply that we have the following equation

y = a(x + 4)(x - 2)

From the question, we have

(x, y) = (1, -5)

This gives

-5 = a(1 + 4)(1 - 2)

Divide

a = 1

Substitute a = 1 in y = a(x + 4)(x - 2)

y = (x + 4)(x - 2)

Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)

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Answer: The answer would be A: f(x) = (x − 2)(x + 4)

Step-by-step explanation: I got it right on my test

Answer: x=5

Step-by-step explanation:

3x appears two times and so does 2x +2. That created the equation 3x + 3x + 2x + 2 + 2x + 2=54. Combine like terms. You get 10x +4=54. Then you solve. Inverse operation: You subtract 4 from 54. Which is 50, then divide by 10. X=5

The value of the x for the given rectangle is 5 units.

The whole distance that a rectangle's boundaries, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides.

Given, The perimeter of the rectangle below is 54 units.

Also given the length of the rectangle = 3x

and the width of rectangle = 2x + 2

Since, Perimeter of rectangle = 2 *( length + width)

Perimeter of rectangle = 2 * (3x + 2x + 2)

Since we have a perimeter

54 = 2 *(5 x + 2)

5x + 2 = 27

5x = 25

x = 5

Therefore, For the given rectangle, the value of x is 5 units.

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Step-by-step explanation:

it's simple:

Answer:

x-6/2=2x/7

7x-42=4x

7x-4x=42

3x= 42

X = 42/3

Answer:

Step-by-step explanation:

Everyone asks about these types of problems,  I feel like math teachers do not know how to teach this type of problem.

these really are just follow the steps , type of problems..

Step 1 :

find the slope

slope = m

given:

point P1 (-4,-6)  in the form (x1,y1)

4x + 5y = 25

because they tell us to find a line perpendicular to the given line,  we are able to use the slope of the given line to find the slope of the line we want.  Perpendicular means  take the reciprocal of the given line's slope.

or

4x + 5y = 25

5y = -4x + 25

y = \(\frac{-4}{5}\) X +5  use the slope intercept formula to know slope m

y= mx + b

m=   \(\frac{-4}{5}\)

take the reciprocal and swap the sign

m = \(\frac{5}{4}\)

Step 2:

put the given information into the point slope formula.  if this seems like a lot to remember it's going to be super super helpful for you to memorize the two formulas,   slope-intercept and point-slope,  you'll use them over and over.

point slope formula

y - y1 = m(x -x1)

y - (-6) =  \(\frac{5}{4}\)(x-(-4))

the (x1,y1) came from the given point above.  Now just solve for Y

y +6 =   \(\frac{5}{4}\)(x+4)

y + 6 =   \(\frac{5}{4}\)x + 5

y  =   \(\frac{5}{4}\)x + 5 -6

y =  \(\frac{5}{4}\)x -1

this is the equation of the line that passes through point (-4,-6)

Note that that is in the form of the slope intercept formula

y = mx + b

where b is just a negative number

There was really just 2 Steps,  and none of that math is really difficult.

recall the two formulas,  and how they are used.  and you are good.

9514 1404 393

Answer:

  4

Step-by-step explanation:

Consider the arcs PQ and P'Q. When turns are made without slipping, these have the same measure. The length of arc PQ is ...

  PQ = CP·θ

The length of arc P'Q is ...

  P'Q = O₂Q·(∠PO₂Q)

Segment O₂A is parallel to CP, so angle AO₂Q is θ. Then ∠PO₂Q = θ+α, where α is the angle by which P' has rotated counterclockwise from A.

We are given that ...

  CP = 5, O₂Q = 1

Using the above relations, we can write ...

  5θ = 1(θ+α)

  α = 4θ

That is, for every full turn θ = 2π, the smaller circle makes turns totalling 4(2π) = 8π, or 4 full turns.

The small circle makes 4 revolutions to arrive at its starting point.

Answer:

y= -4/3x

Step-by-step explanation:

hope this helps :)

If a merchant bought an item for $50.00 and sold it for 30% more (markup), the item's selling price was $65.00.

The markup is the percentage or amount by which an item is sold.

The markup is based on the cost price.  After adding the markup amount, the selling price is determined to generate some profits for the seller.

The purchase price of an item = $50.00

The markup = 30%

Markup factor = 1.3 (1 + 0.3)

The selling price of the item = $65.00 ($50.00 x 1.3)

Thus, for adding 30% more (markup) on the cost of the item, the selling price is determined as $65.00.

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Para planificar su cosecha y garantizar una buena ganancia, Guillerno necesita utilizar la ecuación de utilidad.

En un negocio, la utilidad se refiere a la ganancia neta de una empresa o la diferencia entre el total de dinero que se gana y los gastos o inversión.

La utilidad se calcula a partir de la siguiente ecuación:

Esta ecuación requiere saber los posibles costos y los ingresos totales para calcular la utilidad de un producto y así mismo planear la cantidad del producto a vender.

Nota: Esta pregunta está incompleta porque no hay información sobre los costos, posbiles ganancias, etc. de Guillermo. Debido a lo anterior, la respuesta se basa en conocimiento general.

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Answer:

2 I think let me know if I'm wrong

Step-by-step explanation:

The value of X and Y in the length of each side of an equilateral triangle is X = 3 and Y = 4

In this question we have been given the equations for the three sides of an equilateral triangle.

3X +12, 8X -3 and 5Y + 1

We need to find the value of X and Y.

We know that all sides of an equilateral triangle are equal.

so, 3X +12 = 8X -3 = 5Y + 1

Consider 3X +12 = 8X -3

3X -8X = - 3 - 12

-5X = - 15

X = 3

Now consider an equation 8X - 3 = 5Y + 1

substitute above value of X in this equation.

8(3) -3 = 5Y + 1

24 - 3 = 5Y + 1

21 - 1 = 5Y

5Y = 20

Y = 4

Therefore, the value of X and Y in the length of each side of an equilateral triangle is X = 3 and Y = 4

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Hello!

\(\large\boxed{\text{Infinitely many solutions.}}\)

-3(x - 14) + 9x = 6x + 42

Distribute the coefficient of the parenthesis:

-3(x) - 3(-14) + 9x = 6x + 42

-3x + 42 + 9x = 6x + 42

Combine like terms:

6x + 42 = 6x + 42

Both sides of the equation are the same, therefore:

There are infinitely many solutions.

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______________________

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For solving such problems we need to recall equations .

⠀⠀⠀⠀

When the value of two variable comes equal and zero in an equation then that equation is said to have infinitely many solutions . If the value of a variable have any particular constant then the equation is said to have one solution . If the value of of any variable comes undefine then the equation is said to have no solution .

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➠ - 3 ( x - 14 ) + 9x = 6x + 42

➠ -3x + 42 + 9x = 6x + 42

Now, we will bring the variable on left hand side and constants on right hand side

➠ -3x + 9x - 6x = 42 - 42

➠ -9x + 9x = 42 - 42

➠ 0 = 42 - 42

➠ 0 = 0

As we can see the equation have end with a zero the equation have indefinitely many solutions

➠ Indefinity many solutions

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2 different expressions that involve only outs and powers of 2 which are equivalent 4 2/3 / 8 1/4

1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)

2) (2^5 * 3^1) / (2^6 * 4^-1)

1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)

This expression is equivalent to 4 2/3 / 8 1/4 because it is written in terms of powers of two. 4^2 is equal to 16, which is the numerator in 4 2/3. 2^-1 is the same as 1/2, which is the second fraction in 4 2/3. 3^1 is equal to 3, which is the numerator in 8 1/4. 8^1 is equal to 8, which is the denominator in 8 1/4. 2^-2 is the same as 1/4, which is the second fraction in 8 1/4. 4^-1 is equal to 1/4, which is the first fraction in 8 1/4. When all the terms are multiplied and divided, it is the same as 4 2/3 / 8 1/4.

2) (2^5 * 3^1) / (2^6 * 4^-1)

This expression is also equivalent to 4 2/3 / 8 1/4 because it is written similar to above equation.

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Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, we simplify the expression inside the parentheses:

4 + 2 = 6

Next, we square the result:

6² = 36

Now, we substitute the squared result back into the expression:

6(36) - 32

Next, we perform the multiplication:

6 * 36 = 216

Finally, we subtract 32:

216 - 32 = 184

Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.

Answer:

124 degrees

Step-by-step explanation:

x=24 so if you plug in the value and solve it is 124 degrees

When constructing a confidence interval for the population mean when the standard deviation is unknown, the formula for standard error is: s/√n, where s is the sample standard deviation and n is the sample size.

Begin with a sample: Start with a sample of size n that is representative of the population of interest. The sample is used to estimate the population mean.

Compute the sample standard deviation: Calculate the sample standard deviation, denoted as s, which measures the variability or spread of the sample data. The sample standard deviation is an estimate of the population standard deviation.

Calculate the standard error: The standard error represents the standard deviation of the sampling distribution of the sample mean. It quantifies the variability or uncertainty associated with estimating the population mean based on the sample.

The formula for the standard error is: Standard Error = s / √n

s: Sample standard deviation, which measures the variability of the sample data.

n: Sample size, the number of observations in the sample.

Standard Error = Sample Standard Deviation / √(Sample Size)

By dividing the sample standard deviation by the square root of the sample size, we obtain the standard error.

Interpretation: The standard error gives us an idea of how much the sample means are likely to vary from the true population mean. Smaller standard errors indicate less variability and greater precision in estimating the population mean.

Confidence interval: Once the standard error is calculated, it is used along with the desired level of confidence and critical values from the appropriate distribution (such as the t-distribution or the standard normal distribution) to construct a confidence interval for the population mean.

The confidence interval represents a range of values within which we can be confident, with a specified level of confidence, that the true population mean lies.

To summarize, when constructing a confidence interval for the population mean when the standard deviation is unknown, we calculate the standard error by dividing the sample standard deviation by the square root of the sample size.

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Answer:

yes I think he does because of the distance of the sprinklers reach.

The area οf the actual bridge deck in square feet is 1,280 square feet.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet * 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet * (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Fred's pay for the specified week, with a rate of $11.25 for regular hours and time and a half for overtime, and number of hours worked of 48.5 hours is presented by completing the attached table as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

A payment rate is the amount of payment or money that is received in a unit of time.

The amount Fred earns per hour = $11.25

The number of regular hours Fred works per week = 40

The rate at which he is paid for overtime = Time and a half

The number of hours Fred works in the specified week = 48.5 hours

Therefore, the amount Fred earns for working overtime = 1.5 × $11.25 = $16.875

The amount Fred earns for regular hours during the specified week = 40 × $11.25 = $450

The number of overtime hours Fred works for during the week = 48.5 - 40 = 8.5

The amount Fred earns for the overtime work = 8.5 × $16.875 = $143.4375

Fred's gross payment for the week is therefore; $450 + $143.4375 = $593.4375

The table can therefore be completed by plugging in the above values as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

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To find the variance of the sum of the numbers rolled three times with a biased dice, we need to determine the probabilities of rolling each number.

Let's assume the biased dice has six faces numbered 1 to 6. Let p be the probability of rolling an even number, and 2p be the probability of rolling an odd number. Since the total probability must equal 1, we can express this as:

3p + 3(2p) = 1

3p + 6p = 1

9p = 1

p = 1/9

Therefore, the probability of rolling an even number (1, 2, 4, or 6) is 1/9, and the probability of rolling an odd number (3 or 5) is 2/9.

Now, let's calculate the variance of the sum of the numbers rolled three times. The variance is the average of the squared differences between each outcome and the mean, multiplied by the corresponding probabilities.

The mean of a single roll is calculated as:

(1 * 1/9) + (2 * 1/9) + (3 * 2/9) + (4 * 1/9) + (5 * 2/9) + (6 * 1/9) = 4/3

Now, let's calculate the variance:

Variance = [(1 - 4/3)^2 * (1/9) + (2 - 4/3)^2 * (1/9) + (3 - 4/3)^2 * (2/9) + (4 - 4/3)^2 * (1/9) + (5 - 4/3)^2 * (2/9) + (6 - 4/3)^2 * (1/9)]

Variance = (1/9) * [(-1/3)^2 + (2/3)^2 * 2 + (1/3)^2 + (2/3)^2 * 2 + (5/3)^2 + (2/3)^2]

        = (1/9) * [(1/9 + 4/9) * 2 + 1/9 + (4/9) * 2 + 25/9 + 4/9]

        = (1/9) * [2/3 + 1/9 + 8/9 + 25/9 + 4/9]

        = (1/9) * (40/9)

        = 40/81

Therefore, the variance of the sum of the numbers rolled three times with the biased dice is 40/81.

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The set of all points equidistant from the points A(-2, 4, 4) and B(5, 2, -3) forms a plane. This plane can be described by an equation that represents the locus of points equidistant from A and B.

To find the equation of the plane, we can first calculate the midpoint M between points A and B, which is given by the coordinates (x₀, y₀, z₀) of M, where x₀ = (x₁ + x₂)/2, y₀ = (y₁ + y₂)/2, and z₀ = (z₁ + z₂)/2.
Midpoint M:
x₀ = (-2 + 5)/2 = 3/2
y₀ = (4 + 2)/2 = 3
z₀ = (4 - 3)/2 = 1/2
Next, we calculate the direction vector D from A to B, which is obtained by subtracting the coordinates of A from those of B.
Direction vector D:
dx = 5 - (-2) = 7
dy = 2 - 4 = -2
dz = -3 - 4 = -7
Using the midpoint M and the direction vector D, we can write the equation of the plane as follows:
(x - x₀)/dx = (y - y₀)/dy = (z - z₀)dz
Substituting the values we calculated earlier, the equation becomes:
(x - 3/2)/7 = (y - 3)/(-2) = (z - 1/2)/(-7)
This equation represents the set of all points equidistant from points A(-2, 4, 4) and B(5, 2, -3), and it describes a plane in three-dimensional space.

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Answer:

5275.2 m³

Step-by-step explanation:

We need the radius first:

\(\sqrt{l^2- h^2}\) = 12

Formula for volume = πr²*h/3

Volume = 3.14 * 144 * 35/3

Volume = 5275.2

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