Solve the system by substitution.
y = 2x + 35
y = 9x

Answer:

5x-100-3x=$x

Step-by-step explanation:

The borderline if the linear inequality's symbol is > (greater than) or (greater than or equal to).

In mathematics, an inequality is a connection that does not have an equal sign between two expressions or values. Inequality follows imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Use the not equal symbol, which is most often used, when two values are not equal (). No matter how little or huge the values, various inequalities are employed to contrast them. The two sides can be changed until the variables are all that is left in order to solve several basic inequalities. Unevenness is caused by a number of factors, including: The sum or division of negative values on both sides. The left and right are exchanged.

given

inequality for y

5x – 2y ≤ 10

– 2y ≤ – 5x + 10

y ≥ 5/2x - 5

When dividing by a negative number, remember to switch the inequality sign.

In a linear inequality, you will shade below the boundary line if the sign is (less than) or (less than or equal to).  The borderline if the linear inequality's symbol is > (greater than) or (greater than or equal to).

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Explanation

We will use the volume formula to find the radius,

And if that is the radius, then the diameter must be:

Answer

Approximately 8.6 cm

To forecast using data that has seasonality, one commonly used method is seasonal decomposition of time series (STL). This method separates the time series data into three components: trend, seasonality, and residuals. By isolating the seasonal component, you can forecast future values by extrapolating the pattern observed in previous seasons.

Another approach is the use of seasonal autoregressive integrated moving average (SARIMA) models. SARIMA models are an extension of ARIMA models that incorporate seasonal patterns. These models capture both the trend and seasonality in the data and can be used to make forecasts.

To control volatility in various time series models, a common technique is to use a volatility model, such as the generalized autoregressive conditional heteroskedasticity (GARCH) model. This model estimates the volatility of the time series by incorporating past volatility and squared residuals. By modeling and forecasting the volatility, you can better understand and manage the potential fluctuations in the time series data.

A simple moving average method is a technique used to smooth out fluctuations and identify trends in time series data. It involves calculating the average of a fixed number of data points, often referred to as the window size or period. As new data becomes available, the oldest data point in the window is dropped, and the newest data point is included in the calculation. This process is repeated for each subsequent data point. The resulting moving average values can provide insights into the overall trend of the data, helping to identify patterns or changes over time.

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Answer:

2/3, 2:3, or 2 to 3.

Step-by-step explanation:

The key statement is "boys to girls"

Ratios can be written three different ways:

12/18 -> 6/9 -> 2/3

Best of Luck!

Answer:

108

Step-by-step explanation:

240 x 0.45 = 108

In order to find the percentage of something, turn the percentage into a decimal and multiply it by the number. For example 45% becomes 0.45. Then to find the answer you multiply it by 240, finding what 45% of 240 is.

Answer:

108

Step-by-step explanation:

First find 40% of 240 = 96

Then 5% of 240 = 12

Add both of them together

96 + 12 = 108

Answer:

An invoice is a commercial instrument that states the total amount due.

The proforma invoice is a declaration by the seller to provide products and services on a specified date and time.

Step-by-step explanation:

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An expression that represents the area of the gift shop, in terms of x is 720x² + 464x - 480.

An expression that represents the perimeter of the gift shop, in terms of x is 720x² + 464x - 480.

If the perimeter is going to be 176 feet, the dimensions of the building are 54 feet by 34 feet.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangular gift shop = (20x + 24) × (36x - 20)

Area of rectangular gift shop = 720x² - 400x + 864x - 480

Area of rectangular gift shop = 720x² + 464x - 480

Perimeter of rectangular gift shop = 2(20x + 24 + 36x - 20)

Perimeter of rectangular gift shop = 2(56x + 4)

Perimeter of rectangular gift shop = 112x + 8

176 = 112x + 8

112x = 168

x = 1.5

Length, L = 20(1.5) + 24 = 54 feet.

Width, W = 36(1.5) - 20 = 34 feet.

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Answer:

About 38 dollars

Step-by-step explanation:

If there is a 20 percent tip ten it would be 1/5 of the amount. Then the answer would be 38.

Answer:

The experimental probability is 6% lower than the theoretical probability.

The experimental probability is 6% higher than the theoretical probability.

Both of them are right

Answer:

The experimental probability is 6% lower than the theoretical probability.

Or

The experimental probability is 6% higher than the theoretical probability.

Step-by-step explanation:

Just choice either or both you'll do fine!

Answer:

2y=5x-2

Write the equation in the form of y = mx + b

where m is the gradient and b is the y-intercept.

Therefore, 2y=5x-2 will be:

y = 5/2x - 1

Gradient is 5/2

and y-intercept is (0,-1)

The preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft is approximately $700 million.

To estimate the cost of building a 600-MW fossil-fuel plant, we can use the cost capacity exponent factor and the cost index.

First, let's calculate the cost capacity ratio (CCR) for the 600-MW plant compared to the 200-MW plant:

CCR = (600/200)^0.79

Next, we need to adjust the cost of the 200-MW plant for inflation using the cost index. The cost index ratio (CIR) is given by:

CIR = (current cost index / base cost index)

Using the given information, the base cost index is 400 and the current cost index is 1200. Therefore:

CIR = 1200 / 400 = 3

Now, we can estimate the cost of the 600-MW plant:

Cost of 600-MW plant = Cost of 200-MW plant * CCR * CIR

Using the information provided, the cost of the 200-MW plant is $100 million. Plugging in the values, we have:

Cost of 600-MW plant = $100 million * CCR * CIR

Calculating CCR:

CCR = (600/200)^0.79 ≈ 2.3367

Calculating the cost of the 600-MW plant:

Cost of 600-MW plant = $100 million * 2.3367 * 3

Cost of 600-MW plant ≈ $700 million

Your question is incomplete but most probably your full question was

Suppose that an aircraft manufacturer desires to make a preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of its new long- distance aircraft. It is known that a 200-MW plant cost $100 million 20 years ago when the approximate cost index was 400, and that cost index is now 1,200. The cost capacity exponent factor for a fossil-fuel power plant is 0.79. What is he preliminary estimate of the cost of building a 600-MW fossil-fuel plant for the assembly of the new long-distance aircraft?

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tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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The prediction for the number of inches that Stephen will grow during his 15th year is given as follows:

2.44 inches.

To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function in this problem is given as follows:

y = 0.02x + 2.14.

Hence the estimate during the 15th year, when x = 15, is given as follows:

y = 0.02(15) + 2.14

y = 2.44.

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The two expressions are not equal, so the function f(x) = 2x² is also not linear.

To determine if a function is linear, we need to verify if it satisfies the linearity property, which states that for any x and y in the domain of the function and any scalars α and β, the function should satisfy f(αx + βy) = αf(x) + βf(y).

Let's examine each function and determine if it is linear:

f(x) = 3x - 2

To check linearity, we need to verify if f(αx + βy) = αf(x) + βf(y). Let's substitute the values:

f(αx + βy) = 3(αx + βy) - 2

= 3αx + 3βy - 2

On the other hand:

αf(x) + βf(y) = α(3x - 2) + β(3y - 2)

= 3αx - 2α + 3βy - 2β

Comparing the two expressions, we can see that they are not equal, so the function f(x) = 3x - 2 is not linear.

f(x) = 2x²

Using the same logic, let's check linearity:

f(αx + βy) = 2(αx + βy)²

= 2(α²x² + 2αβxy + β²y²)

= 2α²x² + 4αβxy + 2β²y²

On the other hand:

αf(x) + βf(y) = α(2x²) + β(2y²)

= 2αx² + 2βy²

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

In conclusion, neither of the given functions is linear since they do not satisfy the linearity property.

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The correct answer to the above question is Option B. greater than 1. i.e., The future value of 1 factor will always be greater than 1.

The future value of 1 factor, also known as the future value factor (FVF), is a factor used in finance to calculate the future value of a sum of money. It represents the value that a present sum of money will have in the future at a given interest rate, over a specified period.

The FVF depends on the interest rate and the period. It is always greater than 1 when the interest rate is positive because money invested today will grow with interest over time, resulting in a larger future value. For example, if the FVF is 1.10 for one year, it means that if you invest $1 today at an annual interest rate of 10%, it will grow to $1.10 in one year.

On the other hand, if the interest rate is negative, the FVF will be less than 1. This is because money invested today will decrease in value over time due to the negative interest rate.

Therefore, the correct answer is option b) greater than 1, as the future value of 1 factor will always represent a value greater than the original amount invested or borrowed.

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The scientific notation of the given decimal number is \(4.57\times 10^{-4}\).

The given decimal number is 0.000457.

We need to express the given number in scientific notation.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as \(1.36\times 10^{6}\). It is a form of presenting very large numbers or very small numbers in a simpler form. The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.

The scientific notation of the decimal number 0.000457=\(4.57\times 10^{-4}\).

Therefore, the scientific notation of the given decimal number is \(4.57\times 10^{-4}\).

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Answer:

x plus 1

Step-by-step explanation:

Answer:

x+1

Step-by-step explanation:

if you simplify the equation, you will get x+1

first, you take the parentheses away.  The equation becomes

3x-2x-4+5

then you combine like terms

x+1

There are $42.95 more will be in the account if Cho waits 10 years instead of 5 years.

What is compounded continuously?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

Given:

Cho started a savings account with $2800.

The account pays 0.3% compounded continuously.

Cho wanted to withdraw the money after 5 years, but her friend says she should wait until 10 years.

First to find the amount after 5 years.

 \(P_0 = 2800\), r = 0.3% = 0.003,  t = 5

Consider the compounded continuously formula

\(P = P_0e^r^t\)

Plug the values in the formula,

\(P=2800e^0^.^0^0^3^*^5\)

P = $2842.32

The amount in the account after 5 years is $2842.32.

Now to find the amount in the account after 10 years.

\(P_0 = 2800\),  r = 0.003, t = 10

Plug the values in the formula,

\(P=2800e^0^.^0^0^3^*^1^0\)

P = $2885.27

The amount in the account after 10 years is $2885.27.

Now,

$2885.27 - $2842.32 = $42.95

Hence, there are $42.95 more will be in the account if Cho waits 10 years instead of 5 years.

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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The unit vector in the same direction as v = 5i - 12j is (5i - 12j)/13 and the magnitude of this new unit vector is 1 is verified.

To find the unit vector in the same direction as a given vector, we first need to find the magnitude of the vector. The magnitude of a vector is the square root of the sum of the squares of its components. For the given vector v = 5i - 12j, the magnitude is:

|v| = √(5² + (-12)²) = √(25 + 144) = √169 = 13

To find the unit vector in the same direction as v, we divide v by its magnitude:

u = v/|v| = (5i - 12j)/13

This gives us the unit vector in the same direction as v. To verify that the magnitude of this new unit vector is 1, we need to find its magnitude:

|u| = √[(5/13)² + (-12/13)²] = √(25/169 + 144/169) = √(169/169) = 1

Therefore, the magnitude of the new unit vector is indeed 1, which confirms that it is a unit vector in the same direction as v.

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An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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Since the calculated chi-square value (3.91) is less than the critical value (7.82) and the significance level is 0.05, the null hypothesis cannot be rejected.

The null hypothesis in a chi-square goodness-of-fit test for independent assortment is that the observed data fits the expected data under the assumption of independent assortment. Therefore, we conclude that there is no significant difference between the observed and expected data under the assumption of independent assortment at a significance level of p=0.05.

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Answer:

x=4

Step-by-step explanation:

Answer:

\(New\ Side = 6.9cm\)

Step-by-step explanation:

Given

\(Length = 2.3cm\)

\(Scale\ Factor = 3\)

Required

Determine the length of the new side

This is calculated as follows:

\(New\ Side = Length * Scale\ Factor\)

Substitute values for Length and Scale Factor

\(New\ Side = 2.3cm * 3\)

\(New\ Side = 6.9cm\)

Hence, the length of the new side is 6.9cm

Answer:

Their weekly sales would have to be $10,000 before they can be earning the same amount for the week

Step-by-step explanation:

If they are to be earning the same thing each week, it means whatever Toni is earning is what Nicky would be earning.

We proceed by equating their earnings so we would get x;

800 + 0.07x = 600 + 0.09x

Collect like terms

800-600 = 0.09x -0.07x

200 = 0.02x

x = 200/0.02

x = 10,000

The equation for the ellipse is: \($\frac{x^2}{37}\) + \($\frac{y^2}{25}\) \(= 1$$\)

The standard equation for an ellipse centered at the origin is:

\($\frac{x^2}{a^2}\) + \($\frac{y^2}{b^2}\) \(= 1$$\)

where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex.

In this case, the vertices are located at \($(\pm\sqrt{37}, 0)$\), which means \($a=\sqrt{37}$\). The distance between the foci is \($2c=2\sqrt{12}=2\sqrt{3\times 4}=2\sqrt{3}\times 2=4\sqrt{3}$\), which means \($c=2\sqrt{3}$\).

The value of b can be found using the relationship between a, b, and c in an ellipse:

\($$a^2 = b^2 + c^2$$\)

Substituting the values we know, we get:

\($$37 = b^2 + (2\sqrt{3})^2$$\)

Simplifying:

\($$37 = b^2 + 12$$\)

\($$b^2 = 37 - 12 = 25$$\)

Taking the square root of both sides, we get:

\($$b = \pm 5$$\)

Since the co-vertices are located at \($(0,\pm b)$\), we can see that \($b=5$\) (and not -5, since the ellipse is centered at the origin).

Therefore, the equation for the ellipse is:

\($\frac{x^2}{37}\) + \($\frac{y^2}{25}\) \($ = 1$$\)

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The total number of gums she won is equal to the number of gums she gave away plus the number of gums remaining. Hence, there are 20 students in her class.

Given that Jimmy won 243 pieces of gum playing the bean bag toss at the county fair. She gave eight to every student in her math class. The remaining number of pieces of gum she has is 83. Let us assume the number of students in her class is x. Now, we know that Jimmy gave eight gums to each student in her math class. Therefore, the total number of gums she gave away is 8x. As per the problem, she only has 83 remaining.

243 = 8x + 83

Now, we need to find the value of x by solving the above equation.

243 - 83 = 8xx

= 20

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