Which phrase matches the algebraic expression below?
2(x - 7) + 10
OTwo times the sum of x and seven plus ten
OTwo times the difference of x and seven plus ten
OTwo times x minus seven plus ten
OTwo times x minus the sum of seven and ten

Answer:

20 dollars per month

Step-by-step explanation:

85 = 25 + x3

60 = x3

20 = x

Answer:V = LWH volume = length x width x height240 = (2+H)((6+H)H  = (H^2 + 8H + 12)H =  H^3 + 8H^2 + 12HH^3 + 8H^2 + 12H - 240 = 0while there's no easy way to solve cubics,  try some simple integers.  You need an even integer2 doesn't work,  too small, try 44^3 + 8(4)^2 + 12(4) -240 =0   Height = 4 feetdimensions are 4 x 10 x 6  feet   = 240 ft/63divide h-4 into the cubic to get H^2 + 12H + 60the discriminate = 144-4(60) < 0 so there are no other real solutions4 feet by 6 feet by 10 feet is the only solution

Step-by-step explanation:

The solution to the given differential equation is L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

To solve the differential equation using the convolution theorem, we'll follow these steps:

Take the Laplace transform of both sides of the differential equation.

Use the convolution theorem to simplify the resulting expression.

Take the inverse Laplace transform to obtain the solution in the time domain.

Let's start with step 1:

Given differential equation: d²y/dt² - 4y = t cos 2t

Taking the Laplace transform of both sides, we get:

s²Y(s) - sy(0) - y'(0) - 4Y(s) = L{t cos 2t}

Where Y(s) represents the Laplace transform of y(t), y(0) is the initial condition for y(t) at t = 0, and y'(0) is the initial condition for dy/dt at t = 0.

The Laplace transform of t cos 2t can be found using the Laplace transform table:

L{t cos 2t} = -Im{d/ds[1 / (s² - (2i)²)]}

= -Im{d/ds[1 / (s² + 4)]}

= -Im{(-2s) / [(s² + 4)²]}

= 2Im{(s) / [(s² + 4)²]}

Now let's simplify the expression using the convolution theorem:

The Laplace transform of the convolution of two functions, f(t) and g(t), is given by the product of their individual Laplace transforms:

L{f * g} = F(s) G(s)

In our case, f(t) = y(t) and g(t) = 2Im{(s) / [(s² + 4)²]}.

Therefore, F(s) = Y(s) and G(s) = 2Im{(s) / [(s² + 4)²]}.

Multiplying F(s) and G(s), we get:

Y(s) G(s) = Y(s) 2Im{(s) / [(s² + 4)²]}

Now, we can rewrite the left-hand side of the equation using the convolution theorem:

Y(s) * 2Im{(s) / [(s² + 4)²]} = L{t cos 2t}

Taking the inverse Laplace transform of both sides, we have:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{L{t cos 2t}}

Simplifying the right-hand side using the inverse Laplace transform table, we get:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = t sin 2t / 4

Now, we can apply the convolution theorem to the left-hand side of the equation:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{Y(s)} * L⁻¹{2Im{(s) / [(s² + 4)²]}}

The inverse Laplace transform of 2Im{(s) / [(s² + 4)²]} can be found using the inverse Laplace transform table:

L⁻¹{2Im{(s) / [(s² + 4)²]}} = 1 / 2b³ (sin bt - bt cos bt)

Therefore, we have:

L⁻¹{Y(s)} * 1 / 2b³ (sin bt - bt cos bt) = t sin 2t / 4

From this, we can deduce the inverse Laplace transform of Y(s):

L⁻¹{Y(s)} = (t sin 2t / 4) / (1 / 2b³ (sin bt - bt cos bt))

Simplifying further:

L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

This is the solution to the given differential equation.

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\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Considering the data:

Dilation by a scale factor of 4 from the origin in the form of an A'B'C' reflection over x = 1

<=> The two triangles are comparable to one another since triangles can have the same shape but differ in size, so A′′B′′C′′ is 4 times larger than ABC.

=> the connection between "ABC" and "A"B"C" .

\(\frac{AB}{A"B"} = \frac{1}{4}\)

We settle on C.

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

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Answer:

37.5

Step-by-step explanation:

Answer:

(a) 259.5 days

(b) 284 days

Step-by-step explanation:

Let X represent the pregnancy length in days.

It is provided that \(X\sim N(270,9^{2})\).

(a)

Let a represent the minimum pregnancy length that can be in the top 12% of pregnancy lengths.

Then,

P (X < a) = 0.12

⇒ P (Z < z) = 0.12

The corresponding z-score is, z = -1.17.

*Use a z-table.

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\-1.17=\frac{a-270}{9}\\\\z=270-(9\times 1.17)\\\\z=259.47\\\\z\approx 259.5\)

Thus, the minimum pregnancy length that can be in the top 12% of pregnancy lengths is 259.5 days.

(b)

Let b be the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths.

Then,

P (X > b) = 0.06

⇒ P (X < b) = 0.94

⇒ P (Z < z) = 0.94

The corresponding z-score is, z = 1.56.

*Use a z-table.

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\1.56=\frac{b-270}{9}\\\\z=270+(9\times 1.56)\\\\z=284.04\\\\z\approx 284\)

Thus, the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths is 284 days.

The particular solution to the differential equation with the initial condition y(7) = 0 is:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:

Step 1: Write the given differential equation in the form dy/dx = f(x, y).

  In this case, dy/dx = y² - 4.

Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:

  dy / (y² - 4) = dx.

Step 3: Integrate both sides of the equation:

  ∫ dy / (y² - 4) = ∫ dx.

Let's solve each integral separately:

For the left-hand side integral:

Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).

Using partial fractions, we can decompose the left-hand side integral:

1 / (y² - 4) = A / (y - 2) + B / (y + 2).

Multiply both sides by (y - 2)(y + 2):

1 = A(y + 2) + B(y - 2).

Expanding the equation:

1 = (A + B)y + 2A - 2B.

By equating the coefficients of the like terms on both sides:

A + B = 0, and

2A - 2B = 1.

Solving these equations simultaneously:

From the first equation, A = -B.

Substituting A = -B in the second equation:

2(-B) - 2B = 1,

-4B = 1,

B = -1/4.

Substituting the value of B in the first equation:

A + (-1/4) = 0,

A = 1/4.

Therefore, the decomposition of the left-hand side integral becomes:

1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).

Integrating both sides:

∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.

Integrating the right-hand side:

∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy

= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,

where C₁ is the constant of integration.

For the right-hand side integral:

∫ dx = x + C₂,

where C₂ is the constant of integration.

Combining the results:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.

Simplifying the equation:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).

Combining the constants of integration:

C = C₂ - C₁, where C is a new constant.

Finally, we have the solution to the differential equation that satisfies the initial condition:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.

To find the value of the constant C, we use the initial condition y(7) = 0:

(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.

Simplifying the equation:

(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,

(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,

0 = 7 + C,

C = -7.

Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

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Answer:11

Step-by-step explanation:

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Therefore, the standard error of the mean, σ= 2.53 (approx).

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

Given: A simple random sample of 10 items resulted in a sample mean of 25.

The population standard deviation is = 8.

We have to find out the standard error of the mean, σ/Sample Size n,

so we will first calculate σ as;

σ = Population standard deviation = 8

Sample Size n = 10

Substituting values in the formula to find the standard error of the mean, we get;σ/√n = 8/√10 = 2.53 (Round off the value to two decimal places)

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Answer:

The bag of Takis now costs $4.46.

Step-by-step explanation:

We are given that a bag of Takis costs $5.95. We are also told that a markdown of 30% is applied to the product.

\(\displaystyle 100\%-30\% = 70\%\\\\\frac{70}{100}=0.7\\\\5.95 \times 0.7 = 4.165 \approx \$4.17\)

Our new price is equal to $4.17, but we are told that a sales tax of 7% is also applied to the Takis. Therefore:

\(\displaystyle 100\% + 7\% = 107\%\\\\\frac{107}{100} = 1.07\\\\4.17 \times 1.07 = 4.4619 \approx \$4.46\)

Therefore, the item with a markdown and sales tax applied is approximately $4.46.

Incomplete Question:

The content of the pie chart is as follows:

Hamsters  = 9% ; Snakes  = 10% ; Cats  = 23%

Birds  = 21% ;  Dogs  = 26% ;  Fish  = 11%

Answer:

The number of citizens who chose cat or fish is 47,600

Step-by-step explanation:

Given

Number of citizens = 140,000

Required

Determine the number of those that chose fish or cats

First, we need to calculate the percentage of those whose pets are either cats or fish

\(Percentage = Cat + Fish\)

Substitute 23% for cat and 11% for fish

\(Percentage = 23\% + 11\%\)

\(Percentage = 34\%\)

Next, is to multiply the calculated percentage by the number of citizens

\(Cat\ or\ Fish = Percentage * Number\ of\ Citizens\)

\(Cat\ or\ Fish = 34\% * 140000\)

\(Cat\ or\ fish = 47600\)

Hence, the number of citizens who chose cat or fish is 47,600

the number of citizens who chose cat or fish is 47,600

= Number of citizens × total percentage

\(= 140,000 \times (23\% + 11\%)\\\\= 140,000 \times 34\%\)

= 47,600

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Answer:

Number of different options for Ms. Garcia are

3 * 2 * 8 = 48

So 48 options

Step-by-step explanation:

There are m ways to make 1st selection and n ways to make 2nd selection and p ways to make 3rd selection so thats why I did (m * n * p)

Answer:

Step-by-step explanation:

Well you have to solve for X to find Y simplified.

Since both equations equal Y you can plug them together

3x+3=x-1

-x          -x

2x+3=-1

-3         -3

2x=-4

Divide -4 by 2 and you get X = -2 then plug X into both equations and boom

y= -3

Answer:

D) glucose

Step-by-step explanation:

step 4 of photosynthesis is storing energy in the glucose molecule after you separate and release the oxygen back

To identify the class boundaries for a given relative frequency distribution, we need to know the range of the data and the number of classes in the distribution.

The class boundaries are the numbers that define the intervals or "bins" into which the data is grouped. They are typically slightly larger or smaller than the actual data values in order to ensure that each data point is included in only one bin.

In this case, we have a relative frequency distribution table for IQ scores of a random selection of residents of Alaska. The table should include the range of the data (i.e., the minimum and maximum IQ scores), as well as the number of classes (i.e., the number of bins into which the data is grouped).

Once we have the range and the number of classes, we can calculate the width of each class by dividing the range by the number of classes. The class boundaries are then defined by adding or subtracting half of the class width from each class midpoint.

For example, suppose the range of the IQ scores is from 80 to 140, and we want to group the data into 5 classes. The width of each class would be:

Width = (140 - 80) / 5 = 12

The class boundaries would then be:

Class 1: 68 - 80.9

Class 2: 80.9 - 92.9

Class 3: 92.9 - 104.9

Class 4: 104.9 - 116.9

Class 5: 116.9 - 129

Note that the class boundaries are defined by subtracting 0.5 from the lower class limit and adding 0.5 to the upper class limit. This ensures that each data point falls within a single class.

In conclusion, to identify the class boundaries for a relative frequency distribution, we need to know the range of the data and the number of classes. We can then calculate the width of each class and define the class boundaries by adding or subtracting half of the class width from each class midpoint.

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Answer:

x = (-5+/- √(25 + 12j))/6

Step-by-step explanation:

The solution to this question requires the application of quadratic formula

The domain can be written as 3 <x < 81.75, which includes all x values that are feasible and fit within the constraints of the issue.

The most appropriate domain for this situation is (c) 3 < x < 81.75.

The reason for this is that the taxi charges $3 for the first mile, so x must be greater than 1. After that, the taxi charges $2.25 for every mile after the first, so the domain must exclude x = 0. Additionally, the problem states that the farthest the taxi will travel is 35 miles, so the domain must also include x < 35.

Therefore, the domain can be expressed as 3 < x < 81.75, which allows for all possible values of x that fall within the given parameters of the problem.

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The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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Answer: b. Stability/instability

Step-by-step explanation:

Random variation in a process indicates stability; whereas non-random variation indicates process instability.

When there is random variation in a process, it means that the process is stable and under control such that the only variations are those expected to be in the process.

When the variation is non-random however, it points to instability in process because this variation is special and not inherent in the process.

All of the mentioned hypotheses can potentially explain the cause of hypervolemia in a patient.


1. High aldosterone secretion: Increased aldosterone secretion leads to excessive salt reabsorption, causing water retention to maintain salt concentration balance.
2. Insufficient natriuretic peptides: When there are too few natriuretic peptides released, the stretching of the atria due to excess water volume does not inhibit ADH or aldosterone, causing hypervolemia.
3. Excess antidiuretic hormone secretion: Over-secretion of antidiuretic hormone results in excessive water retention and stimulation of thirst centers, leading to hypervolemia.

Hypervolemia can be caused by various factors, including increased aldosterone secretion, insufficient natriuretic peptides, and excess antidiuretic hormone secretion. Identifying the specific cause in a patient requires further examination and testing.

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Answer: no alike terms

Step-by-step explanation:

6x+12+3x+21+88

Combine Like Terms:

=6x+12+3x+21+88

=(6x+3x)+(12+21+88)

=9x+121

Answer:

=9x+121

We are 95% confident that 12% to 28% of the young women in your community are infected with at least one of the most common STDs.

What is Random Sampling?

Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.

Given Data

Sample Size, n = 100

Number of successes, x = 20.0

Significance level,

α =1- 0.95 = 0.05

95% confidence interval for population proportion p :

Point estimate:

P= x/n

= 20.0 / 100

= 0.2

critical value at α= 0.05 is

Zα/2 = 1.96

from the standard normal distribution table

Margin of error:

ME=Zα/2 * √P(1-P)/n

= 1.96 × √ 0.2 (1- 0.2 )/ 100

= 0.0784

Margin of error is 0.0784

Now

95% confidence interval for population proportion :

CI=P ± ME

=0.2 ± 0.0784

= (0.1216, 0.2784)

= (12%, 28%)

We have a 95% confidence that at least one of the most prevalent STDs is present in 12% to 28% of the young women in your neighborhood.

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Answer:

Step-by-step explanation:

M and N and QR