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a) So the solution to this equation is m = -6.  b) So the solution to this equation is m = -3. c) So the solution to this equation is t = -9.

Explanation:

a) To solve for m, we need to isolate the variable on one side of the equation.

First, we can subtract 4 from both sides:

3m + 4 - 4 = -14 - 4

3m = -18

Then, we can divide both sides by 3:

m = -6

So the solution to this equation is m = -6.

b) Similar to part a, we want to isolate the variable on one side of the equation.

First, we can subtract 4 from both sides:

-3m + 4 - 4 = 13 - 4

-3m = 9

Then, we can divide both sides by -3:

m = -3

So the solution to this equation is m = -3.

c) This equation has a decimal, but we can still solve it the same way as the others.

First, we can add 0.5 to both sides:

5t - 0.5 + 0.5 = -45.5 + 0.5

5t = -45

Then, we can divide both sides by 5:

t = -9

So the solution to this equation is t = -9.

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After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

To find the area of the surface of the part of the plane x + 2y + 3z = 1 that lies inside the cylinder x^2 + y^2 = 3, we can use a parametric representation for the plane and cylinder intersection.

Let x = r * cos(θ) and y = r * sin(θ), where r^2 = 3 (from the cylinder equation). Now, we can find z in terms of r and θ using the plane equation:

z = (1 - x - 2y) / 3
z = (1 - r * cos(θ) - 2r * sin(θ)) / 3

Now, we have the parametric representation of the intersection: (r * cos(θ), r * sin(θ), (1 - r * cos(θ) - 2r * sin(θ)) / 3). To find the surface area, we need to calculate the partial derivatives with respect to r and θ and then find the magnitude of the cross product.

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

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Answer:

1) Yes

2) 2.07 hours/day

Step-by-step explanation:

1)

2.2 + 4 + 2 1/4 + 0 + 1.9 =

= 6.2 + 2.25 + 1.9

= 10.35

She danced a total of 10.35 hours, so she did meet her goal.

2)

10.35/5 = 2.07

She danced an average of 2.07 hours per day.

Answer: 2x=74

Step-by-step explanation:

Every triangle is 180 degrees.

so you will take 180-32= 148

then with that you will add up the x's and there are 4...

so then you will take 148/4 and get the answer of...

148/4=37

x=37

but it asked for 2x

37*2

2x=74

final answer is 74

y₁ and y₂ are linearly independent and constitute the fundamental set of solutions of the given differential equation. Hence, the solution of the differential equation is y(x) = c₁x + c₂xeᵡ,  where c₁ and c₂ are arbitrary constants.

Given differential equation:  x²y'' - x(x + 2)y' + (x + 2)y = 0, x > 0;  

And, y₁ = x, y₂ = xeᵡ

In order to verify whether y₁ and y₂ are solutions of the given differential equation or not, we can substitute the value of y₁ and y₂ in the given differential equation and check if they satisfy the given equation or not. i.e.,

For y₁ = x  

Here,  y₁ = x

Therefore, y₁′ = 1, and y₁″ = 0

Putting the values in the differential equation, we getx²y₁″ - x(x + 2)y₁′ + (x + 2)y₁= x²(0) - x(x + 2)(1) + (x + 2)x

= -x³  + x³ + 2x = 2x

Therefore, LHS ≠ RHS  Therefore, y₁ = x is not the solution of the given differential equation. Now, to check whether y₁ and y₂ constitutes the fundamental set of solutions or not, we have to check whether they are linearly independent or not. i.e., We know that the Wronskian of the given differential equation is given by W[y₁, y₂] = \begin{vmatrix} x & xe^x \\ 1 & e^x + xe^x \end{vmatrix}  = xe²

Therefore, W[y₁, y₂] ≠ 0, ∀x > 0 Therefore, y₁ and y₂ are linearly independent and constitute the fundamental set of solutions of the given differential equation. Hence, the solution of the differential equation is y(x) = c₁x + c₂xeᵡ,  where c₁ and c₂ are arbitrary constants.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Relationships 1, 2, and 3 follow a pattern where the cost is directly proportional to the number of markers with a rate of $3 per 5 markers.

The package relationships have a different pattern of cost proportionality and do not belong with the other relationships.

Based on the information provided, we have the following relationships between the number of markers and their cost:
1. 5 markers → $3
2. 10 markers → $6
3. 15 markers → $9
We also know that there are packages available for purchase:
- Package of 8 markers: $4
- Package of 16 markers: $8
Now, let's analyze which relationship does not belong and describe the pattern shown by each relationship.
For relationships 1, 2, and 3, we can see that the cost increases by $3 for every 5 additional markers.

This pattern suggests that the cost is directly proportional to the number of markers, with a rate of $3 per 5 markers.
For the package relationships, the cost doubles as the number of markers doubles (8 markers for $4 and 16 markers for $8).

This also indicates a directly proportional relationship between the number of markers and their cost.
However, the package relationships don't follow the same pattern as relationships 1, 2, and 3.

If we consider buying markers individually based on the rate in the first three relationships, purchasing 8 markers should cost $4.80 (8 markers * $3 / 5 markers), and 16 markers should cost $9.60 (16 markers * $3 / 5 markers).

This inconsistency makes the package relationships the ones that do not belong.

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Answer:

-0.375

Step-by-step explanation:

you just divide the numbers.

Making P the subject of the formula f = p+13 is P= f-13

The subject of a formula is the variable which is expressed in terms of the other variables.

For example, the formula for volume of a cylinder, ie. V = πr2h. In this formula, the subject is 'V' (volume), because it is expressed in terms of other variables 'r' (radius) and 'h' (height).

In a given formula, we may express any of the variables in terms of the other variables by using the rules applicable in solving an equation. Thus, in a given formula, we may change the subject to the desired one.

Changing the subject of the formula f = P+13 to P

we evacuate all other terms with P

subtracting 13 from both sides

f-13=P+13-13

therefore P= f-13

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Answer:

-11

Step-by-step explanation:

it just is ok im smart

Answer:

-11

Step-by-step explanation:

bc yes

The correct statement is: The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

The rate of change in a linear function represents how the dependent variable (in this case, height) changes with respect to the independent variable (time). To find the rate of change in this scenario, we can calculate the slope of the line that goes through the given points (2, 3) and (4, 6).

The slope of a line is determined by the change in the y-values divided by the change in the x-values. In this case, the change in y is 6 - 3 = 3 inches, and the change in x is 4 - 2 = 2 years.

Therefore, the rate of change is 3 inches / 2 years = 1.5 inches per year. This means that for every additional year of growth, the plant's height increases by an average of 1.5 inches.

Now, let's analyze the given statements:

1. The rate of change of a linear function is always the same.

  This statement is true. In a linear function, the rate of change (slope) remains constant throughout the entire graph.

2. The rate of change of a linear function always increases as the input increases.

  This statement is not necessarily true. The rate of change can be positive or negative, depending on whether the line slopes upward or downward.

3. The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

  This statement is true. We calculated the rate of change to be 1.5 inches per year.

4. The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

  This statement is not necessarily true. The rate of change may vary depending on the specific section of the graph being considered. However, we only calculated the rate of change between 2 and 4 years, so we cannot determine the rate of change over a larger time frame based on this information.

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Answer: -(x - 2)(x + 2)(y - x)(y + x)

Step-by-step explanation:

Factor the following polynomial completely.

-x2y2 + x4 + 4y2 - 4x2

I assume the polynomial is as follows:

-x^2y^2 + x^4 + 4y^2 - 4x^2

Therefore:

-(x - 2)(x + 2)(y - x)(y + x)

The least positive integer that will be divisible by both 15 and 35 will be 105.

The given integers are 15 and 35.
As we know that the least positive integer will be divisible by both 15 and 35 will be LCM ( least common factor) of 15 and 35.
The least common multiple of LCM of two integers is the common multiple of two numbers such that it is the least among all common multiples.
For example, LCM of 3 and 5 will be 15 because among all common multiples of 3 and 5, 15 will be least common multiple.
For LCM of 15 and 35, let's write multiples of both the numbers.
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180,195,210,....
Multiples of 35= 35,70,105,140,175,210,...
We can see that 105 and 210 are two common multiples out of which 105 is the least multiple.
Therefore, the least positive integer that will be divisible by both 15 and 35 will be 105.

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Answer:

(b) The distribution of the last digits of ID numbers in a sample of 100 college students

Step-by-step explanation:

Uniform Distribution Explanation

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely.

The only possibility here is the distribution of the last digits since the last digit can be 0 thru 9 and each is equally likely to appear in a random sample of 100 students

The others can be eliminated

Heights can vary depending on gender, ethnic background etc. In fact heights will follow a normal distribution

Scores can vary, most students will be scoring around the mean follows a  normal distribution

GPAs like scores can vary, most students will have GPAs close to the mean GPA so follows a normal distribution

To find the radius of a sphere on a calculator, you will need to know the surface area of the sphere.

You can use the formula r = √(A/4π), where A is the surface area of the sphere and r is the radius, to find the radius of the sphere.

Here's an example of how to find the radius of a sphere on a calculator:

On some calculators, you may need to use the "^" button to enter an exponent, or you may need to use the "pi" button to enter the value of pi. Consult your calculator's manual for more information on how to use these functions.

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Answer:

2.236067977

Step-by-step explanation:

(√a+√b) = (√3+√2)

            = (√5)

the length of the other side = 2.236067977

Answer:

\(( \frac{1 + \sqrt{6} }{ \sqrt{3} + \sqrt{2} } ) (\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } )\)

\( \sqrt{3} - \sqrt{2} + \sqrt{18} - \sqrt{12} \)

\( \sqrt{3} - \sqrt{2} + 3 \sqrt{2} - 2 \sqrt{3} \)

\(2 \sqrt{2} - \sqrt{3} \)

\( \sqrt{8} - \sqrt{3} \)

So the length of this rectangle is (√8 - √3) meters, or (2√2 - √3) meters.

Answer: The answer is (B)

Step-by-step explanation:

It just took the unit test

Answer:

B

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

-8 and 1

Step-by-step explanation:

-8 x 1 is -8

-8+1 is -7

Answer:

An apple and a pear weigh less than an orange and a peach together, and a pear and an orange weigh less than an apple and a peach together. Which of the pieces of fruit is the heaviest? Step 1: Weigh an apple, a pear, and an orange. Step 2: The apple weighs more than the pear and the orange

The objects are chosen depending on shape, pattern and texture.  The chosen objects are arranged such a way that they also have aesthetic appeal and harmonic configuration.

When choosing items for your still life composition, think about whether their shape, texture, or pattern is more significant.

After selecting your items, the next step is to arrange them in an aesthetically acceptable and harmonic configuration.

Take your time positioning them and move around your composition to try other angles. A changed viewpoint frequently causes a significant compositional shift.

Try to arrange the objects so that some of them overlap to make it apparent which is in front of which.

Create links that guide the viewer's attention around the composition.

As you rearrange the items, seek for the pleasant arrangement.

Delete some items and add others.

Once you've found one that suits you, move around and try a few more.

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Answer:

2 & 3

Step-by-step explanation:

2. High Interest Rates

High-interest rates make it more difficult for businesses to invest. For instance, a small store that is just starting is going to find it hard to make repayments at an interest rate of 20 or 30 percent. It also sucks out money from the economy and re-directs it to the banks. As the interest rates are so high, businesses and consumers reduce their demand for credit. In turn, there is a contraction in the money supply which can lead to deflation.

The effects of high interest rates can be dire if not managed correctly and subtly by central banks. If the interest rates are increased too fast, too high, and too rapidly, we will see the aforementioned effects such as lower business investment and deflation. Therefore, it can contribute to a transition towards an economic contraction in the business cycle.

3. Declining Real Incomes

Inflation can create a drain on consumer incomes as it decreases its value year on year. Therefore, if firms do not increase wages in line with inflation, the average worker will be able to afford less than before.

If real incomes decline, it means consumers have less income to spend on goods and services in the economy. In turn, a prolonged period of decline in real incomes can contribute to an economic contraction in the business cycle.

Answer

is 3 just did it on edge

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

\(I_1=[1],\, I_2=\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right],\,I_3=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right],\,...\) and so on are examples of identity matrices.

The multiplicative inverse of a 2x2 matrix is \(\displaystyle A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]\) where ad-bc represents the determinant. Multiplying this with the original matrix will produce the identity matrix as described previously. Usually, you'll mostly deal with 2x2 matrices when it comes to this topic, but don't worry too much.

a. the costs of non-compliance, enforcement, prevention and evaluation are -75 d/p, -$7500, $17500 and $5000 respectively

b. The percentage of effort devoted to each component is:

a) To calculate the costs of non-compliance, enforcement, prevention, and evaluation, we need to determine the deviations in effort for each component and multiply them by the corresponding cost per person-day.

Non-compliance cost:

Non-compliance cost = Actual effort - Predicted effort

To calculate the actual effort, we need to sum up the effort for each component mentioned:

Actual effort = Plan development + Software development + Reviews + Tests + Training + Methodology

Actual effort = 25 + 75 + 20 + 30 + 20 + 5 = 175 d/p

Non-compliance cost = Actual effort - Predicted effort = 175 - 250 = -75 d/p

Enforcement cost:

Enforcement cost = Non-compliance cost * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the enforcement cost:

Enforcement cost = -75 * $100 = -$7500 (negative value indicates a cost reduction due to underestimation)

Prevention cost:

Prevention cost = Predicted effort * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the prevention cost for each component:

Plan development prevention cost = 25 * $100 = $2500

Software development prevention cost = 75 * $100 = $7500

Reviews prevention cost = 20 * $100 = $2000

Tests prevention cost = 30 * $100 = $3000

Training prevention cost = 20 * $100 = $2000

Methodology prevention cost = 5 * $100 = $500

Total prevention cost = Sum of prevention costs = $2500 + $7500 + $2000 + $3000 + $2000 + $500 = $17500

Evaluation cost:

Evaluation cost = Total project cost - Prevention cost - Enforcement cost

Evaluation cost = $25000 - $17500 - (-$7500) = $5000

b) To calculate the percentage of effort devoted to each component out of the total cost, we can use the following formula:

Percentage of effort = (Effort for a component / Total project cost) * 100

Percentage of effort for each component:

Plan development = (25 / 250) * 100 = 10%

Software development = (75 / 250) * 100 = 30%

Reviews = (20 / 250) * 100 = 8%

Tests = (30 / 250) * 100 = 12%

Training = (20 / 250) * 100 = 8%

Methodology = (5 / 250) * 100 = 2%

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Answer:

\(243.2cm^{2}\)

Step-by-step explanation:

Step 1: Understand what this shape is constructed out of

2 Congruent Trapezoid

2 Congruent Rectangles

1 Small Rectangle

1 Large Rectangle

Step 2: Find the surface area of the shapes

Area of 2 Trapezoids =\((\frac{a+b}{2}h)2=(\frac{4+6}{2}2.8)2=(\frac{10}{2}2.8)2=((5)}(2.8))2= (11.6)(2)=23.2cm^{2}\)

Area of 2 Rectangles = \((3)(10)(2)=(60)(2)=120cm^{2}\)

Area of Smaller Rectangle = \((4)(10)=40cm^{2}\)

Area of Larger Rectangle = \((6)(10)=60cm^{2}\)

Step 3: Add the surface areas up

\(23.2cm^{2} +120cm^{2} +40cm^{2} +60^{2} =243.2cm^{2}\)

Therefore the surface area of the Trapezoidal Prism is \(243.2cm^{2}\)

Answer:

This is a test, please refer to the Academic Integrity and Honor Code

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

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

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

42 degrees

Step-by-step explanation:

Since m and n are parallel, that is a transversal

So 24=(x-18) because of exterior angle property

so x - 18 = 24

We bring - 18 to the other side so it becomes + 18

x = 24 + 18

x = 42

The presence of dappled brown patches on a patient's cheek may indicate a condition called melasma. Melasma is a common skin condition that typically affects women and is associated with hormonal changes, sun exposure, and genetic factors.

Dappled brown patches on the cheek often suggest a condition called melasma. Melasma is a common skin disorder characterized by the development of dark, irregularly shaped patches on the skin. It typically affects women, especially those with darker skin tones, and is often associated with hormonal changes, such as during pregnancy or with the use of birth control pills. Sun exposure is another contributing factor to the development of melasma. Genetic factors also play a role, as it tends to run in families. Melasma is not a harmful or dangerous condition but can cause cosmetic concerns and affect a person's self-esteem.

To manage melasma, various treatment options are available. These include topical creams containing ingredients such as hydroquinone, tretinoin, or corticosteroids, which can help lighten the patches over time.

Chemical peels that involve the application of a chemical solution to exfoliate the skin and reduce hyperpigmentation may also be used. In some cases, laser therapy can be beneficial to target and break up the excess pigment in the affected areas.

It's important to note that melasma may recur, especially with sun exposure, so it's essential to protect the skin from the sun by wearing sunscreen and using protective clothing. Consulting a dermatologist is recommended to determine the most appropriate treatment approach for an individual case of melasma.

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Answer:

i believe x=17

Step-by-step explanation:

if 3x-21=x+13, x=17 once you solve it