3. Students are taking three busses to go on a field trip. On the first bus there were 14 students, on the second, 18 students, and on the third bus there were 12 students. The total number of students would then be: 14+18+12 To calculate the total students, their chaperone, Ms. Flores decides to add 18 and 12 to get 30 and then adds 14 to get 44. What property is Ms. Flores using to add these numbers in this order?​

Let's denote the amount invested at 8% as x and the amount invested at 10% as y.

According to the given information, Karim wants to invest a total of $100,000, and the combined annual income from both investments should be $9,000.

Set up the equations based on the information:

The first equation represents the total amount invested:

x + y = 100,000

The second equation represents the total annual income from the investments:

0.08x + 0.1y = 9,000

Solve the equations:

We can use the substitution or elimination method to solve the system of equations. Let's use the elimination method:

Multiply the first equation by 0.08 to match the coefficients of x:

0.08x + 0.08y = 8,000

Now subtract this equation from the second equation to eliminate x:

(0.08x + 0.1y) - (0.08x + 0.08y) = 9,000 - 8,000

0.02y = 1,000

Divide both sides of the equation by 0.02:

y = 1,000 / 0.02

y = 50,000

Substitute the value of y back into the first equation to solve for x:

x + 50,000 = 100,000

x = 100,000 - 50,000

x = 50,000

Calculate the amounts to invest:

Karim should invest $50,000 at 8% and $50,000 at 10% in order to obtain an annual income of $9,000 from both investments.

Karim should invest $50,000 at 8% and $50,000 at 10% in order to obtain an annual income of $9,000 from his investments.

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Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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6.908 is greater than 6.098 as the second digit from the left is greater.

We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, are two numbers 6.098 and 6.908.

Now, starting from left both the numbers have the same digit so we can't

differentiate.

The digit after the decimal place to the first number is 0 and on the second it is 9 so definitely, the second number is greater.

∴ 6.098 < 6.908.

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Answer:

I think the answer is C but I'm not too sure so if it doesn't sound right don't click it cuz I don't want you get the answer wrong

Answer:

D is the answer

Step-by-step explanation: Explanation:

The domain is the set of

x

-values that can be used to draw the function so,

You are unable to get a square-root of a negative number therefore the value under the square root must be

≥

0

.

Therefore we need all of the

x

-values that result in the value of

4

−

x

being

≥

0

.

4

−

x

≥

0

4

≥

x

x

≤

4

So all

x

-values

≤

4

will work in the equation. Now we right this in terms of all real numbers:

The Domain of

x

is all the real numbers expect when

x

>

4

(This produces a negative under the square root)

brainliest please

Answer:

Option 4.

Step-by-step explanation:

We know if under the square root is a negative, then it will become an imaginary number i.

We see that in order to make the square root negative, we would have to have a number smaller than 4.

√(x - 4)

√(4 - 4) = √0 = 0

√(3 - 4) = √-1 = i

Therefore, in order for f(x) to be real numbers, x ≥ 4, [4, ∞), or {x | x ≥ 4}

The number of simulation trials that would be likely to produce results that are  closest to the actual probability is 25. The correct option is C).

The following steps can be used  in order to determine the number of simulations:

Step 1 - Remember the maximum number of trials gives the maximum chance to produce results that are  closest to the actual probability.

Step 2 - Now, check all the options given in the question and choose the largest one.

From the above steps, it can be concluded that the correct option is C) 25.

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Full question :

Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.

A. 10

B. 15

C. 25

D. 20

Through the SAS rule of congruence, we prove that triangles LMY and LNX are congruent.​

Congruence is the condition when both of the figures have the same size, and shape and are mirror images of each other. SAS rule of congruence states when two sides and one angle is equal to the corresponding sides of the other triangle, then the two triangles are congruent.

Now, we have triangles LMY and LNX

In these two triangles, we have :

LX = LY { equal sides of isosceles triangle }

LM = LN { given}

∠LMY =  ∠LNX {corresponding angles of the equal sides of the isosceles triangle }

Hence, triangles LMY and LNX are congruent by the SAS rule of congruence.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The velocity of the center of mass of the system is -9.16\(\hat{i}\) - 4.26\(\hat{j}\) m/s.

We must compute the weighted average of the velocities of the two masses in order to determine the velocity of the system's center of mass.

The equation: gives the center of mass's velocity (\(V_{cm}\)):

\(V_{cm}\) = (\(m_{A}\) × \(v_{A}\) + \(m_{B}\) × \(v_{A}\))/(\(m_{A}\) + \(m_{B}\))

\(m_{A}\) = 31 kg(mass of A)

\(m_{B}\) = 30 kg(mass of B)

\(v_{A}\) = 11\(\hat{i}\) - 20\(\hat{j}\) (velocity of A)

\(v_{B}\) = -30\(\hat{i}\) + 12\(\hat{j}\) (velocity of B)

Substituting the given values into the equation, we have:

\(V_{cm}\) = (31 kg × (11\(\hat{i}\) - 20\(\hat{j}\)) + 30 kg × (-30\(\hat{i}\) + 12\(\hat{j}\)))/(31 kg + 30 kg)

Simplifying the expression, we get:

\(V_{cm}\) = (341\(\hat{i}\) - 620\(\hat{j}\) - 900\(\hat{i}\) + 360\(\hat{j}\))/61 kg

\(V_{cm}\) = (-559\(\hat{i}\) - 260\(\hat{j}\))/61 kg

Therefore, the velocity of the center of mass of the system is approximately -9.16\(\hat{i}\) - 4.26\(\hat{j}\) m/s.

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The complete question is:

Mass \(M_{A}\) = 31 kg and mass \(M_{B}\) = 30 kg . They have velocities (in m/s) \(\vec{v}_{A}\) = 11\(\hat{i}\) - 20\(\hat{j}\) and \(\vec{v}_{B}\) = -30\(\hat{i}\) + 12\(\hat{j}\). Determine the velocity of the center of mass of the system.

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

Therefore , the solution of the given problem of unitary method comes out to be  A.$10.5 total cost and $ 0.12 .

By first multiply the value with one unit by the number of units needed, one can use the unit method to solve a problem. Simply put, the unit function is used to distinguish a single entity unit from a given many. 40 needles may be purchased for 400 rupees, or the price of one pen. There may be a standard method for figuring this out. only one nation. Everything has a unique quality. Algebra, its dialectic and inversion, and matrix logic are all analogous concepts.

Here,

Given:

A) Estimate :

70 * 1.25

80*1.25

=> 80 + 20 = 100

and

100/30 = 3.33

thus, approx 4 gallons of gas felicia needs

=> 4 * 3.5 = 14

thus, $14 total cost

Exact :

=> 70 * 1.25 = 87.5 miles

=> 87.5/30 = 2.92 gallons

thus, approx 3 gallons of gas felicia needs

=> 3*3.5 =10.5

thus, $10.5 total cost

B)

=> per cost / miles

=> 3.5 / 30 = 0.116

=>$ 0.12

Therefore , the solution of the given problem of unitary method comes out to be  A.$10.5 total cost and $ 0.12 .

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The distance covered by the rover is the perimeter of the trapezoid, and it is 40 meters.

See attachment for the path followed by the rover.

From the attached graph, we have the following lengths

\(AD = 9m\)

\(AB = 2m\)

\(DC = 14m\)

Next, we calculate the distance BC using the following Pythagoras theorem

\(BC^2 = AD^2 + x^2\)

Where:

\(x = 12\)

So, we have:

\(BC^2 = 9^2 + 12^2\)

\(BC^2 = 225\)

Take positive square root of both sides

\(BC = 15\)

The distance covered is the sum of the side lengths of the trapezoid.

So, we have:

\(Distance =AD + AB +DC + BC\)

This gives

\(Distance =9m+ 2m +14m + 15m\)

Add the lengths

\(Distance =40m\)

Hence, the distance covered by the rover is 40 meters

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Slope of the given graph function is -3/2 while the y-intercept: (0, 1)

What is slope intercept?

Finding the equation of a straight line in the coordinate plane is done using the slope intercept form. The connection that any point's coordinates on the line must satisfy is the equation of a straight line. Any point that is not on the line will not have coordinates that satisfy. The answer to this equation is simple to determine.

To Find :  equation of the line, in slope-intercept form

Solution:

Standard/ general form of equation of line in 2 variables is

Ax + By + C = 0

Slope intercept form is

y = mx + c

intercept form is

x/a  + y/b   = 1

Slope intercept form is

y = mx + c

m = Slope = -3/2

c = y intercept  =  1  

y  = (-3/2)x  + 1

equation of the line, in slope-intercept form is   y  = (-3/2)x  + 1.

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Answer:

A vector graphic consists of a set of instructions for creating a picture is a true statement.

Step-by-step explanation:

A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.

These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.

Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.

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Answer:

C. The answer is molecular motion.

Step-by-step explanation:

When a molecule moves it would heat up. Therefore, by moving it would heat up.

Step-by-step explanation:

please mark me as brainlest

Using function concepts, it is found that:

a. The amount of the air in the tank is a function of the number of minutes, as each input is mapped to only one output.

b. The domain is [0,50], and is a continuous domain.

For the relation in this problem, the input and the output are given as follows:

For each minute, there can only be one possible amount, that is, each input is mapped to only one output, hence the amount of the air in the tank is a function of the number of minutes.

The domain of a function is the set that contains all possible values for the function.

The amount of air will be of 0 when:

48t = 2400

t = 2400/48

t = 50.

That is, it will take 50 minutes to remove all air from the tank, hence the domain is [0,50]. The time in minutes can assume decimal values, such as 10.5 minutes, hence the domain is continuous.

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Applying this property to this case:

Answer:

4x +12

Step-by-step explanation:

\(5x + 2 - x + 10\\\\\mathrm{Group\:like\:terms}\\=5x-x+2+10\\\\\mathrm{Add\:similar\:elements:}\:5x-x=4x\\=4x+2+10\\\\\mathrm{Add\:the\:numbers:}\:2+10=12\\=4x+12\)

Interval of increase: (-∞, -1) ∪ (3, +∞)

Interval of decrease: (-1, 3)

Given function is f(x) = x³ - 3x² - 9x + 4

Differentiating with respect to x,

f'(x) = 3x² - 6x - 9

f'(x) = 3 (x² - 2x - 3)

f'(x) = 3 (x² - 3x + x - 3)

f'(x) = 3 (x(x - 3) + (x - 3))

f'(x) = 3 (x - 3) (x + 1)

For increasing or decreasing,

f'(x) = 0

3 (x - 3) (x + 1) = 0

x = - 1, 3

In interval (-∞, -1 ), f'(x) = positive,

⇒ f(x) is increasing on (-∞, -1 ),

In interval (-1, 3), f'(x) = negative,

⇒ f(x) is decreasing on (-1, 3),

In interval (3, ∞), f'(x) = positive,

⇒ f(x) is increasing on (3, ∞),

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Given question is incomplete, the complete question is below

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x³ - 3x² - 9x + 4 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.)

a. The equilibrium solution (y = 0) is stable.

b. The limit of \(\( y(t) \)\) as \(\( t \)\) approaches infinity is 0.

A function's derivative with respect to an independent variable is what is referred to as differentiation. In calculus, differentiation can be used to calculate the function per unit change in the independent variable. Let y = f(x) represent the function of x.

The nonlinear differential equation is given as:

\(\( \frac{{dy}}{{dt}} = -y^2 \)\)

a) Classifying Equilibrium Solutions:

To find the equilibrium solutions, we set the derivative equal to zero:

\(\( -y^2 = 0 \)\)

The only solution is (y = 0). Therefore, the equilibrium solution is (y = 0).

To classify the stability of the equilibrium solution, we examine the sign of the derivative \(\( \frac{{dy}}{{dt}} \)\) around the equilibrium point.

For \(\( y < 0 \), \( \frac{{dy}}{{dt}} > 0 \)\), indicating that the function is increasing and moving away from the equilibrium solution.

For \(\( y > 0 \), \( \frac{{dy}}{{dt}} < 0 \)\), indicating that the function is decreasing and moving towards the equilibrium solution.

Hence, the equilibrium solution (y = 0) is stable.

b) Determining the Limit:

Given that \(\( y(0) = 2 \)\), we need to determine the limit of \(\( y(t) \) as \( t \)\) approaches infinity, if it exists.

The differential equation \(\( \frac{{dy}}{{dt}} = -y^2 \)\) can be separated and solved:

\(\( \frac{{dy}}{{y^2}} = -dt \)\)

Integrating both sides:

\(\( \int \frac{{dy}}{{y^2}} = -\int dt \)\)

\(\( -\frac{1}{y} = -t + C \)\)

Simplifying, we have:

\(\( \frac{1}{y} = t + C \)\)

Rearranging the equation:

\(\( y = \frac{1}{t + C} \)\)

Since we are given \(\( y(0) = 2 \)\), we can substitute this into the equation to find the value of (C):

\(\( 2 = \frac{1}{0 + C} \)\)

Solving for \(\( C \)\), we get \(\( C = \frac{1}{2} \)\).

Therefore, the solution to the differential equation is:

\(\( y = \frac{1}{t + \frac{1}{2}} \)\)

Taking the limit as (t) approaches infinity:

\(\( \lim_{{t \to \infty}} \frac{1}{t + \frac{1}{2}} = 0 \)\)

Hence, the limit of \(\( y(t) \)\) as \(\( t \)\) approaches infinity is 0.

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Answer:

kira

Step-by-step explanation:

1.75*4 is greater than 1*5

The solved vectors are;

(a) 3u - 5v = [-9, 12, 12, 9, 9, -3] - [-5, 40, 0, 10, -15, 25] = [-9 + 5, 12 - 40, 12 - 0, 9 - 10, 9 + 15, -3 - 25] = [-4, -28, 12, -1, 24, -28]

(b) u + 4v - 2w = [-3, 4, 4, 3, 3, -1] + [-4, 32, 0, 8, -12, 20] - [2, 4, -2, 0, 8, -4] = [-3 - 4 + 2, 4 + 32 - 4, 4 + 0 + 2, 3 + 8 - 0, 3 - 12 + 8, -1 + 20 + 4] = [-5, 32, 6, 11, -1, 23]

(c)  4u - 6v + 3w = [-12, 16, 16, 12, 12, -4] - [-6, 48, 0, 12, -18, 30] + [3, 6, -3, 0, 12, -6] = [-12 + 6 - 3, 16 - 48 +

Given the vector u = [-3, 4, 4, 3, 3, -1], we are asked to compute the following vectors: (a) 3u - 5v, (b) u + 4v - 2w, and (c) 4u - 6v + 3w, where v = [-1, 8, 0, 2, -3, 5] and w = [1, 2, -1, 0, 4, -2].

To compute the vector 3u - 5v, we need to multiply each component of u by 3 and subtract 5 times each component of v. This can be done by performing the operations element-wise:

3u - 5v = [3*(-3), 34, 34, 33, 33, 3*(-1)] - [5*(-1), 58, 50, 52, 5(-3), 5*5]

Simplifying the expression, we get:

3u - 5v = [-9, 12, 12, 9, 9, -3] - [-5, 40, 0, 10, -15, 25] = [-9 + 5, 12 - 40, 12 - 0, 9 - 10, 9 + 15, -3 - 25] = [-4, -28, 12, -1, 24, -28]

For the vector u + 4v - 2w, we can apply similar element-wise operations:

u + 4v - 2w = [-3, 4, 4, 3, 3, -1] + 4[-1, 8, 0, 2, -3, 5] - 2[1, 2, -1, 0, 4, -2]

Simplifying, we get:

u + 4v - 2w = [-3, 4, 4, 3, 3, -1] + [-4, 32, 0, 8, -12, 20] - [2, 4, -2, 0, 8, -4] = [-3 - 4 + 2, 4 + 32 - 4, 4 + 0 + 2, 3 + 8 - 0, 3 - 12 + 8, -1 + 20 + 4] = [-5, 32, 6, 11, -1, 23]

Lastly, for the vector 4u - 6v + 3w, we perform the element-wise operations as follows:

4u - 6v + 3w = 4[-3, 4, 4, 3, 3, -1] - 6[-1, 8, 0, 2, -3, 5] + 3[1, 2, -1, 0, 4, -2]

Simplifying, we get:

4u - 6v + 3w = [-12, 16, 16, 12, 12, -4] - [-6, 48, 0, 12, -18, 30] + [3, 6, -3, 0, 12, -6] = [-12 + 6 - 3, 16 - 48 +

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B(x) = 10x

B = money save

x = days

Answer: After the launch, the fireball seems to be speeding up as it’s moving upward. But a measurement of motion shows that this isn’t true, so our observations are sometimes unreliable.

Step-by-step explanation: Exact answer from plato

The narrator refers to, After launch, the fireball seems like be speeding up as it is moving upward. But measurement of the motion shows that this is not true, so our observations are sometimes unreliable.

What is an Unreliable Narrator?

The unreliable narrator is the character that says to you the story with some kind of lack of credibility. This technique could be difficult to pull off but if we do, it could be so effective. As the reader, you feel like you can believe the narrator, they are the one guiding you through the story. However, just because they are the narrator, it does not mean they are the 'good guy and that they can be trusted. Some of the best stories are when the narrator not only deceives the other characters on the book but the readers too.

How to be an unreliable narrator?

There are many roads to use this technique, and I thought that the best way to use it is by thinking outside from the box. The last thing you want to read to expect is what is about is happen, this will completely ruin what you are trying to do. Be bold or imaginative.

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approximately 97.5% of the sample will have values below 600.

The empirical rule states that about 68 % of the sample will be within one standard deviation of the mean, approximately 95 % will be within two standard deviations of the mean, and approximately 99.7 % will be within three standard deviations of the mean.

We must determine the z-score for a value of 600 using the following formula in order to determine the proportion of the sample that has values lower than 600.

z = (x - μ) / σ

If x is the value for which we wish to calculate the probability, is the sample mean, and is the sample standard deviation.

When we enter the values we have, we get:

z = (600 - 500) / 50 = 2

The number of 600 is therefore two standard deviations above the mean.

Approximately 95% of the sample will, under the empirical criterion, lie within two standard deviations of the mean. We can infer that since 600 is two standard deviations above the mean, 2.5% of the sample will have values above 600.

Therefore, approximately 97.5% of the sample will have values below 600.

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No

Because they all are different in taste and smell

True!

Explanation: Apples, potatoes and onions will all taste the same if somehow you were to block your sense of smell (plug your nose).

According to the National Survey on Drug Use and Health, approximately 18.53% of U.S. adults (ages 18 and older) experienced some form of mental illness in 2016.

Approximately 18.53% of U.S. adults suffered from mental illness in 2016. This percentage represents the prevalence of mental health disorders among the adult population, which is important to understand in order to address and provide support for those affected.

This includes a range of conditions such as anxiety disorders, depression, bipolar disorder, and schizophrenia. It's important to note that mental illness can vary in severity and can impact individuals differently, and seeking professional help can greatly improve one's quality of life.

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