Simplify by combining like terms.
-3r - 2r - 6 - 1 - 7r+ 9r

The composite method for determining the location of the center of gravity of a composite body requires integration.

So, the answer is A.

The center of gravity is the point at which the entire weight of a body appears to act when the body is in equilibrium.

The concept of a center of gravity is used to calculate the behavior of a body when subjected to external forces. The composite method for determining the location of the center of gravity of a composite body involves integration.

The center of gravity is found by dividing the sum of the products of individual masses with their corresponding distance from an arbitrary reference line by the total mass of the system. When there is more than one weight distribution involved, the composite method is employed.

Hence, the answer of the question is A.

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201 food calories (kcal) would be sufficient for a well-conditioned athlete to metabolize in doing the same work with an efficiency of 25%

Assuming input the 25% into equation and work

with the help of the equation, we know:

η = work_out / work_in

therefore we get, 0.25 = (2.10e5) / (kcal)

then, kcal = (2.10e5J)/(0.25)

kcal = 2.10e5 J / 0.25

upon dividing the following we get the answer,

kcal = 840e3J

now we need to convert the Joules to kcal and we get,

we know that, 1kcl = 4184J

therefore, 840e3 / 4184 = 201 kcal

hence we know that 201 food calories (kcal) would be sufficient for a well-conditioned athlete to metabolize in doing the same work with an efficiency of 25%

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The probability of drawing two pens of the same color (blue) with replacement is approximately 0.0472, while the probability of drawing two pens of the same color without replacement is approximately 0.0405.

a. Drawing with replacement:

When drawing with replacement, it means that after each draw, the pen is placed back into the bag, and the total number of pens remains the same.

The probability of drawing a blue pen on the first draw is given by the ratio of the number of blue pens to the total number of pens:

P(Blue on first draw) = Number of blue pens / Total number of pens

P(Blue on first draw) = 5 / (8 + 5 + 10) = 5 / 23

Since we are drawing with replacement, the probability of drawing a blue pen on the second draw is also 5/23.

The probability of drawing two pens of the same color (both blue) with replacement is the product of the probabilities of each individual draw:

P(Two blue pens with replacement) = P(Blue on first draw) * P(Blue on second draw)

P(Two blue pens with replacement) = (5/23) * (5/23)

P(Two blue pens with replacement) = 25/529 ≈ 0.0472 (approximately)

b. Drawing without replacement:

When drawing without replacement, it means that after each draw, the pen is not placed back into the bag, and the total number of pens decreases.

The probability of drawing a blue pen on the first draw is the same as before:

P(Blue on first draw) = Number of blue pens / Total number of pens

P(Blue on first draw) = 5 / (8 + 5 + 10) = 5 / 23

After drawing a blue pen on the first draw, there are now 4 blue pens remaining out of a total of 22 pens left in the bag.

The probability of drawing a blue pen on the second draw, without replacement, is:

P(Blue on second draw) = Number of remaining blue pens / Total number of remaining pens

P(Blue on second draw) = 4 / 22 = 2 / 11

The probability of drawing two pens of the same color (both blue) without replacement is the product of the probabilities of each individual draw:

P(Two blue pens without replacement) = P(Blue on first draw) * P(Blue on second draw)

P(Two blue pens without replacement) = (5/23) * (2/11)

P(Two blue pens without replacement) ≈ 0.0405 (approximately)

Therefore, the probability of drawing two pens of the same color (blue) with replacement is approximately 0.0472, while the probability of drawing two pens of the same color without replacement is approximately 0.0405.

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Answer:

in 13 years it will be at 432,480

Step-by-step explanation:

The probability of choosing a uni-color pair of socks from the bag is 199/799.

The probability of choosing a uni-color pair of socks from a large bag with 100 pairs of each of red, blue, black, and white socks is calculated as follows:

Step 1: Calculate the total number of socks in the bag.
There are 100 pairs of each color, and each pair consists of 2 socks, so there are 100 x 2 = 200 socks of each color.
The total number of socks in the bag is 200 x 4 = 800 socks.

Step 2: Calculate the probability of choosing a uni-color pair of socks.
The probability of choosing a red sock on the first draw is 200/800 = 1/4.
The probability of choosing another red sock on the second draw is 199/799.
The probability of choosing a red pair is (1/4) x (199/799) = 199/3196.

Similarly, the probability of choosing a blue pair, a black pair, or a white pair is also 199/3196.

The probability of choosing a uni-color pair is the sum of the probabilities of choosing a red pair, a blue pair, a black pair, and a white pair.

So the probability of choosing a uni-color pair is (199/3196) x 4 = 796/3196 = 199/799.

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The orthogonal projection of [1, -1] onto the line through [-1, 3] and the origin is [0.4, -1.2].

To compute the orthogonal projection of a vector onto a line, we need to find the projection vector that lies on the line and is perpendicular to the vector we want to project.

Let's start by finding a vector that lies on the line through [-1, 3] and the origin. We can obtain this vector by subtracting the origin from any point on the line. Let's choose the point [-1, 3] as our reference point.

The direction vector of the line is the difference between any two points on the line. Since we already have the reference point [-1, 3], we can take the negative of this point to get the direction vector. So, the direction vector is [1, -3].

Next, we need to find the projection vector that lies on the line and is perpendicular to the vector [1, -1] that we want to project.

To find this projection vector, we can use the formula: proj_v(u) = ((u · v) / (v · v)) * v, where u is the vector we want to project and v is the direction vector of the line.

Let's calculate the projection vector:

u = [1, -1]

v = [1, -3]

Dot product of u and v: (1 * 1) + (-1 * -3) = 1 + 3 = 4

Dot product of v and v: (1 * 1) + (-3 * -3) = 1 + 9 = 10

proj_v(u) = ((4) / (10)) * [1, -3] = [0.4, -1.2]

Therefore, the orthogonal projection of [1, -1] onto the line through [-1, 3] and the origin is [0.4, -1.2].

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Answer:

20/27

Step-by-step explanation:

According to the Central Limit Theorem, the mean of the sampling distribution of means will be equal to The mean of the Original Population.

Central Limit theorem:

The central limit theorem (CLT) is a statistical concept that states that the sample mean distribution of a random variable assumes an approximately normal or normal distribution when the sample size is large enough. Simply put, the theorem states that the mean sampling distribution approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

For example:

An investor wants to estimate the return on the ABC stock market index, which consists of 100,000 shares. Due to the large size of the index, the investor cannot analyze each stock individually and instead chooses to use a random his sample to obtain an estimate of the index's total his return. Investors select a sample of stocks. Each sample contains at least 30 strains. Samples should be random and previously selected samples should be replaced by subsequent samples to avoid bias.

If the average return of the first sample was 7.5%, the average return of the next sample could be 7.8%. Due to the nature of random sampling, each sample will produce different results. As you increase the sample size for each selected sample, the sample means begin to form their own distribution.

The distribution of the sample mean approaches a normal distribution as the value of n increases. The average return of the index example stocks estimates the return of the entire index of 100,000 shares, and the average returns follow a normal distribution.

According to the central limit theorem, if a large sample is chosen from an unknown population with mean μ and standard deviation σ, the sampling distribution of the sample mean follows a normal distribution.

The mean and standard deviation of this sampling distribution are:

                        μₐ = μ

                      σₐ = σ/√n

This standard deviation of the sampling distribution of the mean is called the standard error.

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In the given figure:

step 1 has 2 blocks

step 2 has 6 blocks

step 3 has 12 blocks

1)

2) n( n + 1 )

n( n + 1 ) is valid

3)

Since the expression can also write as:

Thus, n^2 +n is also valid

4)

n + n + 1 is not valid

Answer :

b) n( n + 1 )

c) n^2 + n

Answer:

4

Step-by-step explanation:

i just answered it.

The value of the variable x will be 4. Then the correct option is B.

It is a polygon with four sides. The total interior angle is 360 degrees.

A quadrilateral with 90 degree angles.

If all the angles are right angle, then the quadrilateral should be either rectangle or square.

The lengths of the left and right sides are 10 and 2y + 4.

The lengths of the top and bottom sides are 18 and 10 + 2x.

If the adjacent side of the rectangle are same, then the rectangle will become square.

So, the quadrilateral is a rectangle.

Opposite sides of the rectangle are congruent.

Then the value of the variable x will be

10 + 2x = 18

       2x = 18 – 10

       2x = 8

         x = 8 / 2

         x = 4

The value of the variable x will be 4.

Then the correct option is B.

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Answer: I think 10ft apart

Step-by-step explanation:

Mark receives a scale report and on the Math section, he earned a raw score of 39 which is at the 68th percentile, meaning that the total raw score on the Math section is 57

Find out the total score of the Math score, 100th percentile

     Given; raw score- 39 which is at the

                       68th- percentile

For someone to be at the 100th percentile, he or she must have scored all the questions right.

In Mark's case, he had a score of 68 percentile with a score of 39

Total raw score for the Math section;

    state;   If score of 39 = 68 percentile

                          ?                 100 percentile

Cross multiply to solve for the unknown

Thus;  39 * 100 / 68

         =  57

Therefore, total raw score on the Math section is 57, which is at the 100th percentile.

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The evaluation approach described in the given scenario is B.) forced distribution.

Forced distribution is an evaluation approach where performance ratings are distributed among employees according to predetermined percentages. In this case, the professor has predetermined that 10% of the class will receive an "A", 20% will receive a "B", 40% will receive a "C", 20% will receive a "D", and 10% will receive an "F".

This approach imposes a forced ranking system that restricts the distribution of grades based on predetermined proportions. Forced distribution can be useful in certain contexts as it helps differentiate performance levels and prevent grade inflation or deflation.

However, it also has limitations, as it may not accurately reflect individual performance and can create a competitive environment among students. It is important for educators to carefully consider the implications and potential drawbacks of using forced distribution in educational settings.

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Answer:

Step-by-step explanation:

In an arithmetic sequence, we keep adding/subtracting to get the next term in the sequence.

Therefore, we can make an equation that looks like this:

5k-(2k+1) = 7k+2-5k

We can subtract 2k+1 from 5k, and 5k from 7k+2, because from subtracting the difference would be the same. (common difference of sequence is what we would find)

Now, we just need to simplify.

5k-2k-1 = 2k+2

3k-1=2k+2

Now let's combine like terms, and we get:

k=3

Hope this helped!

Answer:   Yes

Step-by-step explanation:

Any number that can be written as a fraction, or in other words the ratio between two numbers, is a rational number. It is also a real number as rational numbers are a sub-set of the collection of real numbers

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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Answer:

they are all expressions except D) 6y + 1z = 7x - 3w which is an equation, B

4x ^ 2

2

- 6 it is not known because it is poorly written.

Step-by-step explanation:

Which of the following is NOT an expression?

A   3x + 1  (expression)

B  4x^2 2- 6 (unknow)

C) 5b (expeession)

D) 6y + 1z = 7x - 3w    (Equation)

Answer:

A 6 units up

Translation rule

Y rule

+= up

-= down

X rule

+= right

-=left

Reflection rule

Reflection over x axis

Y that was once a positive number, is flipped to a negative

example

6,2 reflected over the x axis.

2=-2

Y axis rule example

-2,7 reflected over the y axis

-2=2

Step-by-step explanation:

If it ever says (example,example) like flipped over the x, it will change the y.

Same for a flip over the y, it will change the x

Answer: -1/2

Step-by-step explanation:

\(\frac{3-1}{5-9}=-\frac{1}{2}\)

The slope of line is -1

Take a look at the grid and the line.

Or you can use rise/run

(3,1) and (2,2) which is part of the graph.

\(m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{2 - 1}{2 - 3} \\ m = \frac{1}{ - 1} \\m = - 1\)

If the average waiting time in the line is 18 minutes, it is not possible to determine the number of customers at the carwash without additional information such as the service rate or arrival rate.

The number of customers at the carwash depends on various factors such as the service rate, arrival rate, and the distribution of service times. Without knowing these factors, it is not possible to accurately determine the number of customers at the carwash.

However, we can make some general observations. If the service rate is high, it is likely that the waiting time will be lower, and hence, the number of customers at the carwash will be lower. On the other hand, if the service rate is low, the waiting time will be higher, and hence, the number of customers at the carwash will be higher.

Similarly, if the arrival rate is high, the number of customers at the carwash will be higher, and if the arrival rate is low, the number of customers will be lower. Therefore, to determine the number of customers at the carwash, we need to know both the arrival rate and the service rate.

In conclusion, knowing only the average waiting time in the line is not sufficient to determine the number of customers at the carwash. Additional information such as the arrival rate and service rate is required to make an accurate estimation.

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

I got 8

Step-by-step explanation:

The value of the equation A = (0.2 ) x 40 is A = 8

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the value of A = 0.2 x 40

On simplifying the equation , we get

The value of 0.2 = 1/5

Now , substituting the value of 0.2 in the equation , we get

The value of A = ( 1/5 ) x 40

The value of A = 40/5

The value of A = 8

Therefore , the value of A is 8

The equation can also be solved as

The value of A = 0.2 x 40

The value of A = ( 2 / 10 ) x 40

The equation can be simplified as

The value of A = 80/10

The value of A = 8

Therefore , the value of A is 8

Hence , The value of the equation A = (0.2 ) x 40 is A = 8

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Correlation analysis:

a. The variables used in the research study are "age" and "number of times eaten out in an average month." The level of measurement for age is an interval, and the level of measurement for the number of times eaten out is ratio.

b. Pretest Checklist for NormalityAge Histogram Interpretation:

A histogram with a bell curve, skewness equal to 0, and kurtosis equal to 3 indicates normality.

Mean = 45.17, Standard deviation = 14.89, Skewness = -.08, Kurtosis = -0.71.

The histogram for the age of respondents is approximately bell-shaped, indicating normality.

Number of times eaten out Histogram Interpretation:

A histogram with a bell curve, skewness equal to 0, and kurtosis equal to 3 indicates normality.

Mean = 8.38, Standard deviation = 8.77, Skewness = 2.33, Kurtosis = 9.27.

The histogram for the number of times the respondent eats out in an average month is positively skewed and not normally distributed. Therefore, it is not normally distributed.

Linearity:

Age vs. Number of times Eaten Out

Scatterplot Interpretation:

A scatterplot indicates linearity when there is a straight line and all data points are scattered along it. The scatterplot displays that the number of times respondents eat out increases as they get older. The relationship between the variables is linear and positive.

Homoscedasticity:

Age vs. Number of times Eaten OutScatterplot Interpretation: The scatterplot displays no fan-like pattern around the regression line, which indicates that the assumption of homoscedasticity is met.

c. Bivariate Correlation and Descriptive Statistics

Age and the number of times eaten out in an average month have a correlation coefficient of.

150, which is a small positive correlation and statistically insignificant (p = .077). The mean age of the respondents was 45.17 years, with a standard deviation of 14.89. The mean number of times the respondent eats out in an average month was 8.38, with a standard deviation of 8.77.

The scatterplot with regression line shows a positive slope that indicates a small and insignificant correlation between age and the number of times the respondent eats out in an average month.

d. The research study aimed to determine whether there is a correlation between age and the number of meals eaten outside the home. The data were analyzed using a bivariate correlation analysis, scatterplot with regression line, and descriptive statistics. The results indicated a small positive correlation (r = .150), but this correlation was statistically insignificant (p = .077).

The mean age of the respondents was 45.17 years, with a standard deviation of 14.89. The mean number of times the respondent eats out in an average month was 8.38, with a standard deviation of 8.77. The findings showed that there is no correlation between age and the number of times the respondent eats out in an average month.

Therefore, the researcher cannot conclude that age is a significant factor in the number of times a person eats out. The implications of the findings suggest that other factors may influence a person's decision to eat out, such as income, time constraints, and personal preferences. Further research could be done to determine what factors are significant in the decision to eat out.

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Answer:

I beleive c. i had the same question last year, and i believe i got the answer right. so sorry if its wrong. hope this helps.

Step-by-step explanation:

Answer

x=a 1/2+i / a 1/2

Step-by-step explanation:

Answer:

Solution given:

A.coordinate are

A(-2,3)

B(0,-3)

C(4,5)

B.Each length are :

we have

length \( \sqrt{(x2-x1)²+(y2-y1)²} \)

now

AB:\( \sqrt{(-2-0)²+(3+3)²} \)=\( 2\sqrt{10} \)units

BC:\( \sqrt{(0-4)²+(-3-5)²} \)=\( 4\sqrt{5} \)units

AC:\( \sqrt{(-2-4)²+(3-5)²} \)=\( 2\sqrt{10} \)units

C. the figure:

By using Pythagoras law

base[b]=AB=perpendicular [p]=AC

hypotenuse [h]=BC

we have

h²=p²+b²

substituting value

(\( 4\sqrt{5} \))²=2p²

16*5=2*(\( 2\sqrt{10} \))²

80=2*4*10

80=80

SO IT IS RIGHT ANGLED ISOSCELES TRIANGLE.

Answer:One-half names the same number as two-quarter or as three sixths  or as four-eights . Three-fourths  is equal to six-eighths because they are different ways of expressing the same number.

Step-by-step explanation: