Two​ pulleys, one with radius r 1r1 and the other with radius r 2r2​, are connected by a belt. The pulley with radius r 1r1 rotates at omega 1ω1 revolutions per​ minute, whereas the pulley with radius r 2r2 rotates at omega 2ω2 revolutions per minute. Show that StartFraction r 1 Over r 2 EndFraction equals StartFraction omega 2 Over omega 1 EndFraction r1 r2

Answer:

$y=(7/2)x+20$

Step-by-step explanation:

SInce the gradient of the first line is $-2/7$ then the gradien of the perpendicular line is $7/2$.

Therefore by the point slope formula the line that we are looking for is

$y-6=(7/2)(x+4)$

$y=(7/2)x + 20$

If the first cube has a volume of 125 cm³ and the second cube has a volume of 343 cm³, the difference in the area of one face of the second cube and the area of one face of the first cube is 24cm². The answer is B. 24 cm².

To find the difference in the area of one face of each cube, we first need to find the side length of each cube. Since the volume of a cube is equal to the side length cubed (V = s³), we can find the side length by taking the cube root of the volume.

For the first cube:
Volume = 125 cm³
Side length = cube root of 125 = 5 cm

For the second cube:
Volume = 343 cm³
Side length = cube root of 343 = 7 cm

Next, we find the area of one face of each cube. The area of one face of a cube is equal to the side length squared (A = s²).

Area of one face of the first cube:
A1 = 5² = 25 cm²

Area of one face of the second cube:
A2 = 7² = 49 cm²

Finally, find the difference in the area of one face of each cube:
Difference = A2 - A1 = 49 cm² - 25 cm² = 24 cm²

The answer is B. 24 cm².

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Step-by-step explanation:

XY = 3WX

3WX - XY = 0

X(3W - Y) = 0

By zero product rule, either X = 0 or 3W = Y.

YZ = 6WX = 2XY (From 1st equation)

2XY - YZ = 0

Y(2X - Z) = 0

Again by zero product rule, either Y = 0 or 2X = Z.

Therefore, either both X and Z = 0, or both W and Y = 0. Let's look at the last equation.

WZ = 10WX

10WX - WZ = 0

W(10X - Z) = 0.

Here, either W = 0 or 10X - Z = 0.

- If both X and Z were 0, 10X - Z = 0.

- If both W and Y were 0 instead, W = 0.

Since both ways satisfy the equation, it is proved.

The composite function N(T(t)) = 20082.The time when the bacteria count reaches 20082 is approximately 30.28 hours.

To find the composite function N(T(t)), we need to substitute the expression for T(t) into the function N(T).

Given:

N(T) = 307² - 112T + 75

T(t) = 3t + 1.7

Substituting T(t) into N(T), we get:

N(T(t)) = 307² - 112(3t + 1.7) + 75

Simplifying:

N(T(t)) = 307² - 336t - 190.4 + 75

N(T(t)) = 307² - 336t - 115.4

Now let's find the time when the bacteria count reaches 20082.

N(T(t)) = 20082

307² - 336t - 115.4 = 20082

Taking 115.4 to the other side:

\(307^2\) - 336t = 20082 + 115.4

307² - 336t = 20197.4

336t = 307² - 20197.4

Dividing by 336:

t = (307² - 20197.4) / 336

Calculating the value of t:

t ≈ 30.28

Therefore, the time when the bacteria count reaches 20082 is approximately 30.28 hours.

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It is not advisable to use the sample mean as an estimate of the population mean without including a margin of error.

When estimating a population parameter, such as the population mean, using a sample, it is essential to consider the uncertainty or variability in the sample estimate. This uncertainty is captured by the margin of error.

The sample mean provides an estimate of the population mean based on the available sample data. However, it is subject to sampling variability, meaning that different samples from the same population may yield different sample means. This variability arises due to the inherent randomness in the sampling process.

By including a margin of error, we acknowledge and quantify this sampling variability. The margin of error provides a range within which the true population mean is likely to lie. It accounts for the uncertainty associated with estimating the population parameter based on a finite sample.

Ignoring the margin of error means disregarding the inherent variability in the sample mean and assuming that it perfectly represents the true population mean. This assumption is generally not valid and can lead to inaccurate or misleading conclusions about the population.

By including a margin of error, we convey the level of confidence or precision associated with our estimate and provide a more realistic assessment of the population mean. This helps in making informed decisions or drawing valid statistical inferences based on the sample data.

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Measurements of the Rhombus are Angle 1 = 124°; Angle 2 = 28° ; Angle 4 = 124°; Angle 3 = 28°; Angle 5 = 28°

A rhombus is an equal-sided quadrilateral in Euclidean plane geometry. The term "equilateral triangle" also refers to a quadrilateral whose sides are of the same length. A parallelogram has a unique variation known as a rhombus. In a rhombus, the opposite sides and angles are parallel and equal. A rhombus's diagonal is split in half by a right angle, and each of its sides is the same length. Rhombic diamonds and diamonds are other names for rhombuses. The length of every side is the same. Diagonals are equal in a rhombus. At a 90° angle, parallel lines split in half. 180 degrees is the sum of adjacent angles.

Angle 1 = 180 - (28+28)= 124°

Angle 2 = 28° (equal sides of rhombus)

Angle 4 = 124°

Angle 3 = 28° (Diagonals of a rhombus bisects the angles)

Angle 5 = 28° (Diagonals of a rhombus bisects the angles)

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The given statement " If A and B are n x n and invertible, then A⁻¹B⁻¹ is the inverse of AB." is true because  A and B are invertible matrices, it means that they both have an inverse (A⁻¹and B⁻¹, respectively). The product of A and B, represented by AB, is also an n x n matrix.

To show that A⁻¹B⁻¹is the inverse of AB, we must demonstrate that the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix, which is an n x n matrix with 1s along the diagonal and 0s elsewhere.
To verify this, we'll multiply (AB) with (A⁻¹B⁻¹) and check if the result is the identity matrix:
(AB)(A⁻¹B⁻¹) = A(BA⁻¹)B⁻¹ (associative property of matrix multiplication)
Since B and A^-1 are inverses of each other, their product equals the identity matrix:

A(BA⁻¹)B⁻¹= AI B⁻¹(where I is the identity matrix)
Multiplying A and I doesn't change A:
AI B⁻¹= A B⁻¹
Now, A and B⁻¹are inverses of each other as well, so their product also equals the identity matrix:
A B⁻¹= I
Thus, A⁻¹B⁻¹ is indeed the inverse of AB, as the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix.

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intoTo do this, you just have to plug the value of x or y into the equation and solve to get its corresponding x or y value. So,

*If x = 2

*If y = 3

*If x = 6

*If x = 0

*If x = 3

*If y = 0

*If y = 8

Therefore, the table would be

Now, to find the slope of the line you can solve for y in the equation because that way you will have the equation of the line in its slope-intercept form, that is

So,

Then, in this case

Therefore, the slope of the line is -3.

The probability that at least one of the five sections averages over the average obtained in part a is approximately 1 or 100%.

a. To find the score at which a section's average would exceed only 10% of the time, we need to determine the z-score associated with the 10th percentile.

The z-score formula is given by: z = (x - μ) / σ, where x is the raw score, μ is the population mean, and σ is the standard deviation.

Since the population mean is 78 and the standard deviation is 10, we can rearrange the formula to solve for x: x = z * σ + μ.

To find the z-score associated with the 10th percentile, we look up the corresponding z-value in the standard normal distribution table. The z-score for the 10th percentile is approximately -1.28.

Plugging in the values, we have: x = -1.28 * 10 + 78 = 65.2.

A section's average would exceed only 10% of the time if it scores higher than approximately 65.2.

b. To calculate the probability that at least one of the five sections averages over the average obtained in part a, we need to use the concept of the sampling distribution of the sample mean.

Since each section consists of an equal number of cadets, the distribution of the sample means will also be normally distributed. The mean of the sampling distribution of the sample mean is the same as the population mean, which is 78.

To find the standard deviation of the sampling distribution (also known as the standard error), we divide the population standard deviation by the square root of the sample size. In this case, since there are 5 sections with equal size, each section has 200/5 = 40 cadets.

Standard error (SE) = σ / √n = 10 / √40 ≈ 1.58.

Now, we can find the probability that at least one section averages over 65.2 by calculating the probability of the complement event, which is the probability that none of the sections average over 65.2.

The probability that a section's average is less than or equal to 65.2 is given by the cumulative distribution function (CDF) of the sampling distribution.

P(X ≤ 65.2) = Φ((65.2 - μ) / SE) = Φ((-12.8) / 1.58) ≈ Φ(-8.10) ≈ 0 (since z-scores below -4 are extremely rare).

Since the probability of none of the sections averaging over 65.2 is approximately 0, the probability that at least one section averages over 65.2 is approximately 1 - 0 = 1.

The probability that at least one of the five sections averages over the average obtained in part a is approximately 1 or 100%.

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One sample mean t test is used to to check whether the true average is 59k.

Average:

In statistics, average means a mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

Here we need to find in what test can you use to check whether the true average is 59k.

While we looking into the given question we have identified the following details,

Number of students = 49

True average = 59k

Sample average = 44k

In this given situation, the perfectly suitable test is one sample t test,

Why we used this because of a statistical hypothesis test used to determine whether an unknown population mean is different from a specific value.

Suppose our student center published data that the average starting salary for college graduates is 59k. You randomly sampled 49 college graduates and calculated the sample average salary is 44k.

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Answer: Let X be the amount of money Helen had to start with.

After spending one half of her money on ice cream, she had X - X/2 = X/2 left.

After spending three eighths of her remaining money on soda, she had X/2 - 3X/8 = 5X/8 left.

Since she had $7 left, we have:

5X/8 = 7

X = 56

So, Helen had $56 to start with.

Step-by-step explanation:

He argues that teachers and administrators often label students based on their behavior, appearance, or other factors, which can have a profound impact on students' self-perceptions and future opportunities.

Theoretical perspectives are perspectives that sociologists use to help them better understand and explain human social behavior.

These perspectives encompass various theories and approaches to the study of education.

The following is an overview of three major theoretical perspectives and their associated classic studies of education:

Functionalism perspective

The functionalist perspective is a theoretical approach that views society as a complex system composed of various parts that work together to maintain social order.

Functionalism is also known as structural functionalism.

According to functionalists, education plays an important role in society by providing students with necessary skills and knowledge to become productive members of society.

Classic study of education:

Durkheim's study of education in "The Division of Labor in Society."

In this classic study, Durkheim argues that education serves a crucial function in socializing young people into shared cultural values, beliefs, and norms.

According to symbolic interactionists, education is a process of social interaction in which students learn to make sense of the world around them.

Classic study of education: Becker's study of labeling in "Becoming a Marijuana User.

"In this classic study, Becker demonstrates how schools play an important role in shaping student identities.

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Answer:

255

Step-by-step explanation:

21 ÷ 3 + [27] × 9 + 5

21 ÷ 3 + 243 + 5

7 + 243 + 5

255

1. The linear function that models his distance from Washington, D.C. as a function of time, in hours, is:

d(t) = 109.5 - 55t.

2. The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is of: 0.9 hours = 54 minutes.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In the context of this problem, these parameters are given as follows:

Hence the function is:

d(t) = 109.5 - 55t.

The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is t when d(t) = 60.2 hence:

60.2 = 109.5 - 55t.

55t = 109.5 - 60.2

t = (109.5 - 60.2)/55

t = 0.9 hours = 54 minutes.

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So i think its $4.35.

Step-by-step explanation:

I did addition to find out this answer my calculations seem to be correct.

$3.85 + 50 cents = 4 dollars and 35 cents

Answer:

52

you take 5 ÷ it by 7 the ×it by 595

A ratio is an ordered pair of numbers a and b written as a/b where b is not equal to zero.

if the number of women in the social club is 595 then the number of men in the social club is 425.

A ratio is an ordered pair of numbers a and b written  as:

a / b where b does not equal 0.

A proportion is an equation in which two ratios are equal to each other.

We have,

The ratio of men to women:

= 5:7

= 5/7

Let,

The number of men = 5x

The number of women = 7x

Now,

If the number of women = 595

We have,

7x = 595

Multiplying both sides by 5/7 we get,

5/7 x (7x) = 5/7 x 595

5x = 5/7 x 595

5x = 5 x 85

5x = 425

This means if there are 435 men in the social club if the number of women is 595.

Thus if the number of women in the social club is 595 then the number of men in the social club is 425.

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To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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490

472 <490<500

it fits the criteria

Answer:

Between $59.50 and $61.50

Step-by-step explanation:

Since this is about, we have to round the numbers.

85.58 is rounded to 86

24.98 is rounded to 25

2.49 is rounded to 2.50

Therefore:

86 - 25 - 2.50 = 59.50

So the correct answer is #3

Answer:

Step-by-step explanation:

We can start off by putting this into an equation. Kalil's monthly salary is not a changing value, so that stays put. However, any additional money he gets from selling his stuff, he gets to keep 1.4%.

Thus, we can just add his salary and his commission earnings.

To find the commission, we just multiply 1.4% by $51,000 (the total sales, not his salary).

Thus, Kalil got $3964 in July.

The horizon is about 1,027 miles away if a person is in the international space station about 240 miles above the surface of the earth.

As a general rule, the horizon is located 2.9 miles away from an observer on the Earth's surface, and it is because of the planet's curvature. If a person moves up in the sky, the horizon line will also move up because the person's line of sight is increasing in distance.

In other words, if a person moves to a higher altitude, they will be able to see farther. The calculation to determine the distance of the horizon is based on the following formula:
D = √[(2Rh) + h²]

D is the distance to the horizon

R is the radius of the earth

h is the height above sea level of the observer in meters.

The radius of the Earth is about 6,371 kilometers, and it can be converted to meters by multiplying it by 1,000. The altitude of the International Space Station (ISS) is approximately 408 kilometers above the Earth's surface or 240 miles.

Using this information, we can calculate the distance to the horizon.
D = √[(2 * 6,371,000) + (408,000)²]D = √[(12,742,000) + (166,464,000,000)]D = √[166,476,742,000]D ≈ 408,216 meters
≈ 1,338,381.8 feet ≈ 403.6 km ≈ 252 miles

Therefore, if a person is on the International Space Station about 240 miles above the Earth's surface, the horizon will be around 1,027 miles away.

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To solve the equation 2y − 2.3 = 4.1  for y, we can use algebraic manipulation.

In order to remove the constant term on the left-hand side of the equation, we first add 2.3 to both sides of the equation:

                                 2y - 2.3 = 4.1

                     +2.3                          +2.3

                                   2y = 6.4

Now, we divide both sides by 2 to isolate y:

                                 2y = 6.4

                            ÷2               ÷2

                                  y = 3.2

So, the solution to this equation is  y = 3.2

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We need to isolate the variable on one side of the equation in order to solve an equation like this. By carrying out the same method on both sides of the equation, we can do this. In this example, we divided both sides by 2 to isolate y after adding 2.3 to both sides to remove the constant term on the left-hand side.

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- A term in an algebraic equation that has no variables and is steady is known as a constant term in mathematics. A constant is a fixed, unchanging value. A constant in algebra can be a number on its own or sometimes a letter like a, b, or c to show a fixed integer.

- To separate y from all other terms in an equation, the equation must be rewritten so that y is on one side and all other terms are on the other side. It allows us to calculate the value of y and solve for it.

- Mathematical operations including addition, subtraction, multiplication, and division are used to rearrange algebraic expressions or equations to try to simplify or solve them. This process is known as algebraic manipulation. By doing the opposite operations (undoing) to any equation, algebraic manipulation tries to isolate a variable or simplify an expression in order to solve for a certain variable.

Answer:

x = 11

Step-by-step explanation:

Equation:

(5x+1) + (12x-8) = 180

You are doing this because both sides on a straight line add up to 180 degrees. The two angles would add up to 180 degrees since they are on the one side of the line.

Simplifying:

(5x+12x) + (1-8) = 180

Add your common variables together; keep in mind that variables are placed before numbers.

Adding:

17x-7 = 180

Process:

To do this, you are going to simply do the opposite operation for the number without the variable on both sides of the equal sign.

17x - 7 = 180

     + 7    + 7

------------------

17x = 187

-----   ------

17       17

x = 11

You divided by 17 on both sides because you needed to get the x variable by itself. Hope this helped! :)

The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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1. The probability that no Independents are selected is 0.0304.2.  2. The probability that the sample has one Democrat, one Republican and one Independent is 0.0015.

1. To find out the probability that no Independents are selected, the following will be done. Let’s say that A is the event that a voter is a Democrat, B is the event that a voter is a Republican, and C is the event that a voter is an Independent. The probability of no Independent being selected is P (A and B).

The total number of combinations of 3 voters that can be selected is 40C3. This will be the denominator.The numerator will be 20C1 (15C1). This is because only one Democrat and one Republican can be selected from a total of 20 Democrats and 15 Republicans. Therefore,

P(A and B) = (20C1 * 15C1) / 40C3P (A and B) = 300/9880= 0.03042.

To four decimal places, the answer is 0.0304.2.

2. To find out the probability that the sample has one Democrat, one Republican and one Independent, the following will be done. A, B, and C have the same meaning as above. Let’s assume that the probability of the sample having one Democrat, one Republican, and one Independent is P (A and B and C).

The denominator will be 40C3. There are two ways to find the numerator. One Democrat, one Republican, and one Independent must be chosen. The probability of choosing one Democrat, one Republican, and one Independent is (20C1 * 15C1 * 5C1).

Therefore, the probability that the sample has one Democrat, one Republican, and one Independent is (20C1 * 15C1 * 5C1)/40C3P(A and B and C) = (20C1 * 15C1 * 5C1) / 40C3= 0.00153.

To four decimal places, the answer is 0.0015.

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Answer:

One-sample Z-test

Step-by-step explanation:

As the sample size is greater than 30, assuming the data is a simple random sample, and that the data has a normal distribution, the sociologist should conduct a one-sample z-test to calculate the p-value.