A thin, uniform rod of mass MI and length L, is initially at rest on a frictionless horizontal surface: The moment of inertia of the rod about its center of mass is MIL^2/2_ As shown in Figure I, the rod is struck at point Pby mass m2 whose initial velocity perpendicular t0 the rod. After the collision, mass m2 has velocity -[ / 2v as shown in Figure IL Answerthe following in terms ofthe symbols given. Clearky shon alLwork for each stcp a. Using the principle of conservation of linear momentum; determine the velocity v' of the center of mass of this rod after the collision. b. Using the principle of conservation of angular momentum; determine the angular velocity of the rod about its center of mass after the collision c. Determine the ratio of the final kinetic energy Of the system resulting from the collision to the initial kinetic energy Your finalexpression should bein terms ofthe masses_only

Answer:

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

Volume of cylinder formula:

We are given values:

Substitute and calculate the volume:

Virtual reality has had the most significant impact on de la Pena's journalism career due to its ability to provide a more immersive and engaging news experience and its potential to reach a wider audience.

The question is about the future of news and the impact of virtual reality on de la Pena's journalism career.

In terms of the most significant impact on de la Pena's career, it can be argued that virtual reality has had the most significant impact. This is because virtual reality has revolutionized the way news is presented and consumed.

Virtual reality allows journalists like de la Pena to immerse their audience in a story by providing a more immersive and engaging experience. By using virtual reality, de la Pena has been able to create powerful and impactful stories that allow the audience to experience events and situations firsthand. This has the potential to create a deeper understanding and empathy among viewers.

Furthermore, virtual reality has also expanded the reach of journalism by allowing audiences from different parts of the world to experience stories that they wouldn't have been able to otherwise. This has the potential to foster a more global perspective and increase awareness of important issues.

Overall, virtual reality has had the most significant impact on de la Pena's journalism career due to its ability to provide a more immersive and engaging news experience and its potential to reach a wider audience.

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Step-by-step explanation:

All the explanation in the photo

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

In the given situation:

The independent variable is: Time or months. Delilah's saving and accumulation of money depend on the passage of time.

The dependent variable is: Amount of money saved. The amount of money Delilah has saved is dependent on the number of months that have passed and her consistent savings of $15 each month.\(\)

The least volume of 6.0 M HCl needed to dissolve the excess Mg is 0.028 L.

Calculate the moles of Mg and CuSO4:

Moles of Mg = (0.832 g) / (24.305 g/mol) = 0.0342 mol

Moles of CuSO4 = (1.794 g) / (159.609 g/mol) = 0.0112 mol

Determine the limiting reactant:

The mole ratio between Mg and CuSO4 is 1:1. Since the moles of CuSO4 (0.0112 mol) are less than the moles of Mg (0.0342 mol), CuSO4 is the limiting reactant.

Calculate the moles of excess Mg:

Moles of excess Mg = Moles of Mg - Moles reacted with CuSO4

= 0.0342 mol - 0.0112 mol = 0.0230 mol

Convert moles of excess Mg to grams:

Mass of excess Mg = Moles of excess Mg × Molar mass of Mg

= 0.0230 mol × 24.305 g/mol = 0.559 g

Determine the volume of 6.0 M HCl needed to dissolve the excess Mg:

Use the balanced chemical equation:

Mg + 2HCl → MgCl2 + H2

The stoichiometric ratio between Mg and HCl is 1:2. Therefore, the moles of HCl required will be twice the moles of excess Mg.

Moles of HCl required = 2 × Moles of excess Mg = 2 × 0.0230 mol = 0.0460 mol

Concentration of HCl = 6.0 M, so:

Volume of HCl (L) = Moles of HCl required / Concentration of HCl

= 0.0460 mol / 6.0 mol/L = 0.00767 L = 0.00767 × 1000 mL = 7.67 mL

Therefore, the least volume of 6.0 M HCl needed to dissolve the excess Mg is 7.67 mL.

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The value of the surface integral ∬S​G(x,y,z) dS over the hemisphere x^2 + y^2 + z^2 = 4, z ≥ 0, where G(x,y,z) = 3z^2, is 12π.

the surface integral, we can use a parametric description of the surface. Let's use spherical coordinates to parameterize the hemisphere.

In spherical coordinates, the equation of the hemisphere x^2 + y^2 + z^2 = 4 can be written as ρ = 2, where ρ represents the radial distance from the origin. Since we are considering the hemisphere with z ≥ 0, the spherical coordinates range as follows: 0 ≤ ρ ≤ 2, 0 ≤ θ ≤ 2π, and 0 ≤ φ ≤ π/2.

Now, let's express the function G(x, y, z) = 3z^2 in terms of spherical coordinates. We have z = ρ cos(φ), so G(x, y, z) = 3(ρ cos(φ))^2 = 3ρ^2 cos^2(φ).

The surface area element dS in spherical coordinates is given by dS = ρ^2 sin(φ) dρ dθ. Thus, the surface integral becomes ∬S G(x, y, z) dS = ∫∫ G(ρ, θ, φ) ρ^2 sin(φ) dρ dθ.

Substituting G(ρ, θ, φ) = 3ρ^2 cos^2(φ) and the limits of integration, we have ∬S G(x, y, z) dS = ∫[0,2π]∫[0,π/2] 3ρ^2 cos^2(φ) ρ^2 sin(φ) dφ dθ.

Evaluating this double integral, we get the value of 12π as the result.

Therefore, the value of the surface integral ∬S G(x,y,z) dS over the hemisphere x^2 + y^2 + z^2 = 4, z ≥ 0, using the parametric description, is 12π.

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Answer:  2/3

Step-by-step explanation:

Since the line is going through the origin it slope will use the formula  y/x = k where k is the slope. So you can use any point on the number line to determine the slope.

use the point (3,2)  using the formula y/x = k   divide the y by x.

k = 2/3

Answer: 0.67

Step-by-step explanation:

Look at the points (3,2), (6,4), and (9,6)

Answer:

its the third one

Step-by-step explanation:

1.7x10^9

take care

-tired kitten

who wants to rest forever

There are a total of 15,504 different groups of five students that could be selected for the competition from the 20 students in the math club.

To arrive at this answer, we can use the combination formula, which is given by:

nCk = n! / (k! * (n-k)!)

where n is the total number of students in the math club (20), and k is the number of students selected for the competition (5).

Substituting these values into the formula, we get:

20C5 = 20! / (5! * (20-5)!) = 15,504

Therefore, there are 15,504 different groups of students that could be selected for the competition.

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All multiples of 15 between 0 and 300,inclusive

How?

\(\\ \sf\longmapsto f(x)=15x\)

\(\\ \sf\longmapsto f(0)=15(0)=0\)

\(\\ \sf\longmapsto f(20)=15(20)=300\)

Hence.

\(\\ \sf\longmapsto 0\leqslant R_f\leqslant 300\)

We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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Answer:

What?

Step-by-step explanation:

I think you didn't finish the question. Add it again and I'll go check tell me when you've posted another one if you did.

The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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Answer: 7.1

Step-by-step explanation: 210/255 • x/100. This equals to 7.142857142857142.

Step-by-step explanation:

1. find P of semicircle

perimeter of a semicircle = pi×r+d

=3.14×5+10

=25.7

2.find P of rectangle

P=10×4=40cm

3. add P of semicircle and P of rectangle

25.7+40=65.7cm

Answer:

91

Step-by-step explanation:

You add the two measures of the intercepted arcs and divide by 2 to get the measure of the central angle.

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Answer:

91

Step-by-step explanation:

You add the two measures of the intercepted arcs and divide by 2 to get the measure of the central angle.

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The probability that the sample mean will be larger than 49 can be calculated using the standard normal distribution.



Since we know the population mean and standard deviation, we can use the central limit theorem to assume that the distribution of sample means is normal with a mean of 52 and a standard deviation of 20/√50) = 2.83.

To find the probability that the sample mean will be larger than 49, we can standardize the distribution using the z-score formula:

z = (sample mean - population mean) / (standard deviation / √(sample size))

z = (49 - 52) / (20/√(50)) = -1.77

Using a standard normal distribution table or calculator, we can find that the probability of z being less than -1.77 is approximately 0.0384.

Therefore, the probability that the sample mean will be larger than 49 is:

1 - 0.0384 = 0.9616

or 96.16%.

Calculation:

z = (49 - 52) / (20/√50)) = -1.77

Probability of z being less than -1.77 = 0.0384

Probability of sample mean being larger than 49 = 1 - 0.0384 = 0.9616 or 96.16%.

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The solution to the equation -2/(x - 8) = (x - 1)/(x + 2) is x = 3 after checking for extraneous solutions.

To solve the equation

-2/(x - 8) = (x - 1)/(x + 2)

We can start by cross-multiplying to eliminate the fractions

-2(x + 2) = (x - 1)(x - 8)

Simplifying both sides, we get

-2x - 4 = x² - 9x + 8

Bringing all the terms to one side, we get

x² - 7x + 12 = 0

Now we can factor the quadratic equation to get

(x - 3)(x - 4) = 0

So the solutions are x = 3 and x = 4. However, we need to check for any extraneous solutions that may have been introduced by the original equation.

Plugging in x = 3 to the original equation, we get

-2/(3 - 8) = (3 - 1)/(3 + 2)

Which simplifies to

2/5 = 2/5

Therefore, x = 3 is a valid solution.

Plugging in x = 4 to the original equation, we get

-2/(4 - 8) = (4 - 1)/(4 + 2)

Which simplifies to

1/2 = 3/6

Therefore, x = 4 is not a valid solution.

So the only solution to the equation is x = 3.

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The half-life of U-235 is 704 million years. After one half-life, the amount of U-235 remaining will be 1/2 of the original amount, after two half-lives it will be 1/4, and after three half-lives it will be 1/8.

We can use this information to calculate how much of the sample will remain after three half-lives.

First, we need to calculate how many years have passed in three half-lives.

3 half-lives = 3 x 704 million years = 2,112 million years

So, after 2,112 million years, the amount of U-235 remaining in the sample will be:

(1/2) x (1/2) x (1/2) x 125g = 15.625g

Therefore, the answer is C. 12.5g would remain after 2100 million years had passed.

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It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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The simplification of the addition of two or more fraction with unlike denominator is:

Convert the denominator with like terms and then add the numerators.

Method of simplification of addition of fraction with unlike denominator is:

Therefore, to simplify unlike fractions find least common multiple and add the like fractions.

The given question is incomplete, I answer the question in general according to my knowledge:

Simplification of adding fractions with unlike denominators with  example?

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Answer:

I think it's B.

Step-by-step explanation:

:)

The negative linear correlation coefficient, r = -15.97 indicates a very weak negative relationship between Math SAT scores (x) and scores on Math placement test (y).

Given below is 11 observations of Math SAT scores (x) and scores on Math placement test (y):xy69 94 70 82 87 66 80 85 78 76 81100 97 72 89 85 70 90 89 85 82 92.

To find the linear correlation coefficient, r using the given data. The steps to calculate linear correlation coefficient are as follows:

Calculate the mean of x and y, respectively.  x¯=Σx11 and y¯=Σy11.

Calculate the standard deviation of x, sx=Σ(x−x¯)2n−1 and standard deviation of y, sy=Σ(y−y¯)2n−1.

Calculate the sum of products of deviation of x and deviation of y, Sxy=Σ(x−x¯)(y−y¯)n−1Step 4: Calculate the linear correlation coefficient, r by using the formula r=Sxy/sx.sy.

Here is the calculation:Sx = √(Σ(x−x¯)²/n−1)Sx = √(412.36/10)Sx = √41.236Sx = 6.42Sy = √(Σ(y−y¯)²/n−1)Sy = √(1228.16/10)Sy = √122.816Sy = 11.08Sxy = Σ(x−x¯)(y−y¯)n−1Sxy = (69-81.45)(100-85.82) + (94-81.45)(97-85.82) + (70-81.45)(72-85.82) + (82-81.45)(89-85.82) + (87-81.45)(85-85.82) + (66-81.45)(70-85.82) + (80-81.45)(90-85.82) + (85-81.45)(89-85.82) + (78-81.45)(85-85.82) + (76-81.45)(82-85.82) + (81-81.45)(92-85.82)10Sxy = -1136.645.

R = Sxy/sx.syR = -1136.645/(6.42 × 11.08)R = -1136.645/71.2016R = -15.97.

The main answer to the given question is as follows:Linear correlation coefficient, r = -15.97 (approx.)Therefore, the linear correlation coefficient, r is approximately equal to -15.97.

This value indicates that there is a very weak negative linear relationship between Math SAT scores (x) and scores on Math placement test (y).

Use the formula, Sx = √(Σ(x−x¯)²/n−1) and Sy = √(Σ(y−y¯)²/n−1) to determine the linear correlation coefficient, r.

The negative linear correlation coefficient, r = -15.97 indicates a very weak negative relationship between Math SAT scores (x) and scores on Math placement test (y).

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Answer:

1. Slope is 3/2

2. Slope is -2/3

3. Slope is 3/2

Step-by-step explanation:

Plz mark as Brainliest!

Answer:

Step-by-step explanation:

(-8-4)/(5+3)= -12/8= -3/2

perp. 2/3

y - 4 = 2/3(x + 3)

y - 4 = 2/3x + 2

y = 2/3x + 6

y - 4 = -3/2(x + 3)

y - 8/2 = -3/2x - 9/2

y = -3/2x - 1/2

Answer:

  x=12

Step-by-step explanation:

12+x=-12+3x

-2x=-24

x=12

Answer:

x=12

Step-by-step explanation:

12+x=-3(4-x)

12+x=-12+3x

2x=24

x=12

Answer:

Step-by-step explanation:

Step-by-step explanation:

the situation establishes 2 triangles :

1 has the corners at the helicopter, then straight down on the water, and then the island.

the other had the corners at the helicopter, then the island, and then from there 100ft straight up in the air.

we have enough information to know all angles, we know one side (100 ft altitude). so, we can use the law of sine to get the other sides (incl. the side representing the distance to the island).

a/sin(A) = b/sin(B) = c/sin(C)

where the angles are always opposite of the corresponding sides.

I personally prefer the first triangle.

the angle between the line of sight helicopter-island and the straight down altitude line is complementary to the angle of depression : 90 - 40 = 50°

then the angle between the straight down altitude line and the ground distance to the island is a right angle (90°).

and the angle between the ground distance and the line of sight is then 180 - 90 - 50 = 40°

(remember, the sum of all angles in a triangle is always 180°)

so,

altitude line / sin(40) = ground distance / sin(50)

ground distance = altitude line × sin(50)/sin(40) =

= 100 × sin(50)/sin(40) = 119.18 ft

Answer:

\(c=85\)

Step-by-step explanation:

\(c=180-a-b\) where \(a=62\) and \(b=33\)

Step 1.  Substitute a for 62 and b for 33

\(c=180-(62)-(33)\)

Step 2. Subtract \((180 - 62)\)

\(c=118-33\)

Step 3. Subtract (again)

\(c=85\)

so c = 85

The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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The value of {x} for the given proportion is 853.4.

Given is the proportion as -

x : 8 : : 90120 : x

We know that -

Product of extremes = Product of means

x² = 90120 x 8

x² = 728160

x = 853.4

Therefore, the value of {x} for the given proportion is 853.4.

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