Can somebody help me with these. with solution

1 Two balls are drawn in succession without replacement from a box containing 4 red balls and 3 black balls. Let Y be the random variable, where Y is the number of the red balls. What is the expected value of this random event?

2. Two balls are drawn in succession from a box without repetition containing 3 red 3 blue and four yellow marbles. What is the probability that they are of the same color?

[Your Name]

[Your Address]

[City, State ZIP Code]

[Your Email]

[Date]

[Recipient Name]

[Recipient Position]

[Company Name]

[Address]

[City, State ZIP Code]

Dear [Recipient Name],

I am writing this letter to inform you that I have decided to step down from my position as [Your Position] at [Company Name]. My resignation is effective from [Date].

I have made this decision after much consideration and reflection on my personal and professional goals. While I have greatly enjoyed working at [Company Name] and appreciate the opportunities and support provided by the organization, I have decided that it is time for me to pursue other career opportunities.

I will ensure a smooth transition by completing my pending work and helping my replacement to settle into the role. I am willing to assist in any way possible to ensure that my duties and responsibilities are transferred smoothly to my successor.

I would like to take this opportunity to express my gratitude to [Recipient Name] and the entire management team for their support, guidance, and mentorship during my time at [Company Name]. I have learned a lot from my colleagues, and I am grateful for the professional growth opportunities provided to me.

Please let me know if there is any additional information you need from me or if I can assist in any way during this transition period.

Thank you for understanding my decision.

Sincerely,

[Your Name]

The ampere (/aempr/, US: /mpr/; symbol: A), also known as the amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to one coulomb, or 6.2415090741018 electrons passing through a point in one second.

What is ampere?

The ampere, commonly abbreviated as "amp," is the base unit of electric flow in the International System of Units (SI). It was named after French mathematician and physicist André-Marie Ampère (1775-1836), widely regarded as the father of electrodynamics. The ampere is defined by the International System of Units in terms of other base units by estimating the electromagnetic power between electrical conductors that carry the electric flow. The previous CGS estimation framework employed two distinct definitions of current, one based on SI units and the other on electric charge as the base unit. The charge unit is calculated by measuring the power between two charged metal plates. The ampere was then defined as one coulomb of charge per second. SI defines the coulomb as the unit of charge.

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Answer:

  see attached

Explanation:

You want to construct a triangle with a perimeter of 55 mm and angles in the ratio 2:1:3.

Angles

The 2+1+3 = 6 ratio units represent 180°, the sum of angles in a triangle. Hence each unit in the ratio is 180°/6 = 30°.

The angles are 60° : 30° : 90°.

Perimeter

From your knowledge of "special triangles," you know the side lengths in a 30°-60°-90° triangle have the ratios 1 : √3 : 2.

That is, the perimeter of the triangle is (1+√3 +2) = 3+√3 times the length of the shortest side.

Side lengths

The shortest side of the triangle will have the length ...

  [tex]\dfrac{55\text{ mm}}{3+\sqrt{3}}=\dfrac{(3-\sqrt{3})(55\text{ mm})}{(3-\sqrt{3})(3+\sqrt{3})}= \dfrac{(165-55\sqrt{3})\text{ mm}}{3^2-(\sqrt{3})^2}\\\\\\=(27.5-\dfrac{55}{6}\sqrt{3})\text{ mm}\approx 11.6229\text{ mm}[/tex]

The longest side will be double this length, about 23.2457 mm. The side of intermediate length will be (55√3 -55)/2 ≈ 20.1314 mm.

Construction

If you're doing the drawing using only a compass and straightedge, you will start by constructing perpendicular lines (the right angle). Mark off 1 and two lengths of the shortest side on one of these perpendicular segments. Then draw the hypotenuse as 2 times the short length from the end of the short length. It will intersect the perpendicular segment at √3 times the short length.

The tricky part here is constructing a line segment of the desired irrational length. One way to do this is to construct a 30-60-90 triangle with a unit-length short side, then "unfold" it to a line segment with parts that are 1, √3, and 2 units long. A "proportioning" construction can divide the 55 mm length of the perimeter into these proportions, (10 mm might be a good "unit length" for this.)

__

Additional comment

The desired dimensions are sufficiently small that an accurate compass/straightedge construction will be difficult. It is unlikely your pencil line width is much less than about 0.2 mm, so already the error is about 2% in any length.

The attached drawing was made by telling the software what lengths we wanted in "exact" terms. Its calculation is generally good to 10 sf or better. To scale the drawing properly, you'd have to make the longest side about 23.25 mm, or 0.9152 inches.

Option (C) clogged modulator valve is not a common manual transmission problem. This component is typically associated with automatic transmissions, not manual transmissions.

Explanation

Manual transmission problems can include a range of issues that can affect the performance of the transmission. Here short explanation about other option except C as common manual transmission problems:

Bent shift mechanism.
The shift mechanism in a manual transmission is responsible for moving the gears into the correct position for each gear change. If the shift mechanism is bent or damaged, it can cause difficulty in shifting gears or even prevent the transmission from shifting at all. This can happen due to wear and tear, damage from impact or other causes.Worn thrust washers.
Thrust washers are small components in the transmission that help to control the movement of the gears. If the thrust washers become worn, they can cause excessive play in the gears, leading to difficulty in shifting and even gear slippage. This can happen due to normal wear and tear or improper lubrication.Damaged extension housing.
The extension housing is the outermost component of the transmission on the backside that houses the output shaft. If it becomes damaged due to wear and tear, impact or other causes, it can cause leaks in the transmission or even prevent it from operating altogether. A damaged extension housing can cause the transmission to fail or operate poorly.

Learn more about other manual transmission problems on:

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Here's the Python equivalent of the given code:

```
def main():
a = [0] * 5
b = [0] * 5
c = 0

for i in range(5): # Input
a[i], b[i] = map(float, input().split())

for i in range(5):
c += ((b[i] - a[i] - 1.0) > 0) * (4.0 if (b[i] - a[i] - 1.0) > 4 else (b[i] - a[i] - 1.0))

c /= 0.5
c *= 5000

if c >= 150000:
c *= 0.95
elif c <= 50000:
c *= 1.05

print("{:.0f}".format(c))

main()
```

Note that the `scanf` function has been replaced with Python's `input` function, and the `printf` function has been replaced with Python's `print` function with formatted output.