In a circle, a sector is created by an arc measuring 54 degrees. If the diameter of the circle is 20 in, what is

a) the length of the arc

b) the area of the sector

Answer:  b<-7/4

Step-by-step explanation:

Let's collect numbers with same variables to the same side:

-3-4>9b-5b

-7>4b

b<-7/4

Answer: "An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.

Since 4.284 is not the square root of a negative number, it is not imaginary

Since 4.284 is a rational number from above, 4.284 is not an irrational number"

Step-by-step explanation: /\ I looked at a calculator for irrational numbers. Should be right, considering how it's well explained. Just search for "irrational number calculator". Dont rely on that. But it's there if

you need it! :)

No

It is a rational number since it is a fraction/decimal that isn't non-terminating, not is it pi or

The point (a,2b) is on the line, and the equation of the line passing through (3a,0) and (0,3b) is y = (-a/b)x + 3b

We can use the two-point form of the equation of a straight line to find the equation passing through the points (3a,0) and (0,3b).

The two-point form of a straight line is given by,

y - y1 = m(x - x1)

where (x1, y1) and (x, y) are two points on the line, and m is the slope of the line.

Let's take the point (3a,0) as (x1, y1) and the point (0,3b) as (x, y). Then, we have:

y - 3b = [(0 - 3a)/(3b - 0)](x - 0)

Simplifying this, we get:

y - 3b = (-a/b)x

y = (-a/b)x + 3b

This is the equation of the line passing through (3a,0) and (0,3b).

Now, to show that this line passes through the point (a,2b), we substitute x = a and y = 2b into the equation of line:

2b = (-a/b)a + 3b

2b = -a + 3b

a = b

Therefore, the point (a,2b) is on the line

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Answer: Your welcome!

Step-by-step explanation:

y= 3x-2; This is a linear equation with a slope of 3 and a y-intercept of -2, which has the solution (3,4).

Thanks! #BO

The discounted price of the camera is $270 and the price of the camera after the 40% increase is $378.

When the store offered a 40% discount on the original price of $450, the discounted price of the camera can be calculated as follows:

Discounted price = Original price - Discount

Discounted price = $450 - 40% x $450

Discounted price = $450 - $180

Discounted price = $270

Therefore, the discounted price of the camera is $270.

After the sale, the discounted price of the camera was increased by 40%. We can calculate the new price of the camera as follows:

New price = Discounted price + 40% x Discounted price

New price = $270 + 40% x $270

New price = $270 + $108

New price = $378

Therefore, the price of the camera after the 40% increase is $378.

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The probability of choosing an odd prime number from 1 to 20 is 0.35

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The odd prime numbers between 1 and 20 are 3, 5, 7, 11, 13, 17, and 19. There are 7 odd prime numbers in this range.

The total number of possible choices is 20 (since there are 20 numbers in the range 1 to 20).

Therefore, the probability of choosing an odd prime number is:

number of odd prime numbers / total number of possible choices

= 7 / 20

= 0.35

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Answer:

|a × [ob + (1 - o)a]| = √(7 - 8o(a · o) - 8(a · o)^2)

where k = 7 - 8o(a · o) - 8(a · o)^2.

Step-by-step explanation:

Given the position vectors of two points A and B as a and b respectively, where b is a unit vector, and the magnitude of a is twice that of b, we are asked to show that:

|a × [ob + (1-o)a]| = √k,

where k is a constant to be determined.

We can begin by expanding the vector inside the cross product:

ob + (1 - o)a = ob + a - oa

Since b is a unit vector, we can write:

ob = b - o

Substituting this into the previous equation, we get:

ob + (1 - o)a = b - o + a - oa = b + (1 - o)a - oa

Next, we can use the vector cross product formula:

|a × b| = |a||b|sinθ

where θ is the angle between a and b.

We are given that the angle between a and b is 60°, so we can substitute this value into the formula:

|a × b| = |a||b|sin60° = (2|b|)(1)(√3/2) = √3

Now we can calculate the cross product of a and the vector we just derived:

a × [ob + (1 - o)a] = a × (b + (1 - o)a - oa)

= a × (b + a - oa)

= a × b + a × a - a × oa

Since b is a unit vector, we know that a × b is a vector perpendicular to both a and b, and therefore perpendicular to the plane containing a and b. The vector a × a is 0 since the cross product of a vector with itself is 0. Finally, we can use the vector triple product to simplify a × oa:

a × oa = (a · a)o - (a · o)a = |a|^2 o - (a · o)a

Since |a| is twice |b|, we have:

|a|^2 = 4|b|^2 = 4

Substituting this back in, we get:

a × oa = 4o - (a · o)a

Putting it all together, we have:

a × [ob + (1 - o)a] = a × b + 4o - (a · o)a

Now we can take the magnitude squared of both sides:

|a × [ob + (1 - o)a]|^2 = (a × b + 4o - (a · o)a) · (a × b + 4o - (a · o)a)

Expanding the dot product, we get:

|a × [ob + (1 - o)a]|^2 = |a × b|^2 + 16o^2 + |a|^2(o · o) - 8o(a · o)b + 8(a · o)(a × b) - 2(a · o)^2|a|^2

Substituting the values we derived earlier, we get:

|a × [ob + (1 - o)a]|^2 = 3 + 16o^2 + 4(o · o) - 8o(a · o) + 0 - 2(a · o)^2(4)

= 7 - 8o(a · o) - 8(a · o)^2

Now we need to find the value of k such that the left-hand side equals k:

|a × [ob + (1 - o)a]|^2 = k

Using the vector triple product again, we can simplify the left-hand side as:

|a × [ob + (1 - o)a]|^2 = |a|^2|ob + (1 - o)a|^2 - ((a · [ob + (1 - o)a])^2)

Since we know that the magnitude of a is twice that of b, we have:

|a|^2 = 4|b|^2 = 4

Substituting this back in, we get:

|a × [ob + (1 - o)a]|^2 = 4|ob + (1 - o)a|^2 - ((a · [ob + (1 - o)a])^2)

Now we can substitute the expanded expression for ob + (1 - o)a:

|a × [ob + (1 - o)a]|^2 = 4|b + (1 - o)a|^2 - ((a · [b + (1 - o)a - oa])^2)

= 4|b|^2 + 8|b|(1 - o)(a · b) + 4(1 - o)^2|a|^2 - ((a · b + (1 - o)(a · b) - (a · o)(a · b))^2)

= 4 + 8(1 - o)(a · b) + 4(1 - o)^2(4) - ((a · b + (1 - o)(a · b) - (a · o)(a · b))^2)

= 28 - 8o(a · b) - 8(a · o)^2

Substituting this back into the previous equation, we get:

28 - 8o(a · b) - 8(a · o)^2 = k

Therefore, we have:

|a × [ob + (1 - o)a]| = √(28 - 8o(a · b) - 8(a · o)^2)  and

k = 28 - 8o(a · b) - 8(a · o)^2

Hope this helps! Sorry if it's wrong! If you need more help, ask me! :]

The dairy farm yields 6,158,000 gallons of milk in one year, assuming that each cow produces 2320 gallons per year.

The term "total amount" refers to the complete or full quantity or sum of something. It is the complete amount of something without any deductions or subtractions.

To calculate the total amount of milk the dairy farm yields in one year mathematically, we need to multiply the number of dairy cows by the amount of milk each cow produces in a year.

Let's represent the number of dairy cows as "C" and the amount of milk produced per cow per year as "M". Using this notation, we can write:

Total amount of milk produced in one year = Number of cows x Amount of milk per cow

= C x M

Substituting the given values, we have:

C = 2650 (number of dairy cows)

M = 2320 gallons (amount of milk per cow per year)

Total amount of milk produced in one year = 2650 x 2320

= 6,158,000 gallons

Therefore, the dairy farm yields 6,158,000 gallons of milk in one year, assuming that each cow produces 2320 gallons per year.

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Answer:

6.158 x 10^6

Step-by-step explanation:

Converted answer above to scientific notation.

The line plot shows that the construction company has a number of trucks, each of which is designed to haul different amounts of weight.

If all of these trucks are working at the same time, we can calculate how many tons the trucks can carry in total. In order to do this, we need to look at the range of weight each truck is capable of carrying, and then add all of these numbers together.
In order to determine how many tons the trucks can carry, we need to use the information provided by the line plot. The line plot displays the weight each truck can haul, which is given in pounds. We need to convert the weight in pounds to tons in order to find the total weight that the trucks can carry.

To do this, we can use the following conversion factor:1 ton = 2000 poundsWe can use this conversion factor to convert the weight of each truck from pounds to tons. Once we have done this, we can add up the weights of all the trucks to find the total weight that the trucks can carry. Here are the steps:

Step 1: Convert the weight of each truck from pounds to tons Truck 1: 6,000 pounds ÷ 2,000 pounds/ton = 3 tons Truck 2: 9,000 pounds ÷ 2,000 pounds/ton = 4.5 tons Truck 3: 8,000 pounds ÷ 2,000 pounds/ton = 4 tons Truck 4: 10,000 pounds ÷ 2,000 pounds/ton = 5 tons Truck 5: 11,000 pounds ÷ 2,000 pounds/ton = 5.5 tons Truck 6: 9,500 pounds ÷ 2,000 pounds/ton = 4.75 tons

Step 2: Add up the weights of all the trucks3 + 4.5 + 4 + 5 + 5.5 + 4.75 = 26.75 tons. The trucks can carry 26.75 tons in total.

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Answer:

y = 4x - 16

Step-by-step explanation:

Parallel lines have the same slope. Find slope using the points (-3, -3) and (-1, 5)

slope = m = (5 - -3) / (-1 - -3) = 8/2 = 4

y = mx + b      find b using the point (4, 0), the x-intercept of the parallel line

0 = 4(4) + b

b = -16

equation of the parallel line:

y = 4x - 16

Answer: Domain: All x-values

Range: All y-values

Step-by-step explanation:

Answer:

Hope this helps :)

Step-by-step explanation:

Because x is an absolute value, the value of y is always greater than or equal to zero. I attached the graph below. As you'll see, when x is a negative number, it was the same value as the positive of that value. When x = 1 or x = -1, y = 5.

Tristan has 14 nickels and 7 dimes worth of $1. 40.

This is because 1 nickel is worth 5 cents and 1 dime is worth 10 cents.

Let's use the following variables to represent the number of nickels and dimes Tristan has:

n = number of nickels

d = number of dimes

We know that Tristan has $1.40 worth of nickels and dimes. Each nickel is worth $0.05 and each dime is worth $0.10, so we can write an equation based on their values:

0.05n + 0.1d = 1.4

We also know that Tristan has twice as many nickels as dimes:

n = 2d

We can substitute n = 2d into the first equation and solve for d:

0.05(2d) + 0.1d = 1.4

0.1d + 0.1d = 1.4

0.2d = 1.4

d = 7

So Tristan has 7 dimes. Using n = 2d, we can find the number of nickels:

n = 2(7) = 14

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Therefore, the density of the drink is approximately 1.04 grams per cm³.

Volume is a measure of the amount of space occupied by a three-dimensional object or substance. It is the amount of space inside an object or container and is usually measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

Given by the question.

To calculate the density of the drink, we need to first calculate the total mass of the drink, which is the sum of the masses of apple juice, fruit syrup, and sparkling water.

Mass of apple juice = volume of apple juice x density of apple juice = 35 cm³ x 1.04 g/cm³ = 36.4 g

Mass of fruit syrup = volume of fruit syrup x density of fruit syrup = 25 cm³ x 1.6 g/cm³ = 40 g

Mass of sparkling water = volume of sparkling water x density of sparkling water = 270 cm³ x 0.99 g/cm³ = 267.3 g

Total mass of the drink = mass of apple juice + mass of fruit syrup + mass of sparkling water

= 36.4 g + 40 g + 267.3 g

= 343.7 g

Now we can calculate the density of the drink by dividing the total mass by the volume of the drink:

Density of the drink = total mass of the drink / volume of the drink = 343.7 g / 330 cm³ = 1.04 g/cm³ (approx.)

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The area of each part of the figure and then the whole figure, can be found to be :

The area of Triangle A would be :

= 1 / 2 x  Base x height

= 1 / 2 x ( 2 + 2 + 6 ) x 4

= 1 / 2 x 10 x 4

= 20 units ²

The area of Triangle D is :

= 1 / 2 x base x height

= 1 / 2 x 6 x 2

= 6 units ²

The area of the whole figure would then be:

= 20 + 2 + 4 + 6

= 32 units ²

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The value οf P(2 tails) is 37.5%, the cοrrect οptiοn is B.

Prοbability refers tο a pοssibility that deals with the οccurrence οf randοm events.

The prοbability οf all the events οccurring need tο be 1.

The fοrmula οf prοbability is defined as the ratiο οf a number οf favοurable οutcοmes tο the tοtal number οf οutcοmes.

P(E) = Number οf favοurable οutcοmes / tοtal number οf οutcοmes

We are given that;

The sample space=  {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Nοw,

The sample space fοr tοssing a cοin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, where H represents heads and T represents tails.

Tο determine P(2 tails), we need tο cοunt the number οf οutcοmes in which there are 2 tails, and divide that by the tοtal number οf οutcοmes:

Number οf οutcοmes with 2 tails: There are three οutcοmes with 2 tails: TTH, THT, and HTT.

Tοtal number οf οutcοmes: There are eight οutcοmes in tοtal.

P(2 tails) = number οf οutcοmes with 2 tails / tοtal number οf οutcοmes = 3/8 = 0.375, which is equivalent tο 37.5%.

Therefοre, the prοbability the answer will be 37.5%.

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Answer:

chocolate = $1.25

soft drink = $1.85

Step-by-step explanation:

Given price of chocolate is c and price of soft drink is s

Olivia: 5c + 2s = 9.95

Taylor: 6c + 6s = 18.60

6c + 6s = 18.60

divided by 6, we have

c + s = 3.1

=> s = 3.1 - c

Substitute s = 3.1 - c into

5c + 2s = 9.95

5c + 2(3.1 - c) = 9.95

5c + 6.2 - 2c = 9.95

3c = 9.95 - 6.2

3c = 3.75

c = 3.75/3 = 1.25

s = 3.1 - c = 3.1 - 1.25 = 1.85

According to the solving this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

The Nigerian visitor changed N70200 to rupees at a rate of 3 nairas to 35 rupees. Therefore,

70200 Nigerian naira = 70200 * 35 / 3 = 819500 Indian rupees

He spent 224,000 rupees, so the amount he invested at 41.5% per annum was:

819500 - 224000 = 595500 rupees

The simple interest he earned after 8 months at a rate of 41.5% per annum is:

595500 * (41.5/100) * (8/12) = 129702.5 rupees

So, the total amount he had after 8 months was:

595500 + 129702.5 = 725202.5 rupees

He then transferred this amount to his account in the Modern Bank of Nigeria at a rate of 21 rupees to 2 naira. Therefore,

725202.5 rupees = (725202.5 / 21) * 2 = 580162.5 Nigerian naira

this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.

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Julie is trekking to the Blue Ridge Mountains, therefore she is 10 1/12 miles from the beginning point M.

Distance in mathematics is a numerical representation of the actual area between two points. The shortest distance between those two points is how long the path is. The Pythagorean theorem, which asserts that in a right triangle, the sum of the squares of the lengths of the two legs (the sides perpendicular to one another) is equal to the square of the length of the hypotenuse, is used to determine the distance between two locations in a two-dimensional plane (the longest side, opposite the right angle).

given

We must determine Julie's total distance traveled before we can determine how far she is from the beginning location M. By combining the distances between each location, we may determine this:

3 3/8 miles from M to N

2 1/4 miles from N to P

P returning to M: 4 11/24 miles

We must identify a common denominator in order to aggregate these distances. Because it can be divided by 8, 4, and 3, we may pick 24 as the common denominator.

From M to N, the distance is 3 3/8 miles (or 27/8 kilometers). From N to P, it is 2 1/4 kilometers (or 9 kilometers).

We may now multiply the distances:

27/8 + 9/4 + 107/24 = (81 + 54 + 107) / 24

= 242/24

= 10 1/12

Julie is trekking to the Blue Ridge Mountains, therefore she is 10 1/12 miles from the beginning point M.

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The acceleration due to gravity on Earth is approximately 9.81 meters per second squared (m/s^2)

Acceleration due to gravity is the acceleration experienced by an object when it is dropped or falls freely in a gravitational field. On Earth, the value of acceleration due to gravity is approximately 9.81 meters per second squared. This means that if an object is dropped from a certain height, its velocity will increase by 9.81 m/s^2 for every second it falls.

The formula connecting mass and weight, W = m x g, shows that weight is directly proportional to the acceleration due to gravity. This means that as the value of acceleration due to gravity changes, the weight of an object will also change accordingly. The value of acceleration due to gravity is an important factor in various fields, including physics, engineering, and astronomy.

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By speed formula, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.

What is speed?

Speed is defined as the distance travelled by an object in a given amount of time. Speed is a scalar quantity, meaning that it has magnitude but no direction.

Mathematically, speed is calculated as follows:

speed = distance / time

where "distance" is the distance travelled by the object, and "time" is the time it takes for the object to travel that distance.

Let's assume that Angela's shoveling rate is "a" and Franklin's shoveling rate is "f" (measured in driveways per hour). We can use the formula:

time = distance / rate

where "distance" is the length of the driveway (which we can assume to be 1 driveway) and "rate" is the shoveling rate (in driveways per hour).

According to the problem, Angela can shovel the driveway in 2 hours, so her shoveling rate is:

a = 1/2

When Franklin joins her, they can finish the driveway in 54 minutes, or 9/10 of an hour. Therefore, their combined shoveling rate is:

(a + f) = 1 / (9/10) = 10/9

We can now set up a system of equations to solve for "f".

First, we know that Angela and Franklin can finish the driveway in 9/10 of an hour:

1/2 + f = 1 / (9/10)

Multiplying both sides by 10/9, we get:

5/9 + (10/9)f = 1

Simplifying, we get:

(10/9)f = 4/9

f = (4/9) * (9/10)

f = 4/10

f = 2/5

Therefore, Franklin's shoveling rate is 2/5 of a driveway per hour. To find how long it would take him to shovel the driveway alone, we can use the formula:

time = distance/rate

time = 1 / (2/5)

time = 5/2

time = 2 1/2 hours

Therefore, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.

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The greatest number of tens that can live in the tens house is 9.

The greatest number of tens that can live in the tens house depends on how many digits there are in the number.

Let's start with a two-digit number, like 99. In this number, the leftmost digit represents the number of tens, so we want to find the largest digit that can be in that place.

Since we are limited to using only the digits 0-9, the largest digit that can be in the tens place is 9.

Now, let's consider a three-digit number, like 456. Again, we want to find the largest digit that can be in the hundreds place.

Since we are limited to using only the digits 0-9, the largest digit that can be in the hundreds place is also 9. So, we can have up to 9 groups of ten (or 90) in the hundreds place.

In the tens place, we can again have up to 9 groups of ten, and in the units place, we can have any digit from 0-9.

Therefore, the greatest number of tens that can live in the tens house in a three-digit number is 9.

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Answer:

Miguel's account: M(x) = 320 + 85x

Kala's account: K(x) = 820 + 35x

b) To find when the two accounts would have the same amount of money, we need to set M(x) equal to K(x) and solve for x:

320 + 85x = 820 + 35x

Simplifying the equation, we get:

50x = 500

Dividing both sides by 50, we get:

x = 10

Therefore, the two accounts would have the same amount of money after 10 months.

Answer: 37.5 million

Step-by-step explanation:

I looked it up

Answer:

Step-by-step explanation:

The equation of the line with a slope of 1/6 passes through the point (-6, 5) is y=(1/6)x+6.

What is the equation of a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

Given that a line with a slope of 1/6 passes through the point (-6, 5). Therefore, we can write,

y = mx + c

Substitute the values,

5 = (1/6)(-6) + C

5 = -1 + C

5 + 1 = C

C = 6

Hence, the equation of the line with a slope of 1/6 passes through the point (-6, 5) is y=(1/6)x+6.

Answer:

y = (1/6)x + 7

Step-by-step explanation:

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We know that the line has a slope of 1/6 and passes through the point (-6, 6). To find the y-intercept, we can substitute the values of the point into the equation and solve for b:

y = mx + b

6 = (1/6)(-6) + b

6 = -1 + b

b = 7

Now that we know the slope and y-intercept, we can write the equation of the line in slope-intercept form:

y = (1/6)x + 7

Therefore, the equation of the line in slope-intercept form is y = (1/6)x + 7.

(Please could you kindly mark my answer as brainliest)

The exponential function that relates the mass of the substance to the number of years since 2005 is: [tex]y = 600 \times e^(-0.048t)[/tex]  . [Where t is a number of years since 2005, and y is mass of the substance in milligrams at that time.]

An exponential function is a mathematical function of the form[tex]f(x) = a^x,[/tex] representing a rapid increase or decrease in value as x increases or decreases.

It represents a rapid growth or decay in value as the independent variable changes, and is used to model many natural phenomena such as population growth, compound interest, and radioactive decay.

The radioactive decay of the substance follows an exponential decay model. The formula for exponential decay is:

[tex]y = a * e^(-rt)[/tex]

Where:

y - amount of substance at time t.

a - initial amount of the substance.

r - decay rate per unit of time.

t - time elapsed since the start of the decay.

In this case, we know that the initial mass of the substance in 2005 was 600 milligrams. We also know that the substance decays by [tex]4.8[/tex]  % each year, which means that the decay rate per year is [tex]0.048[/tex]  (4.8% expressed as a decimal).

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Answer: A ‍♀️

Step-by-step explanation:

From the given information provided, the expected value of X = np, the variance of X = npq and the probability that X is odd is 0.4824 rounded to four decimal places.

(a) The probability of finding k defective items out of n can be calculated using the binomial distribution:

P(X=k) = C(n,k) ×[tex]p^k[/tex] × [tex]q^(n-k)[/tex], where C(n,k) is the binomial coefficient.

The possible values of K: 0, 1, 2, ..., n.

To show that the probability that X is even is 1/2[1+(1-2p)ⁿ], we use the binomial theorem to expand (p+q)ⁿ+(q-p)ⁿ as:

(p+q)ⁿ + (q-p)ⁿ = ∑[k=0,n]C(n,k) × [tex]p^k[/tex] × [tex]q^(n-k)[/tex] + ∑[k=0,n]C(n,k) × [tex](-1)^k[/tex] × [tex]p^k[/tex]× [tex]q^(n-k)[/tex]

The first sum corresponds to the probability of finding an even number of defective items, while the second sum corresponds to the probability of finding an odd number of defective items. Therefore,

P(X is even) = (1/2)[(p+q)ⁿ + (q-p)ⁿ]

= (1/2)[(p+q)ⁿ - (p-q)ⁿ] (since q-p = 1-2p)

= (1/2)[(1)ⁿ + (1-2p)ⁿ] (since p+q = 1)

Thus, the probability that X is even is 1/2[1+(1-2p)ⁿ].

(b) The expected value of X is:

E(X) = ∑[k=0,n]k × P(X=k)

= ∑[k=0,n]k × C(n,k) × [tex]p^k[/tex]× [tex]q^(n-k)[/tex]

Using the identity ∑[k=0,n]k × C(n,k) ×[tex]p^k[/tex] × [tex]q^(n-k)[/tex] = np, the expected value simplifies to:

E(X) = np

The variance of X is given by:

Var(X) = E(X²) - [E(X)]²

= ∑[k=0,n]k² × P(X=k) - (np)²

= ∑[k=0,n]k² × C(n,k) × [tex]p^k[/tex] × [tex]q^(n-k)[/tex]- n²p²

Using the identity ∑[k=0,n]k² × C(n,k) ×[tex]p^k[/tex] × [tex]q^(n-k)[/tex] = n(n-1)p² + npq, the variance simplifies to:

Var(X) = n(n-1)p² + npq - n²p²

= npq

(c) Using the formula for the expected value and variance of X, we can write:

0.0125 = E(X) = np

0.9875 = Var(X) = npq

Solving for p and q, we obtain:

p = 0.01 and q = 0.99

Therefore, the probability that X is odd can be calculated using the formula for the probability that X is even derived in part (a):

P(X is odd) = 1 - P(X is even)

= 1 - 1/2[1+(1-2p)ⁿ]

= 1 - 1/2[1+(1-2*0.01)ⁿ]

= 1/2[1-(0.98)ⁿ]

Substituting n = 1/0.98 ln(0.0125/0.01) = 24.68

P(X is odd) = 0.482

Learn more about probability here: brainly.com/question/25870256

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Answer:

The perimeter is the sum of all the sides of the rectangle. So, adding up all the given sides, we get:

Perimeter = 2u + u + 10 + u + 10 + 8u

Simplifying the expression by combining like terms, we get:

Perimeter = 12u + 20

Therefore, the simplified answer for the perimeter is 12u + 20.