The two numbers that fit the description are 27 and 99.
There are two numbers that fit this description. To find them, we can solve the equation:
Difference = Number - Number’s Reverse
Difference = 72
Number - Reverse = 72
Let’s call the two-digit number “x” and its reverse “y”. So, we can rewrite the equation as:
x - y = 72
Now, we can solve the equation using algebraic methods. First, add “y” to both sides of the equation:
x - y + y = 72 + y
x = 72 + y
Next, let’s solve for “y” by subtracting “72” from both sides of the equation:
x - 72 = 72 + y - 72
x - 72 = y
Therefore, we can rewrite the equation as:
x - 72 = y
Now, we can solve for “x” and “y” by plugging in possible values for “x” and “y” and seeing which ones work. Since we’re dealing with two-digit numbers, let’s start with numbers between 10 and 99.
First, let’s try x = 10 and y = 82.
10 - 82 = -72
This doesn’t work, since the difference cannot be negative.
Next, let’s try x = 15 and y = 87.
15 - 87 = -72
Again, this doesn’t work.
Finally, let’s try x = 27 and y = 99.
27 - 99 = -72
This works! So, the two numbers that fit the description are 27 and 99.
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Helppp!!! i’m having a really hard time figuring this out:
Therefore , the solution of the given problem of unitary method comes out to be the composite shape's overall size is 30 square units.
What is a unitary method?Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.
Here,
We must divide the composite shape into smaller shapes and sum up their areas in order to determine the area of the composite shape.
We can see that the composite form is made up of a triangle with a base of four and a height of three, and a rectangle with dimensions of six by four.
=> length times breadth equals six by four, or 24 square units, for a rectangle.
Triangle's area is equal to
=> (1/2) x base times height, or (1/2) x 4 times 3, or 6 square units.
As a result, the composite shape's overall size is:
=> 24 + 6 = 30 square units.
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Suppose you select a number at random from the sample space {-3, -2, -1, 0, 1, 2, 3, 4). Find the probability. P(the number is less than 2 | the number is less than 4)
Evaluate 4!
Evaluate 6!
Evaluate 5!/3!
Answer:
Step-by-step explanation:
There are four numbers in the sample space that are less than 4: -3, -2, -1, and 0. Of these, three are less than 2: -3, -2, and -1. Therefore, the probability P(the number is less than 2 | the number is less than 4) is 3/4.
To evaluate 4!, we perform the multiplication 4 x 3 x 2 x 1, which equals 24.
To evaluate 6!, we perform the multiplication 6 x 5 x 4 x 3 x 2 x 1, which equals 720.
To evaluate 5!/3!, we first calculate 5! (which is equal to 5 x 4 x 3 x 2 x 1, or 120) and then divide by 3! (which is equal to 3 x 2 x 1, or 6). Therefore, 5!/3! = 120/6 = 20.
for the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36}, what will be the least upper bound of elements {8, 12}?
The least upper bound of the elements {8, 12} under the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36} is 24.
To find the least upper bound of a set of elements under a relation, we look for the smallest element in the set that is greater than or equal to all of the elements in the set.
Under the divisibility relation, an element a is said to be divisible by an element b (written as b divides a) if a is a multiple of b, that is, a = b * k for some integer k. For example, 8 divides 24 because 24 = 8 * 3.
We want to find the least upper bound of the elements {8, 12} under this relation on the set {1, 2, 3, 6, 8, 12, 24, 36}. That means we want to find the smallest element in the set that is a multiple of both 8 and 12.
We can list the multiples of 8 and 12 in the set as follows:
Multiples of 8: 8, 24
Multiples of 12: 12, 24, 36
We can see that the smallest element in the set that is a multiple of both 8 and 12 is 24.
Therefore, the least upper bound under the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36} is 24.
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the sum of shannon and john’s ages is 70 shannon is 4 times as old as john
when using sample data to estimate a population-level relationship, why is it necessary to engage in hypothesis testing?
Hypothesis testing is an important step when using sample data to estimate a population-level relationship because it helps ensure that the conclusions drawn from the data are accurate.
Hypothesis testing allows us to determine the probability that the observed results are due to chance, rather than reflecting a real relationship between the variables. When constructing a hypothesis, we set up two competing hypotheses, the null and the alternative. The null hypothesis states that there is no relationship between the variables and that the observed results are due to chance. The alternative hypothesis states that there is a relationship between the variables and that the observed results are not due to chance.
We can then use the sample data to conduct a test of statistical significance to compare the results of the two hypotheses. This test helps us determine whether the observed results are due to chance or if they are significant enough to suggest a real relationship between the variables. In conclusion, hypothesis testing is essential when using sample data to estimate a population-level relationship because it allows us to determine the probability that the observed results are due to chance, rather than reflecting a real relationship between the variables.
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a(n) ? is a device that indicates whether two ac sources to be connected in parallel are in the correct phase relationship.
The device that indicates whether two AC sources to be connected in parallel are in the correct phase relationship is called a synchronizing device.
A synchronizing device is a mechanism that ensures that two AC sources are in sync when they are connected in parallel. It's used to match the voltage, frequency, and phase angle of two alternating current (AC) sources.
It guarantees that the power supplied by both generators is synchronized, allowing them to be combined into a single electrical system without disrupting the balance of the current or causing a short circuit.
As a result, it is critical to the safe and efficient operation of power systems. A phase sequence indicator (PSI) or a synchroscope is often used as a synchronizing device. It works by providing an indication of the voltage difference, the phase angle difference, and the frequency difference between two AC sources that are to be synchronized.
Therefore, a synchronizing device is an instrument that determines whether two alternating current (AC) sources to be connected in parallel are in the appropriate phase relationship.
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Write the integers in order from least to greatest. -6, -2, 3, -9, 2, -4
Answer:
-9, -6, -4, -2, 2, 3
Step-by-step explanation:
the higher the negative the lower it is
in the packet of mixed candies there are 2 fruit centers for every 3 caramel centers. there are 30 candies in the packet
Answer: there are 12 fruit centers and 15 caramel centers
Step-by-step explanation:
The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number?
find the sum for
1 12/15 + 1 5/15
let's firstly convert the mixed fractions to improper fractions and then add them up.
[tex]\stackrel{mixed}{1\frac{12}{15}}\implies \cfrac{1\cdot 15+12}{15}\implies \stackrel{improper}{\cfrac{27}{15}}~\hfill \stackrel{mixed}{1\frac{5}{15}} \implies \cfrac{1\cdot 15+5}{15} \implies \stackrel{improper}{\cfrac{20}{15}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{27}{15}~~ + ~~\cfrac{20}{15}\implies \cfrac{27~~ + ~~20}{\underset{\textit{denominator is the same}}{15}}\implies \cfrac{47}{15}\implies 3\frac{2}{15}[/tex]
george flips an unfair coin $7$ times. the coin has a $\frac{1}{4}$ probability of coming up heads and a $\frac{3}{4}$ probability of coming up tails. what is the probability that he flips exactly $2$ tails?
The probability of getting exactly 2 tails in 7 flips of a coin with a probability of tails being 3/4 is 189/16384 or approximately 0.0115.
We can use the binomial distribution formula to solve this problem. Let X be the number of tails that come up in 7 flips of the coin. Then X follows a binomial distribution with n = 7 and p = 3/4 (since the probability of tails is 3/4).
The probability of getting exactly 2 tails is given by:
P(X = 2) = (7 choose 2) * (3/4)^2 * (1/4)^5
= (21 * 9/16 * 1/1024)
= 189/16384
So the probability that George flips exactly 2 tails is 189/16384, or approximately 0.0115.
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I’ll give brainstorm if you do it but I’m mad confused fr
Hope this helps! You just submitted the picture and never really showed which side was a b c or anything!
By the angle bisector theorem,
[tex]\frac{5}{9}=\frac{2}{x-2}[/tex]
After cross multiplying,
5(x-2) = 2(9)
5x-10 = 18
5x = 28
x = 5.6
Solve the following quadratic function by utilizing the square root method.
Answer:
x = ±9
Step-by-step explanation:
If x² = k, then x = ±√k.
x² - 81 = 0
x² = 81
x = ±√81
x = ±9
a dance delegation of 4 people must be chosen from 5 pairs of dance partners. if 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?
There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.
In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).
Therefore, the calculation is as follows:
total number of ways = nCr
= 5C4
= 5! / 4!(5-4)!
= 5! / 4!1!
= 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1
= 5 x 4 x 3 x 2
= 120
Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
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WILL GIVE BRAINLY
If sin (x) =3 cos(x), then what is sin(x) times cos (x)?
How do I work this out?
a.) The mode for the chart is 24.
b.) The probability that the winning score will be 25 = 7/50
C.)The probability that the winning score will be 23 or more = 37/50.
How to calculate the probability of the selected outcomes?The number of times the game is played = 50 times
The number of games that showed the score of 25= 7
The probability of winning a score of 25 = 7/50
The scores that are 23 and above; 10+14+7+4+2= 37
The probability of winning a score of 23 and above = 37/50
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The speed of the ISS is 27,576 kilometres per hour.
The station travels 42,600 in 1 orbit
Work out the number of full orbits the station does in 1 day.
Answer:
15 Full orbits per day
Step-by-step explanation:
To work out the number of full orbits the ISS does in 1 day, we need to know how long it takes for the ISS to complete one orbit around the Earth.
We can use the information given to us to calculate the time it takes for the ISS to complete one orbit:
Distance traveled in one orbit = 42,600 kilometers
Speed of the ISS = 27,576 kilometers per hour
To calculate the time taken for one orbit:
Time taken = Distance traveled / Speed
Time taken = 42,600 kilometers / 27,576 kilometers per hour
Time taken = 1.54 hours (rounded to 2 decimal places)
So, the ISS takes approximately 1.54 hours to complete one orbit around the Earth.
Now, we can calculate the number of orbits the ISS does in one day:
Number of orbits per day = 24 hours / Time taken for one orbit
Number of orbits per day = 24 hours / 1.54 hours
Number of orbits per day = 15.58 (rounded to 2 decimal places)
Therefore, the ISS completes approximately 15 full orbits around the Earth in one day.
Should christians have supported the counterculture of the 1960’s? Arex there areas today in which Christians must not conform to the dominant culture? Give a specific example
We must prioritize biblical teachings and values over the cultural trends of the day. We should be salt and light to the world and live our lives in a way that honours God.
As Christians, it is our responsibility to be salt and light to the world. The dominant culture may be a reflection of the majority of the population's thoughts, but it may not necessarily align with the Bible's teachings. We should not be swayed by the current trends and instead prioritize God's standards.
The counterculture of the 1960s, according to some, promoted ideas that are contrary to Christian teachings. Many people who were part of this movement advocated for sexual freedom, drug use, and rebellion against authority. Christians should not have supported these behaviours or beliefs since they are inconsistent with biblical principles.
Likewise, in today's world, there are areas in which Christians must not conform to the dominant culture. One of the primary areas where Christians may be tempted to conform is in terms of sexual morality. Many people believe that premarital sex and homosexuality are acceptable practices, but these beliefs are not supported by the Bible.
As a result, Christians should not follow these cultural trends, but rather stick to biblical teachings and live their lives according to God's standards.Another example is in regards to materialism. The desire to accumulate wealth and material possessions is prevalent in modern culture.
Still, Christians must resist the temptation to make money and possessions their god, as this is against the Bible's teachings. Instead, we should focus on using our resources to glorify God and help others.In conclusion, Christians must be cautious about conforming to the dominant culture.
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a census reports that the mean retirement age is 68.3 years. in a random sample, the mean retirement age is 65.8 years. what is the mean of 68.3 years?
The mean retirement age in the census report is 68.3 years.
The given information states that the population mean retirement age is 68.3 years, and a random sample of retirement age has a sample mean of 65.8 years. We can use this information to estimate the population mean with a certain level of confidence.
However, the question asks us to find the mean of 68.3 years, which is simply the given population mean. Therefore, we can state that the mean of 68.3 years remains the same, as it is not affected by the sample mean or any other sample statistic.
In other words, the population mean of 68.3 years is a fixed value, and it does not change based on the sample mean or any other sample statistic. Therefore, we can simply state that the mean retirement age is 68.3 years, which is the given information provided in the question.
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A’(10, 5) is the image of A after a translation along the vector 〈−6, 0〉. What are the coordinates of A?
To perform the opposite translation, we add the opposite of the translation vector to the image point A': the coordinates of point A are (16, 5).
what is a vector?
In mathematics, a vector is an object that represents a quantity having both magnitude (or length) and direction. Vectors can be represented geometrically as arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.
To find the coordinates of point A, we need to perform the opposite translation of moving along the vector 〈−6, 0〉 from the image point A'(10, 5). This is because a translation is a rigid motion that preserves the distance between points, so the distance between A and A' is the same as the distance between their respective translations.
To perform the opposite translation, we add the opposite of the translation vector to the image point A':
A = A' - 〈-6, 0〉 = (10, 5) - (-6, 0) = (16, 5)
Therefore, the coordinates of point A are (16, 5).
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WILL GIVE BRAINLIST TO BEST ANSWER
The population of a certain town was 10,000 at the start of the year 2000. Each year, people moving into town increase the population by a net 3%, while people moving out of town decrease it by 2%. In addition, births increase the population by 5% each year.
Write a Recursive expression f(n), that shows the population at the beginning of the year n, as a function of its population the preceding year, n-1. Support your answer.
The Recursive expression f(n), that shows the population at the beginning of the year n, as a function of its population the preceding year is
f(1) = 10 000f(n) = f(n - 1) * 1.06How to write the recursive expressionThe population at the beginning of the year is given as 10 000
Let P(n) be the population at the beginning of the year n,
where
n is a positive integer.
We can express P(n) in terms of P(n-1) as follows:
P(n) = P(n - 1) + 0.03P(n - 1) - 0.02P(n - 1) + 0.05P(n - 1)
= (1 + 0.03 - 0.02 + 0.05)P(n - 1)
= 1.06P(n - 1)
Therefore, the recursive expression that shows the population at the beginning of the year n as a function of its population the preceding year is:
f(n) = 1.06f(n - 1)
This recursive formula is derived from the fact that each year,
the population increases by 3% due to people moving in and decreases by 2% due to people moving out, the population increases by 5% due to birthsResulting in a total increase of 6% per year.
The formula expresses this increase as a multiplication of the previous year's population by a factor of 1.06, resulting in the population at the beginning of the current year.
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algebra 1a/b opt #1 performance task: task linear regression
Answer:
Step-by-step explanation:
Not sure.
g a group of people were asked if they had run a red light in the last year. responded yes, and responded no. find the probability that if a person is chosen at random, they have run a red light in the last year.
The probability that a person chosen at random has run a red light in the last year can be calculated by taking the number of people who said “yes” to running a red light and dividing it by the total number of people in the group.
For example, if 10 people said “yes” and 20 said “no”, the probability of a person chosen at random running a red light in the last year is 10/30, or 1/3.
The probability of an event happening is calculated using the formula:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
In this case, the favorable outcome is running a red light in the last year, and the total number of outcomes is the total number of people asked.
To calculate the probability, we take the number of people who said “yes” to running a red light in the last year and divide it by the total number of people in the group. In our example, 10/30 = 1/3, so the probability that a person chosen at random has run a red light in the last year is 1/3.
In conclusion, the probability of a person chosen at random having run a red light in the last year is calculated by taking the number of people who responded “yes” and dividing it by the total number of people in the group.
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End of unit 4 assessment right triangle trigonometry
End of unit 4 assessment on right triangle trigonometry is an evaluation of a student's understanding of the basic concepts and applications of trigonometry involving right triangles.
This assessment may cover topics such as the trigonometric functions, Pythagorean theorem, special right triangles, and solving right triangles.
Trigonometry is the study of the relationships between the angles and sides of triangles, particularly right triangles. It is a branch of mathematics that has numerous applications in fields such as physics, engineering, and astronomy.
The trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions can be used to solve problems involving angles and sides of right triangles, such as finding the missing side or angle.
The Pythagorean theorem is another fundamental concept in right triangle trigonometry. It states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Special right triangles, such as the 30-60-90 triangle and the 45-45-90 triangle, have specific ratios of their side lengths that can be used to solve problems more easily.
Solving right triangles involves finding the measures of all the angles and sides of a right triangle given certain information, such as the length of one side and the measure of one angle.
In conclusion, the end of unit 4 assessment on right triangle trigonometry evaluates a student's understanding of the basic concepts and applications of trigonometry involving right triangles. This assessment is important for students to demonstrate their mastery of the subject and to prepare them for further studies in mathematics and related fields.
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End of unit 4 assessment right triangle trigonometry describe the importance of Side ratios in right triangles as a function of the angles ?
Find the coordinates of the vertices of the given points when reflected across the x-axis.
W (-5,0), X (0,2), Y (-1,-3)
As a result, the vertices' values when mirrored along the x-axis are W' (-5,-0), X' (0,-2), and Y'. (-1,3).
The coordinates meaning is unclear?In this case, coordinates refer to the edges of a grid structure. Latitude and longitude are often combined to form GPS measurements. Lines of latitude measure how far north and south are from the center of the earth, which is located at 0 degrees north and south.
When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
For point W (-5,0), reflecting across the x-axis results in the point W' (-5,-0).
For point X (0,2), reflecting across the x-axis results in the point X' (0,-2).
For point Y (-1,-3), reflecting across the x-axis results in the point Y' (-1,3).
Therefore, the coordinates of the vertices when reflected across the x-axis are:
W' (-5,-0), X' (0,-2), Y' (-1,3).
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HELP FAST I DONT HAVE TIME ASAP
Answer:772
Step-by-step explanation:
SA=PH+2b
SA=(10+8+10+8)(17)+2(8x10)
SA=772
Answer:
Step-by-step explanatin
multiply all of them
a rectangle's length is 5cm more than its width, if it has an area of 336 cm squared find the length
The length of the rectangle is 19 cm.
The formula for the area of a rectangle,
Area = Length x Width
Given that the area is 336 cm squared.
So, we can set up an equation,
⇒ 336 = (w + 5)w
where w represents the width of the rectangle.
Expanding this equation,
⇒ 336 = w² + 5w
Moving all terms to one side:
⇒ w² + 5w - 336 = 0
This is a quadratic equation that we can solve using the quadratic formula,
⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))
⇒ w = (-5 ± 23) / 2
We'll take the positive value,
⇒ w = 14
So, the width of the rectangle is 14 cm.
We also know that the length is 5 cm more than the width,
Therefore,
⇒ l = w + 5
⇒ l = 14 + 5
⇒ l = 19
Therefore, the length of the rectangle is 19 cm.
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What is the value of x given the following image?
ans- <CDF+<FDE=90(Being right angle)
or, 2x+x+9=90
or, 3x+9=90
or, 3x=90-9
or, 3x=81
or, x=81/3
:.x=27,,
the fact that the sample averages are not all the same is an illustration of the concept of , and the fact that the sample averages systematically overestimate the true population average is an illustration of the concept of . group of answer choices
The fact that the sample averages are not all the same can be an illustration of the concept of the central limit theorem, while the fact that the sample averages systematically overestimate the true population average can be an illustration of the concept of bias.
The given statement is incomplete, we need additional information in order to provide a solution. It is important to provide the complete statement so that we can help you in the best way possible.
However, based on the given options, we can provide a general explanation of the concepts mentioned, which are the concepts of the central limit theorem and bias.
The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases. In other words, as the sample size increases, the means of the samples drawn from a population tend to be normally distributed. The central limit theorem has important implications for statistics and hypothesis testing.
Bias, on the other hand, refers to a systematic error in data collection or analysis. Bias can be caused by a variety of factors, such as the selection of participants or the measurement instruments used. A biased sample or analysis can lead to inaccurate conclusions about a population.
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A factory produces components of which 1% are defective. The components are
packed in boxes of 10. A box is selected at random
the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.
a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).
Using the binomial probability formula, we get:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸
= 0.90438222
Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).
b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.
Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.
We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:
z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919
Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.
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Complete Question
factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.