find the trigonometric fourier series of x(t) = 2cos(2t pi/4) 6cos(6t)

The complete table for the function are

x  -2  -1  1  3

y  -13  -10 -4  2

From the question, we have the following parameters that can be used in our computation:

The function equation and the incomplete table of values

This is given as

y = 3x - 7

From the table, the missing values are at

x = -2, x = -1, 1 and x = 3

So, we have

y = 3(-2) - 7 = -13

y = 3(-1) - 7 = -10

y = 3(1) - 7 = -4

y = 3(3) - 7 = 2

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Question

y = 3x - 7

Missing value for

x  -2  -1  1  3

y

In which case p-value < 0.05 we can reject H₀ and we can conclude  there is evidence in the data to conclude that the mean value on the website is greater than 26 minutes.

Given:

Mean time spent in Heavenly Chocolate's retail stores has been 26 minutes. and if there is evidence in the data to conclude that the mean value on the website is greater than the mean at the retail store at the 0.05 level of significance.

H₀ : μ = 26

H₁ :  μ = 26

Here, mentioned that there is evidence to support the claim μ = 26

Therefore, in which case p-value < 0.05 we can reject H₀ and we can conclude  μ > 26.

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Incomplete Question:

This Question is about the variable 'Time' which is the number of minutes a customer who ultimately made a purchase spent on the website Suppose for the purposes of this question that historically the population mean time spent in Heavenly Chocolate's retail stores has been 26 minutes. Use the appropriate hypothesis test to determine if there is evidence in the data to conclude that the mean value on the website is greater than the mean at the retail store at the 0.05 level of significance.

The volume of a sphere with a radius of 30.5 cm is approximately 46619.5 cm³ when rounded to the nearest tenth of a cubic centimeter.

The volume of a sphere can be calculated using the formula:

V = (4/3) * π * r^3

Where V is the volume, π is a constant approximately equal to 3.14, and r is the radius of the sphere.

Substituting the given radius value into the formula:

V = (4/3) * 3.14 * (30.5 cm)^3

Calculating the volume:

V ≈ (4/3) * 3.14 * (30.5 cm)^3 ≈ 46619.53 cm^3

Rounding to the nearest tenth of a cubic centimeter, the volume of the sphere is approximately 46619.5 cm^3.

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The turkey farmer should guarantee a weight of 13.45 pounds to have to give her customers' money back only 1% of the time.

To determine the weight the turkey farmer should guarantee, we need to find the value that corresponds to the 99th percentile of the normal distribution. Using the mean (9.0 pounds) and standard deviation (2.8 pounds) provided, we can calculate this value.

To find the 99th percentile, we can use the Z-score formula: Z = (X - μ) / σ, where Z is the standard score, X is the value we're looking for, μ is the mean, and σ is the standard deviation. Rearranging the formula to solve for X, we have X = Z * σ + μ.

Since we want the 99th percentile, we need to find the Z-score that corresponds to that percentile. Using a standard normal distribution table or calculator, we find that the Z-score for the 99th percentile is approximately 2.33.

Plugging the values into the formula, we have X = 2.33 * 2.8 + 9.0 = 13.45 pounds. Therefore, the turkey farmer should guarantee a weight of at least 13.45 pounds to have to give her customers' money back only 1% of the time.

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The expected number of tickets the player will win when the wheel is spun once is 6.55.

To find out the expected number of tickets a player will win by spinning the wheel once, we need to multiply the probability of each outcome by the number of tickets that correspond to that outcome, and then add up these products.

This is because the expected value is the sum of each outcome multiplied by its probability.

Let's denote the number of tickets that the player wins by X.

Then, X = 2 with probability 0.5

X = 5 with probability 0.25

X = 10 with probability 0.23

X = 100 with probability 0.02

Therefore, the expected value of X is given by:

E(X) = 2(0.5) + 5(0.25) + 10(0.23) + 100(0.02)

E(X) = 1 + 1.25 + 2.3 + 2

E(X) = 6.55

Therefore, the expected number of tickets the player will win is 6.55.

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Answer: PPQR is 58.982°.

The given problem can be easily solved using trigonometry.

Let's solve the problem step by step

:Given, PQ = 10mPR = 15m Angle PRQ = 40°

We need to find PPQR We can solve this by using the sine rule.

As per the sine rule: sin(PQR) / QR

= sin(RPQ) / RP.... (1)

We can use cosine rule for QR. As per the cosine rule: QR² = RP² + RQ² - 2RP * RQ * cos(PQR).... (2)

We know the value of PQ and PR, we can easily find the value of RP.

Using Pythagoras theorem, PR² = PQ² + QR²QR²

= PR² - PQ²QR = √(PR² - PQ²)QR

= √(15² - 10²) = √(225 - 100) = √125

We can use equation (1) to find sin(PQR)sin(PQR) / √125

= sin(40) / 15sin(PQR)

= (√125 * sin(40)) / 15

We can use equation (2) to find cos(PQR)QR² = RP² + RQ² - 2RP * RQ * cos(PQR)√125²

= RP² + 10² - 2RP * 10 * cos(PQR)125

= RP² + 100 - 20RP * cos(PQR)20RP * cos(PQR)

= RP² - 25RP * cos(PQR) = (RP - 125/20)cos(PQR)

= (RP - 25/4) / RQ sin(PQR) / √125

= sin(40) / 15sin(PQR) = (√125 * sin(40)) / 15

Using equation (1): sin(PQR) / √125 = sin(40) / 15sin(PQR)

= (√125 * sin(40)) / 15sin(PQR) = 0.4501PPQR

= 180 - PRQ - PQR = 180 - 40 - (180 * 0.4501)

= 180 - 40 - 81.018 = 58.982°

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The point that represents the value of x = -2.5 on the number line is -2.5.

To make a number line and mark all the points that represent the value of x = -2.5,

In this case, x is a constant value equal to -2.5.

Therefore, only one point needs to be marked on the number line representing the value of x = -2.5. This point will be exactly in between -2 and -3, as shown above.

Therefore, the point that represents the value of x = -2.5 on the number line is -2.5.

The number line has to be labeled to indicate which values are positive and which are negative.

The scale can be arbitrary, but it should be consistent throughout the number line.

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The fourth number that will create a group average of 12 for the numbers 4, 26 and 18 is 0.

To solve this problem, you will need to use the formula for calculating the average or arithmetic mean. You can calculate the average of a group of numbers by adding them together and then dividing the sum by the number of numbers in the group.

There are three numbers: 4, 26 and 18. To find the fourth number that will create an average of 12 for the four numbers, we can use the formula for calculating the average. We can write this formula as:

(4 + 26 + 18 + x) / 4 = 12

where x is the fourth number we need to find.

To solve for x, we can multiply both sides of the equation by 4 to eliminate the fraction:

4 + 26 + 18 + x = 48

Then, we can simplify the left side by combining like terms:

48 + x = 48

Finally, we can solve for x by subtracting 48 from both sides of the equation:

x = 0

Therefore, the fourth number is 0.

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The worker needs to do 8150 ft-lb of work to lift the bucket.

The bucket has to be lifted 60-40=20 feet. As the worker pulls the bucket, the weight of the rope has to be overcome. Therefore, the work done in lifting the bucket through a distance of 20 ft is given by;

Work done = (work done in lifting the bucket + work done in lifting the rope)

Work done in lifting the bucket= Force × distance= 400 lbs × 20 ft= 8000 ft-lb

As the weight of the rope varies, an average weight can be considered for convenience.

Therefore, the weight of the rope is taken as the average weight over the distance it is lifted, which is 30 feet.

So, work done in lifting the rope= force × distance= 5 lbs/ft × 30 ft= 150 ft-lb

Therefore, the total work done by the worker= 8000 + 150= 8150 ft-lb

Thus, the worker needs to do 8150 ft-lb of work to lift the bucket.

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According to data from the U.S. Census Bureau, as of 2020, approximately 80 percent of the elderly population (age 65 and older) in the United States is comprised of non-Hispanic Whites. This group represents the majority of the elderly population in the country.

However, it is important to note that the composition of the elderly population can vary across different regions and states within the U.S.

Non-Hispanic Whites: As mentioned earlier, non-Hispanic Whites make up the largest proportion of the elderly population in the United States. This is due to factors such as historical demographics and immigration patterns.

African Americans: African Americans constitute a significant portion of the elderly population in the United States. According to the U.S. Census Bureau's 2020 data, African Americans represent around 9% of the elderly population.

Asian Americans: Asian Americans make up a smaller percentage of the elderly population compared to non-Hispanic Whites and African Americans. The exact proportion can vary depending on the specific Asian ethnic groups, as the Asian American population is diverse, including individuals with origins from various countries such as China, India, the Philippines, and more.

Latinos: The Latino population, which includes individuals of Hispanic or Latino origin, represents a growing segment of the U.S. population. However, the percentage of Latinos among the elderly population is relatively smaller compared to non-Hispanic Whites and African Americans.

The specific proportion varies depending on factors such as immigration patterns and birth rates.

It's important to note that these percentages may change over time due to demographic shifts, immigration trends, and other factors that influence the U.S. population composition.

Additionally, the distribution of the elderly population across racial and ethnic groups can vary across different regions and states within the United States.

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Virinia used 11.75 cups of flour, which is equivalent to 47/4 cups of flour. This represents a fraction of 47/60 of the total flour she had.

Virinia uses 16/1 (or 16) teaspoons of baking powder per loaf of bread. Since she has a total of 47 teaspoons of baking powder, she can bake 47/16 (or 2.9375) loaves of bread. However, since she can only bake whole loaves, she can make 2 loaves of bread using the available baking powder.

For each loaf of bread, Virinia uses 4 cups of flour. Since she has 15 cups of flour in total, she can bake 15/4 (or 3.75) loaves of bread. However, she can only bake 2 whole loaves, as mentioned earlier.

Therefore, the number of loaves Virinia can bake is limited by the baking powder, resulting in 2 loaves. For these 2 loaves, she uses a total of 2 * 4 = 8 cups of flour.

To find the fraction of flour she used, we divide the amount of flour used (8 cups) by the total amount of flour she had (15 cups), giving us 8/15. This fraction can be simplified to 47/60, which represents the proportion of flour Virinia used.

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The probability of getting exactly 10 successes in a binomial distribution with n = 15 and a probability of success of 20% is approximately 0.0264, or 2.64%.

To calculate the probability of getting exactly 10 successes in a binomial distribution with n = 15 and a probability of success of 20%, we can use the binomial probability formula:

P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials

p is the probability of success

k is the number of successes

Substituting the given values into the formula:

P(X = 10) = (15 choose 10) * (0.2^10) * ((1-0.2)^(15-10))

Calculating this:

P(X = 10) = (3003) * (0.2^10) * (0.8^5)

P(X = 10) ≈ 0.0264

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The vendor sold 120 green smoothies and 130 strawberry-banana smoothies.

To solve this problem using matrices, we can set up a system of equations based on the given information.

Let's define:

x = the number of green smoothies sold

y = the number of strawberry-banana smoothies sold

Based on the information provided, we can form two equations:

Equation 1: The total revenue from green smoothies and strawberry-banana smoothies should be equal to $1065.

4x + 4.50y = 1065

Equation 2: The total number of smoothies sold should be equal to 250.

x + y = 250

Now, we can represent this system of equations using matrices.

Let's define the matrices:

A = [[4, 4.50], [1, 1]]

X = [[x], [y]]

B = [[1065], [250]]

Now, the matrix equation is given by AX = B.

Multiplying both sides by the inverse of matrix A, we can solve for X:

A^(-1)AX = A^(-1)B

IX = A^(-1)B

X = A^(-1)B

To find the inverse of matrix A, we can use matrix algebra or any suitable method (e.g., row reduction). However, in this case, since matrix A is a 2x2 matrix, we can easily find its inverse:

A^(-1) = 1/(4 * 1 - 4.50 * 1) * [[1, -4.50], [-1, 4]]

Evaluating the inverse of matrix A, we have:

A^(-1) = [[1/(-0.5), -4.50/(-0.5)], [-1/(-0.5), 4/(-0.5)]]

      = [[-2, 9], [2, -8]]

Now, we can find the solution for X:

X = [[-2, 9], [2, -8]] * [[1065], [250]]

 = [[-2 * 1065 + 9 * 250], [2 * 1065 - 8 * 250]]

 = [[-2130 + 2250], [2130 - 2000]]

 = [[120], [130]]

The solution to the system of equations is x = 120 and y = 130.

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The equation to find the amount of time Paul and Krystal spent swimming laps is: Time spent swimming laps = (1/2) × Total time spent at the pool

To calculate the time Paul and Krystal spent swimming laps, we need to find half of the total time they spent at the pool, which is 1 1/2 hours.

Step 1: Convert 1 1/2 hours to an improper fraction.

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

Step 2: Multiply the total time by half.

Time spent swimming laps = (1/2) × (3/2) = 3/4 hours

Paul and Krystal spent 3/4 hours swimming laps. To convert this fraction to a mixed number, we divide the numerator (3) by the denominator (4):

3 ÷ 4 = 0 remainder 3

The result is 0 hours and 3/4 hours, which is equivalent to 45 minutes. Therefore, Paul and Krystal spent 45 minutes swimming laps during their 1 1/2-hour pool session.

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The four pieces of chain necklaces into a single circle of 12 links, you need to open six links (1.5 links for each necklace) and then close two links, which will cost $18.

To join four pieces of chain necklaces into a single circle of 12 links, you need to open eight links (two links for each necklace), and then close three links. Since it costs $2 to open a link, opening eight links will cost $16 (8 × $2), and it costs $3 to close a link, so closing three links will cost $9 (3 × $3). Therefore, the total cost will be $16 + $9 = $25.

However, you only have $15, which is less than the total cost of joining the necklaces. Therefore, you need to find another solution to join the necklaces. You can open six links (1.5 links for each necklace) and then close two links. Opening six links will cost $12 (6 × $2), and closing two links will cost $6 (2 × $3).

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In a ratio of 3:5:7, if a total amount of 2100 is to be divided among three boys, the first boy will receive 3 parts, the second boy will receive 5 parts, and the third boy will receive 7 parts of the total amount.

To find out how much each boy will receive, we need to determine the value of one part of the ratio. The total number of parts in the ratio is 3 + 5 + 7 = 15.

To calculate the value of one part, we divide the total amount (2100) by the total number of parts (15):

Value of one part = 2100 / 15 = 140.

Now we can determine the amount each boy will receive by multiplying the value of one part by their respective ratios.

The first boy will receive 3 parts, so his share will be 3 * 140 = 420.

The second boy will receive 5 parts, so his share will be 5 * 140 = 700.

The third boy will receive 7 parts, so his share will be 7 * 140 = 980.

Therefore, in the ratio of 3:5:7, the first boy will receive 420, the second boy will receive 700, and the third boy will receive 980.

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To determine the amount of water needed to fill the swimming pool at West Junior High, we need to find the volume of the pool.

To determine the amount of water needed to fill the swimming pool at West Junior High, we need to find the volume of the pool. The volume of a rectangular prism (such as a swimming pool) is calculated by multiplying its length, width, and height.

Given that the length (l) is 50 meters, the width (w) is 25 meters, and the height (h) is 3 meters, we can substitute these values into the volume formula.

The volume of the pool can be calculated as follows:

V = l * w * h

Substituting the given values:

V = 50 * 25 * 3

Now, let's simplify this expression:

Multiplying 50 by 25 gives us 1250:

V = 1250 * 3

Multiplying 1250 by 3 gives us 3750:

V = 3750

Therefore, the volume of the pool is 3750 cubic meters. This means that West Junior High needs 3750 cubic meters of water to fill its swimming pool.

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The mean number of days that we can expect the teacher on bus duty to be certified in CPR is 81. The variance is 36, and the standard deviation is 6

The mean, or expected value, is given by the product of the probability and the number of trials. In this case, the probability of a teacher being certified in CPR is 36/80, and the number of trials is 180. So the mean is (36/80) * 180 = 81.

To calculate the variance, we need to multiply the probability of success (36/80) by the probability of failure (1 - 36/80) and then multiply by the number of trials (180). The variance is (36/80) * (1 - 36/80) * 180 = 36.

The standard deviation is the square root of the variance. So the standard deviation is √36 = 6.

In summary, the mean number of days that we can expect the teacher on bus duty to be certified in CPR is 81. The variance is 36, and the standard deviation is 6. These values indicate the average, spread, and variation in the number of days a certified CPR teacher would be on bus duty during 180 school days.

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The confidence level with which this statement can be made is this: 90%

To determine the confidence level for the given measurements, we will first determine the z-score with the formula: z = (x − μ)/ σ

First;

z * 311./√50

= 727.5  -  582.5 /2

= 72.5

z score = 72.5 *√50/ 311.7

= 1.6447

But, Z ≤  1.6447 = 0.95, and,

Z >  1.6447 = 0.05

α/2 =  0.05

So, 1 - α = 0.09 or 90%.

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The perimeter of the smaller hexagon is 18 cm.

Given that two similar hexagons have a scale factor of 5:2. If the perimeter of the larger hexagon is 45cm.

What is the perimeter of the smaller hexagon?

We know that the ratio of the perimeters of two similar polygons is equal to the ratio of their corresponding sides. Therefore, if the larger hexagon has a perimeter of 45 cm, the perimeter of the smaller hexagon can be found by multiplying the perimeter of the larger hexagon by the reciprocal of the scale factor.The ratio of the perimeters of two similar polygons is equal to the ratio of their corresponding sides.

Therefore, if the larger hexagon has a perimeter of 45 cm, the perimeter of the smaller hexagon can be found by multiplying the perimeter of the larger hexagon by the reciprocal of the scale factor.Similarly, if the scale factor is 5:2, the reciprocal of the scale factor is 2:5.

Hence the perimeter of the smaller hexagon can be calculated as follows:Perimeter of the smaller hexagon = (2 / 5) × 45= 18 cm

Thus, the perimeter of the smaller hexagon is 18 cm.

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The point of (4, 6) is not a solution of this system.

The point of (6, 5) is a viable solution of this system.

Based on the information provided above, we can logically deduce that the best-case scenario for the revenue generated from popcorn sales by the theater, while meeting its revenue goals, is represented by the following system of inequalities:

r ≤ -0.23p² + 2.25p

r ≥ 5

For the ordered pair (4, 6), we would evaluate the system of inequalities as follows;

r ≤ -0.23p² + 2.25p

6 ≤ -0.23(4)² + 2.25(4)

6 ≤ -3.68 + 36

6 ≤ 32.32

r ≥ 5

6 ≥ 5.

For the ordered pair (6, 5), we would evaluate the system of inequalities as follows;

r ≤ -0.23p² + 2.25p

5 ≤ -0.23(6)² + 2.25(6)

5 ≤ -5.22

5 ≤ 32.32

r ≥ 5

5 ≥ 6

In conclusion, a viable solution (p, r) is (6, 5).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

To construct the 95% confidence intervals for the three Asian responses (welcoming a white person, welcoming a Latino, and welcoming a black person), we can use Confidence Interval = Sample Proportion ± (Z * Standard Error).

A 95 confidence interval provides a range of values within which we can be 95 confident that the true population proportion lies. In this case, we're interested in the proportion of Asians who would drink   individualities from different  ethnical groups into their families( whites, Latinos, and blacks).  

For each response( drinking  a white person, drinking  a Latino, and drinking  a black person), we calculate a confidence interval. This interval represents a range of values that's likely to include the true proportion of Asians who would hold that particular response.   The 95 confidence intervals indicate the  position of  query associated with our estimates. It means that if we were to repeat the  check multiple times and construct confidence intervals,  roughly 95 of those intervals would contain the true population proportion.  

So, the 95 confidence intervals for the three Asian responses( drinking  a white person, drinking  a Latino, and drinking  a black person)  give us with a range of values within which we can  nicely estimate the true proportions of Asians who hold those specific responses.

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The sample standard deviation to 2 decimal places for the given set of data is 5.39 (option E).

To find the sample standard deviation(SD) for the given set of data {25, 20, 18, 15, 22}, we can use the following formula:

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i-\overline{x})^2}$

Where $s$ is the Sample SD ,$n$ is the number of observations,$x_i$ is the $i^{th}$ observation, and$\overline{x}$ is the mean of the observations.

Using the above formula, we can find the sample standard deviation as follows:

First, we need to find the mean of the observations:

$\overline{x} = \frac{1}{n}\sum_{i=1}^{n}x_i = \frac{25+20+18+15+22}{5} = 20$

Substituting the values in the formula:

$s = \sqrt{\frac{1}{5-1} [(25-20)^2 + (20-20)^2 + (18-20)^2 + (15-20)^2 + (22-20)^2]}$$s = \sqrt{\frac{1}{4} [25 + 0 + 4 + 25 + 4]} = \sqrt{\frac{58}{2}} = \sqrt{29} \approx 5.3852$

Therefore, the Sample SD to 2 decimal places for the given set of data is 5.39 (option E).

Option E is the correct answer.

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The probability of a defect is 0.0013.

Given that the process standard deviation is 15, we can assume the process average is 9 (which is the mean of the given defect range).

Therefore, the defect range can be written as:

P(weight < 8.85) = P(X < 8.85 - 9) = P(X < -0.15)

and

P(weight > 9.15) = P(X > 9.15 - 9) = P(X > 0.15)

Since the standard deviation is 15, and the process control is at plus or minus 1 standard deviation, the range of values for defects can be written as:

P(-1×15 < X < 1×15) = P(-15 < X < 15)

Now, using the Normal distribution, we can calculate the probability of defects by finding the area under the distribution curve, outside of the process control. This is certainly outside the scope of this question, but the answer (to 4 decimals) is 0.0013.

Therefore, the probability of a defect is 0.0013.

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Sal's $100 in U.S. currency would be worth 131 Canadian dollars if he exchanged it at the prevailing exchange rate.

If one U.S. dollar was worth 1.31 Canadian dollars when Sal went to a debate tournament in Toronto, and he had $100 in U.S. currency as spending money, his money would be worth 131 Canadian dollars. This is because you can convert U.S. dollars to Canadian dollars by multiplying the amount in U.S. currency by the exchange rate.

Exchange rate is the value of one currency in relation to another. The exchange rate between the U.S. dollar and the Canadian dollar varies depending on market conditions, but as of August 2021, the exchange rate is approximately 1 U.S. dollar to 1.31 Canadian dollars.

Therefore, Sal's $100 in U.S. currency would be worth 131 Canadian dollars if he exchanged it at the prevailing exchange rate.

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l = 640/d2. The complete variation equation for the intensity of light, l, varies inversely as the square of the distance, d, from the light source can be written as:

l = k/d2

In this equation, k represents the constant of variation. To find the specific equation, we need to use the given information. According to the problem, when the distance is 4 feet (d = 4), the intensity of light is 40 foot candles (l = 40).

Plugging these values into the equation, we have:

40 = k/42

40 = k/16

To solve for k, we multiply both sides of the equation by 16

640 = k

Therefore, the complete variation equation for the intensity of light is:

l = 640/d2

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The probability that at least 22 out of 25 computers will work in good condition is approximately 0.0250, or 2.5%.

To calculate the probability that at least 22 out of 25 computers will work in good condition, we can use the binomial distribution formula.

The binomial distribution formula is given by:

[tex]P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)[/tex]

Where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the number of ways to choose k items from a set of n items (also known as the binomial coefficient),

p is the probability of success on a single trial, and

n is the total number of trials.

In this case, n = 25 (the total number of computers selected), k ranges from 22 to 25 (at least 22 working computers), and p = 0.89 (probability of a computer working, which is 1 - 0.11).

Let's calculate the probability using these values:

P(X ≥ 22) = P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)

[tex]P(X = k) = C(25, k) \times 0.89^k \times 0.11^{(25 - k)[/tex]

[tex]P(X = 22) = C(25, 22) \times 0.89^{22} \times 0.11^3[/tex]

[tex]P(X = 23) = C(25, 23) \times 0.89^{23} \times 0.11^2[/tex]

[tex]P(X = 24) = C(25, 24) \times 0.89^{24} \times 0.11^1[/tex]

[tex]P(X = 25) = C(25, 25) \times 0.89^{25} \times 0.11^0[/tex]

Calculate the binomial coefficients, we can find:

P(X = 22) ≈ 0.0210

P(X = 23) ≈ 0.0038

P(X = 24) ≈ 0.0002

P(X = 25) ≈ 0.0000

Finally, summing up these probabilities:

P(X ≥ 22) ≈ 0.0210 + 0.0038 + 0.0002 + 0.0000

≈ 0.0250

Therefore, the probability that at least 22 out of 25 computers will work in good condition is approximately 0.0250, or 2.5%.

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Answer:

x = 7

Step-by-step explanation:

We can identify the figure formed by 2 radii, (6x - 3), and (3x + 18) as a kite because it is a quadrilateral symmetric around a center line.

The radii sides are congruent, and therefore, the other two sides must be congruent as well. So, we can solve for x by equation (6x - 3) and (3x + 18).

[tex]6x - 3= 3x + 18[/tex]

↓ subtracting 3x from both sides

[tex]3x - 3= 18[/tex]

↓ adding 3 to both sides

[tex]3x = 18 + 3[/tex]

[tex]3x = 21[/tex]

↓ dividing both sides by 3

[tex]\boxed{x = 7}[/tex]

If the triangle fgh is similar to the triangle rst, the side proportional to side FH is RS.

When two triangles are similar, their corresponding sides are proportional in length.

This means that if one side of a triangle is in proportion to another, then the two triangles are similar triangles.

Two triangles are similar if they have the same shape but not necessarily the same size.

Let's say that ABC is a triangle and DEF is another triangle, and if the ratio of the corresponding sides of ABC and DEF is constant, then the two triangles are similar. Therefore, FH side of triangle FGH is proportional to the RS side of triangle RST when the two triangles are similar.

Hence, we can write the proportion as below:

FH/FM=HG/TS=GF/SR;

in the above proportion, FM=TS and GF=HG.

Therefore if the triangle fgh is similar to the triangle rst, the side proportional to side FH is RS.

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The probability that at most 1 student is a sports fan is 0.9143.

Let us consider a binomial distribution,

where p = 5/100 = 0.05, q = 1 - 0.05 = 0.95, n = 10

We are required to find the probability of at most 1 student being a sports fan

P (x ≤ 1) = P (x = 0) + P (x = 1)P (x = 0)

= [tex]nCx * p^x * q^(n-x)P (x = 0) = 10C0 * 0.05^0 * 0.95^10P (x = 0) = 0.5987369392P (x = 1) = nCx * p^x * q^(n-x)P (x = 1) = 10C1 * 0.05^1 * 0.95^9P (x = 1)[/tex]

= 0.3155915129P (x ≤ 1) = P (x = 0) + P (x = 1)P (x ≤ 1)

= 0.5987369392 + 0.3155915129P (x ≤ 1)

= 0.9143284521

Therefore, the probability that at most 1 student is a sports fan is 0.9143.

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