To study the effect of mindfulness meditation on mental health, an experimental investigation was done by comparing serum cortisol (as an indicator of stress level) between 2 groups of medical students who volunteered to participate in the study. Group 1 took a 4- day meditation program, while Group 2 did not. Volunteers from both groups then had a blood test and their serum cortisol was measured in nmol/L. Results were as follows: Group 1: 267 245 263 316 246 282 379 300 291 306 425 190 346 150 344 Group 2 470 222 443 506 455 518 360 408 375 246 189 368 Do the results support the hypothesis that meditation helps reduce stress level, with 95% confidence? You must properly identify and follow all the necessary steps for this investigation (Hint: for comparing variances, you can use 98% confidence.)
The results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.
To determine if the results support the hypothesis that meditation helps reduce stress levels, we need to perform the necessary statistical analysis. Here are the steps involved:
Step 1: Define the hypothesis:
The null hypothesis (H₀) is that there is no significant difference in stress levels between the two groups.
The alternative hypothesis (Hₐ) is that there is a significant difference in stress levels between the two groups, with meditation reducing stress.
Step 2: Identify the appropriate statistical test:
Since we are comparing the means of two independent groups and want to test if there is a significant difference, we can use an independent samples t-test.
Step 3: Set the significance level:
The significance level (α) is the probability of rejecting the null hypothesis when it is true. In this case, we will use a significance level of 0.05, corresponding to a 95% confidence level.
Step 4: Calculate the sample statistics:
Calculate the means, standard deviations, and sample sizes for both groups.
Group 1:
Mean (x1) = (267 + 245 + 263 + 316 + 246 + 282 + 379 + 300 + 291 + 306 + 425 + 190 + 346 + 150 + 344) / 15 = 290.2
Standard deviation (s1) = 70.764
Sample size (n1) = 15
Group 2:
Mean (x2) = (470 + 222 + 443 + 506 + 455 + 518 + 360 + 408 + 375 + 246 + 189 + 368) / 12 = 377.5
Standard deviation (s2) = 109.057
Sample size (n2) = 12
Step 5: Conduct the statistical test:
We can now perform an independent samples t-test using the sample statistics.
Step 5a: Test for equal variances:
Before conducting the t-test, we need to check if the variances of the two groups are equal. We can use a F-test to compare the variances.
Null hypothesis (H₀): The variances of the two groups are equal.
Alternative hypothesis (Hₐ): The variances of the two groups are not equal.
Using a significance level of 0.02 (98% confidence), we can calculate the F-statistic and compare it to the critical F-value from the F-distribution table.
F = s1² / s2² = 70.764² / 109.057² = 0.428 (approximately)
The critical F-value for a 98% confidence level with (n1-1) = 14 and (n2-1) = 11 degrees of freedom is 3.72.
Since our calculated F-value is smaller than the critical F-value, we fail to reject the null hypothesis. Thus, we can assume equal variances.
Step 5b: Conduct the t-test:
Since the variances are assumed to be equal, we can perform the independent samples t-test using the sample means and pooled standard deviation.
Pooled standard deviation (sp) = √(((n1 - 1) × s1² + (n2 - 1) × s2²) / (n1 + n2 - 2)) = √(((15 - 1) × 70.764² + (12 - 1) × 109.057²) / (15 + 12 - 2)) = 90.362
t = (x1 - x2) / (sp × √(1/n1 + 1/n2)) = (290.2 - 377.5) / (90.362 × √(1/15 + 1/12)) = -2.227
Degrees of freedom (df) = n1 + n2 - 2 = 15 + 12 - 2 = 25
Using the t-distribution table or a statistical software, we can find the critical t-value for a two-tailed test at a significance level of 0.05 with 25 degrees of freedom. The critical t-value is approximately ±2.060.
Since our calculated t-value (-2.227) is smaller than the critical t-value (-2.060), we reject the null hypothesis and accept the alternative hypothesis. Therefore, there is evidence to support the claim that mindfulness meditation helps reduce stress levels, with a 95% confidence level.
In conclusion, the results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.
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what two numbers add up to 6 but multiply to -72?
Answer:
12 x -6 is -72 and -6 + 12 is 6 so 12 and -6 is the answer
Step-by-step explanation:
Answer:
-6 and 12.Step-by-step explanation:
Equations to check:
-6 + 12 = 6.-6 * 12 = -72.The 2 numbers that add up to 6, but multiply to -72 are - 6 and 12.
Brainliest please.
What is the measure of the arc from A to B that does not pass through C?
a. 160 degrees
b. 140 degrees
c. 100 degrees
d. 90 degrees
Answer:
a
Step-by-step explanation:
The scale factor for a model is 8 cm m Model : 11.23cm actual: 40.2 m
My guys do you thing I am giving brainliest
Answer: B
Step-by-step explanation:
How do you find the inverse of a modulo?
You need to find a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This can be done using the extended Euclidean algorithm, and the resulting inverse is the residue of the coefficient modulo the modulus.
Finding the inverse of a modulo involves finding a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This process is important in modular arithmetic, where calculations are performed with remainders of a fixed integer modulus.
To find the inverse of a modulo, you can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor of two integers.
The steps for finding the inverse of a modulo are as follows:
1. Identify the number you want to find the inverse of (let's call it "a") and the modulus (let's call it "m").
2. Use the extended Euclidean algorithm to find the greatest common divisor of "a" and "m", and the coefficients x and y such that ax + my = gcd(a,m).
3. If gcd(a,m) = 1, then "a" has an inverse modulo "m" and the inverse is given by x mod m.
4. If gcd(a,m) is not equal to 1, then "a" does not have an inverse modulo "m".
In step 3, x mod m represents the residue of x modulo m, which is the unique non-negative integer less than m that is congruent to x modulo m. In other words, it is the remainder when x is divided by m.
For example, to find the inverse of 5 modulo 7, we can use the extended Euclidean algorithm to find that 2(5) + (-1)(7) = 1. Therefore, the inverse of 5 modulo 7 is 2.
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what is the distance along the unit circle between any two successive 8th roots of 1?
a. π/8
b. π/6
c. π/4
d. π/2
The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.
To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.
Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.
Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.
Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.
Therefore, the correct answer is option c. π/4.
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Create a table to match the word problem below and solve,
Guorts
Jenny was making omelets for her
farnily for breakfost. For every omelet she used 3 eggs
4 ounces of cheese, How many eggs and ounces of cheese did she use if there ore 5 people in
her family?
Sure! Here's a table to represent the information given in the word problem: Item Amount per Omelet Eggs 3 Cheese 4 ounces To find out how many eggs and ounces of cheese Jenny used for her family.
we need to multiply the amounts per omelet by the number of omelets she made. Since there are 5 people in her family, we assume she made one omelet per person. Therefore, she made a total of 5 omelets Using the table, we can calculate: Eggs: 3 eggs per omelet × 5 omelets = 15 eggs Cheese: 4 ounces of cheese per omelet × 5 omelets = 20 ounces of cheese So, Jenny used 15 eggs and 20 ounces of cheese for her family.
To find out how many eggs and ounces of cheese Jenny used for her family, we need to multiply the amounts per omelet by the total number of omelets she made. Since there are 5 people in her family, she needs to make 5 omelets Using the table, we can calculate Eggs: 3 eggs per omelet × 5 omelets = 15 eggs Cheese: 4 ounces of cheese per omelet × 5 omelets = 20 ounces of cheese.
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For what reason did Franklin take apart essays and put them back together again
Franklin wrote his autobiography for a number of reasons: to "remember" and relive his life, perhaps more perfectly, as he said at the beginning; to provide some genealogical anecdotes to his son; to bow before his friends To their flattery, he owes society an account of his life.
Benjamin Franklin was an American polymath author, scientist, inventor, statesman, diplomat, printer, publisher, forger, and political philosopher. Among the leading intellectuals of the time, Franklin was one of the founding fathers of the United States, the drafter and signer of the American Declaration of Independence, and the first postmaster of the United States.
As a scientist, he was an important figure in American Enlightenment history and physics as he studied electricity and mapped and named the Gulf Stream. As an inventor, he is known for the lightning bolt, bifocal glasses, and the Franklin stove, among others. He founded many civic organizations, including the Library Company, Philadelphia's First Fire Department, and the University of Pennsylvania. Franklin earned the title of "First American" for his early and tireless efforts to unify the colonies and for his work in London as a writer and spokesperson for several colonies. As the first United States Ambassador to France, he exemplified America's rise to power.
Franklin defined the American spirit as the combination of practical values of economy, industry, education, community spirit, self-government, and opposition to political and religious authoritarianism with the values of science and tolerance. clarification. In the words of historian Henry Steele Commager, "In Franklin it was possible to combine the virtues of faultless Puritanism, the lightness of Enlightenment without enthusiasm." Franklin has been called "the most able and influential American inventor in this type of society". America will become.
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A relationship is proportional when the ratio of y over x is
y/x is equivalent to a constant and is equal to [m].
What is the general equation of a Straight line?The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}
(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}
x/a + y/b = 1 {intercept form}
x cos(β) + y sin(β) = L {Normal form}
We have a relationship that is proportional when the ratio of [y] over [x].
The equation of a straight line -
y = mx + c
can be used to represent proportional relationship when [c] = 0. Now -]
y = mx
m = y/x
Now, y/x is equivalent to a constant and is equal to [m].
Therefore, y/x is equivalent to a constant and is equal to [m].
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Which are correct representations of the inequality 6x greater than or equal to 3 + 4(2x-1)? Select three options.
Answer:
I know for sure the first 2 are answers. As for the third, I'm not sure...
Step-by-step explanation:
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied.
Surveying 20 college students and recording their favorite TV showSurveying 20 college students and recording their favorite TV show.
Choose the correct answer below.
A. No, because there are more than two possible outcomes and the trials are not independent.
B. Yes comma because all 4 requirements are satisfied.Yes, because all 4 requirements are satisfied.
C. No comma because there are more than two possible outcomes.No because there are more than two possible outcomes.
D. No, because the probability of success does not remain the same in all trials.
The given procedure does not result in a binomial distribution because it does not satisfy the criteria of having only two possible outcomes and independent trials.
No, this procedure does not result in a binomial distribution. In order for a distribution to be binomial, it must meet four criteria: (1) there must be a fixed number of trials; (2) the trials must be independent; (3) there must be only two possible outcomes (i.e., success or failure); and (4) the probability of success must remain the same in all trials.
In the given procedure, there are more than two possible outcomes (i.e., the different TV shows that the college students can choose) and the trials are not independent. Therefore, the procedure does not satisfy two of the four criteria necessary for a binomial distribution.
A binomial distribution can be described by the formula:
\(P(x) = nCx * p^x * (1 - p)^(n - x)\)
where n is the number of trials, x is the number of successes, and p is the probability of success. Since the given procedure does not meet the criteria for a binomial distribution, this formula does not apply.
The given procedure does not result in a binomial distribution because it does not satisfy the criteria of having only two possible outcomes and independent trials.
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Select one of the options below as your answer:
A. Gary: The balance in his check register is $500 and the balance in his bank statement is $500.
B. Gail: The balance in her check register is $400 and the balance in her bank statement is $500.
C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.
The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.
The check register shows a balance of $500, while the bank statement shows a balance of $510.
In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.
A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.
For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.
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Show that the equation x ^ 3 + 6x - 10 = 0 has a solution between x = 1 and x = 2
Find the percent of decrease. Round to the nearest whole percent.
old: 374 boxes; new: 130 boxes
Answer:
B
Step-by-step explanation:
the graph shows a probability distribution. which probabilities are equal to 0.3? select each correct answer. p(5≤x≤8) p(x≤3) p(x≥3) p(3≤x≤5)
There is no graph provided for reference, but if the graph shows a probability distribution, then the probabilities that are equal to 0.3 would depend on the specific shape and values displayed on the graph.
Without this information, it is impossible to determine which probabilities are equal to 0.3. Based on the given information, the graph represents a probability distribution. To determine which probabilities are equal to 0.3, you would need to analyze the graph (which is not provided). However, I can explain each term:
1. p(5≤x≤8): This represents the probability that x falls between 5 and 8, inclusive.
2. p(x≤3): This denotes the probability that x is less than or equal to 3.
3. p(x≥3): This signifies the probability that x is greater than or equal to 3.
4. p(3≤x≤5): This indicates the probability that x falls between 3 and 5, inclusive.
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g (x) =-3x-4
f (x)=x2-2
Find (g+f) (2)
Answer:
(-3x-4+x^2-2)(2)=(x^2-3x-6)(2)
=(2^2)-3(2)-6
=4-6-6
=-8
a circle has a radius of 16in. find the length s of the arc intercepted by a central angle of π/6 radians. do not round any intermediate computations, and round your answer to the nearest tenth. s=in
Answer:
Central angle intercepted by arc is 0.7 radian
Step-by-step explanation:
What property is 5 · 12 · 25 = 5 · 25 ·12
This is the Communative property of multiplication
Answer:
associative property, 5 can be an associate to both 12 and 25
x - 12 = -48 *
pls help quick
Answer:
x = -36
Step-by-step explanation:
Add 12 to both sides
x - 12 + 12 = x
(12 cancels out)
-48 + 12 = -36
x = -36
you lose one quarter, 2 dimes, and 2 nickels
write the amount as a decimal
and as a fraction
Draw a rectangular array on graph paper for 24 x 18. Solve the problem 24 x 18 using the partial-products algorithm. Use your array to explain why the partial-products algorithm calculates the correct answer to 24 x 18.
To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.
The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.
For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.
The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.
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PLEASE HELP ASAP SHOE YOUR WORK!!!! Best answer gets brainliest :)
Answer:
Height = 3cm
Volume = 50.27cm^3
Step-by-step explanation:
Well to solve for the height with slant height and radius we can use the Pythagorean Theorem,
Which is \(a^2 + b^2 = c^2\).
So we have c and a, so we have to fill those in.
(4)^2 + b^2 = (5)^2
16 + b^2 = 25
-16
b^2 = 9
\(\sqrt{b} \sqrt{9}\)
b = 3cm
So to find the volume of a cone we use the following formula \(\pi r^2 \frac{h}{3}\).
So we have the radius and height so we just fill those in.
(pi)(4)^2(3)/3
(pi)16(1)
pi*16
About 50.27cm^3
question is in the picture
Answer:
18 tables: $143
t tables: $35 + $6t
Step-by-step explanation:
35 + 6t
35 + 6(18) = 35 + 108 = 143
Solve the system by graphing.
y = 4x + 2
y = 3x - 3
F (-2,3)
G. (2,3)
H. (2,3)
I
(2,3)
Answer:
Step-by-step explanation:
The point of intersection is (-5,-18).
Look at the attached image below.
match the type of attention with its impact on the encoding process.
Type of Attention Impact on Encoding Process
1. Sustained attention Facilitates thorough encoding of information.
2. Selective attention Enhances encoding of attended stimuli while filtering out irrelevant information.
3. Divided attention Impairs encoding by dividing attentional resources among multiple tasks.
4. Exogenous attention Captures attention involuntarily, potentially interrupting the encoding process.
5. Endogenous attention Voluntarily directed attention that can prioritize specific information for encoding.
1. Sustained attention: Sustained attention refers to the ability to maintain focus over an extended period. It has a positive impact on the encoding process as it allows for thorough and comprehensive encoding of information.
2. Selective attention: Selective attention involves focusing on specific stimuli while filtering out irrelevant information. It enhances the encoding process by directing attention to the relevant stimuli, promoting their effective encoding.
3. Divided attention: Divided attention refers to the attempt to allocate attention to multiple tasks simultaneously. Dividing attention among multiple tasks impairs the encoding process as attentional resources become fragmented, leading to less effective encoding of information.
4. Exogenous attention: Exogenous attention is captured involuntarily by external stimuli, potentially interrupting the encoding process. It can divert attention away from the intended encoding task, resulting in a negative impact on encoding.
5. Endogenous attention: Endogenous attention is voluntarily directed attention that allows individuals to prioritize specific information for encoding. It enhances the encoding process by selectively focusing on relevant stimuli and allocating cognitive resources accordingly.
Different types of attention have varying impacts on the encoding process. Sustained attention and selective attention positively influence encoding, while divided attention and exogenous attention have negative effects. Endogenous attention, on the other hand, can enhance encoding by prioritizing specific information.
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the population of a small city grows by 600 every year. If there were 900 people initially, find the population of the city 60 years after the city was first established
Answer:
36900
Step-by-step explanation:
It's a linear function with equation P(t)=900+600*t. P(60)=900+600*60=36900
Answer:
36,900
Step-by-step explanation:
First do 600 times 60=36,000
Next add 900
36,000+900=36,900
theres your answer :)
Solve the equation without graphing
21 = 256
Answer:
no solution
Step-by-step explanation:
21 does not equal 256
9 slices from 1 cake =
slices from 2 cakes
Answer:
18?
Step-by-step explanation:
Well uh since it's 2 cakes wouldn't you multiply 9 by 2?
I mean I tried given the little information in the question so
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.
Answer:
Average speed of boat = 3.67 km/h
Average speed of stream = 0.63 km/h
Step-by-step explanation:
30 km upstream in 10 hours gives a speed of 30/10 = 3 km/h relative speed of boat and stream
Same way, 44 km in 10 hrs = 4.4 km/h relative speed of boat and stream.
Let the speed of the stream be y
Let the speed of both be x, then
x - y = 3.... (1)
x + y = 4.4.... (2)
Subtract 1 from 2
2y = 1.4
y = 1.4/2 = 0.7 km/h
substitute value of y in 1
x - 0.7 = 3
x = 3.7 km/h
Also, 40 km upstream in 13 hrs gives speed of 3.08 km/h
55 km in 13 hrs gives 4.2 km/h
Let speed of boat be x and that of stream be y
x - y = 3.08.... (1)
x + y = 4.2..... (2)
Subtract 1 from 2
2y = 1. 12
y = 0.56 km/h
Substitute value of y in 1
x - 0.56 = 3.08
x = 3.64 km/h
Average speed of boat = (3.7 + 3.64)/2
= 3.67 km/h.
Average speed of stream = (0.7 + 0.56)/2 = 0.63 km/h
Answer:
Let the speed of boat in stream be x km/hrAnd the speed of boat in still water be y km/hr.For upstream = x - yFor downstream = x + yAs we know that,
\(\bigstar \: \: \sf Time = \dfrac{Distance}{Speed} \\ \\ \)
\(\bigstar\:\underline{\boldsymbol{According\: to \:the\: Question\:now :}} \\\(
\(:\implies \sf \dfrac{30}{x - y} + \dfrac{44}{x + y} = 10 \\ \\ \\ \)
\(:\implies \sf \dfrac{40}{x - y} + \dfrac{55}{x + y} = 13 \\ \\ \\\)
\(\sf Let \: \dfrac{1}{x - y} = \textsf{\textbf{m}} \sf \: \: and \: \: \sf{\dfrac{1}{x + y} = \textsf{\textbf{n} }}\\ \\ \\\)
\(:\implies \sf 30m + 44n = 10\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (i)}}\Bigg\rgroup \\ \\ \\\)
\(:\implies \sf 40m + 55n = 13\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (ii)}}\Bigg\rgroup \\ \\ \\\)
\(\qquad\tiny \underline{\frak{ Multiply \: equation \: (ii) \: by \: 3 \: and \: equation \: (i) \: by \: 4 :}} \\\)
\(:\implies \sf 120m + 176n = 40\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iii)}}\Bigg\rgroup \\ \\ \\\)
\(:\implies \sf 120m + 165n = 39\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iv)}}\Bigg\rgroup \\ \\ \\\)
\(\qquad\tiny \underline{\frak{ Substracting \: equation \: (iii) \: from \: equation \: (iv) \: we \: get :}} \\\)
\(\sf 120m + 176n = 40 \\ \\
\sf 120m + 165n = 39 \\ \\ \)
\(\sf \: \: ( - ) \:\:\: \: \: ( - ) \: \: \: \: \: \: \: ( - ) \)
_____________________
\(\: \: \: \: \qquad\sf 11n= 1 \\\)
\(\: \: \: \: \: \qquad\sf n= \dfrac{1}{11} \\ \\ \)
\(\qquad\tiny {\frak{ Put\: n = \dfrac{1}{11}\:in\:equation \: (i) \: we \: get :}} \\\)
\(\dashrightarrow\:\:\sf 30m + 44 \times \dfrac{1}{11} = 10 \\ \\ \\\)
\(\dashrightarrow\:\:\sf 30m= 10 - 4 \\ \\ \\\)
\(\dashrightarrow\:\:\sf 30m= 6 \\ \\ \\\)
\(\dashrightarrow\:\:\sf m= \dfrac{6}{30} \\ \\ \\ \)
\(\dashrightarrow\:\:\sf m= \dfrac{1}{5} \\ \\ \\\)
____________________....\(\dashrightarrow\:\:\sf \dfrac{1}{x - y} = m\\ \\ \\\)
\(\dashrightarrow\:\:\sf x - y= 5\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (v)}}\Bigg\rgroup \\ \\ \\\)
\(\dashrightarrow\:\:\sf \dfrac{1}{x + y} = n\\ \\ \\\)
\(\dashrightarrow\:\:\sf x + y= 11\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (vi)}}\Bigg\rgroup \\ \\ \\\)
\(\qquad\tiny {\frak{Adding\:equation \: (v) \: and \: equation \: (vi) \: we \: get :}} \\\)
\(:\implies \sf 2x = 16 \\ \\ \\\)
\(:\implies \underline{ \boxed{ \textsf {\textbf{x = 8 km/hr}}}} \\ \\\)
\(\qquad\tiny {\frak{Putting\:x = 8\: in \: equation \: (v) \: we \: get :}} \\\)
\(:\implies \sf 8 - y = 5 \\ \\ \\ \)
\(:\implies \sf y = 8 - 5 \\ \\ \\\)
\(:\implies \underline{ \boxed{ \textsf {\textbf{y = 3 km/hr}}}} \\ \\\)
_________________....\(\bigstar\:\underline{\sf{Therefore\: speed\: of \:boat\: in\: still \:water\: and\: speed\: of\: stream:}} \\\)
\(\bullet\:\:\textsf{Speed of boat in stream = \textbf{8 km/hr}}\\\)
\(\bullet\:\:\textsf{Speed of boat in still water = \textbf{3 km/hr}}\\\)