Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).
Given that,
One day, a teacher of statistics randomly selected 10 pupils' names from a hat and instructed them to complete as many pushups as they could before class began. The 10 students who were chosen at random performed an average of 15 pushups, with a standard deviation of 9. Assume that the population's distribution of the maximum number of pushups is roughly normal.
We have to find what is the standard error of the mean.
We know that,
For this problem, we have the standard deviation for the sample, thus, the t-distribution is used.
The sample mean is of 15 is x=15 .
The sample standard deviation is of 9 is s=9.
The sample size is of 10 is n=10.
First, we find the number of degrees of freedom, which is the one less than the sample size, thus df = 9.
Then, looking at the t-table or using a calculator, we find the critical value for a 95% confidence interval, with 9 df, thus t = 2.2622
The margin of error is of:
M=ts/n
Then:
M=2.2622(9/√10)
M=6
The confidence interval is:
x±M
x-M=15-6=9
x+M=15+6=21
Therefore, Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).
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12. A clothing store has 621 blouses.
they place these on 9 racks. About the
same number of blouses were placed on
each rack. About how many blouses are
on each rack? (equation & sentence
Answer:
you have to divide
Step-by-step explanation:
621/9=69 so there are 69 blouses on each of the 9 racks
f a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance. true false
True , the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
Given :
f a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
at 10 % significance:
z score = 1.282
at 90 % confidence interval :
z score = 1.645
[tex]H_0 :[/tex] differences between population mean = 1.282
so true the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.
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Let the random variable x represent the amount of money won or lost for a player who pays $1 to play a certain carnival game. The following table shows the probability distribution of x.
The best interpretation of the mean of X is in the long run, a player will lose an average of $0.15 per carnival game played.
What do you mean by Mean?
The average of the specified collection of numbers is what is referred to as mean. It indicates a data set's values are distributed equally.
Given:
Amount = $1 $1 $10
Probability = 0.80 0.15 0.05
In mathematics and statistics, the arithmetic mean is the sum of a set of integers divided by the total number of the numbers in the set. When the context is clear, it is also referred to as the mean or average. A set of experiments or survey findings are typically included in the collection.
Hence, the correct option is (A) In the long run, a player will lose an average of $0.15 per carnival game played.
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It is more than 7+3
It is less than 8+5
Answer:
11 or 12 ....?
Step-by-step explanation:
This seems simple... so simple i feel like im overthinking it (x_x)
9 2 8 7 6 5 1 4 3 show the contents of the array above each time an insertion sort changes it while sorting the array into ascending order.
The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.
A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.
Initial Pass: 2 9 8 7 6 5 1 4 3
The array's first two members are initially compared using an insertion sort.
Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.
Therefore, 2 is currently kept in a sorted sub-array.
Second Pass: Continue with the next two elements and compare them.
2 8 9 7 6 5 1 4 3
Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.
Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.
Moving on to the following two components, which are 9 & 7,
2 7 8 9 6 5 1 4 3
Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.
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Write a rule for g(x)=f(x+2) when f(x)=x+1.
Answer:
g(x) = x+3
Step-by-step explanation:
f(x) = x+1
g(x) = f(x+2)
so g(x) = (x+2)+1
g(x)=x+3
flipping a fair two-sided coin, the probability of getting heads is equal to the probability of getting tails. if the coin is flipped three times consecutively, what is the probability of getting heads at least twice?
The probability of getting heads at least twice is 0.5
Since we are given two-sided coin, where the probability of getting heads is equal to the probability of getting tails.NO of outcomes in this case is 2,The probability of getting a head = 1/2, similarly probability of getting a tail is =1/2 .So when a coin is flipped three times, the sample space for the event will be (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT), H stands for head and T stands for tails, here for tossing the coin the number of outcomes is 8 .So the probability of getting at least two heads is: 4/8= 1/2 =0.5
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5x+4y-2x+3x+3y simplify
The Seinfeld family pays $60 per month for electricity under balanced billing. At the end of the year, they had used less electricity than the balanced billing covered, and the utility company owed them a credit of $35.
What are their total electricity expenses for the year?
Answer:
685
Step-by-step explanation:
they would normally pay 720
but they got 35 credit
720-35 is 685
Educational Technology, Inc. sells software to provide guided homework problems for a statistics course. They would like to know if students who use the software score better on exams. A sample of students who used the software had the following scores: 86, 78,66,83, 84, 81, 84, 109, 65, and 102. Students who did not use the soft-ware had the following scores:91, 71, 75,76, 87, 79, 73, 76,79, 78, 87, 90, 76, and 72. Assume the population standard deviations are not the same. At the .10 significance level, can we conclude that there is a difference in the mean scores for the two groups of students
a. What are the three assumptions for CASE C?
b. State the null and alternative hypothesis for this problem.
c. State the level of significance for this problem.
d. Which distribution (normal or t) should be used in this problem? Explain why.
e. Create a decision rule for this problem. Include the critical value. (USE TEXTBOOK TABLE.) Make sure it agrees with the excel printout.
f. Calculate the test statistic. (BY HAND). Make sure it agrees with the excel printout.
g. What is your conclusion? EXPLAIN IN DETAIL.
h. Estimate the p-value for this problem. Restate the conclusion. What is the actual p-value from the excel printout?
The assumptions are- Sample of students are independent and samples are simple random samples. Distribution is normal (t distribution). The independent variable measures on interval scale.
What is Statistics?The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are within the purview of statistics, a branch of natural science. Research in stats has application in almost all scientific domains, and software concerns in the many science disciplines inspire the creation of new statistical methods and theories. Statistics is a very multidisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the concept that supports such methods.
Uncertainty and variation are two cornerstones of the statistical profession. In science, as well as more broadly in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air.
How to solve?
ts < tc Do not reject H0
P value > α Do not reject H0
There is insufficient data to determine that the mean scores of the two groups of pupils differ.
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a researcher wants to examine the relationship between fat and calories in fast food. data was analyzed using linear regression. fat grams in the food represented x (the independent variable) and total calories in the food item was represented by y. the slope was 13 and the y intercept was 143. predict how many calories would be in a sandwich containing 32 grams of fat?
The predicted number of calories in a sandwich containing 32 grams of fat is 559.
What is the slope intercept form?In algebra, the slope-intercept form of a linear equation is a typical approach to express a line on a graph. A linear equation is written as y = mx + b in standard form.
The y-intercept, or place where the line crosses the y-axis, is represented by the letters b and m, respectively. The point where the lines contacts the y-axis is known as the y-intercept, and the slope is a measurement of how steep the line is. Because it explicitly displays the slope and y-intercept, this equation's form is known as the slope-intercept form.
y = mx + b
Where m is the slope, x is the value of the independent variable, and b is the y-intercept. In this case, the slope is 13 and the y-intercept is 143. So, the equation of the line of best fit is:
y = 13x + 143
To predict the number of calories in a sandwich containing 32 grams of fat, you can plug in 32 for x in the equation:
y = 13 * 32 + 143
y = 416 + 143
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Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?
The inequality x ≤ 20 represents the all possible values of x.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Given that,
Kelli walks not more than 25 dogs on Mondays,
Also,
Kelli walks 5 dogs that belongs to Ms. Lincoln
The inequality to find the number of dogs Kelli walks on Monday x, in addition to Ms. Lincoln's dogs, can be written as,
x+5 ≤ 25
Subtract 5 from both the sides,
x + 5 - 5 ≤ 25 - 5
x ≤ 20
The required inequality is x ≤ 20.
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the population of a town increased from 3050 in 2006 to 5500 in 2009. find the absolute and relative (percent) increase. absolute increase: relative increase: % give answers accurate to at least 1 decimal place.
In the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.
What is the percentage increase?When you want to analyze how a value has evolved over time, a percentage increase is helpful.
Although percentage increase and absolute increase are fairly comparable, the former is more helpful when contrasting different data sets.
For instance, a change from 1 to 51 and a change from 50 to 100 both have an absolute change of 50, but the first change grew significantly more due to the higher percentage growth of 5000% compared to the second change of 100%.
The most popular method of assessing growth is percentage increase because of this.
So, the absolute and relative percentage increase is:
The town's population grew from 3,250 in 2008 to 4,300 in 2010.
2008: P1 = 3250
2010: P2 = 4330
Absolute variation:
Absolute difference = P2 - P1
Absolute difference = 4330 - 3250
Absolute difference = 1050
Relative increase:
Relative percentage = P2 - P1/P1 * 100
Relative percentage = 1050/3250 * 100
Relative percentage = 32.3076
Therefore, in the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.
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Correct question:
The population of the town increased from 3,250 in 2008 to 4,300 in 2010. Find the absolute and relative(percent) increase.
which point on the unit circle corresponds to −π? responses (1, 0) begin ordered pair 1 comma 0 end ordered pair (0, −1) begin ordered pair 0 comma negative 1 end ordered pair (0, 1) begin ordered pair 0 comma 1 end ordered pair (−1, 0) begin ordered pair negative 1 comma 0 end ordered pair
(-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
Option (D) is the correct one.
Given, a unit circle
and we have to mention the point on the unit circle that corresponds to -π.
As, the equation of a unit circle is
x² + y² = 1
now -π is represented by the left side of the x-axis
therefore to represent the given point we have to take a point on x-axis that will be at the left side of the origin and at the unit distance from the origin.
So, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
Hence, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.
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Your question is incomplete kindly find the complete question below.
Which point on a unit circle corresponds to -π ?
(a) (1 , 0)
(a) (0 , -1)
(c) (0 , 1)
(d) (-1 , 0)
Answer:
(-1,0)
Step-by-step explanation:
I just took the quiz :)
Grafica y aproxima el area bajo la curva de f(x)=x³+1 en el intervalo x€[0,2]
The total area bounded by curve f(x)=x³+1 between (0,2) will be 6 units.
What is Integration ?The summing of discrete data is indicated by the integration. To determine the given functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately and integrals are calculated. The concept of limit is employed broadly in calculus whenever algebra and geometry are applied.
Given Graph = x³+1
Area between interval x€[0,2]
To get the desired area we have to integrate between x€[0,2]
[tex]\int\limits^2_0 {(x^3 + 1)} \, dx[/tex]
∫x³dx + ∫1dx
[tex]\frac{x^4}{4}[/tex] + x + c
We can find the area by lower limit - upper limit
Putting x = 0
we get result as c
Putting x = 2
We get result as 6+c
So desired area will be ( 6+c ) - c = 6
Hence the total area bounded by curve between (0,2) will be 6 units.
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What is the value of the expression below when x=3? i need help on evaluating expressions.
7x^2 -2x+2
The value of the expression 7x² - 2x + 2 when x = 3 is 59.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Based on the information given, the expression is:
7x² - 2x + 2
Put x = 3
= 7x² - 2x + 2
= 7(3)² - (2 × 3) + 2
= 63 - 6 + 2
= 59
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Please help! Lots of points and brainliest!
4 bracelets and 3 Necklaces are made by the Jeweler.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us represent Bracelet as B and Necklace as N
B+N=7..(1)
7B+18N=82..(2)
From equation 1,
B=7-N
Now plug in B value in equation 2
7(7-N)+18N=82
49-7N+18N=82
49+11N=82
Subtract 49 on both sides
11N=33
N=3
Now we have to find B
B+N=7
B+3=7
Subtract 3 on both sides
B=4
Hence, 4 bracelets and 3 Necklaces are made by the Jeweler.
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in this fulcrum, the weights are perfectly balanced. how far must the fulcrum be located from the 40 lb. weight if the bar is 9 feet long?
The distance of 40 lb will be 5ft, according to the question.
What do you mean by distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
According to the given question,
We have the given information:
The fulcrum be located from the 40 lb.
The weight of bar is 9ft long.
Now, we will calculate the distance,
40x = 50(x-1)
40x = 50x - 50
40x - 50x = -50
-10x = -50
x = 5
Therefore, the required answer is 5ft.
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PLS HELP!!! CHOICES FOR ANSWERS ARE THE SAME FOR BOTH! 50 PTS
The two-column proof shown above should be completed with the following theorems:
Statements Reasons
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
What are the types of triangle?In Geometry, there are five (5) major types of triangle based on the length of their sides and angles, and these include the following;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleWhat is CPCTC?In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it can be defined as a theorem which states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent.
By applying the corresponding parts of congruent triangles are congruent (CPCTC) theorem to triangle ABC (ΔABC), we have the following;
Statement Reason
AD ≅ CD CPCTC.
What is HL?In Mathematics, HL is an acronym for hypotenuse leg and it can be defined as a theorem which states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.
By applying the hypotenuse leg (HL) theorem to triangle ABC (ΔABC), we have the following;
Statement Reason
ΔADB ≅ ΔCDB HL.
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the time is 11:06 in 2 hours it will be
Answer:
Step-by-step explanation:
01:06
Answer:
1:06
Step-by-step explanation:
11:06 + 2:00 = 13:06
13:06-12:00= 1:6
Uppose there are three pipes filling a tank. The first pipe can fill the tank in 5 hours. The second pipe can fill the tank in 8 hours. The third pipe can fill the tank in 11 hours. How much of the tank can the first pipe fill in one hour? how much of the tank can the second pipe fill in one hour? how much of the tank can the third pipe fill in one hour?
Answer:
Step-by-step explanation:
write a function that computes a hask key for a string. the hash key is the average of the position of each letter in the alphabet divided by the size of the table. you can use the charposition() defined in the previous exercise in your calculation, this correct implementation was provided for you in this exercises.
a function that determines a string's hask key. The average position of each letter in the alphabet divided by the size of the table yields the hash key.
def char_position(char):
alphabet = list("abcdefghijklmnopqrstuvwxyz")
return alphabet.index(char)
def hash_key(string):
total = 0
for char in string.lower():
total += char_position(char)
return total / len(string)
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this exercise involves the formula for the area of a circular sector. the area of a sector of a circle with a central angle of 5????/11 rad is 15 m2. find the radius of the circle. (round your answer to one decimal place.) incorrect: your answer is incorrect. m
The radius of the circle will be 4.6m.
What is area of a circle?
The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value. The area of the circle will be A = [tex]\pi r^{2}[/tex].
The area of the circle given is = 15 m²
Sector of a circle with a central angle of 5π/11 rad
The area will be (1/2) * r² * Ф
15 = (1/2) * r² * (5π/11)
⇒r² = 30 * (11/5π)
⇒r² = 21.00
⇒r=4.6m
Hence, the radius of the circle will be 4.6m.
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How do you find the distance between these two integers? Complete the following statement that answers this question. Count the units between integer and zero. There is______ unit(s) between 0 and 1. There are______ unit(s) between 0 and 1. There are0 and -3. So, the sum of these two values is______ units.
Answer: (A) There is 1 unit between 0 and 1.
(B) There are 1 units between 0 and 1
(C) There are 0 and -3 so the sum of these two values is 3 units.
Step-by-step explanation:
How to find a distance between two integers? Easy!
First find the absolute value! Its gonna help a lot!
What are the missing angle measures in parallelogram rstu? m∠r = 70°, m∠t = 110°, m∠u = 110° m∠r = 110°, m∠t = 110°, m∠u = 70° m∠r = 110°, m∠t = 70°, m∠u = 110° m∠r = 70°, m∠t = 110°, m∠u = 70°
∠R= 110°, ∠U= 70°, ∠T= 110° are the missing angle measures in parallelogram RSTU.
A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.
Because RSTU is a parallelogram, we may use parallelogram characteristics to calculate S=U=70° ( Opposite angles of parallelogram are equal).
Using the property, sum of adjacent angles is equal to 180°, therefore,
⇒∠S+∠R= 180°
⇒70°+∠R= 180°
⇒∠R= 180°- 70°
⇒∠R=110°
Also, ∠R= ∠T= 110° (Opposite angles of parallelogram are equal).
Thus, ∠R=110°, ∠T= 110° and ∠U=70°
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I need help, please answer this?
The Answer is A: 50
just remember that the line in the middle is half of the one on the outside of the triangle
the margin of error is: a. the largest possible sampling error for a specified level of confidence; b. the critical value times the standard error of the sampling distribution; c. the difference between the point estimate and the parameter. a only b only c only a and b b and c a and c all of the above none of the above
The correct is b i.e; the critical value times the standard error of the sampling distribution
Given options are :
a. The biggest sampling error that can be made while maintaining a certain level of confidence.
b. the critical value multiplied by the sampling distribution's standard error
c. the discrepancy between the parameter and the point estimate.
Margin of error
= C * SE
Where C is critical value of on
of is the Standard error
The multiple of Critical Value and Standard error is the margin of error
Correct Option is b i. e the critical value times the Standard error of Sampling distribution
Therefore, The margin of error is the product of Critical Value and Standard Error.
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If Veronica has 4 more nickels than quarters and they have a combined value of 170 cents, how many of each coin does she have?
The total number of nickels and quarters with Veronica are 5 and 9, respectively.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of nickels be represented by x, while the number of quarters be represented by y.
It is known that a nickel is worth 5 cents, while a quarter is worth 25 cents. Therefore, the given statements can be written in the form of equations as,
Veronica has 4 more nickels than quarters,
x = y + 4
Coins have a combined value of 170 cents,
5x + 25y = 170
Substitute the value of x from the first equation in the second,
5x + 25y = 170
5(y + 4) + 25y = 170
5y + 20 + 25y = 170
30y = 170 - 20
30y = 150
y = 150/30
y = 5
Therefore, the number of quarters are 5.
Since, Veronica has 4 more nickels than quarters,
x = y + 4
x = 5 + 4
x = 9
Hence, the total number of nickels and quarters are 5 and 9, respectively.
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a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
If a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals, the dimensions are 90 feet and 120 feet
From the figure
4x + 3y = 720
3y = 720 - 4x
y = 240 - (4/3)x
The area = l × w
Where l is the length
w is the width
Substitute the values in the equation
A = 2x × y
= 2x (240 - (4/3)x)
Apply the distributive property
= 480x - (8/3)x^2
Differentiate the values
0 = (-16/3)x + 480
(16/3) x = 480
x = 480 / (16/3)
x = 90 feet
Then,
y = 240 - (4/3)(90)
= 120 feet
Hence, the dimensions are 90 feet and 120 feet
I have answered the question is general, as the given question is incomplete.
The complete question is
A rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?
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you and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. you both leave from the same point, with you riding mph east and your friend riding mph north. after you have travelled mi, at what rate is the distance between you and your friend changing? after you have travelled mi, the distance between you and your friend is changing at a rate of mph.
The distance between you and your friend is changing at a rate of 20 miles per hour.
What is the Pythagorean theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we
Let the east direction is denoted by x and
the north direction is denoted by y.
dx / dt = 16 miles per hour
dy / dt = 12 miles per hour
x = 4 miles
Let the distance between both the friends be s.
Time is taken by you to travel 4 miles,
time = distance / speed = 4 / 12 = 1/4 hour
Distance traveled by your friend in time t,
y = speed x time = 12 x 1/4 = 3 miles
By Using the Pythagorean theorem,
x² + y² = s² ..... (1)
Substitute, x = 4 mile, y = 3 mile
s² = 16 + 9 = 25
s = 5 miles
Now, Differentiate equation (1) with respect to t, we get
2x dx/dt + 2y dy/dt = 2s ds/dt
4 (16) + 3 (12) = 5 ds/dt
ds/dt = 20 miles per hour
Hence, the distance between you and your friend is changing at a rate of 20 miles per hour.
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