The expected value E(X) of a random variable X is -1.04
The expected value of a random variable is a measure of its central tendency. It represents the average value that would be obtained if the experiment or process that generates the variable is repeated many times.
To find the expected value of a discrete random variable X with probability distribution P(X), we multiply each possible value of X by its corresponding probability and then sum these products. Symbolically, this can be written as:
E(X) = Σ[x * P(X)]
In words, this formula says that we take each possible value of X, multiply it by its probability, and then add up these products to get the expected value.
In the given problem, we are given the probability distribution of X and asked to find its expected value. We can use the formula above to do this, by plugging in the values of x and P(X):
E(X) = (-9 * 0.16) + (-7 * 0.11) + (-5 * 0.14) + (-3 * 0.17) + (-1 * 0.10) + (1 * 0.32)
E(X) = -1.04
Therefore, the expected value of X is -1.04.
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please help
A survey is taken at a movie theater in Winterville. The first 150 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 150 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Winterville.
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.
The population is the number of people in the town of Winterville, and the sample is the number of people who go to the movie theater.
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater is correct.
In this situation, the population refers to the entire group of individuals that are of interest to the survey. In this case, the population is the total number of people who go to the movie theater. The sample, on the other hand, refers to a subset of the population that is actually observed and surveyed. In this case, the sample is the first 150 people who entered the theater and were asked about their favorite type of movie.
It is important to note that the sample should be representative of the population in order to draw valid conclusions from the survey. This means that the individuals in the sample should be selected in a way that reflects the characteristics of the population as a whole.
In summary, the population in this situation is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater who were asked about their favorite type of movie.
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suppose iq scores are normally distributed with μ = 100 and σ = 15. what percent of iq scores are between 85 and 130?
If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we can use the normal distribution properties to find the percentage of IQ scores between 85 and 130.
Specifically, we can standardize the scores and use a normal distribution table or calculator to find the area under the curve between the z-scores corresponding to 85 and 130.To find the percentage of IQ scores between 85 and 130, we first need to standardize the scores by subtracting the mean and dividing by the standard deviation. This gives:
z1 = (85 - 100) / 15 = -1.00
z2 = (130 - 100) / 15 = 2.00
We can then use a normal distribution table or calculator to find the area under the curve between these two z-scores. For example, using a standard normal distribution table, we can find that the area to the left of z = -1.00 is 0.1587 and the area to the left of z = 2.00 is 0.9772. Therefore, the area between these two z-scores is:
0.9772 - 0.1587 = 0.8185
This means that approximately 81.85% of IQ scores are between 85 and 130. Alternatively, we can use a normal distribution calculator to find the same result. For example, using an online calculator, we can input the mean (100), standard deviation (15), and the lower and upper limits (85 and 130) and obtain a probability of 0.8185, or 81.85%.
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On a recent statewide math test, the raw score average was 56 points with a standard deviation of 18. If the scores were normally distributed and 24,000 students took the test, answer the following questions. (d) How many of the 24,000 students receive a scaled score greater than a 90%?
of the following correlation coefficients, the one indicative of the weakest linear relationship is: a. .10 b. - .90 c. - .05 d. .50 e. .85
The correlation coefficient indicative of the weakest linear relationship is option (c) -0.05. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.
Correlation coefficient ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship. Therefore, a correlation coefficient closer to 0 indicates a weaker linear relationship. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.
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4. if you draw three cards from a deck of 52 cards one at a time without replacement, what is the probability that all three cards are diamonds?
The probability of drawing three cards from a deck of 52 cards one at a time without replacement and having all three cards be diamonds is 0.0026, or approximately 0.26%.
To calculate this probability, we can use the formula for conditional probability. The probability of drawing the first diamond is 13/52, since there are 13 diamonds in the deck. Once the first diamond has been drawn, there are 12 diamonds left out of 51 cards. So the probability of drawing a second diamond, given that the first card was a diamond, is 12/51. Finally, once two diamonds have been drawn, there are 11 diamonds left out of 50 cards. So the probability of drawing a third diamond, given that the first two cards were diamonds, is 11/50. Multiplying these three probabilities together gives us the probability of drawing three diamonds in a row, which is approximately 0.0026.
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Sosssssss math problem
Answer:
22
Step-by-step explanation:
whats ur question
the numbers of letters in the mailboxes of 10 houses are given below. identify the stem-and-leaf plot that represents the given data. 10, 13, 8, 5, 4, 16, 12, 11, 7, 2
The stem-and-leaf plot is a data visualization tool that provides a quick way to see the distribution of a set of data.
The given data represents the number of letters in the mailboxes of 10 houses. To construct a stem-and-leaf plot, we group the data by their tens digit and display them as stems on the left side of the plot, and the ones digit is shown as leaves on the right side of the plot. For the given data, the stem-and-leaf plot is:
2 | 2
4 | 4 5
5 | 7 8
7 | 0 1
8 |
10 | 0 2
11 |
12 | 3
13 |
16 |
The plot shows that the majority of houses have between 4 and 13 letters in their mailboxes, with the most common numbers of letters being 7, 8, and 10. The plot also shows that there are two outliers: one house with only 2 letters and another with 16 letters in its mailbox.
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suppose that x varies directly with the square of y and inversely with the cube root of z. of x=6 when y=2 and z=8, find x when y=4 and z=27.
Please answer quick!
The value of x is 16 for the desired values of y and z.
If x varies directly with the square of y and inversely with the cube root of z, then we can write:
[tex]x = k * y^2 / z^{(1/3)[/tex]
where k is a constant of variation.
To find the value of k, we can use the given information that x=6 when y=2 and z=8:
[tex]6 = k * 2^2 / 8^{(1/3)[/tex]
Simplifying this equation:
6 = k * 4 / 2
k = 3
Now we can use this value of k to find x when y=4 and z=27:
[tex]x = 3 * 4^2 / 27^{(1/3)[/tex]
Simplifying this expression:
x = 3 * 16 / 3
x = 16
Therefore, when y=4 and z=27, x is equal to 16.
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Find the value of c.
25 ft
C=
с
Perimeter = 60 feet
feet
15 ft
Which price would lead to a shortage in the market depicted below?
Price
20
19
18
17
16
15
14
13
12
11
10
9
8
0
$10
$13
$16
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x
Quantity
The price would lead to a shortage in the market is $8.
We know that,
When the amount required exceeds the amount supplied at the going rate, there is a shortage.
Three factors primarily contribute to shortages: rising demand, falling supply, and government action.
According to the given data
At $8, there would be a shortage because there is a greater demand than there are available items.
At $8, there is a shortfall of 4 units because only 10 are available while 14 are needed.
Thus,
The price is of $8 lead the shortage.
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Use a sum-to-product formula to show the following. Sin(55°) sin(5°) = sin(65°) use a sum-to-product formula for sine and simplify
sin(55°) + sin(5°) = sin(65°) using a sum-to-product formula for sine
We can use the sum-to-product formula for sine to show that sin(55°) + sin(5°) = sin(65°). The formula is:
sin A + sin B = 2 sin[(A + B)/2] cos[(A - B)/2]
Substituting A = 55° and B = 5°, we get:
sin(55°) + sin(5°) = 2 sin[(55° + 5°)/2] cos[(55° - 5°)/2]
Simplifying, we get:
sin(55°) + sin(5°) = 2 sin(30°) cos(25°)
We know that sin(30°) = 1/2 and cos(25°) = sin(90° - 25°), so we can substitute these into the expression:
sin(55°) + sin(5°) = sin(90° - 25°)
We also know that sin(90° - 25°) = sin(65°), so we can substitute this into the expression:
sin(55°) + sin(5°) = sin(65°)
Therefore, sin(55°) + sin(5°) = sin(65°) using a sum-to-product formula for sine.
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Given question is incomplete, the complete question is below
Show that sin(55°) + sin(5°) = sin(65°)
use a sum-to-product formula for sine and simplify
For 99 Points!! Find x and decide if the triangle is Equilateral, scalene, or isosceles.
I think the triangle is scalene but I need x to be sure. I don't know where to start to find x but if someone could set up an equation I could do it. Please explain and show your work.
The value of x if the triangle is equilateral is x = -16 and x = -10
what is an equilateral triangle?An equilateral triangle is a regular polygon with all three sides of equal length. It is also equiangular, meaning that all three internal angles are congruent to each other and are each 60 degrees
If the triangle is equilateral therefore
5x + 16 = 4x and 5x + 16 = 3x - 4
5x -4x = -16
x = -16
Also, in equation 2
Also, 5x - 3x =-4 -16
2x = -20
therefore,
x = -10
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1 bag of takis cost 2.25 dollars and 1 soda cost 1.50 dollars. if he buy 16 total items and spend 30.75 dollars,how many bags of takis did he buy and how many sodas did he bug
The bags of takis did he bought is 9 and number of sodas is 7
Given data ,
1 bag of takis cost 2.25 dollars and 1 soda cost 1.50 dollars.
Now , total number of items = 16
And total amount spend = $ 30.75
The total number of items bought is 16, so we have the equation:
x + y = 16 (equation 1)
The total amount spent is $30.75, so we have another equation:
2.25x + 1.50y = 30.75 (equation 2)
Multiply equation 1 by 1.50 to make the coefficients of y the same
1.50(x + y) = 1.50(16)
1.50x + 1.50y = 24 (equation 3)
Subtract equation 3 from equation 2 to eliminate y:
(2.25x + 1.50y) - (1.50x + 1.50y) = 30.75 - 24
0.75x = 6.75
x = 6.75 / 0.75
x = 9
Substitute the value of x into equation 1 to find y:
9 + y = 16
y = 16 - 9
y = 7
Hence , the person bought 9 bags of Takis and 7 sodas
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find the area of the surface obtained by rotating the curve x=6e2y x=6e2y from y=0y=0 to y=6y=6 about the yy-axis.
The area of the surface obtained by rotating the curve x = 6e^(2y) from y = 0 to y = 6 about the y-axis is approximately 1337.47 square units.
We can use the formula for surface area obtained by rotating a curve about the y-axis:
SA = 2π∫a^b f(x)√(1+(dy/dx)^2) dx
In this case, the curve is x = 6e^(2y) and we want to rotate it from y = 0 to y = 6. So, we have:
f(x) = 6e^(2y)
dy/dx = (1/2)(1/x) = (1/2e^(2y))
(1 + (dy/dx)^2) = 1 + (1/4e^(4y))
Substituting these values into the formula, we get:
SA = 2π∫0^6 6e^(2y)√(1+(1/4e^(4y))) dy
This integral is difficult to solve analytically, so we can use numerical methods to approximate the value. Using a numerical integration method, we get:
SA ≈ 1337.47
Therefore, the area of the surface obtained by rotating the curve x = 6e^(2y) from y = 0 to y = 6 about the y-axis is approximately 1337.47 square units.
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a random sample of 49 sat scores of students applying for merit scholarships showed an average of 1300 with a standard deviation of 200. find the t value needed to develop the 95% confidence interval for the population mean sat score.
The t-value needed to develop the 95% confidence interval for the population mean SAT score is: t = 2.009
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
To find the t-value needed to develop the 95% confidence interval for the population mean SAT score, we can use the following formula:
t = (x - μ) / (s / √(n))
where:
x = sample mean (1300)
μ = population mean (unknown)
s = sample standard deviation (200)
n = sample size (49)
To find the t-value, we need to find the margin of error (ME) first:
ME = t* (s / √(n))
We know that for a 95% confidence interval, the critical value of t is 2.009 (from t-distribution table or calculator) with 48 degrees of freedom
(df = n-1).
Therefore, the t-value needed to develop the 95% confidence interval for the population mean SAT score is:
t = 2.009.
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Two of the dozen eggs in a carton are cracked. About what percent of the carton is cracked?
Answer:
About 17%.
Step-by-step explanation:
A dozen is 12.
2 out of 12 are cracked.
2 / 12 = 0.16666666666
That equals about 16.7%.
Your problem doesn't say which place to round to but this seems kind of basic so I'd write "about 17%."
HELPPPP GEOMETRY QUESTION
The value of tan(A) is equal to 3/4.
Option B is the correct answer.
We have,
To find the tangent of angle A, we can use the formula for tangent in a right triangle, which is given by:
tan(A) = opposite/adjacent
In this case,
Side a is the length of the side opposite to angle A, and side b is the length of the side adjacent to angle A.
Given that b = 12 and a = 9, we can substitute these values into the formula:
tan(A) = a/b = 9/12 = 3/4
Therefore,
The value of tan(A) is equal to 3/4.
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a triangular parcel of land has sides of lengths 860 feet, 820 feet and 1038 feet. a) what is the area of the parcel of land?
The area of the triangular parcel of land is approximately 305,682.4 square feet.
We can use Heron's formula to find the area of a triangular parcel of land. This formula states that the area of a triangle with sides a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c)/2
Using the lengths of the sides given in the problem, we can calculate the semi-perimeter:
s = (860 + 820 + 1038)/2 = 1759
Then we can plug this value into Heron's formula to find the area:
Area = √(1759(1759-860)(1759-820)(1759-1038))
Area = √(1759×899×939×721)
Area = √(93587715844)
Area = 305682.4 square feet (rounded to the nearest tenth)
Therefore, the area of the triangular parcel of land is approximately 305,682.4 square feet.
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PLEASE HELP RUGHT NOW ILL GIVE ALOT OF POINTS
There are a total of 78 students in a drama club and a yearbook club. The drama club has 12 more students than the yearbook club. How many students are in the drama club? the yearbook club?
Answer: 45
Step-by-step explanation:
Let's call the number of students in the yearbook club "x". Since the drama club has 12 more students, the number of students in the drama club would be "x+12".
We know that the total number of students in both clubs is 78, so we can set up an equation:
x + (x+12) = 78
Simplifying the equation:
2x + 12 = 78
Subtracting 12 from both sides:
2x = 66
Dividing both sides by 2:
x = 33
So there are 33 students in the yearbook club.
To find the number of students in the drama club, we can substitute x = 33 into the equation we set up earlier:
x + 12 = 33 + 12 = 45
Therefore, there are 45 students in the drama club.
Answer:
year book club= 33 people
drama club = 45 people
Step-by-step explanation:
78 students in total
drama : year book
x+12 x
x+12+x=78
2x+12=78
2x=66
x=33
year book= 33
drama= 45
a slice of cheese is cut from a wheel of parmesan, and the wedge approximates the shape of a rectangular pyramid. its base is 4 cm wide and 9 cm long. the wedge is 21 cm tall. what is the volume of the piece of cheese?(1 point)
The volume of the piece of cheese is 252 cubic centimeters (cm³).
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length. It is a type of quadrilateral, a polygon with four sides. The length of the sides that are parallel to each other is called the base, and the length of the sides that are perpendicular to the base is called the height.
The volume of a rectangular pyramid is given by the formula:
V = (1/3) * base area * height
The base area of the wedge is 4 cm * 9 cm = 36 cm².
Substituting the given values into the formula, we have:
V = (1/3) * 36 cm² * 21 cm = 252 cm³
Therefore, the volume of the piece of cheese is 252 cubic centimeters (cm³).
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How many different triangles can be drawn with side lengths of 15 centimeters, 28 centimeters, and 12 centimeters?
A. 0
B. Exactly 1
C. Exactly 2
D infinitely many
(q74) The dye dilution method is used to estimate cardiac output using 7 mg of dye. The dye concentration is modeled by the function c(t) = 2t(4 - t). The dye concentration is expressed in mg/L and t is measured in seconds. Estimate the cardiac output for the time interval [0, 4].
Integrating the concentration between 0 and 4, we can see that the correct option is A.
How to estimate the carciac output?We know that the concentration is given by the quadratic equataion:
c(t) = 2t(4 - t)
To find the cardiatic output for the time interval [0,4 ], we need to integrate over that interval, we will get:
[tex]\int\limits^4_0 {2t*(4 - t)} \, dt = [-(2/3)t^3 + 4t^2 + C]^4_0[/tex]
Where C is the constant of integration.
Evaluating that in the given interval, we will get:
[ -(2/3)*4³ + 4*4² - 0] = 21.33
Then we can see that the correct option is A.
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If P(A) = 3/4, P(B)=1/2, and P(AB)=7/8, what is P(AB)?
a. 5/8
b7/8
c3/8
d1/8
Answer:
We know that P(AB) = P(A) + P(B) - P(A∪B), where P(A∪B) represents the probability that at least one of the events A or B will occur.
To calculate P(A∪B), we can use the formula P(A∪B) = P(A) + P(B) - P(AB), which follows from the addition rule of probability.
Substituting with the given values, we have:
P(A∪B) = P(A) + P(B) - P(AB)
P(A∪B) = 3/4 + 1/2 - 7/8
P(A∪B) = 6/8 + 4/8 - 7/8
P(A∪B) = 3/8
Now, we can calculate P(AB) using the first formula:
P(AB) = P(A) + P(B) - P(A∪B)
P(AB) = 3/4 + 1/2 - 3/8
P(AB) = 6/8 + 4/8 - 3/8
P(AB) = 7/8
Therefore, the correct answer is option b) 7/8.
Step-by-step explanation:
*PLS MUST ANSWER ASAP*
Answer:
[tex]f(x) = -5(x -1)^{2} +6[/tex]
Step-by-step explanation:
[tex]f(x) = a(x - h)^{2} + k[/tex] is the standard form of a quadratic, so the fourth option [tex]f(x) = -5(x -1)^{2} +6[/tex] is in standard dorm
Acellus
Georg predicted that he would find 24 bags
of chocolate chips at the grocery store.
However, he only found 23 bags. What was
Georg's percent error?
Round to the nearest percent.
Georg's percent error is 4.30%.
The predicted value is 24 bags, and the actual value is 23 bags.
To find the percent error, we need to find the absolute value of the difference between the predicted value and the actual value, divide that by the predicted value, and multiply by 100 to get a percentage.
percent error = |(predicted value - actual value) / actual value| x 100%
Substituting the given values, we get:
percent error = |(24 - 23) / 23| x 100%
percent error = |1 / 23| x 100%
percent error = 4.3478%
Therefore, Georg's percent error is 4.30%.
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Find the quadratic equation.
The quadratic equation of the graph is:
x² - 4x = 0
How to find the quadratic equation from the graph?The quadratic equation of a quadratic graph can be found by check the points where the curve cuts or intersect the x-axis. These two x values can then be used to form the quadratic equation.
Looking at the graph, you will notice that the graph cuts the x-axis at points x = 0 and x = 4 (Check the red circles in the attached image). We will then form the equation the x values as follow:
x = 0 and x = 4
x - 0 = 0 and x - 4 = 0
Combining them and simplifying:
(x - 0)(x - 4) = 0
x(x - 4) = 0
x² - 4x = 0
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A closet has 9 jeans and 6 skirts. What is the ratio of jeans to skirts?
Answer:
3 : 2
Step-by-step explanation:
the ratio of jeans : skirts is
9 : 6 ( divide both parts by 3 )
= 3 : 2 ← in simplest form
The ratio of jeans to skirts is 3:2
This can be found by dividing the number of jeans by the number of skirts
ratio of jeans to skirts = number of jeans / number of skirtsratio of jeans to skirts = 9 / 6Simplifying this ratio by dividing both the numerator and denominator by 3ratio of jeans to skirts = 3 / 23:2Find the critical points of f(x,y) = 2x4 + 3y2 - 10xy-3
To find the critical points of a function, we need to determine the points at which the gradient of the function is zero or undefined.
In the case of the given function f(x,y) = 2x^4 + 3y^2 - 10xy - 3, we need to find the values of x and y where the partial derivatives of f with respect to x and y are both zero.
After taking the partial derivatives of the function with respect to x and y, we got two equations.
We solved these equations simultaneously to obtain the values of x and y at which the partial derivatives of f are both zero. The obtained values of x and y are the critical points of the function.
In this case, we got two critical points ( √(25/12), (25/12)√(3/5)), (- √(25/12), -(25/12)√(3/5)).
To check whether these critical points are maximum, minimum, or saddle points, we can use the second derivative test.
We can evaluate the second partial derivatives of f and plug in the values of x and y for each critical point to determine the nature of the critical points.
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a dairy farmer is interested in knowing the true mean april 2023 retail whole milk price ($/gallon) for all us cities. previous studies have shown the standard deviation of the milk prices is $0.60. determine the number of cities that must be sampled in order to estimate the true mean within $.10 with 95% confidence.
The dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.
To estimate the true mean April 2023 retail whole milk price with a margin of error of $0.10 and 95% confidence, a dairy farmer can use the sample size formula for estimating population means. The formula is:
n = (Z² × σ²) / E²
where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and E is the margin of error.
For a 95% confidence level, the z-score (Z) is 1.96. The standard deviation (σ) of milk prices is $0.60, and the margin of error (E) is $0.10. Plugging these values into the formula, we get:
n = (1.96² × 0.60²) / 0.10²
n = (3.8416 × 0.36) / 0.01
n ≈ 138.56
Since the sample size must be a whole number, we round up to the nearest whole number to ensure the desired level of accuracy. Therefore, the dairy farmer needs to sample at least 139 cities to estimate the true mean April 2023 retail whole milk price within $0.10 with 95% confidence.
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what is the straight line distance (meters) from sheehan lake (point a) to the small lake (point b)?
The straight line distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .
The sheehan lake (point A) is at 2000 m .
The small lake ( point B) is at 3700 m .
Distance between the two lake can be calculated by finding the difference between lakes .
To find the distance between sheehan lake and small lake = point B - point A .
Distance = 3700 - 2000
Distance = 1700 m .
The distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .
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The question is incomplete the complete question is :