(a) The coefficient of determination for the given regression line is 0.832. It can be interpreted as the fraction of the variation in sales that can be explained by the variation in total square footage. The remaining fraction of the variation, approximately 16.8%, is unexplained and can be attributed to other factors or sampling error.
(b) The standard error of estimate for the regression line is approximately 77.607 billion dollars. It can be interpreted as the average amount by which the predicted sales deviate from the actual sales. In other words, it represents the variability or scatter of the data points around the regression line.
(a) The coefficient of determination, denoted by R^2, is a measure of how well the regression line fits the data. It ranges between 0 and 1, where 0 indicates that the regression line explains none of the variation in the dependent variable (sales in this case), and 1 indicates a perfect fit where all the variation is explained. In this case, the coefficient of determination is 0.832, which means that approximately 83.2% of the variation in sales can be explained by the variation in total square footage.
(b) The standard error of estimate (SE) is a measure of the accuracy of the predicted values. It represents the average amount by which the predicted sales deviate from the actual sales. The standard error of estimate for this regression line is approximately 77.607 billion dollars, indicating that, on average, the predicted sales may deviate from the actual sales by around this amount.
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Find the area of the square. Round to one decimal place.
Answer:
309.8 mm
Step-by-step explanation:
17.6 x 17.6= 309.76
309.76 rounded is 309.8
Answer:
309.8
Step-by-step explanation:
The formula for area of square is one of its sides times another (or its side squared).
So if one of the side is 17.6, it would be 17.6^2 which is 309.76.
You then round one decimal place and get 309.8
Have a good day
From her eye, which stands 1.75 meters above the ground, Myesha measures the angle of elevation to the top of a prominent skyscraper to be 19 degrees
. If she is standing at a horizontal distance of 337 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.
The height of the skyscraper is approximately 115.25 meters (rounded to the nearest hundredth of a meter).
To find the height of the skyscraper, we can use trigonometry and the information provided about the angle of elevation and the horizontal distance.
Let's denote the height of the skyscraper as h. We are given that Myesha's eye height above the ground is 1.75 meters, and she measures the angle of elevation to be 19 degrees.
In a right triangle formed by Myesha's eye, the top of the skyscraper, and a point on the ground directly below the top of the skyscraper, the angle of elevation (θ) is the angle between the line of sight from Myesha's eye to the top of the skyscraper and the horizontal ground.
The opposite side of the triangle is the height of the skyscraper (h), and the adjacent side is the horizontal distance from Myesha to the base of the skyscraper (337 meters).
Using the trigonometric function tangent (tan), we can set up the following equation:
tan(θ) = h / 337
Since we know the value of the angle of elevation (θ = 19 degrees), we can substitute it into the equation:
tan(19 degrees) = h / 337
Now we can solve for h:
h = tan(19 degrees) * 337
Using a calculator or trigonometric tables, we find that tan(19 degrees) is approximately 0.34202. Substituting this value into the equation:
h = 0.34202 * 337
h ≈ 115.25
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1 Which is an arithmetic sequence?
F)2, 5, 9, 14, ...
G)100, 50, 12.5, 1.6, ...
H)3, 10, 17, 24,...
j) -2,-1,-1/2,-1/4
Answer:
H) 3, 10, 17, 24, ...Step-by-step explanation:
An arithmetic sequence is when the difference of the terms is same
F)2, 5, 9, 14, ...
14 - 9 = 5, 9 - 5 = 4. 5-2 = 35 ≠ 4 ≠ 3, no
G)100, 50, 12.5, 1.6, ...
1.6 - 12.5 = -10.912.5 - 50 = -37.550 - 100 = -50-10.9 ≠ -37.5 ≠ -50, no
H)3, 10, 17, 24,...
24-17 = 717 - 10 = 710 - 3 = 77 is the common difference, yes
j) -2,-1,-1/2,-1/4
-1/4 - (-1/2) = 1/4-1/2 - (-1) = 1/2-1 - (-2) = 11/4 ≠ 1/2 ≠ 1, no
Explain the relationship between evolution, natural selection and mutations.
You must write out a well thought out and cohesive explanation. Use the CER model for this answer.
Answer:
Natural selection is a mechanism, or cause, of evolution. Adaptations are physical or behavioral traits that make an organism better suited to its environment. Heritable variation comes from random mutations. Random mutations are the initial cause of new heritable traits.
Answer:
Darwin's theory of evolution
Charles Darwin developed a theory of evolution to explain the unity and diversity of life, based on the idea of shared common ancestors.
Natural selection
Darwin's theory was based on the mechanism of natural selection, which explains how populations can evolve in such a way that they become better suited to their environments over time.
Light colored mice are more easily seen by predators and are therefore preyed upon more. Dark mice are better adapted to their environment and better able to survive and reproduce.
Light colored mice are more easily seen by predators and are therefore preyed upon more. Dark mice are better adapted to their environment and better able to survive and reproduce.
Natural selection acting on mice population over time.
Individuals have variations within their heritable traits. Some variations make an individual better suited to survive and reproduce in their environment.
If this continues over generations, these favorable adaptations (the heritable features that aid survival and reproduction) will become more and more common in the population.
The population will not only evolve (change in its genetic makeup and inherited traits), but will evolve in such a way that it becomes adapted, or better-suited, to its environment.
Artificial selection
There are other types of selection, in addition to natural selection, that are out there in the world.
Artificial selection, also called "selective breeding”, is where humans select for desirable traits in agricultural products or animals, rather than leaving the species to evolve and change gradually without human interference, like in natural selection.
A timeline showing how dogs became domesticated over a long period of time due to artificial selection.
A timeline showing how dogs became domesticated over a long period of time due to artificial selection.
Dog breeding is a perfect example of how humans select for desirable or fashionable traits. Breeders deliberately mate parents with the hope of producing offspring with specific traits (such as color, size, ear shape, snout length, and so on).
Common mistakes and misconceptions
Evolution is not the same as adaptation or natural selection. Natural selection is a mechanism, or cause, of evolution. Adaptations are physical or behavioral traits that make an organism better suited to its environment.
Heritable variation comes from random mutations. Random mutations are the initial cause of new heritable traits. For example, a rabbit can't choose to have a different fur color. Rather, a genetic mutation causes a difference in fur color, which may help that rabbit hide better in its environment.
Natural selection acts on existing heritable variation. Natural selection needs some starting material, and that starting material is heritable variation. For natural selection to act on a feature, there must already be variation, and that variation must be able to be passed on to offspring.
Natural selection depends on the environment. Natural selection doesn't favor traits that are somehow inherently superior. Instead, it favors traits that are beneficial in a specific environment. Traits that are helpful in one environment might actually be harmful in another.
Step-by-step explanation:
find the missing side x
Answer:
[tex]\sqrt{968}[/tex]
Step-by-step explanation:
Since this is a right triangle, we are able to use pythagorean theorem, a^2+b^2=c^2. In this case x would be the "c", so 22^2+22^2=x^2. Isolate the variable and solve for x. 484+484=x^2
968=x^2
[tex]\sqrt{968\\}[/tex]=x
Which expression is already in its simplified form?
a.) 3t+ (s +t)
b.) 6h + 2(h+ 3k)
c.) 5m + 7mn + 4n
d.) 8 + y3 - 5z2 + 2y3
A recipe uses 6 tablespoons of butter for every 8 oz of cheese. the rate is __ tablespoons for every 1 oz. the raze is __ oz for every 1 tablespoon.
1/4 or .75
6 divided by 4 equal 1/4 or .75
In a local, recreational soccer league there are 252 men and 90 women signed up to play. The organizers need to make sure that everyone is on a team, the teams are the same size, each team has the same number of males; and each team has the same number of females. a. What is the largest possible number of teams? b. How many people will be on each team?
(a) There can be a maximum of 18 teams.
(b) The largest possible number of teams is 18, and there will be a total of 19 players on each team.
Given information:
In a local, recreational soccer league there are 252 men and 90 women signed up to play. The organizers need to make sure that everyone is on a team, the teams are the same size, each team has the same number of males; and each team has the same number of females.
(a) To find the largest possible number of teams, we need to divide the players (252 men and 90 women) into teams, where each team has the same number of males and females. Let's find the GCD (greatest common divisor) of 252 and 90:
GCD of 252 and 90 = GCD (252,90) = 18.
Therefore, there can be a maximum of 18 teams.
(b) Since the number of teams is 18, and we have 252 men and 90 women, there will be a total of 342 players.
Now, we need to divide these 342 players into 18 teams. Each team must have an equal number of males and females. Number of males = 252, Number of females = 90.
To divide the players equally into teams, we need to find the number of males and females that can be in one team.
Number of males in one team = 252/18 = 14
Number of females in one team = 90/18 = 5
Therefore, each team will have 14 males and 5 females, and there will be a total of 19 players on each team (14 + 5).
Thus, the largest possible number of teams is 18, and there will be a total of 19 players on each team.
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A Store owners offers a discount of 20% off the regular price of all jackets. Jessica has a coupon that gives her an additional 5% off the discount price. The original price of jacket Jessica buys is $84. What is the price of the jacket after the discount and Jessica coupon?
Answer:
$63
Step-by-step explanation:
The store is 20% off, Jessica has a coupon that is 5% off add that together and it's 25% off. $84 - 25% = $63
Someone solve this please
Answer:
the pyramid is 80 ft² and the rectangular prism is 240 ft²
Step-by-step explanation:
Find all solutions to the equation 34 – 38 = 3 where a, ß are positive integers (or show there are none). (6) Find all solutions where x and y are integers to the diophantine equation 1/x + 1/y =1/5
a) There are no solutions to the equation.
To find all solutions to the equation 34 - 38 = 3, we can simplify the equation:
34 - 38 = 3
-4 = 3
However, this equation is not true, as -4 is not equal to 3. Therefore, there are no solutions to the equation.
b) Now, let's consider the diophantine equation 1/x + 1/y = 1/5, where x and y are integers. To find all solutions, we can follow these steps:
1: Multiply both sides of the equation by 5xy to eliminate the denominators:
5y + 5x = xy
2: Rearrange the equation:
xy - 5x - 5y = 0
3: Apply Simon's Favorite Factoring Trick:
Add 25 to both sides to complete the square:
xy - 5x - 5y + 25 = 25
xy - 5x - 5y + 25 = 25
(xy - 5x - 5y + 25) + 25 = 25 + 25
(x - 5)(y - 5) = 50
4: List all possible factor pairs of 50:
(1, 50), (2, 25), (5, 10), (-1, -50), (-2, -25), (-5, -10)
5: Solve for x and y in each factor pair:
For (x - 5)(y - 5) = 50:
If x - 5 = 1 and y - 5 = 50, then x = 6 and y = 55.
If x - 5 = 2 and y - 5 = 25, then x = 7 and y = 30.
If x - 5 = 5 and y - 5 = 10, then x = 10 and y = 15.
If x - 5 = -1 and y - 5 = -50, then x = 4 and y = -45.
If x - 5 = -2 and y - 5 = -25, then x = 3 and y = -20.
If x - 5 = -5 and y - 5 = -10, then x = 0 and y = -5.
Therefore, the solutions to the diophantine equation 1/x + 1/y = 1/5, where x and y are integers, are:
(x, y) = (6, 55), (7, 30), (10, 15), (4, -45), (3, -20), (0, -5).
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I need alittle help with this,
9x-5y+3x+2y-4y-y
Answer:
12x - 8y
Step-by-step explanation:
9x - 5y + 3x + 2y - 4y - y
9x + 3x - 5y + 2y - 4y - y
12x - 8y
Answer:
12x - 8y would be the simplified version of this equation if this is not the type of answer your looking for please lmk
Step-by-step explanation:
Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p_1 and p_2 at the given level of significance α using the given sample statistics. Assume the sample statistics are from independent random samples.
Claim: p_1 = p_2, α = 0.05
Sample statistics: x_1 = 32, n_1 = 119 and x_2 = 183, n_2 = 203
C. H_o: p_1 = p_2
H_a:p_1>p_2
D. H_o:p_1
H_a: p_1 = p_2
E. A normal sampling distribution cannot be used, so the claim cannot be tested.
Find the critical values. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The critical values are - z_o = - 1.96 and z_o = 1.96 (Round to two decimal places as needed.)
B. A normal sampling distribution cannot be used, so the claim cannot be tested.
Find the standardized test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. Z= ______(Round to two decimal places as needed.)
B. A normal sampling distribution cannot be used, so the claim cannot be tested.
The normal sampling distribution can be used
The critical values at α = 0.05 are z₀ = -1.96 and z₀ = 1.96
The standardized test statistic is -11.652
Deciding whether the normal sampling distribution can be usedFrom the question, we have the following parameters that can be used in our computation:
Claim: p₁ = p₂, α = 0.05Sample statistics: x₁ = 32, n₁ = 119 and x₂ = 183, n₂ = 203In the above we can see that the sample sizes are greater than 30 as required by the central limit theorem
This means that the normal sampling distribution can be used and the parameters are
H₀: p₁ = p₂
H₁: p₁ > p₂
Finding the critical valueIn (a), we have
α = 0.05
The critical values at α = 0.05 are z₀ = -1.96 and z₀ = 1.96
Finding the standardized test statistic.Start by calculating the pooled sample proportion using
p = (x₁ + x₂)/(n₁ + n₂)
So, we have
p = (32 + 183)/(119 + 203)
p = 0.67
So, we have
z = (x₁/n₁ - x₂/n₂)/√[p(1 - p)/n₁ + p(1 - p)/n₂)
substitute the known values in the above equation, so, we have the following representation
z = (32/119 - 183/203)/√[0.67(1 - 0.67)/119 + 0.67(1 - 0.67)/203]
Evaluate
z = -11.652
Hence, the standardized test statistic is -11.652
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please help, tysm for your assistance if you do :)
Answer:
27/49
plz mark me as brainliest
The distance y (in miles) that a truck travels on x gallons of gasoline is represented by the equation y=18x The graph shows the distance that a car travels. Which vehicle gets the better gas mileage?
Answer:
Car M:
50.4/2 = 25.2
car M uses up 1 gallon every 25.2 miles
Car P:
Just from the graph, you can see that it uses up 1 gallon every 30 miles
The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.
Answer:
Step-by-step explanation:
find w such that 2u v − 3w = 0. u = (−6, 0, 0, 2), v = (−3, 5, 1, 0)
To find the value of w that satisfies the equation 2u v - 3w = 0, where u = (-6, 0, 0, 2) and v = (-3, 5, 1, 0), we can substitute the given values into the equation and solve for w.
Substituting the given values of u and v into the equation 2u v - 3w = 0, we have:
2(-6, 0, 0, 2)(-3, 5, 1, 0) - 3w = 0.
Expanding the scalar multiplication and performing the dot product, we get:
(-12, 0, 0, 4)(-3, 5, 1, 0) - 3w = 0,
(36 + 0 + 0 + 0) - 3w = 0,
36 - 3w = 0.
Simplifying the equation, we have:
36 = 3w,
w = 12.
Therefore, the value of w that satisfies the equation is 12. By substituting w = 12 into the equation 2u v - 3w = 0, we get:
2(-6, 0, 0, 2)(-3, 5, 1, 0) - 3(12) = 0,
(-12, 0, 0, 4)(-3, 5, 1, 0) - 36 = 0,
36 - 36 = 0,
0 = 0.
Hence, the value of w = 12 makes the equation true, satisfying the given condition.
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There’s a picture of my question plz help :)
Answer:
1,534 inches squared
Step-by-step explanation:
To find surface area we just solve for the area of all the sides and add those together. A rectangular prism (a box like above) has 6 sides. There are...
2 sides each of the following dimensions:
2(13×26)=
2(338)=676
2(13×11)=
2(143)=286
2(26×11)=
2(286)=572
Add the area of all 6 sides...
676+286+572=1,534
Remember it is squared not cubed.
PLZZZ HELPPPPPP ILL GIVE BRAINLIESTTTTT
N = visitors
1030 = 1300 - 18(P - 30)
1030 - 1300 = -18(P - 30)
-270 = -18(P - 30)
-270/-18 = (P - 30)
15 = P - 30
45 = P
ANSWER: 45An insurance policy sells for $600. Based on past data, an average of 1 in 50 policyholders will file a $5,000 claim, and average of 1 in 100 policyholders will file a $10,000 claim, and an average of 1 in 200 policyholders will file a $30,000 claim. What is the expected value per policy sold?
Answer:
$250
Step-by-step explanation:
Calculation to determine the expected value per policy sold
Expected value per policy sold =$600-(1/50)*$5,000-(1/100)*$10,000-(1/200)*$30,000
Expected value per policy sold =$600-$100-$100-$150
Expected value per policy sold =$250
Therefore the expected value per policy sold will be $250
. In a volleyball game, Alexis scored 4 points more than twice the
number of points Jessica scored. Jessica scored 3 points. How many
points did Alexis score?
F. 1 point G. 7 points H. 10 points I. 12 points
Answer: 10
Step-by-step explanation:
Alexis Scored 4 more than twice the number of points Jessica scored.
Jessica scored 3
twice the number of 3 would be 3 x 2 which equals six
4 more than twice the number which is 6 would be 10, 4+6=10
To figure out the distance for a trip, you use a ruler to measure the distance from Orlando to Gainesville on the map. You measure 2.3 cm. Find the actual mileage
between the two cities, rounded to the nearest mile.
will give u brainlist
Answer:
The answer is 71
Step-by-step explanation:
Why because
1 cm /31 mi = 2.3 cm / m
1 x m = 31 x 2.3
n = 71.3
71.3 rounded to nearest mile is 71.
What is the equation of the graph below?
y = sec(x – 4)
y = sec(x) – 4
y = sec(x + 4) + 4
y = sec(x + 4) – 4
Answer:
It's A don't listen to the other guy
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
edg 22
The playground at a park is shaped like a trapezoid the dimensions what is the area of the playground in square feet
Answer:
[tex]Area = 1560ft^2[/tex]
Step-by-step explanation:
Given
See attachment for playground
Required
Determine the area
The playground is a trapezoid. So;
[tex]Area = \frac{1}{2}(Sum\ parallel\ sides) * Height[/tex]
From the attachment, the parallel sides are: 68ft and 36ft
The height is: 30ft
So, the area is:
[tex]Area = \frac{1}{2}(68ft + 36ft) * 30ft[/tex]
[tex]Area = \frac{1}{2}(104ft) * 30ft[/tex]
[tex]Area = 52ft * 30ft[/tex]
[tex]Area = 1560ft^2[/tex]
pls help i’ll give brainliest
Answer:
The answer is 56.33 in decimal form but in fraction form the answer is 5633/
100
Step-by-step explanation:
6.55 x 8.6
3. A system of functions is given. Select
ALL values where f(x) = g(x). Round all
answers to the nearest tenth
f(x) = - x - 2x + 6
g(x) = 2x2 + 5x + 3
a) -2.7
b) -1.8
c) -0.6
d) 0.4
e) 4.1
f) 5.1
g)7.0
Answer:
Step-by-step explanation:
The easiest way is to graph both functions and see where they intersect. The intersection is where f(x) = g(x).
f(x) = -x² - 3x + 6
g(x) = 2x² + 5x + 3
*WILL GIVE BRAINLIEST FOR THE BEST ANSWER PLEASE HELP AND IF YOU DONT KNOW THE ANSWER DONT ANSWER!*How many people participated in the survey given the data in the histogram below?
Question 1 options:
7 people
12-15 people
20 people
0 people
Answer:
20 people participated in the survey.
For a random variable X where X ~ N(p, p(1-p)/k) and 0<=p<=1, find the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9
The value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is {0.2^2 p(1-p)}/{1.645^2}
Given a random variable X where X ~ N(p, p(1-p)/k) and 0<=p<=1, we need to find the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9.
In general, if X ~ N(μ,σ²), then
P[|X-μ| < a] = 2Φ(a/σ) - 1
where Φ(z) is the standard normal cumulative distribution function.
Therefore, we can say that
P[|X-p| < 0.2] = 2Φ(0.2/√(p(1-p)/k)) - 1 ≥ 0.9
or 2Φ(0.2/√(p(1-p)/k)) ≥ 1.9
or Φ(0.2/√(p(1-p)/k)) ≥ 0.95
or 0.2/√(p(1-p)/k) ≥ Φ^(-1)(0.95)
where Φ^(-1)(z) is the inverse of the standard normal cumulative distribution function.
Therefore, Φ^(-1)(0.95) = 1.6450.2/√(p(1-p)/k) ≥ 1.645
or k ≤ 0.2²p(1-p)/1.645²
From the above inequality, we get the maximum value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is given by the formula:
k ≤{0.2^2 p(1-p)}/{1.645^2}
Therefore, the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is {0.2^2 p(1-p)}/{1.645^2}
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Let a/m and b/n be rational numbers expressed in lowest terms. Prove that (an + bm)/(mn) is in lowest terms if and only if m and n are relatively prime.
If m and n are relatively prime, the numerator (an + bm) and denominator (mn) have no common factors other than 1, and therefore, (an + bm)/(mn) is in lowest terms.
To prove that (an + bm)/(mn) is in lowest terms if and only if m and n are relatively prime, we will need to establish two separate claims:
Claim 1: If (an + bm)/(mn) is in lowest terms, then m and n are relatively prime.
Claim 2: If m and n are relatively prime, then (an + bm)/(mn) is in lowest terms.
Proof of Claim 1:
Let's assume that (an + bm)/(mn) is in lowest terms. This means that the numerator (an + bm) and the denominator (mn) have no common factors other than 1.
Suppose m and n are not relatively prime, which means they have a common factor greater than 1.
Let's say that factor is d, where d > 1. Then we can express m and n as follows: m = dx and n = dy, where x and y are integers.
Now, we rewrite the numerator (an + bm) as follows:
an + bm = an + b(dx) = n(a + bx/d)
Since m = dx and n = dy, we have (an + bm)/(mn) = (n(a + bx/d))/(dx * dy) = (a + bx/d)/(xy).
We can see that both the numerator (a + bx/d) and the denominator (xy) have the factor d.
This contradicts our assumption that (an + bm)/(mn) is in lowest terms, as they have a common factor greater than 1.
Therefore, m and n must be relatively prime.
Proof of Claim 2:
Now, let's assume that m and n are relatively prime, which means they have no common factors other than 1.
To show that (an + bm)/(mn) is in lowest terms, we need to demonstrate that its numerator and denominator have no common factors other than 1.
Let's suppose that the numerator (an + bm) and the denominator (mn) have a common factor d, where d > 1.
This implies that d divides both an + bm and mn.
Since d divides mn, we can express m and n as follows: m = dx and n = dy, where x and y are integers.
Now, let's rewrite the numerator (an + bm) as follows:
an + bm = an + b(dx) = n(a + bx/d)
We can see that d divides both n and the expression (a + bx/d). Therefore, d also divides the numerator (an + bm).
However, we initially assumed that (an + bm)/(mn) is in lowest terms, which means the numerator and denominator have no common factors other than 1. This contradicts the assumption that they have a common factor d > 1.
Thus, if m and n are relatively prime, the numerator (an + bm) and denominator (mn) have no common factors other than 1, and therefore, (an + bm)/(mn) is in lowest terms.
By proving both Claim 1 and Claim 2, we have established that (an + bm)/(mn) is in lowest terms if and only if m and n are relatively prime.
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a camera has a listed price of $634.95 before tax. if the sales tax rate is 8.75%, find the total cost of the camera with sales tax included. round your answer to nearest cent, as necessary
Answer:
690.50
Step-by-step explanation:
How many students are enrolled in a course either in calculus, discrete mathematics, data structures, 7. or programming languages at a school if there are 507, 292, 312, and 344 students in these courses, respectively; 14 in both calculus and data structures; 213 in both calculus and programming languages; 211 in both discrete mathematics 558 and data structures; 43 in both discrete mathematics and programming languages; and no student may take calculus and discrete mathematics, or data structures and programming languages, concurrently
Answer:
974
Step-by-step explanation:
Let assume that:
The set of student that took part in Calculus be = C
Those that took part in discrete mathematics be = D
Let those that took part in data structures be = DS; &
Those that took part in Programming language be = P
Thus;
{C} = 507
{D} = 292
{DS} = 312
{P} = 344
For intersections:
{C ∩ DS} = 14
{C ∩ P} = 213
{D ∩ DS} = 211
{D ∩ P} =43
{C ∩ D} = 0
{DS ∩ P} = 0
{C ∩ D ∩ DS ∩ P} = 0
According to principle of inclusion-exclusion;
{C ∪ D ∪ DS ∪ P} = {C} + {D} + {DS} + {P} - {C ∩ D} - {C ∩ DS} - {C ∩ P} - {D ∩ DS} - {D ∩ P} - {DS ∩ P}
{C ∪ D ∪ DS ∪ P} = 507 + 292 + 312 + 344 - 14 - 213 - 211 - 43 - 0
{C ∪ D ∪ DS ∪ P} = 974
Hence, the no of students that took part in either course = 974