The true statement is (d) The area of triangle XYZ is equal to the area of triangle X'Y′Z
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y'Z'.
The rotation is a rigid transformation
This means that it does not change the side length and angles of a shape when applies
Using the above as a guide, we have the following:
The image and the preiamage have the same area
Hence, the true statement is (d)
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Complete question
Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y′Z'.
y. z. y. x. x.
Which statement is true?
The sum of the angle measures of triangle XYZ is 90° less than the sum of the angle measures of triangle X'Y′Z'.
The angle measures of triangle XYZ are less than the corresponding angle measures of triangle X'Y′Z'.
Triangle XYZ is not congruent to triangle X'Y′Z'.
The area of triangle XYZ is equal to the area of triangle X'Y′Z
The average daily balance for Pete's credit card last month was a dollars. The finance charge was f dollars. Express the APR algebraically.
The average daily balance for Pete's credit card last month was a dollars. The finance charge was f dollars. APR algebraically is: 12f/a.
What is APR algebraically?Finance charge = Monthly interest rate · Average daily balance
Monthly interest rate = APR/12
Where:
Finance charge = f
Average daily balance = a
f= Monthly interest rate · a
f = APR/12 · a
f/a = APR/12
12.f/a = APR
Therefore APR algebraically is: 12f/a.
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A hiker is starting a hike to his destination. There are four trails (Trail no. 1, 2, 3, and 4) that lead
to his destination. However, each trail divides into two sub-trails along the way and only one of
the two sub-trails leads to hiker’s destination. The hiker has no map available. The hiker decides
to choose one of the four trails by rolling a fair 4-sided die. The hiker also decides to choose
between two sub-trails by flipping a fair coin. What is the probability that the hiker will reach his
destination.
The probability that the hiker will reach his destination is, 1/2
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Since the hiker chooses one of the four trails with equal probability by rolling a fair 4-sided die,
the probability of taking any one trail is 1/4.
Once the hiker is on a trail, there are two sub-trails, and the hiker chooses one of them by flipping a fair coin.
The probability of taking the correct sub-trail is 1/2.
P(reaching destination) = P(trail 1) x P(correct sub-trail on trail 1) + P(trail 2) x P(correct sub-trail on trail 2) + P(trail 3) x P(correct sub-trail on trail 3) + P(trail 4) x P(correct sub-trail on trail 4)
P(reaching destination) = (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2)
P(reaching destination) = 4/8
P(reaching destination) = 1/2
Therefore, the probability that the hiker will reach his destination is 1/2, or 50%.
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A farmer wants to fence a rectangular area of 288 square feet next to a river. Find the length and width of the rectangular which uses the least amount of fencing if no fencing is needed along the river. Assume the length of the fence runs parallel to the river
Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.
What is meant by budget?
Budget is a planning and monitoring tool used by management to coordinate all of the company's activities. Budgeting is the process of estimating income and expenses for a given time frame.For any individual, group of people, organisation, or government. A budget is a plan for financial calculations for a specified time period, usually a month or a year, but not always.Budgeting is the process of estimating a company's revenues and expenses for a given time period.Examples of budgets prepared for this purpose include the sales budget, which makes a projection of the company's sales, and the production budget, which makes a projection of the company's production, among others.Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.
We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.
So we can set up the following system of equations:
x + y = 168 (total amount of punch)
1.57x + 2.41y = 1.66(168) (total cost of punch)
Simplifying the second equation:
1.57x + 2.41y = 278.88
Now we can use substitution or elimination method to solve for x and y.
Using substitution:
x = 168 - y
1.57(168 - y) + 2.41y = 278.88
264.36 - 1.57y + 2.41y = 278.88
0.84y = 14.52
y = 17.29
So Hannah needs 17.29 gallons of fruit drink.
Using x + y = 168, we can find that she needs 150.71 gallons of soda.
Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.
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I need to know why the medians differ relative to the data set and the best measure of center?
Answer: The median is one of several measures of center that can be used to summarize a dataset. The median is the middle value in a set of data when the data is arranged in order from smallest to largest. The median divides a dataset into two equal parts, with half of the data values being smaller than the median and half being larger.
Step-by-step explanation:
The median is one of several measures of center that can be used to summarize a dataset. The median is the middle value in a set of data when the data is arranged in order from smallest to largest. The median divides a dataset into two equal parts, with half of the data values being smaller than the median and half being larger.
The reason why the median can differ relative to the data set is because it is affected by extreme values, or outliers, in the data. For example, if a dataset has a few very large or very small values, the median can be significantly different from the mean (another measure of center), which is affected by all values in the dataset. In these cases, the median provides a better measure of center because it is less sensitive to outliers.
In general, the median is considered the best measure of center when the data is skewed (not symmetrical) or has outliers. In these cases, the median provides a better representation of the "typical" value in the dataset. However, when the data is symmetrical and does not have outliers, the mean can be a good measure of center because it takes into account all values in the dataset.
In conclusion, the best measure of center depends on the shape and distribution of the data. When the data is skewed or has outliers, the median is the best measure of center, while in symmetrical and non-outlier datasets, the mean can provide a good measure of center.
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-4x - 15y = -10
x + 3y = 1
Answer:
This system of equations can be solved using substitution or elimination methods.
Using substitution, we can solve for one of the variables in one of the equations and substitute that expression into the other equation.
Solving for x in the second equation:
x + 3y = 1
x = 1 - 3y
Substituting this expression for x into the first equation:
-4(1 - 3y) - 15y = -10
Expanding and solving for y:
-4 + 12y - 15y = -10
12y - 4 = -10
12y = -6
y = -1/2
Now that we know y = -1/2, we can substitute this value back into the expression for x:
x = 1 - 3(-1/2) = 1 + 3/2 = 7/2
So the solution to the system of equations is (7/2, -1/2).
Checking the solution in both equations:
-4(7/2) - 15(-1/2) = -4(7/2) + 15/
Step-by-step explanation:
what is the total population if 15% is 36,000 people
pls help
About 3,500 tourists visit the Granite Falls overlook each year. After the construction of a new nature center with exhibits and hands-on activities, that number is expected to increase 5% each year. Assuming the same growth continues, you can use a function to approximate the number of annual visitors to the overlook x years after the nature center is built.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answer:
Step-by-step explanation:
Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:
Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:
y0 = 3,500
Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:
r = 0.05
Write the equation for exponential growth. The formula for exponential growth is given by:
y = y0 × (1 + r)^x
where x is the number of years after the nature center is built.
So, the equation for the function in this case would be:
f(x) = 3,500 × (1 + 0.05)^x
This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.
5 Practice
6a of 6
Question 6a
If a truck carrying 3 tons of wheat unloads 1, 000 pounds, what is the weight of the
wheat still in the truck?
Answer: the weight of the wheat still in the truck is 5000 pounds.
Step-by-step explanation:
Here are the steps to calculate the weight of the wheat still in the truck:
Convert the weight of the unloaded wheat to tons. To convert from pounds to tons, divide by 2,000:
1000 lbs / 2000 lbs/ton = 0.5 tons
Subtract the weight of the unloaded wheat from the original weight:
3 tons - 0.5 tons = 2.5 tons
Convert the answer back to pounds:
2.5 tons * 2000 lbs/ton = 5000 lbs
Therefore, the weight of the wheat still in the truck is 5000 pounds.
How did you calculate the total mass of boys
Express the following in the form; a+jb
1. Cos(e^j)
2.exp(e^j)
3.(sqrt(j))^sqrt(j)
Using Euler's formula, the expressions can be rewritten as Im = sin(e^j) - sinh(1), exp(e^j) = e^(cos(1) + j*sin(1)) and e^[(1/2)√(2)e^(j(π/4+2π*n))] respectively
What is the expression in a + jb1.
Cos(e^j) can be expressed using Euler's formula as:
Cos(e^j) = (e^(je^j) + e^(-je^j)) / 2
= (cos(e^j) + cosh(1)) + j(sin(e^j) - sinh(1))
Re = cos(e^j) + cosh(1)
Im = sin(e^j) - sinh(1)
2.
exp(e^j) can also be expressed using Euler's formula as:
exp(e^j) = e^(cos(1) + j*sin(1))
3.
(sqrt(j))^sqrt(j) can be written as:
(sqrt(j))^sqrt(j) = e^[(1/2)√(2)e^(j(π/4+2π*n))]
where n is an integer. This is because the logarithm of a complex number has infinitely many possible values due to the periodicity of the exponential function.
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Can someone please help me with this question please
Answer:
77.5°
Step-by-step explanation:
You want the measures of the angles formed when ray OX bisects the 155° angle AOB.
BisectorThe angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...
155°/2 = 77.5°
If it takes 6 people 8 hours to finish the job, how long would it take 4 people?
12 hours
If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours
Answer:
5.333 hours.
Step-by-step explanation:
Put this on a chart:
6 people = 8 hours
4 people = ? hours
To find ? Use crisscross multiplication and solve:
? = (4 * 8) / 6
? = 32 / 6
? = 5.333
Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.
Which statements correctly describe how the graph of the geometric sequence below should appear?
640, 160, 40, 10, ...
Select two options.
Answer:
Step-by-step explanation:
The graph of the geometric sequence 640, 160, 40, 10, ... should have the following characteristics:
Decreasing: The values in the sequence decrease at a constant rate, so the graph should decrease as well.
Straight Line: Since the sequence is a geometric sequence, the graph will be a straight line when plotted on logarithmic axes.
Negative Slope: The slope of the line should be negative, since the values are decreasing.
Non-Linear: When plotted on linear axes, the graph will not be a straight line and will curve downward, since the difference between consecutive terms is decreasing.
Therefore, the graph of the geometric sequence should appear as a straight line with a negative slope when plotted on logarithmic axes, and as a non-linear curve with a downward slope when plotted on linear axes.
Equation: -140
Answer: x =
= -10x
=
Please help me with my following homework problem
The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.
How to make the decisionThe test statistic for this hypothesis test can be calculated as follows:
t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)
Plugging in the values, we get:
t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36
Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator.
Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.
Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.
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A recent conference had 850 people in attendance. In one exhibit room of 60 people, there were 46 teachers and 14 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 652 principals in attendance.
There were about 453 principals in attendance.
There were about 259 principals in attendance.
There were about 198 principals in attendance.
The predicted number of principals in attendance at the conference can be 161
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
A recent conference had 850 people in attendance.
In one exhibit room of 60 people, there were 46 teachers and 14 principals.
The predicated number of principals = ?
The ratio of teachers to principals = 60/14
= 30/7
In the same ratio there will be total teachers and principals:
Suppose, the number of teachers = x
the number of principals = y
x + y = 850
x/y = 30/7
x = (30/7)y
(30/7)y + y = 850
37y = 850 x 7
y = 161 (approx)
Hence, the number of principals cab be 161
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Answer:
D
Step-by-step explanation:
There were about 198 principals in attendance. EZ
Suppose ABC Inc Can Produce 20 Units of Output Using any of the 4 Techniques Below TECHNIQUE TI 12 13 Т4 LAND LABOR CAPITAL 10 18 12 10 20 8 10 22 6 10 24 3 Further Suppose That The Output sells for $20 Per Unit In The Market. And the prices of land, labor, And capital are $8, $6, & $4, respectively.
11. Which technique should this firm use to maximize profit?
12. This firm will earn a profit equal to ________ dollars.
13. This firm will earn a Revenue equal to _____ dollars.
14. The profit associated with T1 is equal to _______ dollars.
15. If the price of labor falls to $2, ceteris paribus, this firm will earn a profit of
______dollars.
The height of a triangle is 8 m more than twice the length of the base. The area of the triangle is 21 m². Find the height of the triangle.
Answer:
The height of the triangle is 14 m,
Step-by-step explanation:
Let the base be x, then the height is:
2x + 8The area is half the product of base and height.
Set up equation and solve for x:
x(2x + 8)/2 = 21x(x + 4) = 21x² + 4x = 21x² + 4x - 21 = 0x² + 7x - 3x - 21 = 0x(x + 7) - 3(x + 7) = 0(x + 7)(x - 3) = 0x = - 7 or x = 3The first root is discarded as negative. The second root is the answer.
The base is 3 m, so the height is:
2*3 + 8 = 14 mAnswer:
The height of the triangle is 14 m.
Step-by-step explanation:
The area of a triangle can be found by using the following formula:
[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]
where:
b is the base of the triangle.h is the height of the triangle.If the height of a triangle is 8 m more than twice the length of the base, then an expression for h in terms of b is:
[tex]h = 2b + 8[/tex]
Rewrite this equation to make b the subject:
[tex]\implies 2b=h-8[/tex]
[tex]\implies b=\dfrac{1}{2}h-4[/tex]
Given the area of the triangle is 21 m², substitute this value along with the found expression for b into the formula for area of a triangle:
[tex]\implies \dfrac{1}{2}\left(\dfrac{1}{2}h-4\right)h=21[/tex]
To find the height of the triangle, solve the equation for h.
[tex]\implies \dfrac{1}{4}h^2-2h=21[/tex]
[tex]\implies h^2-8h=84[/tex]
[tex]\implies h^2-8h-84=0[/tex]
[tex]\implies h^2-14h+6h-84=0[/tex]
[tex]\implies h(h-14)+6(h-14)=0[/tex]
[tex]\implies (h+6)(h-14)=0[/tex]
Apply the zero-product property:
[tex]h+6=0 \implies h=-6[/tex]
[tex]h-14=0 \implies h=14[/tex]
As length cannot be negative, the height of the triangle is 14 m.
2-step Word problemas please help my
Answer:
1: 9 polar bears and 38 penguins
2: 47 snowglobes
3: 130 snowballs
4: 97 penguins
Step-by-step explanation:
i did the math
Sean M(2,5) el punto medio de P(a,-2) y Q(-5,b) ¿como hallar el valor de (a+2b)
Solving the provided question, we can say that equatiοn of slope intercept will me as y -y1 = m(x-x1) => 3x - y = -1
What is slope intercept?In mathematics, the intersectiοn point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crοsses on a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equation fοr the straight line to show this.
The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept fοrm. When an equatiοn has the intercept form (y=mx+b), the slοpe is m and the y-intercept is b. Sοme equations can also be rewritten such that they seem to be slοpe intercepts. If y=x is rewritten as y=1x+0, fοr instance, the slοpe and y-intercept are bοth changed to 1.
Here,
coordinates are
M(2,5) and P(a,-2)
equation of slope intercept will me as
y -y1 = m(x-x1)
y - 5 = 3x-4
3x - y = -1
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How many millimeters long is 3 inches
Answer:
3 inches is approximately equal to 76.2 millimeters.
Step-by-step explanation:
Answer:
3 inches = 76.2 millimeters
Step-by-step explanation:
Amy has three times as many Star Wars toys as Carly. Total they have 312 Star Wars toys. how many Star Wars toys does Amy have?
Answer:
the answer to this question is 936
a 17 meter ladder leans against a building the base of the ladder from the building is 6 meters.Find the angle in degrees
The angle of the base and the ladder is 69. 34 degrees
How to determine the valueNote that the six trigonometric identities are;
sinetangentcosinecotangentcosecantsecantFrom the information given, we have that;
Hypotenuse = 17 meters
Adjacent = 6 meters
The identity to use is the cosine
cos θ = adjacent/hypotenuse
Substitute the values
cos θ = 6/17
cos θ =,0. 3529
Take inverse of cos
θ = 69. 34 degrees
Hence, the value is 69. 34 degrees
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**Image **Find the value of x. Show your steps.
The value of x is 9 by using the concept of corresponding angles.
What are corresponding angles?Corresponding angles are the angles formed when two parallel lines are crossed by any other line. It may also be generated in matching edges(corners) or corresponding corners with the transversal.
From the information given:
(8x + 9) is corresponding to the opposite side of the transversal with an angle of 99 degrees.
Using the sum of angles on a straight line.
Step 1: (8x + 9)° + 99 = 180°
Step 2: 8x + 108 = 180
Step 3: 8x = 72
Step 4: x = 9
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A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution. How many liters
of the 10% and how many liters of the 70% solutions will be used?
Liters of 10% solution =
Liters of 70% solution=
Liters of 10% solution = 1 liters
Liters of 70% solution = 5 liters
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x +3 = 8 is an equation.
We have,
10% solution = x
70% solution = y
Now,
A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution.
This means,
We can make two equations.
0.10x + 0.70y = 6 x 0.20
0.10x + 0.70y = 1.2 ______(1)
x + y = 6 ______(2)
Solve for x and y.
From (2),
x = 6 - y
Substituting in (1) we get,
0.10x + 0.70y = 1.2
0.10 (6 - y) + 0.70y = 1.2
0.6 - 0.10y + 0.70y = 1.2
0.6 + 0.60y = 1.2
0.60y = 1.2 - 0.6
0.60y = 0.6
y = 1
And,
x = 6 - y
x = 6 - 1
x = 5
Thus,
10% solution = 1 liter
70% solution = 5 liters
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HelpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss WILL GIVE 20 POINTS EASY
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.
What's meant by rate?
A rate in calculation displays how numerous times one number is contained in another. The rate of oranges to failures, for case, is eight to six if there are eight oranges and six failures in a coliseum of fruit. The proportions of oranges to the overall quantum of fruit are 814 for oranges and 68 for failures, independently. An equation in which two rates are made equal is known as a chance. As an illustration, you could express the rate as 1 3 if there's 1 joe and 3 girls( for every one boy there are 3 girls)Areas If the scale factor of the sides of two analogous polygons is m/ n
also the rate of the areas is (m/n)^2.
Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.
It's given that, the rate of peripheries of two analogous quadrilateral is 2 4
now,
to find the rate of area, we can take two quadrilaterals, say square.
Square ABCD of side 2 units and Square PQRS of side 4 units.
now rate of areas,
[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]
[tex]=\frac{2 \times 2}{4 \times 4}[/tex]
= 4/16
= 1/4
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89392i÷5×5+788 what is the answer
Answer:
89392i + 788
Step-by-step explanation:
The divide by 5 and the multiply by 5 cancel out, and we cannot simplify 89392i + 788 any further, since we don't know what i is. Therefore the answer is 89392i + 788.
Hope that helps!
What is the solution of the system
of equations?
y = __
2
3 x + 5
7x − 3y = 15
(0, 5)
B (2,19/3)
(4, 23/3)
(6, 9)
Answer:
2,19/3 this is answer this is correct
One reason to compute a correlation coefficient to measure the strength of the relationship between two variables is that ______.
One reason to compute a correlation coefficient to measure the strength of the relationship between two variables is that quantify the strength and direction of the correlation in a precise and standardized way..
When we have two variables that are related, we say that there is a correlation between them. The most common way to visually represent a correlation is by plotting the data on a scatter plot, where each point represents a pair of values for the two variables.
While a scatter plot is a useful tool to visualize the relationship between two variables, it doesn't tell us how strong or weak the correlation is. For instance, two variables might show a positive correlation, but the scatter plot might be quite dispersed, indicating that there is a lot of variability in the data. In this case, we would say that the correlation is weak. On the other hand, if the scatter plot is tightly clustered around the line, we would say that the correlation is strong.
This is where the correlation coefficient comes in. The correlation coefficient is a mathematical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation.
To compute the correlation coefficient, we first need to calculate the covariance between the two variables. Covariance is a measure of how much the two variables vary together, and it is defined as the sum of the products of the deviations of the values from their respective means. Once we have the covariance, we can divide it by the product of the standard deviations of the two variables to get the correlation coefficient.
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