Answer:
x=9
Step-by-step explanation:
this is solved by using cover and cancel so we can isolate the x variable
1) first add 72 to both sides.
6x=54
2) second divide both sides by 6
3) x=9
which direction does the gradient v point in the direction of maximum increase or maximum decrease in v
The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.
The gradient of a scalar-valued function is a vector that points in the direction of the maximum increase of the function.
In other words, if we consider a point in the domain of the function and take the gradient at that point, the direction of the gradient vector indicates the order in which the function increases the most from that point. Conversely, the negative gradient points in the direction of the maximum decrease of the function.
Specifically, let f be a scalar-valued function of n variables [tex](f: R^n - > R),[/tex]and let x be a point in the domain of f. The gradient of f at x is defined as the vector:
[tex]grad f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)[/tex]
where ∂f/∂xi denotes the partial derivative of f with respect to xi evaluated at x, the direction of the gradient vector grad f(x) at x is the direction in which f increases the most from x, and the magnitude of the gradient vector is the rate of change of f at x in that direction.
The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.
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Write a quadratic function f whose zeros is 7
The quadratic function, x2 + 14x + 49 f, would have 7 as the lone zero.
What are function?Any subset of a Cartesian product is a relation.
For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."
These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.
A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).
A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.
As you can see from these definitions, every function is a relation from X to Y, but not vice versa .
(x - 7)(x - 7)
⇒ (x - 7)²
⇒ x² + 7²+ 2 × 7 × x
⇒ x² + 49 + 14x
⇒ x² + 14x + 49
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Thomas bought 120 whistles, 168 yo-yos and 192 tops . He packed an equal amount of items in each bag.
a) What is the maximum number of bag that he can get?
Answer:
To find the maximum number of bags that Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192.
Prime factorizing the three numbers:
120 = 2^3 x 3 x 5
168 = 2^3 x 3 x 7
192 = 2^6 x 3
The GCD is the product of the common prime factors with the lowest exponents, which is 2^3 x 3 = 24.
So, Thomas can pack the items into 24 bags, each containing an equal number of whistles, yo-yos, and tops.
Answer:
Step-by-step explanation:
To find the maximum number of bags that Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192.
We can start by finding the prime factorization of each number:
120 = 2^3 × 3 × 5
168 = 2^3 × 3 × 7
192 = 2^6 × 3
Then we can find the GCD by taking the product of the smallest power of each common prime factor:
GCD = 2^3 × 3 = 24
Therefore, Thomas can pack a maximum of 24 bags.
y=4(x+5)^2+16 can you help me
To solve this equation, begin by expanding the parentheses.
y = 4x² + 40x + 100 + 16
Then, collect like terms on the left hand side.
y = 4x² + 40x + 116
Finally, rearrange the equation to get y on the left side.
4x² + 40x - (y - 116) = 0
The final answer will be a quadratic equation.
PLEASE ANSWER THIS QUESTION, 20 POINTS!!
Answer:
∠1 = 50
∠2 = 50
∠3 = 80
∠4 = 130
∠5 = 130
Step-by-step explanation:
∠1 = 180 - 130 = 50
∠2 = ∠1 = 50
∠3 = 180 - ∠1 - ∠2 = 180 - 50 - 50 = 80
∠4 = 180 - ∠2 = 180 - 50 = 130
∠5 = ∠4 = 130
A convex, 11-sided polygon can have at most how many acute interior angles?
Note: Convex means that each interior angle measure is less than 180 degrees
Answer: At most 18 acute angles
Step-by-step explanation:
The sum of the interior angles of an n-sided polygon is (n-2) × 180 degrees. In a convex polygon, each interior angle is less than 180 degrees.
Let a₁, a₂, ..., a₁₁ be the interior angles of the 11-sided polygon. Then the sum of the interior angles is:
a₁ + a₂ + ... + a₁₁ = (11-2) × 180 = 1620 degrees
Since each angle is acute, we know that each angle is less than 90 degrees. Let A be the number of acute angles. Then the sum of the acute angles is at most:
A × 90
So we have:
a₁ + a₂ + ... + a₁₁ ≤ A × 90
Substituting the sum of the interior angles, we get:
1620 ≤ A × 90
Solving for A, we get:
A ≤ 18
Therefore, the polygon can have at most 18 acute angles.
PLEASEE HELP!
Draw an angle that is 150 degrees.
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to draw an angle that is 150}^{\circ}.[/tex]
[tex]\textsf{We will need a Protractor to draw this angle.}[/tex]
[tex]\large\underline{\textsf{To Draw an Angle with a Protractor;}}[/tex]
[tex]\textsf{First, notice a point at the bottom of the Protractor. This is where we will start.}[/tex]
[tex]\textsf{Draw a Straight Line from the point to the 0}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Secondly, use a ruler to carefully draw a straight line towards the 150}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Note that some Protractors may be different from others. Similar steps should apply.}[/tex]
[tex]\textsf{Refer to the picture. It represents what the angle should look like afterwards.}[/tex]
To do :-
To draw a angle of 150° .Instruments required:-
A pair of compasses ,A ruler ,A pencil ,and a protactorSteps of construction:-
Draw a line segment of desired length.Taking a point on the line , draw a semicircle using a compass .Taking G as centre cut an arc on the semicircle mark the point of intersection as I .Taking I as centre cut another arc on the semicircle , mark it as point J .Taking J and I as center, cut an arc such that both the arcs intersect each other, mark it as point D .Join C and D .Taking F as centre again cut an arc on the semicircle, mark it as point E .Join E and C .Using a protactor you can check whether the angle formed is 150° or not .Hence angle ECB represents 150° .
Precaution:- do not change the arm length of the compass.
and we are done!
13) Raymond and Kevin want to purchase a house. They offer $235,000 with 30% down payment. They are pre-qualified for a 30-year loan at 3.8%. Calculate their anticipated monthly payments.
Answer:
Step-by-step explanation:
The down payment is 30% of $235,000, which is $70,500. This means they are financing the remaining amount of $164,500.
Using the loan amount, interest rate, and loan term, we can calculate the monthly payment using the formula for a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
where:
M = monthly payment
P = loan amount
i = monthly interest rate (annual rate divided by 12)
n = total number of payments (loan term in years multiplied by 12)
Plugging in the numbers, we get:
M = 164500 [ 0.038/12 (1 + 0.038/12)^360 ] / [ (1 + 0.038/12)^360 – 1]
Simplifying this expression, we get:
M = $765.84
Therefore, their anticipated monthly payments would be $765.84.
PLEASE HELP AND SHOW THE WORK
An equation of the line that goes through the point (-1, -3) and (3, 5) is y = 2x - 1.
An equation of the line in slope-intercept form that is perpendicular to the equation for obstacle 1 is y = -x/2 + 3.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (-1, -3), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - (-3) = \frac{(5- (-3))}{(3-(-1))}(x -(-1))\\\\y +3 = \frac{(5+3)}{(3+1)}(x +1)[/tex]
y + 3 = 2(x + 1)
y = 2x + 2 - 3
y = 2x - 1
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
2 × m₂ = -1
m₂ = -1/2.
At point (-4, 5), an equation of the line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x + 4)
y = -x/2 - 2 + 5
y = -x/2 + 3
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In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $750, which is a profit of $749. If you lose, you lose $1. Your probability of winning is 0.001.
The expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
What is outcome?The term "outcome" generally refers to the result or effect of an action, process, or event. It refers to what happens as a consequence of a particular decision, activity, or circumstance.
According to question:To calculate the expected value, we multiply the possible outcomes by their probabilities and then sum them up.
Let's start with the possible outcomes:
If you win, you make a profit of $749, so the outcome is $749.
If you lose, you lose $1, so the outcome is -$1.
The probabilities are:
Probability of winning is 0.001.
Now we can calculate the expected value:
Expected value = (0.001 * $749) + (0.999 * -$1)
Expected value = $0.748 - $0.999
Expected value = -$0.251
Therefore, the expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
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A test consists of 30 multiple choice questions, each with five possible answers, only one of which is correct. find the mean and the standard deviation of the number of correct answers. round the answers to the nearest hundredth.
The mean and standard deviation for 30 multiple-choice questions for the number of correct answers is Mean(μ) = 6 and Standard deviation(σ) = 2.19.
What is mean?
A collection of values are averaged to form the mean. The total points were divided by the total scores. When population samples are tiny, the mean is sensitive to extreme scores. For example, if two students in a class of 20 earned significantly higher than the rest, the mean will be skewed higher than the other students' scores might suggest. When using means, larger sample sizes are preferable.
Define standard deviation.
In statistics, a measure of variability known as the standard deviation ( standard deviation ) is frequently used. It demonstrates how different things are from the norm. (mean). When the SD is low, the data tend to be close to the mean, while when it is high, the data are dispersed over a wide variety of values.
Given: number of questions(n) = 30, p = [tex]\frac{1}{5}[/tex], q = [tex]\frac{4}{5}[/tex]
Mean μ = n*p
= 30 *[tex]\frac{1}{5}[/tex]
μ = 6
Standard deviation σ = [tex]\sqrt{n*p*q}[/tex]
= [tex]\sqrt{30*\frac{1}{5}*\frac{4}{5}}[/tex]
= [tex]\sqrt{4.8}[/tex]
σ = 2.19
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the answer is supposed to be 799 & 7188, but I don't know how to get there
Doing simple algebra with the two summations we can see that:
[tex]\Sigma x = 799\\\\\Sigma x^2 = 7,188[/tex]
How to find the values of the two summations?First, we know that there are 97 passengers, and we know that the summation:
[tex]\Sigma (x - 5) = 314[/tex]
Where x represents the weights.
Then we can rewrite that sum as:
[tex]\Sigma (x - 5) = \Sigma x - 97*5[/tex]
And replace that in the original equation to get:
[tex]\Sigma x - 97*5 = 314\\\Sigma x = 314 + 5*97 = 799[/tex]
So that is the first summation, now let's get the second one, we can rewrite the summation as:
[tex]\Sigma (x - 5)^2 = \Sigma x^2 - 10x +25 \\\\\Sigma x^2 - \Sigma 10x + \Sigma 25[/tex]
Where remember we have 97 terms, and the summation is equal to 1623, then:
[tex]\Sigma x^2 - \Sigma 10x + 25*97 = 1623[/tex]
Now we can replace the second term by the thing we found earlier:
[tex]\Sigma x^2 - 10\Sigma x + 25*97 = 1623\\\\\Sigma x^2 - 10*799 + 25*97 = 1623\\\\\Sigma x^2 = 1623 + 10*799 - 25*97\\\\\Sigma x^2 = 7,188[/tex]
That is the answer.
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You roll one six-sided die. A friend looks at the number and tells you that it is an odd number. What is the probability that you rolled a 3?
Answer: 1/3 chance or 33.33333%
Step-by-step explanation: There are only 3 odd numbers on the die, 1,3,5 so there is a 1/3 chance it is 3
Consider the following algebraic statements and determine the values of x for which each statement is true.
8=-|x|
Answer:
This is false.
Step-by-step explanation:
Since absolute value bars change negatives into positives and positive into themselves (positives) we can put the example:
[tex]-|8|\\[/tex]
When we remove the absolute value bars, 8 will still equal 8. But, we have a negative, therefore the 8 has a negative after being simplified with absolute value.
x = -8, not positive 8.
Answer:
Ther are no values of x that would make this statement true. There is no solution.
Step-by-step explanation:
here are the factors of sixteen and twenty. click the factors that are common to both numbers. (choose 3)
The common factors of sixteen and twenty are 1, 2, and 4.
The factors of sixteen are 1, 2, 4, 8, and 16. The factors of twenty are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, and 4.
To calculate the factors of sixteen, we can start by dividing sixteen by two until we cannot divide any further. We can start with sixteen divided by two, which equals eight. Eight divided by two equals four. Four divided by two equals two. Two divided by two equals one. As we can see, the factors of sixteen are 1, 2, 4, 8, and 16
To calculate the factors of twenty, we can start by dividing twenty by two until we cannot divide any further. We can start with twenty divided by two, which equals ten. Ten divided by two equals five. Five divided by two equals two. Two divided by two equals one. As we can see, the factors of twenty are 1, 2, 4, 5, 10, and 20.The common factors of sixteen and twenty are 1, 2, and 4. This can be determined by comparing the two lists of factors. As we can see, 1, 2, and 4 are present in both lists.
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Complete question
What are the common factors of sixteen and twenty ?
Help please! Appreciate the help
For the given statements for domain and range, option 3 and option 4 are correct answers.
What is domain and range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. With functions, we enter various numbers, and the output is a new set of numbers. The two essential characteristics of functions are domain and range. A function's domain and range are its constituent parts.
The domain of the function are all the input values while the range are the output values of the function for the given input.
In the given options, option 3 and 4 are correct as the functions have the same input but not the same output.
That is, they have the same domain, all real numbers, but not the same range.
Hence, for the given statements for domain and range, option 3 and option 4 are correct answers.
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Please help I-readyyyyyy
A large drug company must determine how many sales representatives to assign to each of four sales districts. The cost of having ???? (???? > 0) representatives in a district is 88,000 + 80,000???? dollars per year, and you only pay 88,000 fixed cost if there is at least one sales representative at that district. If a sales rep is based in a given district, the time it takes to complete a call on a doctor (i.e., the sales rep travels to the doctor’s office) in each of the actual sales call district is given in the following table, where times are in hours: Actual Sales Call District Rep’s Base District 1 2 3 4 1 1 4 5 7 2 4 1 3 5 3 5 3 1 2 4 7 5 2 1 Each sales rep can work up to 160 hours per month. Each month a certain number of calls, given in the following table, must be made in each district (i.e., this is the total number of calls to be completed by all of the sales reps). Number of calls District 1 50 District 2 80 District 3 100 District 4 60 A fractional number of representatives in a district is not permissible. Determine how many representatives should be assigned to each district.
Answer:
Dont understand. Repeat question?
Step-by-step explanation:
Can someone pls help me it would mean so much to me
Answer: y = 3x-2 (for first question)
Step-by-step explanation:
Equation of the line: y = mx+c. For A, it passes through (0, -2) and has a gradient of 3. So, you substitute the values inside the equation.
x = 0
y = -2
m = 3
-2 = 0+c
c= -2
ans: y = 3x-2
Use the same method to complete the rest of the questions. GL
Note: I am just a student, if I get this wrong I hope someone corrects me, thanks
convert 49% to a fraction
Answer:
To convert 49% to a fraction, we can simply write it as 49/100. This is because a percentage is a way of expressing a number as a fraction of 100. So 49% means 49 out of 100, which can be written as the fraction 49/100.
Answer:
49/100
Step-by-step explanation:
Percent means out of 100.
49%
49/100
change these fractions to decimals 1/35
Answer:
Step-by-step explanation:
ASAP PLEASE FOR A TEST!!!A line passes through (-1, 7) and (2, 10).
Which answer is the equation of the line?
O-3x+y=4
Ox+y=12
O = x+y=8
-3x+y=16
Answer:
i think this is the answer!! good luck
Mortgage
Status Current Past
Due In
Foreclosure Repossessed Total
Number 156,330 58,310 8,550 5,590 228,780
(The four categories are mutually exclusive; for instance, "Past Due" refers to a mortgage whose payment status is past due but is not in foreclosure, and "In Foreclosure" refers to a mortgage that is in the process of being foreclosed but not yet repossessed.)
(a)
Find the probability that a randomly selected subprime mortgage in the state during November 2008 was neither in foreclosure nor repossessed. HINT [See Example 1.] (Round your answer to two decimal places.)
(b)
What is the probability that a randomly selected subprime mortgage in the state during November 2008 was not current? (Round your answer to two decimal places.)
a) The probability that a randomly selected subprime mortgage in the state during November 2008 was neither in foreclosure nor repossessed is 0.50.
b) The probability that a randomly selected subprime mortgage in the state during November 2008 was not current is 0.32.
What is the probability?Probability describes the chance or likelihood that an expected outcome or event does or does not occur.
Probability is the quotient of the expected outcome over the total number of possible outcomes or events.
Probabilities can be stated in ratios (fractions, decimals, or percentages).
Mortgage Status
Current Past Due In Foreclosure Repossessed Total
Number 156,330 58,310 8,550 5,590 228,780
The number of subprime mortgage neither in foreclosure nor repossessed = 114,640 (156,330 + 58,310)
The probability that a subprime mortgage in the state was neither in foreclosure nor repossessed = 0.50 (114,640/228,780).
The number of subprime mortgage that was not current = 72,450 (58,310 + 8,550 + 5,590) or (228,780 - 156,330)
The probability that a subprime mortgage in the state was not current = 0.32 (72,450/228,780).
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Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation.
The result of the division in ordinary decimal notation is 300.
Scientific notation, also known as standard form or exponential notation, is a method of expressing very large or very small numbers in a compact and standardized way.
To perform the indicated operation, we need to divide 0.00036 by 0.0000012.
First, let's express both numbers in scientific notation
0.00036 = 3.6 x 10^(-4)
0.0000012 = 1.2 x 10^(-6)
Now we can divide the two numbers and simplify
3.6 x 10^(-4) / 1.2 x 10^(-6) = (3.6 / 1.2) x 10^(-4-(-6)) = 3 x 10^(2)
Finally, we can convert this result back to ordinary decimal notation
3 x 10^(2) = 300
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The given question is incomplete, the complete question is:
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation. 0.00036/0.0000012
light of 650 nm wavelength illuminates a single slit of width 0.20 mm . (figure 1) shows the intensity pattern seen on a screen behind the slit.
the intensity pattern visible on a screen at 1.168 metres behind the slit.
That is the answer to the question "650 nm light shines on two slits that are separated by 0.20 mm. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).
How far away from you is the screen?"
It is possible to specify that the distance to the screen is d=1.168m.
The answer to the question is that 650 nm light illuminates two slits that are 0.20 mm apart. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).
How far is the screen from you?
The equation for the distance is typically presented mathematically as
d=1.168m
As a result,
d=1.168m is the distance to the screen.
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Given two points (x1, y1) and (x2, y2) in the cartesian plane, show that the slope
m of a line is of the form
m =y2 − y1÷x2 − x1
assuming that x2≠ x1
therefore, we have shown that: [tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex] assuming that x2 ≠ x1.
What is slope?Slope refers to the measure of steepness of a line or a curve. In mathematics, slope is usually denoted by the letter "m" and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on a line.
The formula for calculating the slope between two points (x1, y1) and (x2, y2) on a line is:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex]
by the question.
To finds the slope of a line passing through two points (x1, y1) and (x2, y2), we use the slope formula:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex]
This formula represents the change in y divided by the change in x between the two points.
Now, assuming that x2 ≠ x1, we can simplify the formula as follows:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})*(1/1)[/tex]
Multiplying the numerator and denominator by 1, which in this case is (x2 - x1) / (x2 - x1), we get:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})*(x_{2}-x_{1})/(x_{2}-x_{1})[/tex]
Simplifying the numerator, we have:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})/[(x_{2}-x_{1})*1][/tex]
The term (x2 - x1) cancels out, leaving us with:
[tex]m=(y_{2}-y_{1} /1[/tex]
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From the given graph, how many students worked at least 10 hours per week?
Answer:
39.
Step-by-step explanation:
From the group of 10-14 hours worked per week, 8 students.
From the group of 15-19 hours worked per week, 4 students.
From the group of 20-24 hours worked per week, 12 students.
From the group of 25-29 hours worked per week, 8 students.
From the group of 30-34 hours worked per week, 4 students.
And finally, from the group of 35+ hours worked per week, 3 students.
So, 8+4+12+8+4+3 = 39 students.
Simplify without calculator: (-5) (7)+4×5 (Show all calculations)
Step-by-step explanation:
this is the answerrr
without calculator
h=p√m2+n find the value of h when p = 3, n=20 , m=6
Answer:
We can substitute the given values of p, m, and n into the formula for h:
h = p√(m^2 + n)
h = 3√(6^2 + 20)
h = 3√(36 + 20)
h = 3√56
We can simplify this by factoring 56 into its prime factors:
h = 3√(2^3 × 7)
h = 3 × √(2^2 × 7) × √2
h = 3 × 2√7
Therefore, when p = 3, n = 20, and m = 6, the value of h is 6√7 or approximately 13.42.
Imagine we have a simple linear model, with one X predicting one Y, where R-squared is equal to .81. What was the correlation between X and Y?A) .81 (or maybe -.81)B) There is not enough information to tell.C) .66 (or maybe -.66)D) .90 (or maybe -.90)
The correlation between X and Y can be calculated using the formula r = SQRT(R-squared).The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1
In this case, the R-squared value is 0.81, so the correlation between X and Y is r = SQRT(0.81) = 0.9 (or -0.9 depending on the direction of the relationship).The correlation between X and Y can be calculated using the formula r = SQRT(R-squared). The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1, where -1 is a perfectly negative linear relationship, 0 is no linear relationship, and 1 is a perfectly positive linear relationship. In this case, the correlation between X and Y was 0.9, indicating a strong linear relationship between the two variables.
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