1/3 of a full rotation: (-0.5, √3/2)
1/2 of a full rotation: (-1, 0)
2/3 of a full rotation: (0.5, -√3/2)
These are the coordinates of point P after the corresponding rotations around the unit circle's center.
To find the coordinates of point P after the unit circle rotates a certain amount counter-clockwise around its center, we can use the properties of the unit circle and the trigonometric functions.
1/3 of a full rotation:
A full rotation in the unit circle corresponds to 360 degrees or 2π radians. Therefore, 1/3 of a full rotation is equal to (1/3) * 360 degrees or (1/3) * 2π radians.
When the unit circle rotates 1/3 of a full rotation, point P will end up at an angle of (1/3) * 2π radians or 120 degrees from the positive x-axis.
In the unit circle, the x-coordinate of a point on the circle represents the cosine of the angle, and the y-coordinate represents the sine of the angle.
At an angle of 120 degrees or (1/3) * 2π radians, the cosine is -0.5 and the sine is √3/2.
Therefore, the coordinates of point P after rotating 1/3 of a full rotation are (-0.5, √3/2).
1/2 of a full rotation:
Similarly, 1/2 of a full rotation is equal to (1/2) * 360 degrees or (1/2) * 2π radians.
When the unit circle rotates 1/2 of a full rotation, point P will end up at an angle of (1/2) * 2π radians or 180 degrees from the positive x-axis.
At an angle of 180 degrees or (1/2) * 2π radians, the cosine is -1 and the sine is 0.
Therefore, the coordinates of point P after rotating 1/2 of a full rotation are (-1, 0).
2/3 of a full rotation:
Again, 2/3 of a full rotation is equal to (2/3) * 360 degrees or (2/3) * 2π radians.
When the unit circle rotates 2/3 of a full rotation, point P will end up at an angle of (2/3) * 2π radians or 240 degrees from the positive x-axis.
At an angle of 240 degrees or (2/3) * 2π radians, the cosine is 0.5 and the sine is -√3/2.
Therefore, the coordinates of point P after rotating 2/3 of a full rotation are (0.5, -√3/2).
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Part A: solve the equation---
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
but i have to use the values x= -4,0,5. can some one please help me? i'm am so confused!!!
Answer:
Step-by-step explanation:
I understand your confusion. Let's go through the steps together to solve the equation correctly:
Given equation: 5 + x - 12 = 2x - 7
Combine like terms on the left side and the right side of the equation:
x - 7 = 2x - 7
Now, let's isolate the variable x. Subtract x from both sides of the equation:
x - x - 7 = 2x - x - 7
Simplifying:
-7 = x - 7
Next, add 7 to both sides of the equation:
-7 + 7 = x - 7 + 7
Simplifying:
0 = x
Therefore, the solution to the equation is x = 0.
If you need to use the values x = -4, 0, and 5, you can substitute each value into the original equation to check if it satisfies the equation. Let's do that:
For x = -4:
5 + (-4) - 12 = 2(-4) - 7
-11 = -15 - 7
-11 = -22
The equation is not satisfied for x = -4.
For x = 0:
5 + 0 - 12 = 2(0) - 7
-7 = -7
The equation is satisfied for x = 0.
For x = 5:
5 + 5 - 12 = 2(5) - 7
-2 = 3
The equation is not satisfied for x = 5.
Therefore, the correct solution to the equation is x = 0. The values x = -4 and x = 5 do not satisfy the equation.
Cara used the order of operations to evaluate the expression below. StartFraction 4 (7 minus 13) over 3 EndFraction + (negative 4) squared minus 2 (6 minus 2) = StartFraction 28 minus 13 over 3 EndFraction + (negative 4) squared minus 2 (4) = StartFraction 15 over 3 EndFraction + 16 minus 18 = 5 + 16 minus 8 = 13. What was Cara’s first error?
Cara's first error occurred when she simplified the expression (negative 4) squared.
According to the order of operations (PEMDAS/BODMAS), exponentiation should be performed before any other operations. However, Cara incorrectly squared only the negative sign and not the entire number.
As a result, she obtained a value of positive 4 instead of 16.
To correct the error, Cara should have squared the entire value of -4. Squaring a negative number yields a positive result. Thus, (-4) squared is equal to 16. By failing to correctly apply this rule, Cara ended up with an incorrect value in her expression.
The correct evaluation of the expression should have been:
StartFraction 4 (7 minus 13) over 3 EndFraction + (negative 4) squared minus 2 (6 minus 2) = StartFraction 4 (-6) over 3 EndFraction + 16 minus 2 (4) = -8 + 16 - 8 = 0.
Therefore, Cara's first error was in incorrectly squaring only the negative sign and obtaining a value of 4 instead of 16.
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HELP PLEASEEE!!
Drake predicted that he would be able to make 16 more pancakes with the remainder of his mix. however, he only made 10 pancakes. What was Drake's percent error?
Answer:
60%
Step-by-step explanation:
To find percent error, use the following equation:
Percent error = [tex]\frac{prediction-actual}{actual}[/tex]×100
=[tex]\frac{16-10}{10}[/tex]
=[tex]\frac{6}{10}[/tex]×100
=0.6×100
Drake's percent error is 60%.
The values in the table represent a function.
x
-6
7
4
3
-5
f(x)
8
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
(3) is
f(x)=-5 when x is
Done
The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (-6, 8).
f(x) = -5 when x is 4.
In function notation, we represent the input value as 'x' and the corresponding output value as 'f(x)'.
Looking at the first row of the table, we see that when x is -6, the corresponding value of f(x) is 8.
Therefore, we can write this ordered pair as (-6, 8) in function notation.
Similarly, we can determine that f(x) = -5 when x is 4 by examining the second row of the table.
The value of f(x) is -5 when x is 4, so we can express it as f(4) = -5.
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Whats the answer to this?
Answer: [tex]x=200[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]
[tex]\frac{1}{5}x-\frac{2}{3}(15)=30[/tex]
[tex]\frac{1}{5}x-10=30[/tex]
[tex]\frac{1}{5}x=40[/tex]
[tex]x=\frac{40}{\frac{1}{5}}[/tex]
[tex]x=40*\frac{5}{1}[/tex]
[tex]x=200[/tex]
Find Tan A 6-11, please?
Answer:
5) tan A = 0.42
6) Acute angle is less than 90°
7) Right angle is exactly 90°
8) Obtuse angle is greater than 90° but less than 180°
9) Straight angle is exactly 180°
10) Complementary angles add up to 90°
11) Supplementary angles add up to 180°
Step-by-step explanation:
tan A = opposite / adjacent
= 5/12
= 0.42
A solid oblique pyramid has a triangular base with a length of 8 inches and a height of 6 inches. The slant height of each triangular face is 10 inches. What is the volume of this pyramid?
a) 160 cubic inches
b) 200 cubic inches
c) 240 cubic inches
d) 280 cubic inches
The correct value of volume of the pyramid is 48 cubic inches.
To find the volume of the solid oblique pyramid, we can use the formula V = (1/3) * Base Area * Height. The base of the pyramid is a triangle, and the height is given as 6 inches.The formula for the area of a triangle is (1/2) * base * height. In this case, the base length is 8 inches and the height is 6 inches. Base Area = (1/2) * 8 * 6 = 24 square inches
Now, we can calculate the volume of the pyramid:
V = (1/3) * Base Area * Height
V = (1/3) * 24 * 6
V = 48 cubic inches
Therefore, the volume of the pyramid is 48 cubic inches.
None of the provided options (a, b, c, d) match the calculated volume of 48 cubic inches. Please double-check the given options or provide the correct options for further comparison.
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Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
Need Help
Answer: -27
Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
We can start by looking at the differences between consecutive terms in the list:
9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12
Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:
-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21
Therefore, we predict that the most probable next number in the list is -27.
GEOMETRY 50POINTS
FIND THE ANGLE OD DEPRESSION OF THE SLOPE
TYSM
Answer:
23.6°
Step-by-step explanation:
The angle of depression, x, is congruent to the bottom right angle of the triangle.
sin x = opp/hyp
sin x = 100/250 = 0.4
x = sin^-1 0.4
x = 23.6°
Assets Liabilities and Net Worth Reserves $51 Checkable Deposits $140 Loans 109 Stock Shares 130 Securities 100 Property 10 Refer to the accompanying consolidated balance sheet for the commercial banking system. Assume the required reserve ratio is 30 percent. All figures are in billions. If the commercial banking system actually loans the maximum amount it is able to lend, excess reserves will be reduced to
If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:
Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.
Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.
This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.
This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
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The lines shown below are parallel. if the green line has a slope of 3 what is the slope of the red line?
Answer:
3
Step-by-step explanation:
parallel lines have the same gradient
Brittany invests $1000 into a savings account with an annual simple interest rate of 3%. Her bank charges no annual fees. How much will Suzy have after 5 years? Show your work.
Answer:
$150
Step-by-step explanation:
Original Savings (Year 0): $1,000
Convert Interest rate into a decimal: 3 / 100 = 0.03
therefore the interest rate is 1.03
How much will be added each year?
$1,000 x 1.03 = $1,030--> $30this shows that $30 dollars will be added per year, the interest is a simple rate and so it will not increase per year.5 years = $30 x 5 = $150
Final sum: $1,000 x $150 = $1,150
Suzy will have $1,150 in her account at the end of a five year period.
What is the volume of this
figure?
A 774 cm³
B 3,546 cm³
C 843 cm3
D 2,250 cm³
Hello!
V
= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)
= 1,620cm³ + 630cm³
= 2,250cm³
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4
What was Brooke’s error?
She found the incorrect slope in step 1.
She mixed up the x- and y-coordinates when she plugged in the point in step 2.
She found the incorrect y-intercept in step 2.
She mixed up the slope and y-intercept when she wrote the equation in step 3
Answer:
she mixed up the slope and y- intercept in step 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
she correctly calculated the slope as m = - 4 and the y- intercept b = - 3
thus equation she should have is
y = - 4x - 3
Brooke's error was that she found the incorrect slope in step 1.
The slope formula is: m = (y₂ - y₁) / (x₂ - x₁)
Using the given points: m = (13 - 25) / (-4 - (-7)) m = -12 / 3 m = -4
So, the slope is -4, not -12/3 as Brooke calculated in step 1.
The correct equation for the line passing through the points (-7, 25) and (-4, 13) is: y = -4x - 3 (as found in step 3)
Which of the following is the graph of y=-(x-2)³-5?
-5-4-3-2-1
-5-4-3
S
-2+
-3
? 4
-4
-5
997
-6
-7
-8.
-9
& co
-10
1 2 3 45 x
1
2345
X
Answer:
Step-by-step explanation:
I cannot see the graphs.
Cecilia se compra un libro con la cuarta parte de su dinero y un cómic con la mitad del dinero que le quedaba. Al salir de la librería se da cuenta que le sobraron $8. ¿Cuál es la ecuación para conocer la cantidad de dinero que tenía en un inicio?
The equation to determine the initial amount of money Cecilia had is x = 0.
Let's denote the initial amount of money Cecilia had as "x" dollars.
According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.
Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.
Since she had $8 left, we can set up the equation:
((x - (1/4)x) - ((1/2)x - 8)) = 8
To simplify the equation, we can first combine like terms:
(x - (1/4)x - (1/2)x + 8) = 8
Now, let's solve the equation step by step:
(x - (1/4)x - (1/2)x + 8) = 8
Multiplying the fractions by their common denominator, which is 4, we get:
(4x - x - 2x + 32) = 32
Simplifying further:
(x + 32) = 32
Subtracting 32 from both sides:
x = 0
Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.
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The overnight temperature drops from 11°C to -2°C. B how many degrees has the temperature dropped?
Answer: I'm pretty sure it's 13.
Step-by-step explanation: Hope this helped!!
Mia makes $15.50 per hour. For the Memorial holiday she worked 6 hours and 30 minutes on Friday. On Saturday, she worked for 1 hour and 10 minutes less than she did on Friday and on Monday she worked 4 hours and 10 minutes. How much money did Mia make for the Memorial holiday?
Answer:
$248.00
Step-by-step explanation:
Hours worked on Friday: 6 hr and 30 min = 6.5 hr
Money earned on Friday: $15.5/hr x 6.5 hr = $100.75
Hours worked on Saturday: 6.5 hr - 1.167 hr = 5.33 *10 min = 10/60 = 0.1667 hr
Money earned on Saturday: $15.50 x 5.33 hr = $82.67
Hours worked on Monday: 4.167 hr
Money earned on Monday: $15.50/hr x 4.167 hr = $64.58
Total money made: 100.75 + 82.67 + 64.58 = $248.00
What will be the result of substituting 2 for x in both expressions below?
+4
x+6-x-2
O Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
O Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
O One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
Equivalent Algebraic expressions:Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expressionns.
Given the algebraic expressions,
[tex]\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2[/tex]
Substituting 2 for x in the first expression gives:
(1/2 × 2) + 4
1 + 4
5
Substituting 2 for x in the second expression gives:
2 + 6 - (1/2 ×2) - 2
8 - 1 - 2
8 - 3
5
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
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What is the solution for t in the equation?
2/3t-1/5t=2
Answer:
Step-by-step explanation:
To solve the equation (2/3)t - (1/5)t = 2 for t, we need to combine like terms and isolate the variable t. Here are the steps:
(2/3)t - (1/5)t = 2
To combine the fractions, we need to find a common denominator for 3 and 5, which is 15.
[(2/3)(5/5)]t - [(1/5)(3/3)]t = 2
(10/15)t - (3/15)t = 2
[(10 - 3)/15]t = 2
(7/15)t = 2
To isolate t, we can multiply both sides of the equation by the reciprocal of (7/15), which is (15/7).
[(7/15)t][(15/7)] = 2[(15/7)]
t = (2 * 15) / 7
t = 30/7
Therefore, the solution for t in the equation (2/3)t - (1/5)t = 2 is t = 30/7 or t ≈ 4.286.
WHOEVER CAN ANSWER 50 POINTS IF U CAN SOLVE IT PLEASE IM DESPERATE
Answer:
First, the graph is overall decreasing with two local maximums and two local minimums.
Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.
Considering the above observations we can state that:
The degree of f(x) is odd;The leading coefficient is negative;There are 5 distinct zeros;There are 2 relative maximum values.Please i give 25 points
71)
Mia buys 4 calculators and 2 pens for $20.60
Heidi buys 5 calculators and 3 pens for $26.90.
Write down a pair of simultaneous equations and solve
cost of a pen.
Answer:
Therefore, the cost of a pen is $2.30.
Step-by-step explanation:
Let's assign variables to represent the cost of a calculator and the cost of a pen.
Let c represent the cost of a calculator.
Let p represent the cost of a pen.
Based on the given information, we can form the following pair of simultaneous equations:
Equation 1: 4c + 2p = 20.60 (Mia buys 4 calculators and 2 pens for $20.60)
Equation 2: 5c + 3p = 26.90 (Heidi buys 5 calculators and 3 pens for $26.90)
To solve for the cost of a pen, we'll eliminate the variable c by multiplying Equation 1 by 5 and Equation 2 by 4. Then we'll subtract Equation 1 from Equation 2:
5 * (4c + 2p) = 5 * 20.60
4 * (5c + 3p) = 4 * 26.90
20c + 10p = 103.00
20c + 12p = 107.60
Subtracting Equation 1 from Equation 2:
(20c + 12p) - (20c + 10p) = 107.60 - 103.00
20c - 20c + 12p - 10p = 4.60
2p = 4.60
p = 4.60 / 2
p = 2.30
Therefore, the cost of a pen is $2.30.
Answer:
Let's assume that the cost of a calculator is x and the cost of a pen is y. Then we can write the following pair of equations:
4x + 2y = 20.60 (equation 1)
5x + 3y = 26.90 (equation 2)
To solve for the cost of a pen, we need to eliminate x from the equations. We can do this by multiplying equation 1 by 5 and equation 2 by -4, and then adding them:
(5)(4x + 2y = 20.60) becomes 20x + 10y = 103 (equation 3)
(-4)(5x + 3y = 26.90) becomes -20x - 12y = -107.60 (equation 4)
Adding Equation 3 and Equation 4 gives:
-2y = -4.60
Divide both sides by -2:
y = 2.30
Therefore, the cost of a pen is $2.30.
Step-by-step explanation:
MARK ME BRAINLIST
PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Pregunta 1
Resuelve el siguiente problema aplicando las estrategias de solución de problemas.
• El área de un triángulo es de 30 pies cuadrados y la base mide 5 pies. ¿Cuál es la
altura del triángulo en pulgadas?
Answer:
I can't understand the language but try people who can
Indefinite Integral for the equation
The antiderivative of ∫[[tex]x^\frac{1}{11}[/tex] - 7sin(x)]dx is:
[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex]
What is the indefinite integral?The indefinite integral, denoted as ∫f(x)dx, represents the antiderivative of a function f(x). It involves finding a function whose derivative is equal to the given function f(x).
Let's evaluate the indefinite integral of [tex]\int [x^\frac{1}{11} - 7sin(x)]dx[/tex]
To find the antiderivative of [tex]x^\frac{1}{11}[/tex], we add 1 to the exponent and divide by the new exponent:
[tex]\int x^\frac{1}{11} dx = (11/12)x^\frac{12}{11} + C_1[/tex], where C₁ is the constant of integration.
∫7sin(x)dx:
To find the antiderivative of 7sin(x), we use the trigonometric identity that the antiderivative of sin(x) is -cos(x):
∫7sin(x)dx = -7cos(x) + C₂, where C₂ is another constant of integration.
Combining the two results, the indefinite integral of [tex]\int[x^\frac{1}{11} - 7sin(x)]dx[/tex] is:
[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex],
where C = C₁ + C₂ represents the constant of integration.
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Complex fractions level 4
By algebra properties, the simplified form of the complex fraction is - (x - 4) / [120 · (x - 1)].
How to simplify a complex fraction
In this problem we find the case of a complex fraction that must be simplified by algebra properties. A simple fraction must be found. First, write the entire expression:
[1 / (3 · x² - 3)] / [5 / (x + 1) - (x + 4) / (x² - 3 · x - 4)]
Second, factor the parts of the fraction:
[1 / [3 · (x - 1) · (x +1)]] / [5 / (x + 1) - (x + 4) / [(x - 4) · (x + 1)]]
[1 / [3 · (x - 1) · (x +1)]] / [[5 · (x - 4) - (x + 4)] / [(x - 4) · (x + 1)]]
Third, eliminate the rational fraction:
[(x - 4) · (x + 1)] / [- 120 · (x - 1) · (x + 1)]
Fourth, eliminate common binomials:
- (x - 4) / [120 · (x - 1)]
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on a scale drawing 9 inches represents 11 miles how many inches represent 55 miles
Answer:
45 inches represent 55 miles on the scale drawing.
Step-by-step explanation:
To solve this proportion, we can set up the following ratio:
9 inches / 11 miles = x inches / 55 miles
We can cross-multiply to solve for x:
9 inches * 55 miles = 11 miles * x inches
495 inches = 11 miles * x inches
Now, we can isolate x by dividing both sides by 11 miles:
495 inches / 11 miles = x inches
Simplifying the expression:
45 inches = x inches
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
B. Lenghts of the diagonals
Step-by-step explanation:
in this chart, × is the length of a persons forearm in centimeters and y is the persons height in centimeters. the question is if someones forearm (x) is 24.5 cm, how tall would they be? how do i find this? and how would i make a linear regression graph? thanks
The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.
How to construct and plot the data in a scatter plot?In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;
y = 3.01x + 89.63
Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;
y = 3.01x + 89.63
y = 3.01(24.5) + 89.63
y = 163.375 ≈ 163.38 centimeters.
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