The total number (n) of distinct solutions of the equation (x + y + z = 15) with the assumption that x, y and z are all nonnegative integers is 153.
The generating function for the number of solutions of the equation (x + y + z = n) is given by the binomial coefficient (n+2)C2, where C2 is the number of ways to choose 2 objects from a set of n+2 objects.
The number of solutions for the given equation (x + y + z = 15) is then given by:
(15+2)C2 = (17C2)
We can also use the formula for binomial coefficient: nCr = n! / (r! (n-r)!)
17C2 = (17!) / (2! * 15!) = 153
So the total number of distinct solutions of the equation (x + y + z = 15) with x, y, z non-negative integers is 153.
"
Complete question
what is the total number n of distinct solutions the equation (x + y + z = 15) after we impose that x, y and z are all nonnegative integers?
"
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What is the equation of the line that passes through the point (3,-6) and has a slope of -3?
Answer:
y = -3x + 3
Step-by-step explanation:
the equation of a line in point-slope form is.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (-6) = -3 (x - 3)
y+6 = -3x+9
Answer:
y = -3x+3
Step-by-step explanation:
Remember that y = mx+c
The slope is m aka the gradient and we know that that's -3.
So just chuck it into the equation:
y = -3x + c
We still have to find c (which is the y intercept)
So substitute the point (3,-6) into the equation
We will have: -6 = -3(3) +c
Once you do algebra you'll get 3=c
So substitute that back into the equation (without the point (3,-6) since we only need the equation)
y = -3x + 3
Maya is spending money at the average rate of 3 dollars per day. After 14 days she has 68 dollars left. The amount of money left depends on the amount of days that have passed.
Answer:
$110 is what she started with
Step-by-step explanation:
i need the answer because i dont know
The functions f and have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.
What is a graph ?
Graph can be defined as the visual representation of the given data using ordered pairs.
Graph of f(x)
You can read the y-intercept on the graph. It is the value of y-coordinate when x = 0; so ti is y = 6.
The axis of simmetry is the vertical line that split the graph into two symmetrical forms. That is the same that the vertical line that passes through the vertex. You can see that it is x = 2
2) Table of values of g(x)
The y-intercept is the value of y-coordinate when x = 0, so it is y = 8.
The axis of symmetry is x = 2.
Hence, The functions f and have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.
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calculate the sample covariance. b. calculate the sample correlation coefficient. c. describe the relationship between x and y.
The relationship between x and y can be described based on the value of the sample correlation coefficient.
Sample covariance measures the degree to which two variables are linearly related and the direction of their linear relationship. The formula for sample covariance is:
[tex]Cov(x,y) = (1/(n-1)) * \Sigma(x-\bar x)(y- \bar y)[/tex] where,
[tex]\bar x[/tex] and [tex]\bar y[/tex] are the sample means of x and y, respectivelyn is the sample size.The sample correlation coefficient, also known as Pearson's correlation coefficient, measures the degree to which two variables are linearly related and the direction of their linear relationship. It is a normalized version of the sample covariance, with a value between -1 and 1. The formula for the sample correlation coefficient is:
r = Cov(x,y) / (s1 * s2) where,
s1 and s2 are the sample standard deviations of x and y, respectively.To calculate the sample covariance and sample correlation coefficient, we need to have a sample of data containing the variables x and y. Once we have the data, we can calculate the sample means, and sample standard deviations, and then use the formulas above to calculate the sample covariance and sample correlation coefficient.
The relationship between x and y can be described based on the value of the sample correlation coefficient.
A value close to 1 indicates a strong positive linear relationshipA value close to -1 indicates a strong negative linear relationship A value close to 0 indicates no linear relationship.Learn more about covariance here:
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The complete question is:
Given a sample of data containing the variables x and y, calculate the sample covariance and the sample correlation coefficient, and describe the relationship between x and y.
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1/10(x+16)=-2(3-X)
X=?
Answer: 2) x=60
Step-by-step explanation:
a researcher randomly draws samples of iq scores for 50 individuals. what proportion of samples will have means less than 80?
A whopping 95% of people fall within the IQ ranges of 70 and 130. 99.7% of people in the world have IQs between 55 and 145. Only about 0.3% of people have IQ scores that fall outside of this range (less than 55 or higher than 145).
According to the one-standard-deviation rule, 32 percent of the population has an IQ score that is at least 15 points off from 100: 16 percent have IQs over 115, and 16 percent have IQs below 85.
The equation IQ=mc100, where m is the mental age and c is the chromological age, determines a person's IQ. Find the range of their mental ages if a group of 12-year-old youngsters has an IQ between 80 and 140.
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I need the parent equations please and thank you
The parent function by reversing rigid transformations are, respectively:
Case 6: f(x) = x³
Case 7: f(x) = √x
Case 8: f(x) = ㏒ x
Case 9: f(x) = |x|
Case 10: f(x) = x²
How to determine the parent function
Parent functions are the most simple form of a kind of expression (i.e. power, exponential, logarithms, roots). In this problem we find five cases of images of parent functions, that is, versions modified by rigid transformations. The most common rigid transformations are, respectively:
Horizontal translation
f(x) → f(x - k)
Vertical translation
f(x) → f(x) + k
Reflection about x-axis
f(x) → - f(x)
Reflection about y-axis
f(x) → f(- x)
Vertical dilation
f(x) → k · f(x)
Horizontal dilation
f(x) → f(k · x)
Now we proceed to revert the rigid transformations used in each function:
Case 6
f(x) = 2 · (x + 6)³ + 11
Vertical translation - Horizontal translation - Vertical dilation
f(x) = x³
Case 7
f(x) = 7 + (1 / 2) · √(x - 3)
Vertical translation - Horizontal translation - Vertical dilation
f(x) = √x
Case 8
f(x) = 5 - ㏒ (x + 1)
Vertical translation - Reflection about x-axis - Horizontal translation
f(x) = ㏒ x
Case 9
f(x) = - 3 · |x + 10| + 7
Vertical translation - Reflection about x-axis - Dilation - Horizontal translation
f(x) = |x|
Case 10
f(x) = (3 / 5) · (x - 8)² - 4
Vertical translation - Dilation - Horizontal translation
f(x) = x²
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Todd made a table to show different plans he
can use to save $500. Complete the table. Which
plan can Todd use to save $500 in less than
16 weeks and have $20 extra
Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.
The number of weeks and y, which is the equation we wish to utilise, stand in for the total amount saved. Our equation will then be 15 x. Instead of the other way around, he will save 330.
Plan Amount saved per week Total amount saved in 16 weeks
1 $31.25 $500
2 $35 $560 (with $60 extra)
3 $40 $640 (with $140 extra)
Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.
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Use a graphing calculator to solve (1/2)^7x+1=-9
Answer:approximatly -1.63092975357148
Step-by-step explanation:To solve the equation (1/2)^7x+1 = -9, we first need to get all the terms on one side of the equation by subtracting 1 from both sides. This gives us (1/2)^7x = -10.
Next, we need to get x by itself, so we take the log base 2 of both sides.
This gives us log base 2 of (1/2)^7x = log base 2 of -10.
The log base 2 of (1/2)^7 is -7, so we have -7x = log base 2 of -10
Finally, we divide both sides by -7 and get x = log base 2 of -10/-7
Using a calculator we can calculate this value which is approximatly -1.63092975357148
x = log base 2 of -10/-7 = -1.63092975357148
A number is doubled and the result is increased by 8. If the final result is 36. What is the number?
Answer:
14
Step-by-step explanation:
This question can be expressed as the following linear equation:
2x+8=36, where x is our unknown number.
From here,
2x+8=36
2x=28 (-8 both sides)
x=14 (/2 both sides)
Therefore the number is 14
Lauren deposited $300 to start her savings account. After one year, she had $312 in
her account. If she did not deposit or withdraw any money that year, how much
interest did she earn?
N
Answer:
12 dollars
Step-by-step explanation:
she started with 300 and didn't add any money or take any away... sooo she earned $12 in interest
quadrilateral PQRS is a parallelogram
Check the picture below.
what is the slope and intercept of the linear plot of the given arrhenius equation using semilogy function?
The slope is -Ea/R and the intercept is equal to ln(A)
The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant of a chemical reaction and temperature:
k = Ae^(-Ea/RT)
where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
The slope and intercept of the linear plot of the Arrhenius equation using a semilogarithmic (semilog) plot can be determined by transforming the equation into a linear form. The semilog plot is created by taking the logarithm of the rate constant (k) on the y-axis and the reciprocal of the temperature (1/T) on the x-axis:
ln(k) = ln(A) - Ea / RT
The slope of the plot is equal to -Ea/R and the intercept is equal to ln(A). By fitting a straight line to the semilog plot, the values of Ea and A can be determined.
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Set up a system of equations for the given information by filling in the boxes with the coefficients of the variables and the constant values, where is the amount invested in stocks, is the amount invested in bonds, and is the amount invested in CD's.
If there is no visible coefficient, then enter
for the coefficient.
If a specific variable is not present in the equation, then enter
for the coefficient.
Country Day's scholarship fund receives a gift of $200000. The money is invested in stocks, bonds, and CDs. CDs pay 5% interest, bonds pay 2.9% interest, and stocks pay 10.9% interest. Country day invests $20000 more in bonds than in CDs. The total amount earned from the investments is $11165.
Total amount invested:
+ +
=
Total amount earned from investements:
+ +
=
Relation of bonds and CDs:
+ + =
Answer: Total amount invested:
= 200000
Total amount earned from investements:
0.109x + 0.029y + 0.05z = 11165
Relation of bonds and CDs:
= +20000
Step-by-step explanation:
It takes 2 h for students to plabt seeds in 3/8 of a community garden. Vanessa says it will take 4 h for the students to plant seeds for the whole garden. Is vanessa corect? Explain your reasoning
Students can plant seeds in a whole community garden in 5 1/3 h. Hence, Vanessa is not correct.
In the example question, students must plant seeds in 3/8 of a community garden in two hours.
The children will need 4 hours to plant the seeds for the entire garden, according to Vanessa.
We must confirm whether Vanessa is correct.
Within two hours, students plant seeds in 3/8 of the community garden.
Students can therefore plant seeds in 1 community garden in = 2/(3/8) h.
In one of the community gardens, students can sow seeds in = 2/3 * 8 hours.
In one of the communal gardens, students can plant seedlings in 16/3 hours.
In one of the communal gardens, students can sow seeds in 5 1/3 hours.
Students can therefore plant seeds in the entire community garden in 5 1/3 hours. Hence, Vanessa is not correct.
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Example 4: ABC~FED
A) Write the scale factor.
B) Find the value of x.
C) Find measure of f
D) Find the value of y.
E) Find the value of z.
The required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°.
What is Similarity in triangles?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal. Consequently, if A = X and AB/XY = AC/XZ, then ABC XYZ.
According to question:Because of similarity, Corresponding angles are equal and corresponding sides are Proportional.
So,
In ΔABC
∠A = 180 - 60 - 36
∠A = 180 - 96 = 86°
Which is equal to ∠F
So,D) angle ∠F = 86°
A) Scale factor = AB/EF
= 5/3
So Scale factor is 5/3.
We can say length of side ΔABC = 5/3 Side of ΔDEF.
So, For x
25 = 5x/3
x = 15
For y
y = 5(12)/3
y = 20
And value of z,
4z = 60 degree
z = 15 degree.
Thus, required values are A) 5/3, B) 15, C) 20, D) 86°, E) 15°
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BOOKSHELVES A bookshelf consists of two vertical planks with five horizontal shelves. Are each of the four sections for books rectangles? Explain.
Yes, each of the four sections for books is a rectangle because all four sides of the section are straight lines and the opposite sides are the same length.
Are each of the four sections for books rectangles?Yes, each of the four sections for books would be rectangles. A rectangle is a four-sided figure with four right angles, meaning that all of the angles measure 90 degrees. In the case of a bookshelf, the two vertical planks and the five horizontal shelves form a rectangle because the angles between the two planks and the five shelves are all right angles.The top section of the bookshelf is the first rectangle. It is formed between the top horizontal shelf and the two vertical planks. The second rectangle is formed between the second shelf from the top and the two vertical planks. The third rectangle is formed between the third shelf from the top and the two vertical planks. Finally, the fourth section is formed between the fourth shelf from the top and the two vertical planks.Each of the four sections of the bookshelf is a rectangle because the angles between the two vertical planks and the five horizontal shelves are all right angles. The two vertical planks form the length of the rectangle, while the five horizontal shelves form the width. This makes all four sections of the bookshelf a rectangle.To learn more about A rectangle refer to:
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Every quadrilateral that has exactly one pair of parallel sides
Answer:
False. This may be true with a trapezoid but not with a square or rectangle, seeing they have 2.
Step-by-step explanation:
Hope it helps! =D
The y-intercept of f(x) has the same value as the
x-intercept of f inverse
y-intercept of f inverse
x-intercept of f
The function f-1(x) has range including all values greater than or equal to 0;therefore, the _____ does also
range of f
domain of f
domain of f inverse
The y-intercept for function f(x) has the same value as the x-intercept of f-inverse.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
As
we can see from figure that y-intercept for f(x)=3
and x-intercept for f inverse = 3
Hence,
The y-intercept for function f(x) has the same value as the x-intercept of f-inverse
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Answer:
x-intercept
domain of f
Step-by-step explanation:
i just did it
ABCD → A’B’C’D’ is a reflection. Use this to answer the questions below.
All the solution of the blank words are given below.
What is a reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.
Given:
Figure ABCD is the pre-image.
And A'B'C'D' is the image.
The line of the reflection is y = 0.
The coordinates of the output:
A'(3, -6), B;(1, -1), C'(11, - 1) and D'(6, -6)
Therefore, all the blank words are given above.
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3.25x -1.5y=1.25
13x-6y=10
Answer:
¿Qué quieres comer?
Step-by-step explanation:
12.5% as a fraction (simplified)
Answer: 12.5% is 1/8
Answer: 25/2 would be your answer, as it is already in it's simplest form. I hope this helps! :)
Step-by-step explanation:
using these data, estimate the mean and standard deviation for hand grip-strength for this population. what assumption about the distribution do you need to make? g
Hand-grip strength is a sign of general toughness and a good indicator of significant consequences.
For grip strength measurements, current, population-specific reference values are required to interpret the results appropriately.
Objectives
To offer grip-strength reference values and formulae based on population for US citizens ages 18 to 85.
Methods
In this cross-sectional study, hand-grip data from 1232 participants, aged 18 to 85, were taken from the database of the 2011 normative phase of the US National Institutes of Health Toolbox project. Equations and descriptive reference values were derived from the data.
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The question is incomplete
the standard deviation for hand grip strength. what Objectives and Methods of the distribution
Solve for x.
y = x-11
y = 15
Simplify your answer as much as possible.
The solution for the given equations is x = 26, y = 15.
What is the linear equation in two variables?
A linear equation in two variables is an equation that can be written in the form of "ax + by = c", where a, b, and c are constants, and x and y are the variables.
To solve the equation y = x-11 for x, we can add 11 to both sides of the equation, resulting in y+11 = x.
To solve the equation y=15 for x, we can substitute 15 in the place of y in the first equation
15 = x - 11
So, x = 26
Hence, the solution for the given equations is x = 26, y = 15.
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Graph △ABC with vertices A(2,3), B(2,0), and C(3,2) and its image after a 90 degrees clockwise rotation about the origin and a reflection in the y-axis.
The coordinates of the final image are
A'' (3, 2)
B'' (0, 2)
C'' (2, 3)
How to find the coordinates of the final imageThe coordinates of the preimage are A(2,3), B(2,0), and C(3,2)
The transformation rule for a 90 degrees clockwise rotation is
(x, y) → (y,-x)
hence we have
A(2,3), → (3,-2)
B(2,0) → (0,-2)
C(3,2) → (2,-3)
The transformation rule for reflection in the y axis is
(x, y) → (x,-y)
hence we have
A'(3,-2) → (3, 2)
B'(0,-2) → (0, 2)
C'(2,-3) → (2, 3)
The image is plotted and attached
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor this expression completely and then place the factors in the proper location on the grid. Note: Place factors alphabetically in the grid!
mn-4m-5n+20
The factors of the expression mn-4m-5n+20 are (m-5)(n-4)
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression mn-4m-5n+20, we need to factorize it,
On factorizing the expression, mn-4m-5n+20, we get,
= mn-4m-5n+20
= m·n-4·m-5·n+5·4
= m(n-4)-5(n-4)
= (m-5)(n-4)
Hence, the factors of the expression mn-4m-5n+20 are (m-5)(n-4)
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find the largest prime number that divides the quantity $0! (1!) \times 1 (2!) \times 2 (3!) \times 3 \cdots (50!) \times 50$.
The largest prime number that divides the given expression is 229.
Largest Prime Factor of 50!We can factorize the given expression as follows:
[tex]$0! \times 1 \times 1! \times 2 \times 2! \times 3 \times 3! \times \cdots \times 50! \times 50$[/tex]
Now, we can cancel out all the factorials from both sides, leaving us with:
[tex]$1 \times 1 \times 2 \times 2 \times 3 \times 3 \times \cdots \times 50 \times 50$.[/tex]
The largest prime factor of any composite number is the largest prime factor of its prime factorization. By the fundamental theorem of arithmetic, we know that the prime factorization of any composite number is unique.
The prime factorization of a number can be found by dividing the number by prime numbers and keeping dividing the quotient by prime numbers until the quotient is prime.
Now, we can start dividing the given number (the product of all numbers from 1 to 50) by the smallest prime number, 2, and keep dividing the quotient by the next prime number until the quotient is prime.
The largest prime factor of the given expression is the largest prime factor of the final quotient.
The final quotient is
[tex]2^{24} \times 3^{12} \times 5^9 \times 7^7 \times 11^5 \times 13^4 \times 17^3 \times 19^3 \times 23^2 \times 29^2 \times 31^2 \times 37^2 \times 41^2 \times 43^2 \times 47^2 \times 53^2 \times 59^2 \times 61^2 \times 67^2 \times 71^2 \times 73^2 \times 79^2 \times 83^2 \times 89^2 \times 97^2 \times 101^2 \times 103^2 \times 107^2 \times 109^2 \times 113^2 \times 127^2 \times 131^2 \times 137^2 \times 139^2 \times 149^2 \times 151^2 \times 157^2[/tex]
[tex]\times 163^2 \times 167^2 \times 173^2 \times 179^2 \times 181^2 \times 191^2 \times 193^2 \times 197^2 \times 199^2 \times 211^2 \times 223^2 \times 227^2 \times 229^2$[/tex]
The largest prime factor of the final quotient is the largest prime factor of the prime factorization, which is 229.
So the largest prime number that divides the given expression is 229.
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To make ends meet, Ms.
Farnsby works three jobs. Her total income last year was $48,000. Her income from teaching was just $6000 more than her income from house painting. Royalties from her textbook sales were one-seventh of the total money she received from teaching and house painting. How much did she make from each source last year?
The money that a organisation earns in return for their labour or products is referred to as income.She make from each source last year $6000.
What is income?The money that a person or organisation earns in return for their labour or products is referred to as income.
Salary, rent, capital gains, company revenue, and income from other sources are a few typical sources of income. Understanding how each type of income is taxed is not always simple, and you may require an income tax calculator to do so.
Let t=teaching income, p=painting income, and b=book sales income.
t=p+6000 b=(t+p)/7 b+t+p=48000 (t+p)/7 +p+6000+p=48000 substitute (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000 multiply each side by 7 to eliminate the fraction.
substitution (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000
2p+6000+7p+42000+7p=336000
16p+48000=336000
16p=336000-48000
16p=288000 \s16p/16=288000/16
p=$18,000.
t=18000+6000
t=$24,000.
b=(24000+18000)/7
=42000/7
=$6000.
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Roberto's parents open a savings account for him by depositing $250 on his birthday. The account earns simple interest at an annual rate of 5%. How much will be in Roberto's account after 5 years
To calculate the amount of money in Roberto's savings account after 5 years, you can use the formula for simple interest:
I = Prt
Where:
I = Interest earned
P = Principal (original amount of money in the account)
r = Annual interest rate (expressed as a decimal)
t = Number of years
In this case, the principal is $250, the annual interest rate is 5% (or 0.05 as a decimal), and the number of years is 5.
So, you can plug these values into the formula:
I = 250 * 0.05 * 5
To find out the total amount of money in the account after 5 years, you need to add the interest to the principal:
250 + I = 250 + (250 * 0.05 * 5) = 250 + 62.5 = $312.5
Roberto's account will have $312.5 after 5 years.
Jonathan compared the ounces in and prices of several different cereals at the grocery store. Here are his results:
Ounces Price (in dollars)
32 $3.89
28 $2.79
42 $4.19
8 $1.00
27 $3.15
12 $2.25
Find the line of best fit for the data. Round any decimals to the hundredths place.
Estimate the price when you have a weight of 48 ounces.
State the correlation coefficient and then explain what it means in the context of the problem.
PLLLLLZZZZZ HELP!!!
Answer:
20
Step-by-step explanation:
To find the line of best fit, we can use the equation for a linear regression: y = mx + b, where y is the price, x is the weight in ounces, m is the slope of the line, and b is the y-intercept.
To estimate the price when the weight is 48 ounces, we can plug in x = 48 into the equation: y = mx + b, and solve for y.
The correlation coefficient, denoted by r, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.
In this case, the correlation coefficient means that how strong and direction of the relationship between the price and weight of cereal. A correlation coefficient of 1 means that there is a perfect positive correlation between the two variables, which means that as the weight of the cereal increases, so does the price. A correlation coefficient of -1 means that there is a perfect negative correlation between the two variables, which means that as the weight of the cereal increases, the price decreases. A correlation coefficient of 0 means that there is no correlation between the two variables, which means that there is no relationship between the weight of the cereal and the price.