The point(s)) where the fire road intersects the outer boundary of the service area is found using the equation of circle which is (0,20) and (-12,-16).
What is the equation of circle?
A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:
(x-h)² + (y-k)² = r²
The equation of the circle is given as - x² + y² = 400 .... (1)
The equation of the fire road is given as - y - 3x = 20 .... (2)
Write the equation of fire road in slope-intercept form - y = mx + b
y = 3x + 20
Substitute the value of y in equation (1) -
x² + y² = 400
x² + (3x + 20)² = 400
Follow the (a + b)² rule, (a + b)² = a² + 2ab + b²
x² + (3x + 20)² = 400
x² + 9x² + 120x + 400 = 400
10x² + 120x + 0 = 0
x² + 12x = 0
x(x+12) = 0
x = 0, x = -12
Substituting the values of x in equation (2).
First calculate for x = 0.
y - 3x = 20
y - 3(0) = 20
y = 20
Now, calculate for x = -12.
y - 3x = 20
y - 3(-12) = 20
y + 36 = 20
y = 20 - 36
y = -16
Therefore, the points of intersection are (0,20) and (-12,-16).
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how many repetitions should be done for each exercise in the preparation drill? group of answer choices seven nine five three
Five repetitions should be done for each exercise in the preparation drill.
Preparation drills are an important part of any fitness routine, as they allow the muscles and joints to be prepared for the workout ahead. Doing the correct number of repetitions for each exercise in the preparation drill is key to getting the most out of the workout. Generally, five repetitions is recommended for each exercise. This should give the body just enough time to get used to the exercise while still providing enough of a challenge. Doing too many repetitions may lead to fatigue or overstretching, leading to injury. Doing too few repetitions may not be enough to prepare the body and prevent injury. Five repetitions is the ideal number for most preparation drills.
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Please help I need the answers ASAP!
Answer:
Refer to the step-by-step
Step-by-step explanation:
Since ∠1 and ∠2 are alternate exterior angles, m∠2=108°
Mr. Bernard needs to order boxes for his 18-inch diameter "Super Pizza. "
What is the approximate circumference of the Super Pizza? Use 3. 14 for π. Show your work.
What is the approximate area of the Super Pizza? Use 3. 14 for π. Show your work.
Please help and hurry!! Ty!!
The circumference of the Super Pizza is 56.52 inches and approximate area of the Super Pizza 253.34 inches2.
To calculate the circumference of the Super Pizza
Circumference = π x diameter
Circumference = 3.14 x 18
Circumference = 56.52 inches
To calculate the area of the Super Pizza
Area = π x radius2
Area = 3.14 x (18/2)2
Area = 3.14 x 81
Area = 253.34 inches2
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A local company manufactures custom truck parts for big rigs. The company's average profit can be modeled by a(p) = 60p-3p, where alp) is the average profit in dollars per p parts produced. What is a reasonable domain for this function?
A. 0 to 10 parts
B. 0 to 14 parts
C. 0 to 18 parts
D. 0 to 20 parts
The reasonable domain for the Funtion is 0 to 14 parts. So,the correct option is B.
This function's domain is the set of all potential input values for the variable p. Because the variable p reflects the number of components generated, it must be non-negative.
Because the function is defined for p is larger than or equal to 0, the domain includes all non-negative p values. Because the function is linear, it is defined for all non-negative real numbers; however, in this case, the company manufactures custom truck parts for big rigs.
Which means the company may have a limit on the number of parts it can produce; this limit is 14 parts, so the reasonable domain for this function is 0 to 14 parts.
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33. let a d 2 4 1 0 4 0 3 2 2 6 3 3 5 and b d 2 4 4 1 4 3 5 . denote the columns of a by a 1, a 2, a 3, and let w d span fa 1; a 2; a 3g. a. is b in fa 1; a 2; a 3g? how many vectors are in fa 1; a 2; a 3g? b. is b in w ? how many vectors are in w ? c. show that a 1 is in w . [hint: row operations are unneces-sary.]
a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.
a. No, b is not in fa 1; a 2; a 3g. There are 3 vectors in fa 1; a 2; a 3g.
b. Yes, b is in w. There are 4 vectors in w.
c. To show that a1 is in w, we need to show that a1 is a combination of the vectors in w. We can do this by constructing a linear combination of the vectors in w that results in a1. In this case, we can take w1 = (2, 4, 1, 0), w2 = (4, 0, 3, 2), and w3 = (2, 6, 3, 3). Now we can set up a linear combination of these vectors, with coefficients c1, c2, and c3, to equal a1. Thus, we have: c1(2, 4, 1, 0) + c2(4, 0, 3, 2) + c3(2, 6, 3, 3) = (2, 0, 0, 0). Solving for c1, c2, and c3, we get c1 = 2, c2 = -2, and c3 = 0. Therefore, a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.
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Helen has to buy all the butter she needs to make 60 biscuits.
She buys the butter in 250 g packs.
What is the exact amount of butter she needs?
For making of 60 biscuits the quantity and packs of butter required by Helen is :
a. The exact amount of butter is 480 grams to make 60 biscuits.
b. Number of packs of butter Helen needs to buy is 2 packs.
Amount of sugar need to make 15 biscuits = 60 grams
Flour is three time of sugar to make 15 biscuits = 60 × 3
= 180 grams
Amount of flour to make 60 biscuits = 180 × 4
= 720 grams
Butter is two times as sugar to make 15 biscuits= 60 × 2
= 120grams
a. Exact amount of butter to make 60 biscuits is:
Butter required to make 60 biscuits = 120 × 4
= 480 grams
b. One pack is of 250 grams
Number of packs of butter she need to buy = 480 / 250
= 1,92
≈ 2packs
Therefore, the quantity of butter and number of packs of butter is given by :
a. The exact amount of butter required to make 60 biscuits is 480 grams.
b. The number of packs she needs to purchase is 2 packs.
The above question is incomplete, the complete question is :
Helen has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250g packs.
(i) What is the exact amount of butter she needs?
(ii) How many packs of butter will she have to buy?
Figure is attached.
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Help!!
Find the value of x
A. X=2
B. X=3
C. X=4
D. X=6
The value of x is 3. Option B
How to determine the valueIt is important to note that the given shape is a parallelogram.
The properties of a parallelogram are;
Opposite sides of the parallelogram are parallelOpposite sides are equalOpposite angles are equalThe interior angles are supplementaryDiagonal of a parallelogram separates it into two congruent trianglesThe diagonals of a parallelogram bisect each other at right angleNow, let's equate the sides, we have;
4x - 1 = 6x - 5
collect like terms
4x - 6x = -5 -1
Subtract like terms
-2x = -6
Make 'x' the subject of formula
x = -6/-2
x = 3
Hence, the value is 3
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(Simple)......Classify the transformation pls
find the surface area of a sphere with a diameter of 12 m.
A) 452.2 m
B) 150.7 m
C) 113.0 m
D) 904.3 m
Find the volume of a sphere with a redius of 4 ft.
A) 33.5 ft
B) 67.0 ft
C) 267.9 ft
D) 803.8 ft
Answer:
First question: 452.2
Second question: 267.9
Step-by-step explanation:
Not a hundred percent sure on second ques
Mr Musk bought a £75000 car at the beginning of the year 2016.
Each year the value of the car decreased by 8%.
a) Calculate the value of the car at the beginning of the year 2020.
Give your answer correct to the nearest £100
Answer:
53700
Step-by-step explanation:
Depreciation of every year is 8%, 2016-2017-18-19-20 - 4 years
in the beginning of 2017 it'll be 0.92*75000
so it'll be (1-8%)^4 = 0.71639
multiply by 75000 = 53729. to the nearest 100 = 53700
Olivia flips a coin and rolls a number cube with sides labeled 1, 2, 3, 4, 5, and 6. After 90 trials of the experiment, the relative frequency of flipping heads and rolling a number less than 3 is 2/15 . What is the difference between the number of expected outcomes and the number of actual outcomes?
Answer:
3
Step-by-step explanation:
Experimental probability is based on the actual outcomes of an experiment (gathered by experimenting repeatedly).
Theoretical probability is based on the possible outcomes (expected outcomes).
Probability formula
[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Theoretical probability of flipping a head
A coin has two sides: one side is a "head", the other side is a "tail".
The number of ways flipping a head can occur is 1.
The total number of possible outcomes is 2.
Therefore, the theoretical probability of flipping a head is 1/2.
Theoretical probability of rolling a number less than 3
The cube has six sides labelled 1, 2, 3, 4, 5 and 6.
The number of ways that rolling less than 3 can occur is 2 (rolling 1 or 2).
The total number of possible outcomes is 6.
Therefore, the theoretical probability of rolling a number less than 3 is 2/6 = 1/3.
Therefore, the theoretical probability of flipping a head and rolling a number less than 3 is:
[tex]\sf P(head)\; and\; P(X < 3)=\dfrac{1}{2} \times \dfrac{1}{3}=\dfrac{1}{6}[/tex]
To calculate the number of actual outcomes and expected outcomes after 90 trials, multiply the number of trials by the probability for each outcome:
[tex]\textsf{Number of actual outcomes}=90 \times \dfrac{2}{15}=12[/tex]
[tex]\textsf{Number of expected outcomes}=90 \times \dfrac{1}{6}=15[/tex]
Therefore, the difference between the number of expected outcomes and the number of actual outcomes is:
[tex]\implies 15-12=3[/tex]
Note: If Olivia continued to flip the coin and roll the number cube, as the number of trials increased, we would expect the experimental probability of 2/15 to get nearer to the theoretical probability of 1/6 and so the difference between the number of actual and expected outcomes would become smaller.
identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative). time in line to buy groceries
Time in Line to Buy Groceries is Quantitative-Discrete type of data. So the option C is correct.
We can observe data in a straightforward integer format or monitor quantitative discrete data in a real line at regular intervals.
We need to utilize an integer time point, which cannot be a decimal, to keep track of time while standing in line for groceries. It cannot be delivered in 2.45 days because a grocery store is unable to provide a delivery schedule in fractions.
The correct solution is therefore quantitative discrete.
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The complete question is:
Identify the type of data that would be used to describe a response.
Time in Line to Buy Groceries
A. Qualitative (Categorical)
B. Quantitative - Continuous
C. Quantitative - Discrete
Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass. Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.
a) When will they have the same amount of money saved up? How much money will they both have?
b) How long will it take each of them to save up for the season pass?
They needed a total of 8 weeks to save the same amount of money, and after 8 weeks, everyone would have $200.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass.
Since Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.
To save up for the season pass:
Harper needs = 1300$
Since, She earns 25$ a week
Harper needs total weeks = 1300/25
Harper needs total weeks = 52 weeks
joe also needs 1300 $
Since, joe already has $80 and plans to save $15 of her weekly allowance.
Joe needs total weeks = (1300 -80)/15
Joe needs total weeks = 81.33
To have the same amount of money saved up:
Let "x" be the weeks they required to save the equal money:
25 *x = 80 + 15*x
10*x = 80
x = 8
Everyone will have = 25 * 8
Everyone will have = 200$
Therefore, they required total of 8 weeks to have the same amount of money saved up and everyone will have 200$ after 8 weeks.
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a car dealership has 24 sedans and 18 sports coupes on its lot. what is the ratio of sedans to sports coupes on the lot? responses 2:3 2 colon 3 3:2 3 colon 2 3:4 3 colon 4 4:3
The ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed as 3:2, 3:4, or 4:3. This means that there are two sedans for every three sports coupes, or three sedans for every two sports coupes, etc.
The ratio of sedans to sports coupes on the lot can be expressed as a fraction, which is the number of sedans divided by the number of sports coupes. In this case, there are 24 sedans and 18 sports coupes, which can be written as 24/18. This fraction can be simplified to 2/3, which is equivalent to the ratio 2:3. This ratio can also be expressed as 3:2, 3:4, or 4:3, which means that there are two sedans for every three sports coupes, three sedans for every two sports coupes, three sedans for every four sports coupes, or four sedans for every three sports coupes. In summary, the ratio of sedans to sports coupes on the lot is 2:3, which can also be expressed in several other ways.
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Express tan Y as a fraction in simplest terms.
In parallelogram lmno, what is the measure of angle m? 20° 60° 80° 100°
In parallelogram lmno measure of angle m m∠M = 80°
In a parallelogram, opposite sides and opposite angles are congruent to each other.
⇒ m∠N = m∠L and m∠M = m∠O ..........(1)
Also, the sum of any two consecutive angles of a parallelogram is supplementary that is 180°
⇒ m∠M + m∠L = 180° ...........(2)
Now, using equation (1)
m∠N = m∠L
⇒ 5x = 3x + 40
⇒ 5x - 3x = 40
⇒ 2x = 40
⇒ x = 20
⇒ m∠N = m∠L = 5x = 100°
Now, from equation (2)
m∠M + m∠L = 180°
⇒ m∠M + 100 = 180
⇒ m∠M = 80°
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If $1,800 gains $882 in interest in seven years, what was the interest rate per year?
Answer:
rate = 7%
Step-by-step explanation:
From the question
Principal = $1,800
Time = 7 years
simple interest = $882
Rate = ?
rate = 100 × ST
P × T
rate = 100 × $882
$1,800 × 7
rate = $88200
12,600
rate = 7%
if you have a logical statement in five variables how many rows do you need in the truth table that you would use to evaluate it?
32 rows are needed in the truth table that we would use to evaluate a logical statement in five variables
As per the given data:
If we have a logical statement in five variables then we have to determine how many rows we need in the truth table that you would use to evaluate it.
It is calculated by both from truth table and by using the formula.
A table with rows and columns is created for a compound statement, and the number of rows depends on the number of statements.
As we know that the formula for number of rows need in the truth table.
Number of rows = [tex]2^{n}[/tex]
Where n = Number of variables
Here given number of variables are 5.
n = 5
[tex]2^{n}[/tex] = [tex]2^{5}[/tex]
= 32
Therefore 32 rows are needed in the truth table.
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For the vectors u = (-4,-1) and v= (1,3), express u as the sum u=p+n, where p is parallel to v and n is orthogonal to v. + 7 21 33 11 u=p+n= 10 10 10 10 (Type integers or simplified fractions. List the terms in the same order as they appear in the original list.)
The vector u can be expressed as a sum of n and p when n= (-33/10, 11/10) and p= (-7/10, -21/10).
To find the vector p that is parallel to v, we need to project u onto v. We can use the formula for projection:
p = (u . v) / (||v||^2) * v
where . represents dot product and ||v|| represents the magnitude of v.
First, we need to find the dot product of u and v:
(-4,-1) . (1,3) = -4*1 + -1*3 = -4 + -3 = -7
Next, we need to find the magnitude of v:
||v|| = sqrt(1^2 + 3^2) = sqrt(1 + 9) = sqrt(10)
Then, we can plug these values into the projection formula:
p = (-7) / (sqrt(10))^2 * (1,3) = (-7/10) * (1,3) = (-7/10, -21/10)
So the vector p that is parallel to v is (-7/10, -21/10)
To find the vector n that is orthogonal to v, we can subtract p from u:
n = u - p = (-4,-1) - (-7/10, -21/10) = (-4 + 7/10, -1 + 21/10) = (-33/10, 11/10)
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Find the value for the following determinant.
[ 2 3]
[ 1 4]
-5
5
11
Answer:
5
Step-by-step explanation:
(2x4)-(3x1)
=(8)-(3)
= 5
So its 5
Find the distance between the two points.
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~2 - (-3)~~)^2 + (~~3 - (-2)~~)^2} \implies d=\sqrt{(2 +3)^2 + (3 +2)^2} \\\\\\ d=\sqrt{( 5 )^2 + ( 5 )^2} \implies d=\sqrt{ 25 + 25 } \implies d=\sqrt{ 50 }[/tex]
2 cups ofcoffee and 5 bottles of water cost $12
7 cups of coffe and 4 bottles of water cost $15
use c to represent the cost of a cup of coffe and w to represent the cost of a bottle of water
Answer:They use the process of photosynthesis to transform water, sunlight, and carbon dioxide into oxygen, and simple sugars that the plant uses as fuel. These primary producers form the base of an ecosystem and fuel the next trophic levels
Step-by-step explanation:
Factor completely.
-3x² + 6x + 9 =
Answer:
-3(x - 3) (x + 1)
Step-by-step explanation:
Let's check
-3(x - 3) (x + 1)
(-3x + 9) (x + 1)
-3[tex]x^{2}[/tex] -3x + 9x + 9
-3[tex]x^{2}[/tex] + 6x + 9
Answer:
-3(x-3)(x+1)
Step-by-step explanation:
A common factor that all three numbers share is that they are divisible by 3, so we can factor 3 out. Typically, I take out the negative first:
-3([tex]x^2-2x-3[/tex]) (always remember to change signs!)
Now, we are left with [tex]x^2-2x-3[/tex], and to factor that out, we need to find two numbers that add up to -2 and multiply to -3. These two numbers will be 1 and -3, so we can write our factor like this:
(x-3)(x+1)
Let's add back in the -3 from earlier to complete our factoring:
-3(x-3)(x+1)
is the tendency for extreme scores on one variable to be followed by, or accompany, less extreme scores on another. a. the extreme return effect b. regression to the mean c. the robust average effect d. extreme minimization
The majority of human physical, mental, and personality factors have a mean in the middle of the distribution, where there are also the most cases. For example, in baseball, the rookie of the year often has a poor second season.
Correct answer is b) regression to the mean.
Regression to the mean is the propensity of outcomes that are extreme by chance on the first measurement to move closer to the average when tested a second time. Results that are susceptible to regression to the mean are those that are vulnerable to some degree of chance. When exceptional scores are the result of chance or a fluke, it's improbable that those extreme scores will be obtained again.
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A cylindrical rod measures 8 inches long and the circumference of one of its bases is 8π inches. The rod is cut into two equally-sized pieces and then all surfaces are painted.
What is the area that is painted?
Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
128π in.² ≈ 402.1 in.²
Step-by-step explanation:
The rod can be cut into two equal sized pieces in different ways, so there are different answers to this question. I assume the question is asking when the rod's length is cut in half, so now there are two rods, each one being a cylinder with 4 inch height.
We need the area of the original rod and then add two more base areas.
C = 8π in.
r = 4 in.
total surface area = lateral area + 4 × area of base
SA = 8 in. × 8π in. + 4 × π × (4 in.)²
SA = 64π in.² + 64π in.²
SA = 128π in.² ≈ 402.1 in.²
Answer:
401.9
Step-by-step explanation:
I got this question wrong on my quiz
The ratio of the angle measures in a triangle is 1:2:3. What is the measure of the largest angle?
Answer:
Step-by-step explanation:
Let the 3 angles be x , 2x , and 3x
notice x:2x:3x = 1:2:3
we know x+2x+3x = 180
6x = 180
x = 30
so the largest angle is 3(30) or 90 degrees
What kind of triangle is this please help me find the relationship and value please.
Answer: x=14°
Step-by-step explanation:
All angles of a triangle added together is 180°. So we can add the angles together.
7x-11+5x-2+2x-3=180 [combine like terms]
14x-16=180 [add both sides by 16]
14x=196 [divide both sides by 14]
x=14
Therefore, x=14°.
a person or object that is a member of the group being studied.
A population is a person or object that is a member of the sample being studied while a sample is the entire group that is being studied.
In a research study, a sample is a relatively small group of people from whom data is collected. The population is the bigger group to whom the information is then generalized.
All citizens, whether they are living there permanently or are only visiting, are referred to as the "people."
This indicator shows the average population density of a given area. The annual population fluctuations brought on by births, deaths, and net migration are known as growth rates.
A population is any large group that has at least one attribute in common. Not all populations are made up of people.
Populations can include, but are not limited to, people, animals, groups, organizations, buildings, houses, trucks, farms, and things.
Of the 7.8 billion people on the planet, 1%, or around 78 million individuals, would be there. One percent of the 7.8 billion people on the planet, or 78 million people, live there.
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Complete question -
A person or object that is a member of the group being studied is called ______.
PLSS HELP
What is the radical form of each of the given expressions?
Drag the answer into the box to correctly match each expression.
Answer:
SEE ATTACHED
Step-by-step explanation:
1. Provide an appropriate response.
Calculate the coefficient of determination, given that the linear correlation coefficient, r, is .845. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?
2. Provide an appropriate response.
Calculate the coefficient of determination, given that the linear correlation coefficient, r, is 1. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?
3. Provide an appropriate response.
Find the standard error of estimate, se, for the data below, given that = -2.5x.
x -1 -2 -3 -4
y 2 6 7 10
4. Provide an appropriate response.
The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Find the standard error of estimate, se, given that y = 1.523x + 6.343
Gestation x -- 8, 2.1, 1.3, 1, 11.5, 5.3, 3.8, 24.3
Life Span y -- 30, 12, 6, 3, 25, 12, 20, 40
Answer: The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 0.845^2 = 0.7146. This tells us that 71.46% of the variation in the data is explained by the regression line, while 28.54% is unexplained.
The coefficient of determination, r^2, is a measure of how well a linear regression model fits the data. It is calculated by squaring the linear correlation coefficient, r. In this case, r^2 = 1^2 = 1. This tells us that 100% of the variation in the data is explained by the regression line, and 0% is unexplained.
The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = -2.5x, so we can use this equation to find the predicted values and then calculate the SSE and SEE.
The standard error of estimate (SEE) for a linear regression model is a measure of the average difference between the predicted values and the actual values. In this case, we can use the formula SEE = sqrt(SSE/n) where SSE is the sum of the squared differences between the predicted and actual values, and n is the number of observations. The given equation is y = 1.523x + 6.343, so we can use this equation to find the predicted values and then calculate the SSE and SEE by using the given data.