Find the least-squares regression line y^=b0+b1xy^=b0+b1x
through the points
(1 point) Find the least-squares regression line û = b + b₁ through the points (-1,2), (2, 9), (5, 15), (8, 19), (12, 27). For what value of a is ŷ = 0? I =

The standard form of the equation of the line

The equation of the line can be expressed in several forms. One of them is the standard form:

Ax + By = C

Where A, B, and C are constants, and x and y are the variables.

We have the equation:

Multiplying by 3:

Subtracting 4x:

Is the required standard form of the line

Quick question: Is this a multiple choice question and if so, may you provide the multiple choice answers before I give you a proper answer?

Answer:

Step-by-step explanation:

Plugin x = 0 & y = -2 in the LHS of the equation. After substituting, if you get the RHS, then this point is the solution of the equation.

x - 2y = 0 - 2*(-2)

         = 0 + 4

         = 4  = RHS.

(0,-2) is solution of the equation.

The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

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Answer:

Step-by-step explanation:

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Answer=4/5

The fraction of his original money does he have left = 4/5 .

What is a fraction in math?

A boy has = 800 and spends = 160

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Therefore, his original money left =4/5

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The estimate for the total number of bees in her hive is 190 bees

She catches 90 of the bees on Monday and she puts mark on each bees and return them to her hive.

On Tuesday she catches 120 of the bees. She find out that 20 of the bees has been marked.

This means only 100 bees have not been marked on Tuesday.

Therefore, the total number of bee in her hives is as follows:

total number = 90 + (120 - 20)

total number = 90 + 100

total number = 190 bees

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The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

\(Given~quadratic ~function : 1=x^2-6x\)

\(here,a=1,b=-6\)

\(so, the~numbers~which ~we ~need ~to ~add....\)

➜ \((\frac{b}{2} )^2\)

➜ \(=(\frac{-6}{2})^2\)

➜\(=(-3)^2\)

➜ \(=9\)

---------------------

hope it helps...

have a great day!!

Answer:

y = 20

Step-by-step explanation:

48 = 3y - 12

Divide by 3 to have one "y'

16 = y - 4

Add 4 to isolate variable

20 = y

So y is equal to 20.

Answer:

y=20

Step-by-step explanation:

Move all terms containing y to the left, all other terms to the right.

Add -3y to each side of the equation.

48 + -3y = -12 + 3y + -3y

Combine like terms: 3y + -3y = 0

48 + -3y = -12 + 0

48 + -3y = -12

Add -48 to each side of the equation.

48 + -48 + -3y = -12 + -48

Combine like terms: 48 + -48 = 0

0 + -3y = -12 + -48

-3y = -12 + -48

Combine like terms: -12 + -48 = -60

-3y = -60

Divide each side by -3.

y = 20

Simplifying

y = 20

1. The total number of students who took the exam is 40 is option c.

2. The probability that the five cards picked are suited is approximately is option d. 0.0020.

Probability is a branch of mathematics that deals with the likelihood of events occurring. In this response, we will provide detailed solutions to two probability problems. We will explain the steps involved in solving each problem using mathematical terms.

Solution to Problem 1:

Let's denote the number of students who took the exam as 'x.' We are given that the probability of passing Chemistry is 70% and Physics is 50%. None of the students failed in both subjects, and 8 students passed both subjects.

To solve this problem, we can use the principle of inclusion-exclusion. The principle states that to find the total number of students who passed at least one subject, we need to sum the number of students who passed Chemistry, the number of students who passed Physics, and then subtract the number of students who passed both subjects.

Let's calculate the number of students who passed at least one subject:

Number of students who passed Chemistry = 0.7x

Number of students who passed Physics = 0.5x

Number of students who passed both subjects = 8

Total number of students who passed at least one subject = (Number of students who passed Chemistry) + (Number of students who passed Physics) - (Number of students who passed both subjects)

Substituting in the values, we have:

Total number of students who passed at least one subject = 0.7x + 0.5x - 8

Since none of the students failed in both subjects, the number of students who passed at least one subject is equal to the total number of students. Therefore, we can set the equation equal to 'x' and solve for it:

0.7x + 0.5x - 8 = x

Simplifying the equation:

1.2x - 8 = x

0.2x = 8

x = 8 / 0.2

x = 40

Therefore, the total number of students who took the exam is 40.

Hence, the answer to Problem 1 is option c. 40.

Solution to Problem 2:

We are given that we are picking five cards from a standard deck of 52 cards. We need to find the probability that all five cards picked are suited, meaning they all belong to the same suit.

To solve this problem, we can use the concept of combinations. The number of ways to choose five cards from a particular suit is denoted as C(13, 5), as there are 13 cards in each suit (hearts, diamonds, clubs, spades) and we need to choose 5 cards. Similarly, the total number of ways to choose any five cards from the deck is C(52, 5).

The probability of picking five suited cards can be calculated as:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Number of favorable outcomes = Number of ways to choose 5 cards from a single suit = C(13, 5)

Total number of possible outcomes = Number of ways to choose any 5 cards from the deck = C(52, 5)

Using the formula for combinations, we have:

C(n, r) = n! / (r!(n-r)!)

Substituting in the values, we get:

Number of favorable outcomes = C(13, 5) = 13! / (5!(13-5)!)

Total number of possible outcomes = C(52, 5) = 52! / (5!(52-5)!)

Calculating the values:

Number of favorable outcomes = 1,287

Total number of possible outcomes = 2,598,960

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1,287 / 2,598,960

Simplifying the fraction:

Probability ≈ 0.000495

Therefore, the probability that the five cards picked are suited is approximately 0.000495.

Hence, the answer to Problem 2 is option d. 0.0020.

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Using an online finance calculator, the annual percentage rate (APR) of an $800 installment loan with a finance charge of $40.72 for 36 monthly payments is 1.656%.

The annual percentage rate (APR) is the cost of borrowing, including the interest and other fees, expressed as a percentage of the debt.

The APR is always computed as an annual rate to show the cost of borrowing or finance charge over a year.

N (# of periods) = 36 months

PV (Present Value) = $800

PMT (Periodic Payment) = $0

FV (Future Value) = $-840.72

I/Y = 1.656% if interest compounds 12 times per year (APR)

I/Y = 1.669% if interest compounds once per year (APY)

I/period = 0.138% interest per period

Total Interest = $40.72

Thus, for Betty Arca's installment loan of $800, the APR is 1.656%.

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Answer:

-3<x<1

(-3,1)

Step-by-step explanation:

it is shown as (-3,1) because x is anything inbetween -3 and 1 and those numbers are not included so you use ( ) as opposed to [ ]

Answer:

13.) 314.2 in²

15.) 181.5 ft²

Step-by-step explanation:

The area of a circle is found using the equation:

A = πr²

In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).

For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".

A = πr²

A = π(10)²

A = π x (100)

A = 314.2 in²

For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.

diameter = 15.2 ft
radius = 7.6 ft

A = πr²

A = π(7.6)²

A = π x (57.76)

A = 181.5 ft²

Karen that has a piece of fabric that is 1 187/240 yards long needs to trim 227/240 yards

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Data of the problem:

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

The value of the denominator is multiplied by the integer component.

The result is added to the numerator of the fraction.

We transform the mixed fractions into improper fractions and we have:

1 187/240 =

[(240*1) + 187)] /240=

[240+ 187] /240=

427/240

Calculating how many yards should she trim:

Yards to trim: 427/240 - 5/6

Yards to trim: (427 - 200) / 240

Yards to trim: 227/240

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Answer: The correct answer is b

Step-by-step explanation:

25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08

Answer:

Step-by-step explanation:

To find the frequency for which the particular solution to the differential equation has the largest amplitude, we first need to know the differential equation we are working with. However, since you didn't provide the specific differential equation, let's work with a general example: a forced harmonic oscillator. The equation for a forced harmonic oscillator can be written as:

m * d²x/dt² + c * dx/dt + k * x = F0 * cos(ωt)

where:

m is the mass of the oscillator

x is the displacement of the oscillator

c is the damping coefficient

k is the spring constant

F0 is the amplitude of the external force

ω is the angular frequency of the external force

For this type of equation, we can find the particular solution in the form:

x_p(t) = X * cos(ωt - δ)

where:

X is the amplitude of the particular solution

δ is the phase angle

We can rewrite the differential equation in the frequency domain by substituting x(t) = X * cos(ωt - δ) and its derivatives into the original equation, then applying the trigonometric identities. After simplifying, we can find the expression for X, the amplitude of the particular solution:

X = F0 / sqrt((k - mω²)² + (cω)²)

To find the frequency for which the particular solution has the largest amplitude, we need to maximize X with respect to ω. To do this, we can find the critical points by differentiating X with respect to ω and setting the result to zero:

dX/dω = 0

To simplify the problem, we can define the damping ratio ζ = c / (2 * sqrt(m * k)) and the undamped natural frequency ω_n = sqrt(k / m). The expression for X becomes:

X = F0 / sqrt((ω_n² - ω²)² + (2 * ζ * ω_n * ω)²)

Now, we differentiate X with respect to ω and set it to zero. Solving for ω, we get:

ω = ω_n * sqrt(1 - 2ζ²)

This is the frequency for which the particular solution to the differential equation has the largest amplitude, assuming a positive frequency and that the damping ratio ζ is less than 1 / sqrt(2). Otherwise, the system will be overdamped, and there will be no resonant frequency.

the frequency for which the particular solution to the differential equation has the largest amplitude is:

ω = √(γ/2 - β^2)

To find the frequency for which the particular solution to the differential equation has the largest amplitude, we can assume that the particular solution is of the form:

y(t) = A*cos(ωt + φ)

where A is the amplitude, ω is the frequency, and φ is the phase angle.

Substituting this form of y(t) into the differential equation gives:

-ω^2Acos(ωt + φ) - 2βωAsin(ωt + φ) + γA*cos(ωt + φ) = f(t)

Simplifying this equation gives:

(A/|D|)[γcos(ωt + φ) - ω^2cos(ωt + φ) - 2βω*sin(ωt + φ)] = f(t)

where |D| is the modulus of the denominator of A*cos(ωt + φ) and is given by:

|D| = √[ (γ - ω^2)^2 + (2βω)^2 ]

To find the frequency for which the amplitude of the particular solution is largest, we need to minimize the modulus of the denominator |D| over all frequencies ω. We can do this by finding the critical points of |D| with respect to ω and then checking which of these critical points correspond to a minimum.

Differentiating |D| with respect to ω gives:

d|D|/dω = [2ω(γ - ω^2) - 4β^2ω]/|D|

Setting this equal to zero and solving for ω gives:

ω = ±√(γ/2 - β^2)

We can see that there are two critical points for |D|, one positive and one negative. To check which of these corresponds to a minimum, we can use the second derivative test:

d^2|D|/dω^2 = (2γ - 6ω^2)/|D|^3

Substituting ω = ±√(γ/2 - β^2) into this expression gives:

d^2|D|/dω^2 = ±4√2β^3/γ^(3/2)

Since β and γ are both positive, the second derivative is negative for both critical points, which means that they both correspond to maxima of |D|. The positive critical point corresponds to the frequency for which the amplitude of the particular solution is largest.

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Answer:

15

Step-by-step explanation:

2/5x = 6

x=15

Or

2/5x = 6

1/5x = 3

3 x 5 = 15

Answer:

15

Step-by-step explanation:

Answer:

Pantalones = $600.00 × 2

$ 1,200.00

Blusas = $350.00 × 4

$ 1,400.00

Calcetas = $120.00 × 3

$ 360.00

Par de tenis = $950.00 × 2

$ 1,900.00

Total a pagar = $4,850.00

$5,000.00

- $4,860.00

Sobrante = $140.00

Answer:

6.92820323028

Step-by-step explanation:

Answer: 4√3 in.

Step-by-step explanation: If the side of a square is S, then the area of the square is S^2, and since we know the area of the square, we can create an equation to solve for the side; S^2=48. We take the square root of both side s and then get √48=√16×√3=4√3!

Answer:

x = 3 and x = \(\frac{9}{2}\)

Step-by-step explanation:

(a)

2(5x - 3) = 24 ( divide both sides by 2 )

5x - 3 = 12 ( add 3 to both sides )

5x = 15 ( divide both sides by 5 )

x = 3

(b)

5(2x + 1) = 50 ( divide both sides by 5 )

2x + 1 = 10 ( subtract 1 from both sides )

2x = 9 ( divide both sides by 2 )

x = \(\frac{9}{2}\)

The parametric equations for the line segment from (-3, 18, 31) to (11, -4, 48) can be expressed as follows:

x(t) = -3 + (11 - (-3))t

y(t) = 18 + (-4 - 18)t

z(t) = 31 + (48 - 31)t

In these equations, t represents the parameter that varies along the line segment. By plugging in different values of t, we can obtain corresponding points on the line segment.

The x(t) equation represents the x-coordinate of the line segment, where -3 is the initial x-coordinate and (11 - (-3)) represents the change in the x-coordinate over the segment. By multiplying this change by t, we can determine the specific x-coordinate at any point along the line segment.

Similarly, the y(t) equation represents the y-coordinate, where 18 is the initial y-coordinate and (-4 - 18) represents the change in the y-coordinate. Multiplying this change by t gives us the y-coordinate at any point.

Lastly, the z(t) equation represents the z-coordinate, where 31 is the initial z-coordinate and (48 - 31) represents the change in the z-coordinate. Multiplying this change by t allows us to determine the z-coordinate at any point along the line segment.

By using these parametric equations, we can generate points that lie on the line segment connecting the given two points and describe the entire line segment in three-dimensional space.

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Approximate height to the statue's actual height of 120 feet, 3 inches from heel to top of head is 123.75 feet.

To estimate the height of the statue, the student can use the method of similar triangles. Since the length of the statue's right arm is 45 feet and the length of the student's right arm is 2 feet, the ratio of the lengths of the arms is 45/2 = 22.5. If we assume that the ratio of the heights of the statue and the student is also 22.5, then the height of the statue can be estimated as:

height of statue = height of student x ratio of heights

height of statue = 5.5 x 22.5

height of statue = 123.75 feet

This estimated height of the statue is close to the actual height of 120 feet, 3 inches. It should be noted that this method of estimation assumes that the ratio of the heights of the statue and the student is the same as the ratio of the lengths of their arms. This may not be completely accurate, as the proportions of the statue and the student may be different.

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Step-by-step explanation:

Notice that:

15x = 5 * 3x and 10y = 5 * 2y.

Since there is a common factor of 5,

we can take out the factor.

=> 15x + 10y = (5)(3x) + (5)(2y) = 5(3x + 2y).

EXPLANATION

The greatest common of pairs is:

6 and 3:

Prime factorization of 6: 2*3

Prime factorization of 3: 3

The prime factors common to 6,3 are

=3 [Not a valid option]

30 and 36:

Prime factorization of 30: 2*3*5

Prime factorization of 36: 2*2*3*3

The prime factors common to 30,36 are

=2*3=6 [Valid option]

24 and 48:

Prime factorization of 24: 2*2*2*3

Prime factorization of 48: 2*2*2*2*3*3

The prime factors common to 24,48 are

=2*2*2*3=24 [Not a valid option]

60 and 88:

The prime factors common to 60,88 are

=2*2=4 [Not a valid option]

18 and 66:

The prime factors common to 18,66 are

=2*3=6 [Valid option]

72 and 84:

The prime factors common to 72,84 are

=2*2*3=12 [Valid option]

The right options are 2. 30 and 36 and 5. 18 and 66

Answer:

4 burritos cost 56

5 burritos cost 70

10 burritos cost 140

Answer:

wdexxewew

Step-by-step explanation:

exewew

Answer:

80

Step-by-step explanation:

firstly, I divide both sides by 80,I.e

80/80=6,400/80=80

Answer:

The rabbit will get hit because the car takes too long to break

Step-by-step explanation:

The revenue from muffins was $8,000. To find the revenue from doughnuts: 4.5x = 4.5 * 8,000 = $36,000 Therefore, the cupcake delight shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.

Let's use the given terms and set up a system of equations to solve this problem:

Let x be the revenue from muffins, and y be the revenue from doughnuts. We know the following:

1. y = 4.5x (Cupcake Delight Shop made 4 1/2 times as much revenue on doughnuts as muffins)
2. x + y = 44,000 (Total sales were $44,000)

Now we'll solve the system of equations step-by-step:

Step 1: Replace y with 4.5x in the second equation (using equation 1):
x + 4.5x = 44,000

Step 2: Combine the x terms:
5.5x = 44,000

Step 3: Divide both sides by 5.5 to solve for x:
x = 8,000

Step 4: Plug x back into equation 1 to find y:
y = 4.5 * 8,000
y = 36,000

So, Cupcake Delight Shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.

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The dollar amount of muffins sold is $8,000, and the dollar amount of doughnuts sold is $36,000.

To solve this problem, let's assign variables to the revenue for doughnuts and muffins:
Let D = revenue from doughnuts
Let M = revenue from muffins
We are given that the shop made 4 1/2 times as much revenue on doughnuts as muffins:
D = 4.5M
We are also given that the total sales were $44,000:
D + M = 44,000
Now, we can solve for the dollar amount of each item sold:
Replace D with 4.5M in the second equation:
4.5M + M = 44,000
Combine like terms:
5.5M = 44,000
Divide by 5.5 to isolate M:
M = 44,000 / 5.5
M = 8,000
Plug the value of M back into the first equation to find the value of D:
D = 4.5M
D = 4.5 × 8,000
D = 36,000.

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Answer:

Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24.

Step-by-step explanation:

Answer:

calculator?

Step-by-step explanation:

calculator?