For the line of best fit in the least-squares method, O a) the sum of the squares of the residuals has the greatest possible value b) the sum of the squares of the residuals has the least possible value

Answer:

Step-by-step explanation:

(1 + 3)/(3-1) = 4/2 = 2

y - 1 = 2(x - 3)

y - 1 = 2x - 6

y = 2x - 5

Answer:

D

I guess you just have to add them

Answer:

D

Step-by-step explanation:

Which of the following is equivalent to (a^1/2 * b^1/3)^1/2?

Note: To distribute exponents in a parentheses where the two variables are being multiplied, you can distribute it to the powers. For example:

(4 * 5)² = 20² = 400

Or, we can rewrite it like:

(4 * 5)² = 4² * 5² = 16 * 25 = 400

Now, onto the problem.

First, multiply the exponents with the one outside the parentheses.

a^(1/2 * 1/2) * b^(1/3 * 1/2)

Simplify.

a^(1/4) * b^(1/6)

So, the answer is D.

Just in case, let's double check the answer.

Let's pretend that a=16 and b=64.

Then,

(a^(1/2) * b^(1/3))^(1/2) = a^(1/4) * b^(1/6)

(16^(1/2) * 64^(1/3))^(1/2) = 16^(1/4) * 64^(1/6)

(4 * 4) ^ (1/2) = 2 * 2

16 ^ (1/2) = 4

4 = 4

Thus, the answer is correct.

Answer:

-5(3x+4) = 25

-15x-20=25

-15x=25+20

-15x=45

>then divide both side by -15

Therefore: X=-3

4(x+2)-3(2x-4)=10

4x+8-6x+12=10

-2x+20=10

-2x=-10

> divide both sides by -2

Therefore: x= 5

Answer:

x=o.23854485

Step-by-step explanation:

the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years is 0.0564 rounded to three decimal places. The final answer is 0.056.

The problem given can be solved by using the central limit theorem.

According to the central limit theorem, if the sample size is sufficiently large, then the sample mean will follow a normal distribution with a mean of μ and a standard deviation of σ/√n, where n is the sample size.Using this formula, we can find the probability that the average age of a randomly selected sample of 100 students will be less than 21.8 years. The formula is:

P(Z < (X-μ)/(σ/√n))

where Z is the standard normal distribution, X is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X = 21.8, μ = 22, σ = 2, and n = 100. Plugging these values into the formula, we get:

P(Z < (21.8-22)/(2/√100)) = P(Z < -1.58)

Using Excel or a standard normal distribution table, we can find that the probability of Z being less than -1.58 is 0.0564.

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Answer:

Step-by-step explanation:

what do you not understand

The scientific notation form of the given number 1,345,080,000 is 1.34508 × 10⁹.

Given the number in the question;

1,345,080,000

To convert to scientific notation;

First, move the decimal so there is one non-zero digit to the left of the decimal point.

Now, the number of decimal places you move will be the exponent on the 10

Note that; if the decimal is being moved to the right, the exponent will be negative, also, If the decimal is being moved to the left, the exponent will be positive.

1.345080000

We moved 9 decimal places to the left

1.34508 × 10⁹

Therefore the scientific notation form of the given number 1,345,080,000 is 1.34508 × 10⁹.

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Answer: The Jacobian of the transformation is: J = 8v(4w)3u - 8u(4v)3w = 24uvw

Step-by-step explanation:

To determine the Jacobian of the transformation, we first need to get the partial derivatives of x, y, and z with respect to u, v, and w:

∂x/∂u = 8v

∂x/∂v = 8u

∂x/∂w = 0∂y/∂u = 0

∂y/∂v = 4w

∂y/∂w = 4v∂z/∂u = 3w

∂z/∂v = 0

∂z/∂w = 3u

The Jacobian matrix J is then:

| ∂x/∂u ∂x/∂v ∂x/∂w |

| ∂y/∂u ∂y/∂v ∂y/∂w |

| ∂z/∂u ∂z/∂v ∂z/∂w |

Substituting in the partial derivatives we found above, we get:

| 8v 8u 0 |

| 0 4w 4v |

| 3w 0 3u |

So, the Jacobian of the transformation is:J = 8v(4w)3u - 8u(4v)3w = 24uvw

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Answer:

oopppppp yes

Step-by-step explanation:

Answer:

Yes

Good luck, and have the most amazing day!

The rational number, which expresses a loss of $ 25. 30 is -253/10 = -25.30. So, option(b) is right one. Similarly, The rational number, which expresses a gain of $ 31.10 = 311/10 = 31.10. So, option(a) is right one.

A rational number is a number that can be represented as the quotient or fraction \( \frac{p}{q}\) of two numbers, a numerator p and a non-zero denominator q. Loss always implies something lose or decrease and profit represents something gain or increase. So, loss denotes by negative sign and profit by positive sign. We have to determine rational numbers that expresses a loss of $25.30 and a profit of $31.10. First we consider the loss, to express in rational number form, Loss

= -253 ÷ 10

= -25.3

In case of Profit, express in form of rational numbers as profit, 31.10 = 3110 ÷100 = 311 ÷ 10

= 311/10 = 31.1

Hence, the rational number that expresses a loss of $ 25. 30 is -25.3, and the rational number that represents a profit of $ 31.10 is 31.1.

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Complete question :

The rational number that expresses a loss of $25.30 is ?

a) +$25.30

b) -$25.30

c) +$2.53

d) -$2.53.

and the rational number that represents a profit of $31.10 is

a) +$31. 10

b) -$31. 10

c) +$3. 11

d) -$3. 11.

Answer:

The equation of line t, which is perpendicular to line s and passes through (-2, 9), is y = -3x + 3 in slope-intercept form.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. The slope of line s, given by the equation y = (1/3)x - 5, is 1/3. Therefore, the slope of line t must be -3, which is the negative reciprocal of 1/3.

To find the equation of line t, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

We are given that line t passes through the point (-2, 9) and has a slope of -3. Substituting these values into the point-slope form, we get:

y - 9 = -3(x - (-2))

Simplifying the expression on the right side and rearranging, we get:

y - 9 = -3x - 6

Adding 9 to both sides, we get:

y = -3x + 3

Therefore, the equation of line t in slope-intercept form is y = -3x + 3, where the slope is -3 and the y-intercept is 3.

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Answer:

Step-by-step explanation:

Answer:

185

Step-by-step explanation:

Hope this helps

Answer:  8.94 is the length of GI

Step-by-step explanation: The two triangles are similar, so the ratios of the sides to each other will be the same.

the unknown length of GI in triangle FIG corresponds to the known length 20 of IH in Triangle GIH, and the known length 4 of side FI in triangle FIG corresponds to GI in Triangle GIH. So the ratio looks like 4:x as x:20

4/x = x/20  multiply both sides by x and 20 to "cancel" the denominators.

20x(4/x) = 20x(x/20)

80 = x²    Calculate the square roots  

√x² = x . √80 = 8.94

Answer:

Step-by-step explanation:

Answer:

3.25

Step-by-step explanation:

Answer:

Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular arrangement of numbers into rows and columns. For example, matrix A has two rows and three columns.

Step-by-step explanation:

Rows and columns of numbers are arranged in a matrix.

The term "matrix" refers to an assortment of numbers put up in rows and columns to form a rectangular array. The elements, or entries, of the matrix are the integers. A rectangular table of numbers is known as a matrix, or more generally, a table made up of abstract quantities that may be multiplied and added.

In a matrix, the horizontal lines are referred to as rows, and the vertical lines as columns. An m-by-n matrix is one that has m rows and n columns; m and n are referred to as the matrix's dimensions. Always list the number of rows before listing the number of columns when describing a matrix's dimensions.

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Answer:

Slope = 6, y-intercept = -12.

Step-by-step explanation:

Slope is the coefficient of the x-term, which is 6 in this case.

The y intercept is the constant term that comes after the x-term, which is -12.

The correct answer is h(t) = 14.25 + 0.25 * sin((π/26) * t)

To model the hours of daylight in a year using a sinusoidal equation, we can consider the average length of daylight, the amplitude of the variation, and the period of the function.

Given:

Summer solstice (longest day) is 14.5 hours

Winter solstice (longest night) is 14 hours

Let's analyze the information:

Average daylight: The average daylight throughout the year would be the average of the summer and winter solstices. It can be calculated as:

Average daylight = (14.5 + 14) / 2 = 14.25 hours

Amplitude: The difference between the average daylight and the longest day or night is the amplitude. In this case, the amplitude is half the difference between the summer and winter solstices. It can be calculated as:

Amplitude = (14.5 - 14) / 2 = 0.25 hours

Period: We are modeling the function over a year, which we'll consider as 52 weeks. Since we want to measure time in weeks (t), the period of the function is 52 weeks.

Putting all the information together, we can write the sinusoidal equation:

h(t) = Average daylight + Amplitude * sin((2π / Period) * t)

Substituting the values we calculated:

h(t) = 14.25 + 0.25 * sin((2π / 52) * t)

Simplifying further, the sinusoidal equation modeling the hours of daylight in a year is:

h(t) = 14.25 + 0.25 * sin(π/26 * t)

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Answer:

3

Step-by-step explanation:

Michael must find the smallest number possible that can divide 60 and 45 then take the two quotients after dividing the 2 types of cookies by the smallest number possible.

2 is not possible as 45 is an odd number

3 can divide both 60 and 45

60/3 = 20 oatmeal cookies in each container.

45/3 = 15 chocolate chip cookies in each container.

Brooklyn will read 1 1/3 books i.e one complete book and one-third of a book at the given rate.

By determining the number of books read in one day, we can use this as a unit rate to determine how many books she will read in 20 days.

Multiplying the unit rate by the number of days gives us the total amount of reading she will do in that time period.

Here we have

Brooklyn read 1/3 of a book in the series she was reading in 5 days

If Brooklyn read 1/3 of a book in 5 days,

The fraction of the book she reads in one day = 1/3 ÷ 5 = 1/15

This implies Brooklyn reads 1/15 of a book in one day.

To find out how many books Brooklyn will have read in 20 days at the same rate, we can multiply the fraction of a book she reads in one day by the number of days:

= (1/15) x 20 = 4/3 = 1 1/3

Therefore,

Brooklyn will read 1 1/3 books i.e one complete book and one-third of a book at the given rate.

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Answer:

It will have a rise of 20.

Step-by-step explanation:

We can use ratios:

Rise : Run = 16 : 4 = 4 : 1 = 20 : 5

Hope this helps!

The second power series solution is:

y₂(x) = \(1 - 6x^2/2! + 36x^4/4! - 216x^6/6! + ...\)

The given differential equation is:

\((x^2 + 1)y'' - 6y = 0\)

To find the power series solution about the ordinary point x = 0, we assume that y(x) can be expressed as a power series in x:

y(x) = \(\sum_(_n_=_0_)^\infty a_n x^n\)

where \(a_n\) are constants to be determined.

We then find the first and second derivatives of y(x) with respect to x:

\(y'(x) =\) \(\sum_(_n_=_1_)^\infty n a_n x^(^n^-^1^)\)

\(y''(x) = \sum_(_n_=_2_)^\infty n(n-1)a_n x^(^n^-^2^)\)

Substituting these into the differential equation, we obtain:

\((x^2 + 1) \sum_(_n_=_2_)^\infty n(n-1)a_n x^(n-2) - 6 \sum_(_n_=_0_)^\infty a_n x^n = 0\)

Simplifying and regrouping terms, we get:

\(\sum_(_n_=_0_)^\infty [(n+2)(n+1)a_(_n_+_2_) - 6a_n] x^n = 0\)

Since this expression must hold for all values of x, the coefficients of each power of x must be zero. Therefore, we have the following recurrence relation:

\((n+2)(n+1)a_(_n_+_2_) - 6a_n = 0\)

which can be simplified to:

\(a_(_n_+_2_) = 6a_n / ((n+2)(n+1))\)

We can use this recurrence relation to compute the coefficients aₙ for n = 0, 1, 2, 3, 4, and so on.

For the first solution, we choose a₀ = 1 and a₁ = 0. Substituting these into the recurrence relation, we get:

We can see that all the even coefficients are zero, and the odd coefficients are given by:

\(a_(_2_k_+_1) = 6a_(_2_k_-_1_) / (2k+1)(2k)\)

Therefore, the first power series solution is:

\(y_1(x) = x - 6x^3/3! + 68x^5/5! - 6810*x^7/7! + ...\)

Simplifying, we get:

\(y_1(x) = x - 3x^3 + 4x^5/5 - 8x^7/7! + ...\)

For the second solution, we choose a₀ = 0 and a₁ = 1. Substituting these into the recurrence relation, we get:

We can see that all the odd coefficients are zero, and the even coefficients are given by:

\(a_(_2_k_) = (-6)^k / (2k)!\)

Therefore, the second power series solution is:

\(y_2(x) = 1 - 6x^2/2! + 36x^4/4! - 216x^6/6! + ...\)

Simplifying, we get:

\(y_2(x) = 1 - 3x^2 + 3x^4/2 -\)

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Answer:

I guess that the equations are:

P*P = Q*6

and

Q - P = 3

now, in the second equation we have:

Q = 3 + P

we can replace it in the first equation:

P^2 = (3 + P)*6 = 6P + 18

then we have the quadratic equation:

P^2  -6P - 18 = 0

Now, we can find the solutions of these equations are:

\(P = \frac{+6 +-\sqrt{(-6)^2 - 4*1*(-18)} }{2} =\frac{6 +- 10.4}{2}\)

then the solutions are:

P = (6 + 10.4)/2 = 8.2

and

P = (6 - |0.4)/2 = -2.2

Then, if P = 8.2, then we must have Q = 11.2

and if P = -2.2, then Q = 0.8

Answer:

Step-by-step explanation:

volume=7.3×1760×3×30×1760×3×1/12=73×176×90×440=508780800 ft³

Answer:

508,780,800 ft³ of rain

Step-by-step explanation:

In order to do the computation, we need to express all the given lengths in feet.

recall that 1 mile = 5280 feet

hence,

width = 7.3 miles = 7.3 x 5280 = 38,544 feet

length = 30 miles = 30 x 5280 = 158,400 feet

also recall that 1 inch = 1/12 feet

hence,

depth of rainfall = 1 inch = 1/12 feet

Volume of rain = width of beach x length of beach x depth of rainfall

= 38,544 x 158,400 x (1/12)

= 508,780,800 ft³ of rain

Answer: \(80.2\ ft\)

Step-by-step explanation:

Given

Zipline begins \(h=46\ ft\) in the air

The angle of elevation is \(35^{\circ}\)

Assume the length of the cable is l

from the figure, we can write

\(\Rightarrow \sin 35^{\circ}=\dfrac{46}{l}\\\\\Rightarrow l=\dfrac{46}{\sin 35^{\circ}}\\\\\Rightarrow l=80.19\approx 80.2\ ft\)

Answer:

$30.41

Step-by-step explanation:

24.20 + 24.20(0.05) + 5 =

24.20 + 1.21 + 5 = 30.41

the 1.21 represents the amount she paid in sales tax

Answer:

-2 -7

0   -1

1     2

3    8

Step-by-step explanation:

Answer:

B: x=19

Step-by-step explanation:

You want to add (x+18)+(6x+29) and set that equal to 180degrees.

(x+18)+(6x+29)=180

7x+47=180

7x=133

x=19