Why do we minimize the e2 in order to find the best fitted line for bivariate data? Why not just minimizing ei? Why the following assumptions must be met in order for us to use linear regression? i. The errors 81,..,6n are random and independent. In particular, the magnitude of any error & does not influence the value of the next error &+1. ii. The errors a, ,an all have mean 0. iii, The errors ε ,G, all have the same variance, which we denote by σ. iv. The errorsare normally distributed.

Answer:

The angle SQR is half the intercepted arc SR which is 43°

I recommend that Ronald Lau build the pilot plant first to maximize his expected payoff. The expected payoff for this decision is $55,000.

To help Ronald Lau maximize his expected payoff, we can use decision analysis to evaluate the potential outcomes and probabilities of each decision.

The first decision is whether to build the new facility directly or to build the pilot plant first and then decide whether to build the complete facility.

If the new facility is built directly, the expected payoff is $200,000 × 0.5 + (-$190,000) × 0.5 = $5,000.

If the pilot plant is built first, the expected payoff is:

$5,000 + $200,000 × 0.75 × 0.6 + (-$190,000) × 0.25 × 0.6 = $55,000

or

$5,000 + (-$190,000) × 0.75 × 0.4 + $200,000 × 0.25 × 0.4 = -$45,000

The best decision is to build the pilot plant first since this decision has a higher expected payoff of $55,000 compared to the expected payoff of $5,000 for building the new facility directly.

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Answer:

2x^(3) - 4x^(2) - 4x - 4.

Step-by-step explanation:

2x^(3)-3x^(2)-3x^(2)+2x^(2)-4x-9

Bring like terms together:

= 2x^(3) - 3x^(2) - 3x^(2) + 2x^(2) - 4x + 5 - 9

Now simplify:

= 2x^(3) - 4x^(2) - 4x - 4.

Answer:

\(2x^3-4x^2-4x-4\)

Step-by-step explanation:

Subtract the numbers

\(2x^3-3x^2+5-3x^2+2x^2-4x-9\)

\(2^3-3^2-4-3^2+2^2-4\)

Combine like terms

\(2x^3-3x^2-4-3x^2+2x^2-4x\)

\(2^3-4^2-4-4\)

Rearrange terms

\(2x^3-4x^2-4-4x\)

\(2^3-4^2-4-4\)

Solution:

\(2x^3-4x^2-4x-4\)

Answer:

39 ft^2

Step-by-step explanation:

area of small rectangle

length = 3 ft

breadth = 1 ft

area of rectangle = l*b

=3*1

=3 ft^2

area of big rectangle

length = 12 ft

breadth = 3 ft

area of rectangle = l*b

=12*3

=36 ft^2

area of the figure = area of small rectangle + area of big rectangle

=3 + 36 ft^2

=39 ft^2

The amount you could save per month would be 25% of your discretionary money.

Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.

The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses

Amount to be saved = 25% of discretionary money

Amount to be saved = 0.25 * (Realized income - Fixed expenses)

Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.

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Answer:

1st Option

Step-by-step explanation:

All angles in a triangle must add up to 180°.

Step 1: Set up equation

40° + 60° + 16x = 180°

Step 2: Rewrite

60° + 16x + 40° = 180°

Answer:

Option: A.

Step-by-step explanation:

Hey there!

In the given triangle;

60° +16x° + 40° = 180° { Sum of interior angle of a triangle}

100° + 16x= 180°

16x = 180° - 100°

\(x = \frac{80}{16} \)

Therefore, X= 5°.

So, Option A (equation) is used for solving the value of"X".

Hope it helps...

Answer and Explanation:

m∠1 = 43° because opposite angles are congruent

m∠2 = 137° because ∠2 and 43° are supplementary, so m∠2 + 43° = 180°

m∠3 = 137° because opposite angles are congruent, so m∠3 = m∠2

m∠5 = 43° because alternate angles are congruent

m∠6 = 137° because ∠5 and ∠6 are supplementary, so 43° + m∠6 = 180°

m∠7 = 137° because alternate exterior angles are congruent, so m∠7 = m∠2

m∠8 = 43° because alternate exterior angles are congruent, so m∠8 = m∠1

Answer:

angle 1: 43

angle 2: 137

Step-by-step explanation:

Lets find angle 1 first :)

Since oposite diagonal angles are the same, this will make angle 1 43 degrees :)

Now lets find angle 2!

Since 1 was 43 degrees, and a flat line is 180 degrees we must subtract!

Lets do that now!

180 - 43 = 137

Angle 2 will be 137 degrees!

Have an amazing day!!

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Bill will pay 50$. ... ... ...........,..........

Answer:

1+1=2

Step-by-step explanation:

easy lol

The slope of the line is -3/4.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

The points on the line are (-4, 5), (0,2), (4, -1).

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ -  y₁)/(x₂ -  x₁).

The slope of the line is

(2 - 5)/(0 - (-4)) = -3/4

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The value of surplus each month of $2492.33.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given monthly expenditure:

Fixed expenses = $1720

Living expenses = $1021

Annual expenses = $135

⇒ total monthly expenditure = 1720 + 1021 + 135 = $2,876

Given annual income:

Annual net income = $64,420

⇒ total monthly net income = 64,420 ÷ 12 = $5,368.33 (nearest cent)

Comparing the monthly income and expenditure, we can see that he earns more than he spends, so there will be a surplus.

⇒ total monthly net income - total monthly expenditure

= 5368.33 - 2876 = $2492.33

So, there is a surplus each month of $2492.33.

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Answer:

−0.989010989010

Step-by-step explanation:

what is the 45th term of a sequence generated by the formula tn=(-1)^n * (2n/2n+1)?

When n= 45

tn=(-1)^n*(2n/2n+1)

tn = (-1)^45 * ( 2(45) / 2(45) + 1

= -1 * 90 / (90+1)

= -90 / 91

= −0.989010989010

The 45th term of the sequence generated by the formula tn=(-1)^n*(2n/2n+1) is −0.989010989010

Answer:

r = 22.3m circa

Step-by-step explanation:

We know that the perimeter of a circle can be calculated as follows:

p = 2\(\pi\)r

So half of perimeter will be:

p/2 = \(\pi\)r

We know that p/s = 70m, therefore:

r = 70m /\(\pi \\\) = 22.3 m circa.

We would expect that 4 of the next 9 children to enroll will be elementary school students.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

If 8 out of the last 18 children to enroll at the daycare center were elementary school students,

We can find the fraction of elementary school students in that group by dividing the number of elementary school students by the total number of children:

= 8/18

= 4/9

This means that 4 out of every 9 children enrolled were elementary school students.

If we want to predict how many of the next 9 children to enroll will be elementary school students,

We can use this ratio:

4/9 of 9 children

= (4/9) x 9

= 4

Therefore,

We would expect that 4 of the next 9 children to enroll will be elementary school students.

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Answer: 8 times.

Step-by-step explanation:

I will answer in English:

This says:

The volume of a cube is 125cm^3

How many times the volume will increase if we duplicate the lenght of the side?

If L is the lenght of the side, we have that the volume of the cube is:

V = L^3

If we duplicate the lenght of the side, the new volume is:

V = (2*L)^3 = 8*L^3

So we can see that the volume of the new cube is 8 times the volume of the previous cube.

Now,  we can do the math, for our original cube we have:

L^3 = 125cm^3

L = 5cm

the new cube has L' = 2*L = 10cm

The volume of this cube is:

V' = L'^3 = 10cm^3 = 1000cm^3

the ratio V'/V is:

1000cm^3/125cm^3 = 8

A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.

The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.

The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.

The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.

It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.

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Answer:

Step-by-step explanation:

This is a system of equations problem. The first equation comes from the fact that there are 5 times as many pens in box a as there are in box b; that means that if we multiply the amount in b by 5, it will be equal to what's in a:

a = 5b

That's the first equation. The second one comes from when 76 pens are moved from box a to box b. They are equal when this happens; therefore:

a - 76 = b

Using substitution:

5b - 76 = b and

4b = 76. Therefore,

b = 19.

If a = 5b, then a = 5(19) which gives us that there are 95 pens in box a.

Given that,

Let's assume there are x pens in box B.

Now, there will be 5x pens in box A.(Because there are 5 times as many pens in box A than in box B).

They had the same number of pens when Tom moves 76 pens from box A to box B.

So, after moving 76 pens from box A to box B:

Box A contains 5x-76 pens.

Box B contains x+76.

Now, Box A and Box B have the same number of pens.

We have to equate the number of pens in both boxes:

5x-76=x+76

4x=152

x=38

5x=190

Box A has 190 pens.

Answer:

Layla bu la 520 and glue 729

Step-by-step explanation:

Answer:

13 65/72 is your answer.

Step-by-step explanation:

Answer:

13 65/72

Step-by-step explanation:

a) The area of the first circle is approximately 254.34 square inches

b) The area of the second circle is approximately 70650 square inches.

a) The area of a circle can be calculated using the formula A = πr², where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

For the first circle with a diameter of 18 inches, we can find the radius by dividing the diameter by 2:

r = 18/2 = 9 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 9² = 254.34 square inches

Therefore, the area of the first circle is approximately 254.34 square inches.

b) For the second circle with a diameter of 25 feet, we need to convert the diameter to inches, since our formula uses radius in inches:

25 feet = 25 x 12 inches = 300 inches

Then we can find the radius by dividing by 2:

r = 300/2 = 150 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 150² = 70650 square inches

Therefore, the area of the second circle is approximately 70650 square inches.

Note that the units for the second calculation are in square inches, not square feet, because we used the formula that requires radius in inches.

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The word "and" in probability implies that we use the Multiplication rule.

The correct option is Option D.

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

The relationship between two events is explained by the probability multiplication rule.

Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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Answer:

a) (x, y) = (1, 7)

Step-by-step explanation:

Let be the following system of inequalties:

\(y > x^{2}-4\cdot x -5\)

\(y < -x^{2}-5\cdot x +6\)

We can find the right option by evaluating each option in the system of inequalities:

a) (x, y) = (1, 7)

\(7 > 1^{2}-4\cdot (1) -5\)

\(7 < -1^{2}-5\cdot (1) +6\)

Then,

\(7>-8\) (TRUE)

\(7<0\) (FALSE)

(1, 7) is not a solution of the system of inequalities.

b) (x, y) = (1, -7)

\(-7 > 1^{2}-4\cdot (1) -5\)

\(-7 < -1^{2}-5\cdot (1) +6\)

Then,

\(-7 > - 8\) (TRUE)

\(-7< 0\) (TRUE)

(1, -7) is a solution of the system of inequalities.

c) (x, y) = (1, -5)

\(-5 > 1^{2}-4\cdot (1) -5\)

\(-5 < -1^{2}-5\cdot (1) +6\)

Then,

\(-5 > - 8\) (TRUE)

\(-5< 0\) (TRUE)

(1, -5) is a solution of the system of inequalities.

d) (x, y) = (-1, 6)

\(6 > (-1)^{2}-4\cdot (-1) -5\)

\(6 <(-1)^{2}-5\cdot (-1)+6\)

Then,

\(6>0\) (TRUE)

\(6 < 12\) (TRUE)

(-1, 6) is a solution of the system of inequalties.

Therefore, we conclude that correct answer is A.

Answer:

Its Not (1,7) i took the test and missed it

Step-by-step explanation:

The probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053.

We can use the concept of combinations.

The total number of ways to choose 4 elk out of 24 is given by the combination formula:

C(24, 4) = 24! / (4!(24-4)!) = 10,626

Now, we need to consider the number of ways to choose 3 tagged elk out of the 8 tagged elk and 1 untagged elk. The number of ways to do this is given by:

C(8, 3) * C(1, 1) = 8! / (3!(8-3)!) * 1! / (1!(1-1)!) = 56

Therefore, the probability that 3 out of the 4 captured elk have been tagged is:

P = (Number of ways to choose 3 tagged elk out of 8 tagged elk and 1 untagged elk) / (Total number of ways to choose 4 elk out of 24)

P = 56 / 10,626

Calculating this division gives us the probability:

P ≈ 0.0053

So, the probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053 .

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Answer:

Step-by-step explanation:

Volume of the cone:

Substitute values and solve for r:

The image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

A rotation of 270 degrees counterclockwise about the origin corresponds to a transformation in which every point in the plane is rotated 270 degrees counterclockwise about the origin.

To find the image of the point (0,1) under this transformation, we can use the following formula for a counterclockwise rotation of a point (x,y) about the origin by an angle of θ:

x' = x cos(θ) - y sin(θ)

y' = x sin(θ) + y cos(θ)

Plugging in the values x = 0, y = 1, and θ = 270 degrees, we get:

x' = 0 cos(270°) - 1 sin(270°) = 0 - (-1) = 1

y' = 0 sin(270°) + 1 cos(270°) = 0 + 0 = 0

Therefore, the image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).

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It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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               \(\rule{50}{1}\large\blue\textsf{\textbf{\underline{Given question:-}}}\rule{50}{1}\)

           What is the value of c in the quadratic \(\large\text{$x^2+28=-11x$}\)?

          \(\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}\)

           Before starting to solve, you should notice something - the

quadratic is not in its standard form!

We can easily fix it by adding \(\large\textit{11x}\) on both sides:-

\(\large\text{$x^2+28-11x=0$}\)

We can switch the order of 28 and -11x:-

\(\large\text{$x^2-11x+28=0$}\)

  Now, the quadratic is in its standard form, so we can get down to

finding the value of "c".

Remember, the standard form of a quadratic looks like so:-

Now we can just write our quadratic here:-

Now, can you see what the value of "c" is?

An easy way to remember "c" in quadratics is:-

The "c" in quadratics is the constant.

Henceforth, we conclude that the value of "c" in the given quadratic is:-

 \(\Large\textbf{28}\Large\checkmark\)

        \(\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}\)    

Answer:

\(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).

Step-by-step explanation:

According to the Rational Root Theorem, the potential roots of a polynomial are

\(x=\pm\dfrac{p}{q}\)  

where, p is a factor of constant and q is a factor of leading term.

The given polynomial is

\(f(x)=9x^8+9x^6-12x+7\)

Here, 9 is the leading term and 7 is constant.

Factors of 9 are ±1, ±3, ±9.

Factors of 7 are ±1, ±7.

Using rational root theorem, the rational or potential roots are

\(x=\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\)

Therefore, the potential root of f(x) are \(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).  

Answer:

its D, 3/7.

Step-by-step explanation:

just did it egen2020