4(2x+3)+4(3x+2) simplify and expand answer

The residual for the observed value (2, 810) is -4.

We are given the least squares regression line as ŷ = 800 + 7x and an observed value of (2, 810). We need to find the residual for this observed value.

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable based on the regression line. Mathematically, the residual can be calculated as:

residual = observed value - predicted value

For the observed value (2, 810), the predicted value can be found by plugging in x = 2 in the regression equation:

ŷ = 800 + 7x = 800 + 7(2) = 814

So, the predicted value for the observed value (2, 810) is 814. Now, we can calculate the residual:

residual = observed value - predicted value = 810 - 814 = -4

Therefore, the residual for the observed value (2, 810) is -4.

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(a) In the equilibrium bidding strategy, bidders bid below their cost. The difference between a contractor's quote and their cost represents their strategic behavior in the auction.

By bidding below their cost, contractors try to increase their chances of winning the auction and securing the project.

This strategy allows them to potentially earn a higher profit if they win the auction and their cost turns out to be lower than their bid.

(b) The probability of contractor A winning when she submits a quote equal to b and contractor B submits a quote according to the equilibrium bidding function β(⋅) can be calculated as follows:

P(A wins) = P(A's bid ≤ B's bid)

Since the contractors' costs are independently drawn from a Uniform [0,1] distribution, the probability can be expressed as:

P(A wins) = P(A's cost + A's bid ≤ B's cost + B's bid)

Given that A's bid is b and B's bid is β∗(B's cost), the probability becomes:

P(A wins) = P(A's cost + b ≤ B's cost + β∗(B's cost))

(c) Contractor A's expected payoff when she has a cost of completing the project equal to c and submits a quote equal to b, while her rival bids according to the equilibrium strategy βx(⋅), can be calculated as follows:

Payoff(A) = P(A wins) × (b - c)

Using the probability expression from part (b), the expected payoff can be written as:

Payoff(A) = P(A's cost + b ≤ B's cost + βx(B's cost) × (b - c)

(d) To show that the bidding strategy βx(c) = 2/(1+c) is a (symmetric) Bayesian Nash Equilibrium, we need to verify two conditions:

(i) the strategy is optimal for a contractor given the strategies of other bidders, and

(ii) no bidder has an incentive to deviate from the equilibrium strategy.

(i) Optimality: Given the bidding strategy βx(c) = 2/(1+c), a bidder's expected payoff is maximized when they follow this strategy. This can be shown by calculating the expected payoff for a bidder who anticipates a cost of completing the project as c and submits a quote equal to βx(c). The expected payoff is maximized when the bidder follows the equilibrium strategy.

(ii) No incentive to deviate: Suppose a bidder deviates from the equilibrium strategy and chooses a different bidding strategy. In this case, the bidder's expected payoff would be lower than or equal to the expected payoff obtained by following the equilibrium strategy. Therefore, no bidder has an incentive to deviate from the equilibrium strategy, indicating that βx(c) = 2/(1+c) is a Bayesian Nash Equilibrium.

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Answer:

6

Step-by-step explanation:

Sin = adjacent ÷ hypotenuse

Sin 45 = x ÷ 9

0.71 = x ÷ 9

0.71 × 9 = x

x = 6.36

~6.

hope it helps. :)

Answer:

The smaller angle is 45 degrees.

Step-by-step explanation:

Angles measure 180º. If there are two angles and one of them is three times the other, you would just divide 180 by 4.

The equation would look like:

3x + x = 180

First, the x would be added together:

4x = 180

Then, divide both sides by 4:

x = 45

The equation of height of each pyramid inside the cube is,

⇒ h = 2V / B

The equation that represent the volume of each pyramid is,

⇒ V = LWH / 3

The equation that represent the volume of each pyramid if the height of each pyramid is h and area of the base is B,

⇒ V = 1/3 (B × h)

Given that;

To find the formula for height and volume of pyramid.

Now, We know that;

The equation of height of each pyramid inside the cube is,

⇒ h = 2V / B

And, The equation that represent the volume of each pyramid is,

⇒ V = LWH / 3

And, The equation that represent the volume of each pyramid if the height of each pyramid is h and area of the base is B,

⇒ V = 1/3 (B × h)

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Using the Central Limit Theorem, the given statements are true or false in following

a) True

b) True

c) True

d)True

e) True

a) From the definition of central limit theorem, by law of large number to sample average converge almost slowly to the population average.

So, based on CLT the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large i.e ., True.

b) Same reason as (a) , based on CLT the usually considers that sample 51Z6 30 is sufficiently large is true

c) If we generate 1000 samples of Binomial (10;0.3)distribution are plot a histogram then it looks like normal distribution.

So, the Central Limit Theorem be applied to both discrete and continols Fandom variables is true.

d) Whatever be the parent distribution , if sample size ,n is large then sample mean means

converges in probability to the population mean.

So, the given option (d) is true .

e) If population size is normally distributed then sample mean is also normally distributed for all sample size.

So, option(e) is also true.

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Complete question:

Problem Central Limit Theorem) _ Are the following statements true or false?

a)Easy. Based the Central Limit Theorem_ the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large.

b)Easy. Then applying the Central Limit Theorem. l usually conziders that sample 51Z6 30 is sufficiently large.

c)Easy. the Central Limit Theorem be applied to both discrete and continols Fandom variables .

d): Assuming that the sample size is sufficiently large the Central Limit Theorem permits draw conclusions about the population based strictly sample data. and without having aIV knowledge about the distribution of the underlying population:

(e) Moderate_ Assuming that the population is normally distributed_ the sampling distribution of the sample mean is normally distributed for samples of all sizes_

The correct number of different ways 10 identical balloons can be given to four children if each child receives at least two balloons is 11. This can be answered by the concept of Combination.

To solve this problem, we can use generating functions, which are a powerful tool in combinatorics for counting the number of ways to distribute objects. Let's define a generating function for each child, representing the number of balloons they receive.

Let the generating function for the first child be represented as x², as each child must receive at least two balloons. Similarly, the generating functions for the other three children would also be x² each.

Now, we can multiply these generating functions together to represent the combined number of balloons given to all four children. Multiplying x² four times gives us (x²)⁴, which simplifies to x⁸.

Finally, we need to find the coefficient of x¹⁰ in the expansion of x⁸. This represents the number of ways to distribute 10 identical balloons among the four children, with each child receiving at least two balloons.

Using the binomial theorem or simply by expanding (x²)⁴, we get the coefficient of x¹⁰ to be 11.

Therefore, The correct number of different ways 10 identical balloons can be given to four children if each child receives at least two balloons is 11

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Hi, there!

 ________

\(\textsc{key:}\)

. . . . . . . . . . . . .

The formula is

\(\longrightarrow\Large\boxed{A=\dfrac{r^2\theta}{2}}\)

. . . . . . . . . . . . . . .

Here

» A=Sector Area, or arc length

» r is the radius (it's squared‼)

» θ is the angle

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Now, we can substitute our parameters, and work out the answer.

\(\bf{A}\sf{=\dfrac{12^2\times65}{2}}\)

\(\bf{A}\sf{=\dfrac{144\times65}{2}}\)

\(\bf{A}=\sf{\dfrac{9360}{2}\)

\(\bf{A}=\sf{4,680 \ centimeters^2}\)

Hope the answer - and explanation - made sense,

happy studying!!                                                                     \(\tiny \boldsymbol{Frozen \ melody}\)

The margin of error is multiplied by √2. The correct option is B.

The margin of error is affected by the sample size and the standard deviation of the population. When the sample size is cut in half, the margin of error increases because there is more uncertainty in estimating the population mean. The formula for margin of error is:

Margin of Error = Z * (Standard Deviation / √Sample Size)
When the sample size is cut in half, the new margin of error becomes:
New Margin of Error = Z * (Standard Deviation / √(Sample Size / 2))
By factoring out the square root, we get:
New Margin of Error = Z * (Standard Deviation / (√Sample Size * √0.5))
This shows that the original margin of error is multiplied by √2 when the sample size is cut in half.

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Answer:

B. 2/5 barrel/hour

Step-by-step explanation:

cross multiply 1/5 and 2/1

=2/5

Answer:

Step-by-step explanation:yes

The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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The average rate of change for the function on the interval [-3, 1] is approximately -0.333 (rounded to 3 decimals).

To evaluate the average rate of change for the function (t² - 4)(t + 1) / (t² + 3) on the interval [-3, 1], we can use the following formula:

Average Rate of Change = (f(b) - f(a)) / (b - a),

where f(b) represents the value of the function at the upper limit of the interval, f(a) represents the value of the function at the lower limit of the interval, and (b - a) represents the width of the interval.

Let's calculate it step by step:

Substitute t = -3 into the function:

f(-3) = (-3² - 4)(-3 + 1) / (-3² + 3)

= (9 - 4)(-2) / (9 + 3)

= 5(-2) / 12

= -10/12

= -5/6.

Substitute t = 1 into the function:

f(1) = (1² - 4)(1 + 1) / (1² + 3)

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

= -6/4

= -3/2.

Calculate the width of the interval:

(b - a) = (1 - (-3))

= 4.

Calculate the average rate of change:

Average Rate of Change = (f(1) - f(-3)) / (1 - (-3))

= (-3/2 - (-5/6)) / 4

= (-3/2 + 5/6) / 4

= (-9/6 + 5/6) / 4

= -4/6 / 4

= -2/6

= -1/3.

Therefore, the average rate of change for the function on the interval [-3, 1] is approximately -0.333 (rounded to 3 decimals).

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Solve x

The solution set for x is [2,10)

Answer:

6.5 miles per day

Step-by-step explanation:

Take the number of miles and divide by the number of days

39 miles/ 6 days

6.5 miles per day

Answer: 6.5 miles per day is correct

Step-by-step explanation:

You would just need to divide 39 by 6 to find the total miles per day. Therefore C: 6.5 is correct!

The approximate solution for the equation \(x^3 - x - 1 = 0\) using the fixed-point iteration method with an initial guess

p0 = 1 is

p3 ≈ 1.4049.

To solve the equation x^3 - x - 1 = 0 using a fixed-point iteration method with three iterations and an initial guess p0 = 1, we can use the fixed-point iteration formula:

p_n+1 = g(p_n)

where g(x) is a function that transforms the equation into the form x = g(x).

First, let's rearrange the equation to isolate x:

x^3 - x - 1 = 0

x^3 = x + 1

x = (x + 1)^(1/3)

Now, we can define our fixed-point iteration function:

g(x) = (x + 1)^(1/3)

Let's perform the iterations:

Iteration 1:

p1 = g(p0)

= (p0 + 1)^(1/3)

= (1 + 1)^(1/3)

= 2^(1/3)

≈ 1.2599

Iteration 2:

p2 = g(p1)

= (p1 + 1)^(1/3)

= (1.2599 + 1)^(1/3)

≈ 1.5214

Iteration 3:

p3 = g(p2)

= (p2 + 1)^(1/3)

= (1.5214 + 1)^(1/3)

≈ 1.4049

After three iterations, the approximate solution for the equation \(x^3 - x - 1 = 0\) using the fixed-point iteration method with an initial guess

p0 = 1 is

p3 ≈ 1.4049.

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For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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well, the difference is £20 - £3 simply £17.

now, if we take £20 to be the 100%, what is £17 off of it in percentage?

\(\begin{array}{ccll} \pounds &\%\\ \cline{1-2} 20 & 100\\ 17& x \end{array} \implies \cfrac{20}{17}=\cfrac{100}{x}\implies 20x=1700 \\\\\\ x=\cfrac{1700}{20}\implies x=85\)

The area of the regular hexagon with a 48-inch perimeter is 96√3 square inches.

A regular hexagon is a polygon with six equal sides and six equal angles. All of the sides and angles of a regular polygon are equal.

To find the area of a regular hexagon with a 48-inch perimeter, we need to use the formula for the perimeter of a regular hexagon, which is:

P = 6s

where P is the perimeter and s is the length of each side.

Since we know that the perimeter is 48 inches, we can solve for s:

48 = 6s

s = 8 inches

Now that we know the length of each side, we can use the formula for the area of a regular hexagon:

A = (3√3/2) s²

where A is the area and s is the length of each side.

Substituting s = 8 inches into the formula, we get:

A = (3√3/2) (8 inches)²

A = (3√3/2) (64 square inches)

A = 96√3 square inches

Therefore, the area of the regular hexagon is 96√3 square inches.

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The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The confidence interval = 95%

And, Size of sample = 17

Now,

Since, The confidence interval = 95%

And, Size of sample (n) = 17

Hence, The degree of freedom (n - 1) = 16

Thus, The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

Therefore, The value of the t score for a 95% confidence interval for degree of freedom 16 will be 2.120.

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Answer:

54°

Step-by-step explanation:

m and the 54° angle are VERTICAL ANGLES. That means they are the same measure.

Answer:

Step-by-step explanation:

54 degree

Answer:

67

Step-by-step explanation:

Answer:

The volume of the gas under these circumstances is 30 cm³.

Step-by-step explanation:

To determine the variation equation for this situation, we start with the formula V = Tk/P

where k is the constant of variation.

To solve for k, we use the initial values of V, T, and P

V = 42 cm³, T = 84 °C, P = 50 mmHg

Substituting these values into the formula, we get

42 = 84k/50

Solving for k, we have

k = (42 x 50)/84 = 25

Therefore, the variation equation for this situation is

V = 25T/P

To find the volume of gas when T = 48 °C and P = 40 mmHg, we substitute these values into the variation equation

V = 25 x 48/40 = 30 cm³

Therefore, the volume of the gas under these circumstances is 30 cm³.

Answer:

42 degrees

Step-by-step explanation:

The measure of ∠S to the nearest degree is 42°.

Law of cosines of triangle states that for three length of sides of the triangle, a, b and c opposite to the angles A, B and C respectively can be related as,

a² = b² + c² - 2bc cos(A)

Given a triangle QRS.

Given,

q = 73 inches

r = 40 inches

s = 51 inches

We have to find the measure of angle S.

By law of cosines,

s² = r² + q² - (2rq)cos(S)

51² = 40² + 73² - (2×40×73) cos (S)

(2×40×73) cos (S) = 4328

cos (S) = 0.741

S = 42.175° ≈ 42°

Hence the measure of angle S is 42°.

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Step-by-step explanation:

it's a right angled triangle

B. acute

C. scalene ( as all sides are different)

E. right

Answer:

Step-by-step explanation:

Answer:

The standard form of such an equation is Ax + By + C = 0 or Ax + By = C. When you rearrange this equation to get y by itself on the left side, it takes the form y = mx +b. This is called slope intercept form because m is equal to the slope of the line, and b is the value of y when x = 0, which makes it the y-intercept.

Step-by-step explanation:

Answer:

46.50

Step-by-step explanation:

The value of 12 gallons of gas is 46.5 dollars.

P = 3.75 g + 1.5

where,

p is the total cost,

g is the gallons of gas.

g=12

Substituting the value of g in the linear model,

P = 3.75 g + 1.5

P = 3.75 (12) + 1.5

P = 45 + 1.5

p = 46.5

Hence, the value of 12 gallons of gas is 46.5 dollars.

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Answer:

3200

Step-by-step explanation:

Answer:

3200

Step-by-step explanation:

one kilometer = 1000

3.2 * 1000