use quadratic regression to find the equation of the parabola going through these 3 points. (-1,-23), (-3,-67), (2,13)

The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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The circumference of the table is 9.42 feet

The circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

For a example a circular ball with diameter 7 cm will have a circumference of 44cm

The circumference of a circle is expressed as:

C = πd

C = 3.14 ×3

C = 9.42 feet

Therefore the circumference of the table is 9.42 feet.

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The scientist that made a more concentrated salt solution is scientist A.

Since Scientist A dissolved 1.0 kilogram of salt in 3.0 liters of water. The concentration will be:

= 1/3 = 0.33

Scientist B dissolved 2.0 pounds of salt into 7.0 pints of water. The concentration will be:

= 2/7

= 0.285

Therefore, the scientist that made a more concentrated salt solution is scientist A.

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Answer: The formula solved for L is E/100M = L.

Step-by-step explanation:

So far we have the givens:

E, is measured by the formula E = 100M/L, where M = number monsters and L= level of monsters and solve for L.

Thus, isolate L to solve for it.

E = 100M/L

Divide each side by 100M to get rid of it and to free L.

E/100M = L

Hence your answer!

Answer: 50M/E is correct

Step-by-step explanation: I got it right :D

The fill up of the missing points are:

Using the image attached, one can see that m<1 and m<2 creates a kind of  linear pair hence one can say they are both supplementary using the law of LINEAR POSTULATE THEOREM.

Based on the fact that the supplementary angles add up to 180 degrees, therefore:

m<1 + m<2 = 180   - will be equation 1

Since the interior angles m<2 and m<3 are known to be equal based on the CONGRUENCE POSTULATE THEOREM. Therefore

m<2 = m<3 ---  will be equation 2

Then place eqn. 2 into eqn. 2

m <1 + m <3 = 180

This connote that m<1 and m<3 are supplementary.

Hence, The fill up of the missing points are:

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d)An error because d cannot be negative.

According to the data, effect sizes such as Cohen's d typically range from 0 to positive values, and negative values do not make sense in this context. Therefore, an effect size of d = -63 is likely an error or a typo.

Assuming that the correct effect size is a positive value, the magnitude of the effect size can be described as follows based on Cohen's convention:

However, it's important to note that the interpretation of effect sizes also depends on the context and the specific field of study.

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The critical value of the correlation coefficient for a two-tailed test at alpha = 0.05 with a sample size of n = 23 is approximately plus/minus 0.497.

To understand why this is the case, we need to consider the distribution of the correlation coefficient, which follows a t-distribution. In a two-tailed test, we divide the significance level (alpha) equally between the two tails of the distribution. Since alpha = 0.05, we allocate 0.025 to each tail.

With a sample size of n = 23, we need to find the critical t-value that corresponds to a cumulative probability of 0.025 in both tails. Using a t-distribution table or statistical software, we find that the critical t-value is approximately 2.069.

Since the correlation coefficient is a standardized measure, we divide the critical t-value by the square root of the degrees of freedom, which is n - 2. In this case, n - 2 = 23 - 2 = 21.

Hence, the critical value of the correlation coefficient is approximately 2.069 / √21 ≈ 0.497.

Therefore, the correct answer is A. Plus/minus 0.497.

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Answer:

9 is the answer

Step-by-step explanation:

You will multiply 3x3 and 9x1 it will have the least common denominator

The number  300 can be written as 300/1 as a quotient of integers to show that it is rational.

A rational number is a number of the form p/q, where q not equal to 0 and p  and q must be co-primes.

To write a number in the form of quotient of integer, we write it as , where p/q.

Here,  300 can be written as  300/1 or 600/2 .

But we should also take care that p and q must be co-primes.

Co-primes are the pairs of numbers that have only one common factor which is 1.

So, 300 can be written as 300/1

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a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

a. The extreme points of the feasible region are the vertices of the polygon formed by the intersection of the constraint lines. In this case, the extreme points are (0,0), (5,0), (3.75, 3.75), (3.5,4.5), and (0,8).

b. To find the optimal solution and the objective function value, we evaluate the objective function at each extreme point and choose the point that maximizes the objective function. In this case, the point (3.5, 4.5) maximizes the objective function with a value of 59.5. Therefore, the optimal solution is x = 3.5 and y = 4.5, and the objective function value is 59.5.

c. The slack variables represent the surplus or slack in each constraint. We calculate the slack variables by subtracting the actual value of the left-hand side of each constraint from the right-hand side. In this case, the values of the slack variables are s1 = 0 (indicating no slack in the first constraint), s2 = 2 (indicating a surplus of 2 in the second constraint), and s3 = 0 (indicating no slack in the third constraint).

Therefore, the correct option is:

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

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The total number of different telephone numbers are possible in city  is 6561.

A term permutation relates to a mathematical process that determines the number of possible arrangements of a given set.

Now, according to the question;

Because the first three digits are fixed, we must select the next four digits.

A total number of available telephone numbers is increased by selecting one of nine numbers for the fourth digit;

nine numbers for the fifth digit;

nine numbers for the sixth digit;

and nine numbers for the seventh digit.

Thus,

= 9×9×9×9

= 6561

Therefore, the total number of ways in which telephone numbers are possible in city are 6561.

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The double integral of sin(xy) over the rectangle r equals 1 when a is approximately equal to 0.986, with 0 ≤ a ≤ π.

The iterated integral to compute the double integral over the rectangle r = {(x,y) : 0 ≤ x ≤ π, 0 ≤ y ≤ a} of sin(xy) is given by:

∫∫r sin(xy) dA = ∫₀^a ∫₀^π sin(xy) dx dy

Integrating with respect to x first, we have:

∫₀^a ∫₀^π sin(xy) dx dy = ∫₀^a [-cos(πy) + cos(0)] dy

= ∫₀^a (1 - (-1)^n) dy

= a - (a/π)sin(πa)

For what values of a is ∫∫r sin(xy) dA equal to 1?

We need to solve the equation:

a - (a/π)sin(πa) = 1

Multiplying both sides by π, we get:

aπ - a sin(πa) = π

Now, let f(a) = aπ - a sin(πa) - π. We need to find the values of a such that f(a) = 0.

Using numerical methods, we can find that there is only one solution in the interval [0,π], which is approximately a = 0.986.

Therefore, the double integral of sin(xy) over the rectangle r equals 1 when a is approximately equal to 0.986, with 0 ≤ a ≤ π.

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Answer:

60

Step-by-step explanation:

Answer:

The train is 0839

Step-by-step explanation:

First off, 0620 and 0746 are not available options, as Jean would've immediately know, as they're the only one with non-repeated minutes.

Now, when Marie says "I'm sure neither does Jean", it means she didn't get 06 or 07, as those are the number that has 0620 and 0746, which then she cannot ensure that Jean doesn't know the train arrival.

We're left with 0825, 0839, 0917, 0925 and 0950

After that, Jean said he knows the train number. So, he couldnt've gotten 25, as it is repeated in the 5 options we pick. => we're left with 0839, 0917 and 0950.

And then, Marie responds now she does as well, which it cannot be 09, as it is repeated.

So, the train number is 0839.

Answer:

the answer to your question is ten

Pair 2 shows one figure rotated 180 degrees compared to the other, and translated as well. So they are congruent (ie the same).

Pair 4 shows one triangle reflected over the vertical line x = 22 to get the other triangle; which shows they are the same triangle.

The other pairs are not congruent. You can show that the areas of each figure being different is enough to prove they aren't the same figure.

1) If you want to calculate how much larger the output elasticity with respect to labor is in 1989 versus 1983, you can split the data into two datasets, one for each year, and estimate the output elasticity with respect to labor for each dataset.

2) You can compute a Wald statistic using the equation,  W = (β1,1989 - β1,1983)^2 / [Var(β1,1989) + Var(β1,1983)]

1) Split the data into two separate datasets, one for 1983 and another for 1989, and calculate the output elasticity with respect to labor for each dataset. Then you can compare the two elasticities to determine how much larger the elasticity is in 1989 relative to 1983.

To calculate the output elasticity with respect to labor, you can use the following formula:

Output elasticity with respect to labor = (% change in output) / (% change in labor)

You can estimate the percentage changes in output and labor using the data from each year, and then use the formula above to calculate the output elasticity with respect to labor for each year.

2) To compute a Wald statistic to test the null hypothesis that the intercept and the two elasticities are the same in 1983 as in 1989, you can use the following steps:

Step 1: Estimate the two regression models separately for each year (i.e., 1983 and 1989) using the data from each year.

Step 2: Use the estimated coefficients from each regression model to construct the null hypothesis that the intercept and the two elasticities are the same in 1983 as in 1989.

Step 3: Estimate a new regression model that combines the data from both years and includes a dummy variable for year (i.e., 1983 = 0, 1989 = 1). The regression model should take the form:

Output = β0 + β1 Labor + β2 Land + β3 Year + ε

Step 4: Compute the Wald statistic for the null hypothesis using the following formula:

W = (β1,1989 - β1,1983)^2 / [Var(β1,1989) + Var(β1,1983)]

where β1,1989 and β1,1983 are the estimates of the output elasticity with respect to labor for 1989 and 1983, respectively, and Var(β1,1989) and Var(β1,1983) are the variances of these estimates.

Step 5: Compare the computed Wald statistic to a critical value from the chi-squared distribution with one degree of freedom. If the computed Wald statistic exceeds the critical value, reject the null hypothesis that the intercept and the two elasticities are the same in 1983 as in 1989.

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By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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Answer: 5x = 10

Hope this helped =)

Answer: 5x=10

                 x=2

Step-by-step explanation:

2(5x+4/2)=7(2)

5x+4=14

    -4   -4

5x=10

x=2

The answer is \(3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right]\)

To solve the given expression, we have to first know about matrix addition and scalar multiplication.

Matrix addition is possible only when both matrices have equal dimensions. Scalar multiplication is the multiplication of a real number and a matrix. Each element of the matrix is multiplied by a scalar value in scalar multiplication.

To solve the given problem, first, substitute the value of A and B in the formula,

\(3A+3B=3\left[\begin{array}{cc}-4&-3\\6&1\end{array}\right] +3\left[\begin{array}{cc}2&-4\\0&0\end{array}\right]\)

Using scalar multiplication, multiply the real number and the matrix. So we get,

\(\begin{aligned}3A+3B&=\left[\begin{array}{ccc}3(-4)&3(-3)\\3(6)&3(1)\end{array}\right] +\left[\begin{array}{ccc}3(2)&3(-4)\\3(0)&3(0)\end{array}\right]\\&=\left[\begin{array}{ccc}-12&-9\\18&3\end{array}\right] +\left[\begin{array}{ccc}6&-12\\0&0\end{array}\right]\end{aligned}\)

To add two matrices with the same dimension, add their corresponding element. So we get,

\(\begin{aligned}3A+3B&=\left[\begin{array}{ccc}-12+6&-9-12\\18+0&3+0\end{array}\right] \\&=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right]\end{aligned}\)

Therefore, the answer is \(3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right]\)

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Answer:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-2.45 times 10 squared is -245 while square root of 93 is 9.643650761 so 6.387 is the smallest then square root of 93 then -2.45 times 10 squared.

Answer:

The answer for this is the 2nd one

Answer:

f(5)= 4(5)-1

=20-1

=21

The evaluated value of f(5) is 19, which is determined by performing the arithmetic operations.

The linear function is given as follows:

f(x) = 4x - 1

To evaluate the function f(x) = 4x - 1 and find f(5), we substitute x = 5 into the function.

f(5) = 4(5) - 1

= 20 - 1

= 19

Therefore, f(5) is equal to 19.

The function f(x) = 4x - 1 represents a linear equation. In this case, when x is equal to 5, the value of f(x) can be calculated by substituting x = 5 into the equation.

By performing the necessary arithmetic operations, we find that f(5) is 19.

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Answer:

(9√3 - 3π) cm²  or ≈ 6.16 cm²

Step-by-step explanation:

Refer to attached pictures

We have equilateral triangle with side of 6 cm and inscribed circle, we need to find the shaded area inside the triangle not covered by the circle.

The shaded are is the difference of areas of the triangle and circle

Area of equilateral triangle is calculated as per formula:

Area of circle is calculated as per formula:

Let's find the value of r:

Δ ADB is the right triangle with angles 30° and 60°

It has sides of 3 cm, 6 cm and AD= m cm

As per attached, m is the long leg and equal to a√3, so

also,

We can find AO in the same way as above using Δ AOF

AO= 2r as it is the hypotenuse and the hypotenuse is twice a short leg in the right triangle with angles 30° and 60°

So,  

Now we can get the area of circle:

Shaded are is:

The three numbers are x = y = 9.625 and z = 0.75, and the maximum value of the quantity 2 is 20.375

We can use the AM-GM inequality to maximize the quantity 2.

From the given equation, we have:

1/yxz = 20

Multiplying both sides by yxz, we get:

1 = 20yxz

yxz = 1/20

Now, let's consider the sum of the three numbers:

x + y + z = 20

Using the AM-GM inequality, we have:

\((x + y + z)/3 > = (xyz)^{(1/3)}\)

Substituting the value of xyz, we get:

\((x + y + z)/3 > = (1/20)^{(1/3)}\)

(x + y + z)/3 >= 0.25

Multiplying both sides by 3, we get:

x + y + z >= 0.75

Since we want the sum of the numbers to be exactly 20, we can rewrite this as:

20 - x - y >= 0.75

x + y <= 19.25

So, the sum of x and y must be less than or equal to 19.25.

To maximize the quantity 2, we can take x = y = 9.625 and z = 0.75,

since this makes the sum of x and y as close to 19.25 as possible while still satisfying the equation and being positive.

Therefore, the three numbers are x = y = 9.625 and z = 0.75, and the maximum value of the quantity 2 is:

2(x + yz) = 2(9.625 + 0.75*0.75) = 20.375/

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To find positive number whose sum is 20 and the quantity 2 is maximized, we can use the AM-GM inequality. According to this inequality, the arithmetic mean of a set of positive numbers is always greater than or equal to their geometric mean. That is,

(a + b + c)/3 ≥ (abc)^(1/3)

Now, we need to rearrange the equation 1/yxz = 20 to get the values of a, b, and c. We can rewrite it as yxz = 1/20.

Next, we can assume that a + b + c = 20 and apply the AM-GM inequality to the product abc to maximize the value of 2. That is,

2 = 2(abc)^(1/3) ≤ (a + b + c)/3

Hence, the maximum value of 2 is 2(20/3)^(1/3), which occurs when a = b = c = 20/3.

Therefore, the positive numbers whose sum is 20 and the quantity 2 is maximized are 20/3, 20/3, and 20/3.
To maximize the quantity 2 with the given equation 1/(yxz) = 20 and positive numbers whose sum is 20 (x+y+z=20), we first rewrite the equation as yxz = 1/20. Now, using the Arithmetic Mean-Geometric Mean (AM-GM) inequality, we have:

(x+y+z)/3 ≥ ((xyz)^(1/3))

Since x, y, and z are positive, we can say that:

20/3 ≥ ((1/20)^(1/3))

From here, we find that x, y, and z should be as close to each other as possible to maximize the quantity 2. One such possible solution is x = y = 19/3 and z = 2/3. Therefore, the positive numbers x, y, and z are approximately 19/3, 19/3, and 2/3, which maximizes the quantity 2.

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The absolute deviation of the data set 7 10 14 and 20 is 4.25.

What is the mean deviation method?

When calculating the average departure from the mean value of a particular data set, statisticians employ a measure known as the mean deviation. Following the steps below will make it simple to determine the mean deviation of the data values.

In statistics, the term "deviation" refers to the discrepancy between the observed value of a data point and its expected value. As a result, mean deviation, also known as mean absolute deviation, is the typical departure of a data point from the mean, median, or mode of the data collection.

data set is 7, 10, 14, 20,

Mean = m = 51/4 = 12.75

So the MAD is 1/4 |7-12.75| |10-12.75| |14-12.75| 20-12.75|

MAD = 17/4 = 4.25

Hence the mean absolute deviation of the data set 7 10 14 and 20 is 4.25.

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(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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