Check if (1,6) is the solution to the system shown below

The ordinary least-squares estimators are used in regression analysis. In order to make the least-squares estimators of α and β BLUE, some assumptions must be met.

Assumptions of Linear Regression Model: In order to apply the OLS estimation technique, the following assumptions must be met :

Linearity - The linear regression analysis's relationship between independent and dependent variables should be linear.

If this assumption is not met, the linear regression will not be able to offer a good estimate of the relationship between variables.

Homoscedasticity - The variances of the residuals should be equal for all values of X.

In addition, the error term should have a constant variance. When this assumption is not met, the model is referred to as heteroscedasticity. Normality - The error term must be normally distributed.

This assumption's significance is critical since OLS depends on normality, and the model's failure to meet this assumption can be disastrous.

Independence - The values of the dependent variable must be independent of one another.

In other words, there should be no correlation between consecutive error terms, and each of the errors should have an average of 0.

Zero Conditional Mean - The X variable is exogenous, meaning it is uncorrelated with the error term.

This is known as the assumption of exogeneity. When this assumption is met, we say that the error has a zero mean or is orthogonal to X, which implies that E(u|X)=0.

The BLUE stands for Best Linear Unbiased Estimators. When OLS meets these five assumptions, the least-squares estimators of α and β are the BLUE.

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The correct answer we get from the Quantitative variable. i.e. "a. number of car in college per day".

The correct answer is "a. number of car in college per day".

Quantitative variable:

The quantitative variable is used to indicate a variable that takes on numerical values. It is a type of statistical variable that is numeric and uses an objective measure to determine its value.

The variable measures the count, amount, or size of something.

To find out which of the given options is an example of a quantitative variable, we need to understand what it is.

So, the given options are:

a. number of cars in college per day. (Quantitative variable)

b. Gender of students. (Non-quantitative variable)

c. College major. (Non-quantitative variable)

d. Type of favored food. (Non-quantitative variable)

Thus, option a. number of cars in college per day is an example of a quantitative variable.

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The vector x in terms of the basis B is [x]B = [a].

The vector x can be written as a linear combination of the basis vectors V₁ and V₂ as shown below:

[x]B = a₁V₁ + a₂V₂

Since B is a basis of R², every vector in R² can be represented as a linear combination of V₁ and V₂.

Using the coordinates of x with respect to B, we have:[x]B = a₁V₁ + a₂V₂ = [8; 3]

We can represent V₁ and V₂ in terms of the standard basis of R² as follows:V₁ = [1; 0] and V₂ = [0; 1]

Therefore,[x]B = a₁[1; 0] + a₂[0; 1] = [a₁; a₂]Hence, we can conclude that a = [8; 3] with respect to the standard basis of R².

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Answer:

$20,783

Step-by-step explanation:

The original value of the car is given as $36,601.

Now, the residual value of the car after a 3 - year lease is given as $15,818.

Residual value is the amount that the person leasing this car can purchase it after the 3 years lease is expired.

Formula for his residual value is usually;

Residual value = original value - depreciation value

Where depreciation value is the amount of the cars original value the Person getting the vehicle on lease for 3 years would pay to cover that period.

Thus;

Depreciation value = 36601 - 15818 = $20783

Answer:

scale factor is 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

5:15. 8:24. 9:27. they are all a ratio of 3

The value of the integral using substitution is 1.96 and using approximation it can be truncated as it is an infinite series.

We need to evaluate the integral f(5/1-4a²) da directly and using a series approximation.

Substitution Method:

Consider ax = sin, then a = sin(x)/x.

On differentiating,

da/dx = cos(x)/x - sin(x)/x²; da/dx = 1/x cos²x.

We know that

1-4a² = 1-4(sin²x)/(x²) = cos(2x)/x²

So the given integral f(5/1-4a²) da can be written as

f (5/x² cos²x cos(2x)) dx = 5 f (cos(2x)/x²) dx

Integrating w.r.t x,

5 f (cos(2x)/x²) dx = (5/2) f (cos(2x)/x²) + C

Using the given values, we can find the value of integral which is 1.96. Thus, the answer is 1.96.

Approximation Method:

As we need to use a series approximation, we can use Taylor series for approximating the integral, which is:

f(x) = f(a) + (x - a) f'(a) + (x - a)² f''(a) / 2 + ... ∞

We know that the function f(5/1-4a²) can be written as

f(x) = 5 / (1 - 4x²), where a = 0.

Substituting the value of f(x) and f'(x) in the Taylor series formula, we get:

f(x) = f(0) + xf'(0) + x²f''(0) / 2! + x³f'''(0) / 3! + ...

The first derivative is given by:

f'(x) = -40x / (1 - 4x²)²

Substituting the value of f(0) = 5 and f'(0) = 0 in the Taylor series formula, we get:

f(x) = 5 - 40x² + 320x^4 - ...

This is an infinite series. Hence, we can truncate it after a few terms to get an approximate value of the integral. Thus, we can find an approximation for the given integral.

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The amount of paint she should buy is 2 gallons and it will cost $36.02.

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The room takes the shape of a cuboid with the dimensions 30 by 15 by 8

Charlotte will be left with 5 surfaces to paint i.e

The ceiling and the other 4 walls.

Therefore the total surface area of the portion to be painted = lh + lh + lb + bh + bh

where l = 20, b = 15 , h = 8

= 20 × 8 +120× 8 + 20×15 + 15× 8 + 15 × 8

= 160+160+300+120+120

= 860 ft²

Let's assume the windows and doors take area of 60ft²

The area to be painted is 800ft²

1 gallon of paint will go for 400ft²

therefore the number of gallon for 800ft² = 800/400 = 2 gallons.

The cost of 1 gallon is $ 16.99

2 gallons = 2 × 16.99 = $33.98

Sales tax = 6%

= 6/100 × 33.98

= $2.04

Total cost = 33.98 + 2.04

= $36.02

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Answer:

(2x+1)(2x-1)

Step-by-step explanation:

4x^2-1

(2x)^2-1

(2x)^2-1^2

(2x+1)(2x-1)

Answer:

21 degrees.

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

as BC ║DE ⇒ ∠CBA=∠BAD

⇒ ∠x=180-∠BAD -∠CAB

⇒ ∠x=180-105-54=21

The inverse Laplace transform of F(S) = (s + 1)(s + 5) is δ''(t) + δ'(t) + 5δ(t), where δ(t) represents the Dirac delta function.

To obtain the inverse Laplace transform of F(S) = (s + 1)(s + 5), we can use the linearity property and the inverse Laplace transform table.

The table states that the inverse Laplace transform of s + a is equal to the Dirac delta function δ(t - a), and the inverse Laplace transform of a constant times F(S) is equal to the constant times the inverse Laplace transform of F(S).

Applying these properties, we can write:

F(S) = (s + 1)(s + 5)

= s^2 + 6s + 5

Using the linearity property, we can split this expression into three terms:

F(S) = s^2 + 6s + 5 = s^2 + s + 5s + 5

Taking the inverse Laplace transform of each term separately, we have:

L^(-1){s^2} + L^(-1){s} + 5L^(-1){s} + 5L^(-1){1}

Referring to the inverse Laplace transform table, we find that:

L^(-1){s^2} = δ''(t)

L^(-1){s} = δ'(t)

L^(-1){1} = δ(t)

Therefore, the inverse Laplace transform of F(S) = (s + 1)(s + 5) is:

L^(-1){F(S)} = δ''(t) + δ'(t) + 5δ(t)

In summary, the inverse Laplace transform of F(S) = (s + 1)(s + 5) is given by δ''(t) + δ'(t) + 5δ(t).

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Step-by-step explanation:

This seems like you just want to figure out the circumference of the manhole cover. The formula for the circumference of a circle is pi (3.14) multiplied by the diameter (d) of the circle so, circumference=πd. (π is the symbol for pi and approx. equals 3.14)

Circumference = πd

= 3.14(d)

= 3.14(3)

= 9.42 ft.

The length of the brass grip-strip will be 9.42 ft.

If the problem was stated in terms of the radius of the manhole cover then the formula would be circumference = 2πr which is the radius multiplied by 2 then multiplied by pi.

The radius of a circle is the distance from the center to the edge and the diameter is the distance from one edge of the circle to the other passing through the center of the circle.

Well, if the grip strip were of no width and could be straightened out to a line (which a piece of rubber cut in a circle couldn't be), then the length of the grip would correspond to the circumference of the manhole cover.

Circumference = 2*PI*radius = PI*diameter so your answer is 3*PI feet long.

2  =

3  =

6 : 9  =

Step-by-step explanation:

Here are some solutions! Hope this helps.

-Lei

Answer: $112

Step-by-step explanation:

700x0.04=28x4=112

Answer: B - one who cannot decide between two sides, as in war or argument

Step-by-step explanation:

Answer:

divide the earnings number by the time, and then subtract the quotient by the slope of tylers graph.

if i was you i wouldnt do that that could be inaporpiet

Answer: 0.416666667 yards

Answer:

2/5 of a yard

Step-by-step explanation:

Hope this helps and have a wonderful day!!!!

9514 1404 393

Answer:

  1135.2 in³

Step-by-step explanation:

The volume of a sphere is given by the formula ...

  V = (4/3)πr^3

The difference in volume will be ...

  ∆V = Vb -Vs = (4/3)π(10^3 -9^3) = (4/3)π(1000 -729) = 4/3π·271 . . . cubic in

  ∆V ≈ 1135.2 . . . cubic inches

The basketball has a volume that is 1135.2 cubic inches greater.

_____

If you use 3.14 for π, your answer is 1134.6 in^3.

Answer:

y= -6

Step-by-step explanation:

-2y - 5y= -7y

-7y=42

42/-7=

y= -6

Answer:

b>a

Step-by-step explanation:

correct just divide then subtract

Answer:

120

Step-by-step explanation:

The polygon shown is a parallelogram with a base length of 15 and a height of 8

The area of a parallelogram can easily be calculated by multiplying the height by the base length

So A = 15 * 8

15 * 8 = 120

Hence, the area of the polygon is 120 square units

Based on a survey, 24% of 205 single women and 27% of 270 single men said they "definitely want to have children."

To construct a confidence interval for the difference between two proportions, we use the formula:

(p₁ - p₂) ± z * sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))

Here, p₁ represents the proportion of single women who want to have children, p₂ represents the proportion of single men who want to have children, n₁ is the sample size of single women, and n₂ is the sample size of single men. The z-value corresponds to the desired confidence level.

Substituting the given values (p₁ = 0.24, n₁ = 205, p₂ = 0.27, n₂ = 270) and the appropriate z-value for a 99% confidence level, we can calculate the lower and upper bounds of the confidence interval.

If the confidence interval includes 0, it suggests that the difference between the proportions is not statistically significant, indicating no evidence of a gender gap. On the other hand, if the confidence interval does not include 0, it suggests a statistically significant difference, indicating evidence of a gender gap.

Therefore, based on the 99% confidence interval estimate, if the interval includes 0 (option A), there is no evidence of a gender gap. If the interval does not include 0 (option B), there is evidence of a gender gap.

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Answer: 100 years

Step-by-step explanation:

A risk ratio less than one suggests a negative association between exercise and future cardiac events.

In a cohort study, the risk ratio (also known as relative risk) is a measure used to assess the association between an exposure (in this case, exercise) and an outcome (future cardiac events). The risk ratio compares the risk of experiencing the outcome in the exposed group (those who exercise) to the risk in the unexposed group (those who do not exercise).

When the risk ratio is less than one, it indicates a lower risk of the outcome among the exposed group compared to the unexposed group. In this context, a risk ratio less than one suggests a negative association between exercise and future cardiac events. It implies that individuals who engage in regular exercise have a reduced risk of experiencing cardiac events compared to those who do not exercise.

It is important to note that a risk ratio less than one does not imply a complete absence of risk or a guarantee of protection. It simply indicates a lower relative risk among individuals who exercise. Other factors and confounding variables should also be considered in interpreting the results of a cohort study and drawing conclusions about the association between exercise and future cardiac events.

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(a) The point estimate for p is 0.5763.

(b) The 99% confidence interval for p is (0.5645, 0.5882).

(c) The normal approximation to the binomial can't be used in this problem.

(a) Let p represent the proportion of all Colorado physicians who provide some charity care.

Find a point estimate for p.

From the given data, the proportion of Colorado physicians who provide charity care (p) is:

p = 3305 / 5724= 0.5763

The point estimate for p is 0.5763 (rounded to four decimal places).

(b) Find a 99% confidence interval for p.

A 99% confidence interval for p is given by:

p ± z * sqrt[p(1-p)/n], where n = 5724, z = 2.576 (for a 99% confidence level)

Lower limit = 0.5645 Upper limit = 0.5882

The 99% confidence interval for p is (0.5645, 0.5882).

We are 99% confident that the true proportion of Colorado physicians providing at least some charity care falls within this interval.

(c) No; np > 5 and ng < 5.

In general, the normal approximation to the binomial is valid when np and n(1-p) are both at least 5.

Here, n = 5724 and p = 0.5763.

So, np = 5724 × 0.5763 = 3303.9620

≈ 3304n(1-p)

= 5724 × (1 - 0.5763)

= 2419.0380

≈ 2419

Neither np nor n(1-p) is less than 5.

So, the normal approximation to the binomial can't be used in this problem.

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Answer:

Yes

Step-by-step explanation:

A trapezoid with two right angles is a quadrilateral with two right angles.  

Answer:

The mode is 78, for it keeps repeating.