y=f(x)=x+3÷2,x€{1,5,-3
​

the criteria used when deciding upon the inclusion of a variable are A - Theory, B - t-statistic, C - Bias, and D - Adjusted R^2.

When deciding upon the inclusion of a variable, the following criteria are commonly used:

A - Theory: Theoretical justification is often considered to include a variable in a model. It involves assessing whether the variable is relevant and aligns with the underlying theory or conceptual framework.

B - t-statistic: The t-statistic is used to determine the statistical significance of a variable. A variable with a significant t-statistic suggests that it has a meaningful relationship with the dependent variable and may be included in the model.

C - Bias: Bias refers to the presence of systematic errors in the estimation of model parameters. It is important to consider the potential bias introduced by including or excluding a variable and assess whether it aligns with the research objectives.

D - Adjusted R^2: Adjusted R^2 is a measure of the goodness of fit of a regression model. It considers the trade-off between the number of variables included and the overall fit of the model. Adjusted R^2 helps in assessing whether the inclusion of a variable improves the model's explanatory power.

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The commission which real estate agency gets is $16885.

The commission which the agent get is $76750

The selling price for a house = $ 307,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 25 %

So, the commission which real estate agency gets:

= 5.5 % of $307,000

= 0.055 × $ 307,000

= $16885

The commission which agent get:

= 25% of $ 382,000

= 0.25 × $ 307,000

= $76750

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For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

The "Rule of 72" is a quick estimation method to determine the time it takes for an investment or savings to double in value. By dividing 72 by the interest rate, you can obtain an approximation of the doubling time. For an interest rate of 3%, it would take approximately 24 years for the savings to double. For an interest rate of 8%, it would take around 9 years for the savings to double.

To calculate the doubling time using the Rule of 72, divide 72 by the interest rate. This provides an approximation of the number of years it takes for an investment or savings to double in value.

For an interest rate of 3%, we divide 72 by 3: 72 / 3 = 24. Therefore, it would take approximately 24 years for the savings to double.

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

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Answer:40sec

Step-by-step explanation:you get the lcm of the seconds

2 8 20

2 4 10

2 2 5

5 1 5

1 1

2×2×2×5×1=40sec

Answer:

Depends on the pool you are pulling them from.

There are currently 11 different denomination accessible.

That would be 1 out of 11.

But considering that 4 of those bills are uncommon, the odds become 1 out of 7

Then to pull 2 of the same would mean you multiply 1/11 by 1/11 = 1/121

for the 1/7 it would become 1/49

The housing supply function is given by h(I,R) = a log1 + bR + cR log1. The housing supply responds to changes in I with a rate of a, and to changes in R with a rate of b + c log1.

Based on the given equation, the housing supply (h) is determined by two variables: I and R. The equation shows that h is a function of R, with a log-linear relationship. The variable I only appears as a constant (a) in the equation, so changes in I do not directly affect the supply of houses.
On the other hand, changes in R (or OR, which is the same variable) do affect the supply of houses. Specifically, an increase in R leads to an increase in the supply of houses. The magnitude of this increase depends on the values of b and c in the equation.
To see this, we can take the partial derivative of h with respect to R:
dh/dR = b + cR/(ln(10))
This equation tells us how much the housing supply changes in response to a change in R. The derivative is positive (i.e. the supply increases) as long as c is positive. The larger c is, the greater the increase in supply for a given increase in R.
Therefore, the correct answer is:
b + cR/(ln(10))

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The answers are:

a). The required monthly percentage rate of APR of 19% is 1.59%.

b). The Monthly percentage rate is 2.08%

c). Oscar pays $0.96 more than Felix.

a). Felix received a card with an APR of 19%; it is unknown what his monthly percentage rate was.

APR = 19%

Given that APR is increased monthly throughout the year,

Monthly rate = 19% / number of months in year

Monthly rate = 19% / 12

Monthly rate = 1.59%

Therefore, 1.59% is the minimum monthly percentage rate for an APR of 19%.

b) Oscar received a credit card with a 21% APR.

Monthly percentage rate = 21%/12 = 1.75%

c). We are informed that for a particular month, each of them had an average daily amount of $800.

Thus;

Felix's payments in full = 800 * 1.63%

Felix's payments in full  = $13.04

Amount Oscar issued = 800 * 1.75%

Amount Oscar issued = $14

Variation in Payments = $14 - $13.04 = $0.96

Thus, Oscar pays $0.96 more than Felix.

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The population parameter is the average amount of time for all students to complete the standardized test. The 90% confidence interval [108.6, 143.4] means that we are 90% assured that the true population means lies within this range.

The population parameter in this case is the average amount of time, in minutes, for all students to complete the standardized test.

The interpretation of the 90% confidence interval [108.6, 143.4] is that we are 90% confident that the true population means that it falls within this interval. It means that if we were to repeat the sampling process multiple times and construct 90% confidence intervals, approximately 90% of these intervals would capture the true population mean. In this specific case, we can be 90% assured that the average time for all students taken to complete the standardized test must be between 108.6 and 143.4 minutes.

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For the given scenario: the Probability of making both shots are A. 0.64 and B. 0.72

a) If a player makes 80% of his foul shots, the probability of making a single foul shot is 0.8. Since the two shots are considered independent events, the probability of making both shots is the product of the individual probabilities.

Therefore, the probability of making both shots is 0.8 * 0.8 = 0.64.

To calculate the probability of making exactly one shot, we need to consider two scenarios: making the first shot and missing the second, or missing the first shot and making the second. Each scenario has a probability of 0.8 * 0.2 = 0.16.

Therefore, the probability of making exactly one shot is 0.16 + 0.16 = 0.32.

Similarly, the probability of missing both shots is 0.2 * 0.2 = 0.04.

b) In this case, the outcome of the second shot depends on the outcome of the first shot. If the player makes the first shot (with a probability of 0.8), the probability of making the second shot is 0.9.

Therefore, the probability of making both shots is 0.8 * 0.9 = 0.72.

If the player misses the first shot (with a probability of 0.2), the probability of making the second shot is 0.7.

Therefore, the probability of making exactly one shot is 0.2 * 0.7 = 0.14.

Since there are only two possible outcomes (making both shots or making exactly one shot), the probability of neither shot being made is 1 - (0.72 + 0.14) = 0.14.

Therefore, for the given scenario:

a) Probability of making both shots: 0.64

  Probability of making exactly one shot: 0.32

  Probability of missing both shots: 0.04

b) Probability of making both shots: 0.72

  Probability of making exactly one shot: 0.14

  Probability of missing both shots: 0.14

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The 95% confidence interval for μ is (80.52, 82.68).

To find the 95% confidence interval for the population mean (μ), we can use the following formula

CI = X ± z* (σ / √n)

where X is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z* is the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 95%).

The critical value z* can be found using a standard normal distribution table or calculator, or using a statistical software. For a 95% confidence level, the z* value is 1.96.

Plugging in the values given, we get

CI = 81.6 ± 1.96 × (5.4 / √100)

Simplifying this expression, we get

CI = 81.6 ± 1.08

=  (80.52, 82.68)

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The given question is incomplete, the complete question is:

A random sample of 100 observations from a normally distributed population possesses a mean equal to 81.6 and a standard deviation equal to 5.4 .  Find a 95% confidence interval for μ

Answer:

10/9

Step-by-step explanation:

10/9

Just flip-flop the numerator and denominator

Answer: see below

Step-by-step explanation:

Set up two equations, one for each scenario

88w + 21b = 5840

84w + 82b = 9044

Use one equation and isolate one of the variables. We'll isolate w in the first equation.

88w + 21b = 5840

88w = 5840 - 21b

w = (5840 - 21b)/88

Then substitute that into the second equation.

84w + 82b = 9044

42w + 41b = 4522 (simplified)

42((5840 - 21b)/88) + 41b = 4522

21((5840 - 21b)/44) + 41b = 4522 (simplified)

(122640 - 441b)/44 + 1804b/44 = 4522

(122640 - 441b + 1804b)/44 = 4522

122640 + 1363b = 198968

1363b = 76328

b = 56

Now that we know belts are $56, we can substitute that back into any equation and solve for w.

w = (5840 - 21b)/88

w = (5840 - 21(56))/88

w = (5840 - 1176)/88

w = 4664/88

w = 53

Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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Answer:

Two Zeros

Step-by-step explanation:

59200/925

Which is equal to  64

No doubt, the expeced answer is 2. This is because you would ordinarily change the problem to 59200/925 for long division by hand.

For this quotient, you don't need any, because the quotient is 64, a multiple of 4, so the numbers being subtracted are always integers.

_____

If you were dividing 591 by 9.25, you would need an infinite number of zeros—because the decimal portion of the quotient is a repeating decimal with a period of 3 digits.

The cross product of (2i -3j + 4k) and (i + j -7k) is -9i + 18j - 11k.

To calculate this,

use the formula for the cross product, which is:
AxBy - AyBx

The cross product of (2i -3j + 4k) and (i + j -7k) is

(2 × -7) - (-3 × 1)i + (2 × 1) - (4 × -7)j + (3 × -7) - (2 × 1)k

Simplifying the above expression yields -9i + 18j - 11k.

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Answer: 82.5 inches

Step-by-step explanation: We know that each plantar has a base of 5.5 by 1 2/3. So if we multiply 5.5 by 1 2/3 we can get 9.166666667. However, there is 9 planters because 3 times 3 is 9. So if we multiply 9.166666667 by 9 we will get 82.5 inches

Answer:

c

Step-by-step explanation:

The numbers in this problem are classified as follows:

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A statement which explains best whether Martin's points represent a function is : D Martin's points represent a function because any vertical line drawn on the coordinate plane will intersect at most one point

To determine whether Martin's points represent a function, we need to check if each x-value corresponds to a unique y-value. In other words, for each x-value, there should be only one y-value associated with it.

By examining the given points (0,4), (1,4), (2,5), (3,6), (4,7), (5,5), we can see that each x-value is paired with a distinct y-value. This means that for every value of x, there is only one corresponding y-value.

The statement in option D, "Martin's points represent a function because any vertical line drawn on the coordinate plane will intersect at most one point," accurately explains that the given points represent a function.

In a function, for every x-value, there can be at most one y-value, and this is satisfied by the given set of points. When we draw a vertical line on the coordinate plane, it intersects the graph at most once, indicating that the points satisfy the vertical line test for a function.

Correct option is D Martin's points represent a function because any vertical line drawn on the coordinate plane will intersect at most one point.

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The length of side b is approximately 13.904 cm.

Trigonometric ratios are ratios of the sides of a right triangle to its angles. In a right triangle, which is a triangle with one angle measuring 90 degrees, we can define three basic trigonometric ratios: sine, cosine, and tangent.

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted by sin(theta) or sin(theta) = opposite/hypotenuse.

The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It is denoted by cos(theta) or cos(theta) = adjacent/hypotenuse.

The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. It is denoted by tan(theta) or tan(theta) = opposite/adjacent.

We can use trigonometric ratios to find the length of side b in a right triangle where we know the angle ∠A and side a. Specifically, we can use the tangent ratio, which relates the opposite side to the adjacent side of an angle in a right triangle.

In this case, we want to find the length of side b, which is the adjacent side to angle A. So we can use the tangent of angle A:

tan A = opposite/adjacent = b/a

Rearranging this equation, we get:

b = a * tan A

Substituting the given values, we get:

b = 16 cm * tan 41°

Using a calculator, we can evaluate the tangent of 41 degrees:

tan 41° ≈ 0.869

So, the length of side b is:

b = 16 cm * 0.869 ≈ 13.904 cm

Therefore, the length of side b is approximately 13.904 cm.

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The results are given below.

Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'

Consider the first triangles,

Given, L is the midpoint of KN and MP.

To find ΔMKL ≅ΔPNL

Using side-angle-side congruency ,

Here, the corresponding sides , KM and MP, KL and LP are equivalent.

But the angle ∠L is not an included angle.

So this triangles are non congruent.

Consider the next triangles.

BD bisects ∠ABC ∠BAD≅∠BCD

To find ΔABC≅BCD

By side- side-side congruency,

The corresponding sides AB and BD, AD and DC, BD are equivalent.

Therefore this ΔABC≅BCD  proved.

Hence the proof.

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9514 1404 393

Answer:

Step-by-step explanation:

1. A point on a graph is a maximum if there are no points on the graph that are higher.

A point on a graph is a minimum if there are no points on the graph that are lower.

Sometimes you're interested in a "local" maximum or minimum. In that case, the "no points higher/lower" rule refers to points in the immediate vicinity of the one of interest.

Sometimes you're interested in a maximum or minimum on an interval. In that case, the rule applies to points contained within the interval. (The maximum or minimum may be at the end of the interval.)

__

2. Average rate of change is defined over some interval. That is, you are given the end points of the interval of interest. The average rate of change is the slope of a straight line between those end points. The slope formula applies:

  \(m=\dfrac{y_2-y_1}{x_2-x_1} \quad\text{where the end points of the interval are $(x_1,y_1)$ and $(x_2,y_2)$}\)

The solution to the inequality is x ≤ 2.5 .

Given data:

To solve the inequality 6x + 4 ≥ 8x - 1, we need to isolate the variable x. Here's the step-by-step solution:

6x + 4 ≥ 8x - 1

Subtract 6x from both sides:

4 ≥ 2x - 1

Add 1 to both sides:

5 ≥ 2x

Divide both sides by 2 (note: since we are dividing by a positive number, the inequality direction remains the same):

5/2 ≥ x

Simplifying:

2.5 ≥ x

Therefore, the solution to the inequality is x ≤ 2.5.

Hence, in interval notation, the solution can be represented as (-∞, 2.5], indicating that x is less than or equal to 2.5 and can take any value less than or equal to that.

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Based on the number of batches of cupcakes, the pounds of sugar in each batch can be found to be 3 / 16 pounds

Find out more below

The total number of pounds of sugar that Polly used was 15/16 pounds of sugar and she used these to make 5 batches of cupcakes.

Each of this batches of cookies used the same amount of sugar so the amount of sugar per batch of cookie is:

= Total number of pounds of sugar used / Number of batches of sugar

Solving for the pounds of sugar gives:

= 15/16 ÷ 5

= 15/16 x 1/5

= 15 / 80

= 3 / 16 pounds

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Answer:

35

Step-by-step explanation:

3 1/2 x 10 =35

make 3 1/2 into an improper fraction: 3 x 2 + 1 = 7/2

make 10 into a fraction: 10/1

find the LCD (least common denominator) for each number:

10/1 = 20/2

7/2 = 7/2

20/2 x 7/2 = 70/2 = 35

:)

Answer:

35

Step-by-step explanation:

For 1 cup of flour, you make 10 muffins. Just by reading the problem, you see that the number of muffins, 10, is 10 times the number of cups of flour, 1.

For 3 1/2 cups of flour, you make 10 times that number muffins.

3 1/2 × 10 = 3.5 × 10 = 35

Answer: 35 muffins

You can also use a proportion.

1 cup flour is to 10 muffins as 3.5 cups flour is to x muffins.

1/10 = 3.5/x

Cross multiply:

1 × x = 10 × 3.5

x = 35

Answer: 35 muffins

If a sequence is defined using previous terms, it is known as a recursively defined sequence.

This type of sequence relies on the previous terms to determine the next term in the sequence. The number of terms that are required to define a recursively defined sequence varies depending on the specific sequence. However, if the first few terms of the sequence are given, it can help determine the pattern and the formula used to generate subsequent terms. A good understanding of recursive sequences can be helpful in many areas, including computer programming, mathematics, and finance. A sequence that is defined using its initial terms and a rule relating its subsequent terms to the previous ones is called a recursively defined sequence. In such sequences, each term's value depends on one or more earlier terms. The first few terms serve as the basis, and the recursive formula generates the remaining terms. This approach allows us to find any term in the sequence based on previous ones, ensuring a consistent pattern and progression.

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The foil method is an effective method because you are able to successfully remember the other at which you multiply the brackets to open them using F.O.I.L, so its not only easy to remember but very good to use for quadratic, cubic and to an extent, polynomials.

The FOIL Method stands for First Outer Inner Last. This is a standard method for multiplying two binomials together. It is also a valid method for solving quadratic equations and simplifying expressions.

The FOIL method is a valid method because it helps to simplify complicated expressions, and it is easy to use. It is used to multiply two binomials together.

By following the steps, the user can easily find the product of two binomials. The steps are as follows:

The FOIL method is valid because it helps to simplify expressions by breaking them down into smaller parts. This makes it easier to see how the parts relate to each other and how they combine to create the final expression. It is a straightforward method, and it is easy to use.

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