which of the following would be an indication that the normality condition has been met for a t -test for the slope of a regression model? a residual plot with no apparent pattern in the residuals a histogram of the residuals that is centered at 0, unimodal, and symmetric a dotplot of the residuals that is centered at 0 and strongly skewed to the left with outliers responses i only 1 only ii only 2 only i and ii only 1 and 2 only ii and iii only 2 and 3 only i , ii , and iii

a. The equilibrium interest rate,  is determined by the risk-free interest rate, the probability of repayment, and the cost of default.

b. The probability of the government repaying its loan can be calculated using the loan repayment threshold and the distribution of the output.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default.

a. To find the equilibrium interest rate,  we need to consider the risk-free interest rate, the probability of repayment, and the cost of default. The equilibrium interest rate is given by the formula: r = r + (c/p), where r is the risk-free interest rate, c is the cost of default, and p is the probability of repayment.

b. The probability that the government will repay its loan can be calculated by determining the percentage of the output distribution that exceeds the loan repayment threshold. Since 0.5 of the output is required to repay the loan, we need to calculate the probability that the output exceeds L/0.5.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default. This can be proven by comparing the repayment threshold (L/0.5) with the loan repayment amount (L + Lr). If the repayment threshold is greater than the loan repayment amount, the borrowing country would default.

Calculations and further details would be required to provide specific numerical answers for each part of the question.

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Therefore, there are 4 vertices in this graph.

Let V be the number of vertices in the graph. The sum of the degrees of all vertices in an undirected graph is twice the number of edges, so in this case, the sum of degrees is 2 * 10 = 20.

We know that two vertices have degree 4, so the degrees of the remaining vertices must add up to 20 - 2 * 4 = 12.

If there are v vertices of degree 3, then the total degree contributed by those vertices is 3v, so we have:

3v + 2 * 4 = 20

3v = 12

v = 4

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Answer:

1/8

Step-by-step explanation:

[1/2 - (1/2 x 1/2)] - (1/4 x 1/2)  =  1/2 - 1/4 - 1/8  =  2/8 - 1/8 = 1/8

The constants that we have to multiply to eliminate one variable from the system are 12 and 5.

The equations are

5x+13y = 232

12x + 7y = 218

Here we can cancel both x term and y terms, lets choose x terms  and apply the elimination method

The coefficient of x in first equation is 5 and 12 in second equation

We have to make it same

Prime factorization

5 = 5×1

12 = 2×2×3

LCM (5, 12 ) = 2×2×3×5 = 60

Multiply the first equation by 12 and second equation by 5

60x + 156y = 2784

60x + 35y = 1090

Subtract equation 2 from equation 1

121y = 1694

Here we have eliminated x term

Hence, the constants that we have to multiply to eliminate one variable from the system are 12 and 5.

The complete question is:

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232

12x + 7y = 218

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The area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

The area of the circle is the space occupied by it. It can be given as,

\(A=\pi r^2\)

Here (r) is the radius of the circle.

In this diagram, three concentric circles' rectangle.

The radius of the smallest circle is 3.

\(r_1=3\rm\unit\)

Thus, the area of it is,

\(A=\pi (3)^2\\A=28.27\rm\; unit^2\)

Let suppose the mid-point of the rectangle is D. Here, OB is the diagonal of the rectangle in which,

\(OD=BD\)  

The radius of the yellow ring's outer face from point O is,

\(r_3=OD+BD\\r_3=OD+OD\\r_3=2OD\\\)

OD is the radius of the small circle, which is 3 units long. Thus,

\(r_3=2\times3\\r_3=6\rm\; units\)

The line segment OC is the radius of the white circle from point O. In the triangle COB from the Pythagoras theorem, the radius r₂ of the middle circle is,

\(r_2=\sqrt{r_3^2-r_1^2}\\r_2=\sqrt{6^2-3^2}\\r_2=3\sqrt3\)

Thus, the area of the yellow ring is,

\(A_y=\pi r_3^2-\pi r_2^2\\A_y=\pi (6)^2-\pi (3\sqrt{3})^2\\A_y=28.27\rm\; unit^2\)

The area of white ring is,

\(A_w=\pi r_2^2-\pi r_1^2\\A_w=\pi (3\sqrt{3})^2-\pi (3)^2\\A_w=56.55\rm\; unit^2\)

Hence, the area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

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Answer:

Bottle A started with 88 and bottle B started with 40

Step-by-step explanation:

To find out what they started with I got the ounces they finished with an the equation they did to get there.

Ended in 64 oz.

To get there:

A => B

B => A

A => B

Every time a pour is made the bottle to the right is doubled so I got 64 and divided it by 2 to see what B had before the pour of bottle A.

B had 32 oz. and A had 96 oz. before the last pour. I got 96 oz. because for them to end up with 64 oz. A has to have 32 oz. + 64 oz. since you are pouring 32 oz. into bottle B.

Now you have this equation:

A => B

B => A

96 oz. => 32 oz.

64 oz.

I then do the same thing I did to find 96 and 32. Since B is giving to A now it has to have more then A but it has to end up with 34 oz. for this is got 96 oz. and I divided it by 2 which got me 48. So on the second pour A started with 48 and B had to have given A 48 plus have 32 so it could end up with 34 therefore making it have 80 oz.

Now you have this equation:

A => B

80 oz. => 48 oz.

96 oz. => 32 oz.

64 oz.

For the last part to get the first ounces to answer the question you will do the same steps. Get half of 80 to see what B had before the 2nd pour which will be 40 and then you have to get 48 + 40 sine bottle A has to have the same amount of soda as B plus 48 oz. that it ends up with. This will have bottle A as 88 oz.

The Answer:

88 oz. => 40 oz.

80 oz. => 48 oz.

96 oz. => 32 oz.

Both will end up with 64 oz.

Answer:

B)7 units

Step-by-step explanation:

In this case, with a significance level of 0.87, the corresponding level of confidence would be 0.13, or 13%.

It seems there may be some confusion in your question. The significance level and confidence level are two different concepts in statistical inference.

The significance level (also known as alpha, α) is a pre-determined threshold used in hypothesis testing. It represents the probability of incorrectly rejecting a true null hypothesis. Typically, the significance level is set at 0.05 (or 5%) in many statistical analyses. It determines the critical region, and if the calculated test statistic falls within that region, the null hypothesis is rejected.

On the other hand, the confidence level is associated with confidence intervals, which are used to estimate a population parameter. It represents the probability that the confidence interval captures the true value of the parameter. Commonly used confidence levels are 90%, 95%, and 99%.

To determine the level of confidence corresponding to a given significance level, you need to subtract the significance level from 1. In this case, if the significance level is 0.87, the corresponding level of confidence would be:

Level of confidence = 1 - Significance level = 1 - 0.87 = 0.13

Therefore, the level of confidence associated with a significance level of 0.87 is 0.13, or 13%.

The significance level and the confidence level are distinct concepts in statistical inference. The significance level determines the probability of incorrectly rejecting a true null hypothesis, while the confidence level represents the probability that a confidence interval contains the true value of the parameter.

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By performing the desired calculation using each arrangement and squaring the difference between the result and the target value, you can determine the arrangement that yields the largest squared difference.

To find the arrangement of the 6 numbers that generates the biggest difference squared, you need to consider all possible permutations of the numbers. For each arrangement, perform the desired calculation using the given, such as addition, subtraction, multiplication, or any other specified operation.

Once you have the calculated result for each arrangement, calculate the squared difference between the result and the target value. This is done by subtracting the target value from the calculated result and then squaring the difference.

By comparing the squared differences obtained for each arrangement, you can identify the arrangement that yields the largest squared difference. This arrangement will have the maximum difference squared between the calculated result and the target value.

It's important to note that the specific calculation or operation to be performed is not mentioned in the question. Therefore, you need to specify the operation or provide more information to determine the exact steps for performing the calculation.

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Step-by-step explanation:

3x+5x+4+3

=8x+7

hope it helps

Answer:

6x+7

Step-by-step explanation:

x+4+5x+3

Combine like terms

x+5x   +4+4

6x+7

The steps for using a compass and straightedge to construct a square is:

Given:

Let AB the length of one side given.

Steps:

a. Using your straightedge, draw a reference line, if one is not provided.

b. Copy the side of the square onto the reference line, starting at a point labeled A'.

c. Construct a perpendicular at point B' to the line through \(AB\).

d. Place your compass point at B', and copy the side of the square onto the perpendicular B'G. Label the end of the segment copy as point C.

e. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.

f. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.

g. Connect points A' to D, D to C, and C to B' to form a square.

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The probability for Sebastian's rainy city that there will be more than 100 days of rain next year in his city is 3/8 .

Probability: probability is a branch of mathematics, in which chance of occurrence of result is calculated. It is denoted by "P" . Probability is a ratio of favourable outcomes to the total possible outcomes.

We have given that

Sebastain lives in rainy city.

In 9 of the past 24 years there have been more than 100 days of rain.

Probability that there will be more than 100 days of rain next year = 9/24

= 3/8

= 0.375

= 37.5%

Hence , the required probability is 3/8 or 37.5% ..

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There are no whole numbers n that satisfy this characteristic

The difference of n and 10 must be a negative number for it to be less than 1, and no whole number can be negative.

Whole numbers are those that can only be represented as integers and don't include any fractional or decimal elements. They also go by the names "counting numbers" or "natural numbers," and they consist of the digits 0 through 9, including 1, 2, 3, 4, 5, 6, 7,, 8, and so on.

A whole number that can be either positive, negative, or zero is known as an integer. A group of integers that are not a fraction or a decimal, such as..., -2, -1, 0, 1, 2,..., are referred to as an integer in mathematics. The natural numbers (1, 2, 3,...), their opposites (-1, -2, -3,...), and zero are all included in the set of integers. Mathematicians employ integers for many various purposes, such as counting, organising, and performing arithmetic operations.

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Answer:

Look in the explanation

Step-by-step explanation:

This is the graph of a parabolic function

The hang time is 3 seconds

The maximum height is about 11 meters

for t between t=0 , t=1.5, the height is increasing

Answer:

b>19

Step-by-step explanation:

15<b−4

Rewrite so b is on the left side of the inequality.

b−4>15

Move all terms not containing b to the right side of the inequality.

Add 4 to both sides of the inequality.

b>15+4

Add 15 and 4.

b>19

b>19

The result can be shown in multiple forms.

Inequality Form:

b>19

Interval Notation:

(19,∞)

The composition of functions g and f, denoted as \(\(g \circ f\)\)is a function that maps elements from the domain of f to the codomain of g. In this case, we have \(\(g: a \to b\)\) and \(\(f: b \to c\)\), where \(\(a = b = c = \{1, 2, 3, 4\}\)\).

The function g is given by \(\(\{(1, 4), (2, 1), (3, 1), (4, 2)\}\)\), and f is given by \(\(\{(1, 3), (2, 2), (3, 4), (4, 2)\}\)\). The composition \(\(g \circ f\)\) is a function that maps elements from the domain of f to the codomain of g. In other words, it combines the mappings of g and f in a way that the output of f becomes the input for g.

To compute \(\(g \circ f\)\), we start with the elements in the domain of f, which is \(\(b = \{1, 2, 3, 4\}\)\). For each element x in b, we apply f to get f(x), and then apply g to get g(f(x)).

The composition \(\(g \circ f\)\) is calculated as follows:

\(\[g \circ f = \{(1, g(f(1))), (2, g(f(2))), (3, g(f(3))), (4, g(f(4)))\}\]\)

Substituting the values from the given functions, we have:

\(\[g \circ f = \{(1, g(3)), (2, g(2)), (3, g(4)), (4, g(2))\}\]\)

Now, we substitute the values of g for the respective inputs:

\(\[g \circ f = \{(1, 2), (2, 4), (3, 2), (4, 1)\}\]\)

Therefore, the composition \(\(g \circ f\)\) is given by \(\(\{(1, 2), (2, 4), (3, 2), (4, 1)\}\)\).

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Answer:D

Step-by-step explanation:

Answer:

the answer is no solution

Work Shown:

x³ + x² + x + 1

(x³ + x²) + (x + 1)

x²(x+1) + 1(x + 1)

(x² + 1)(x + 1)

The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.

The factored form of x³ + x² + x + 1 is (x²+1)(x+1).

A number or other mathematical item is factored (or factorised; see English spelling changes) or factored by a number of factors, usually smaller or simpler things of the same kind.

We have,

x³ + x² + x + 1

Now, making groups as

(x³ + x²) + (x + 1)

= x² (x + 1) + (x+1)

= (x²+1)(x+1)

So, resulting expression is  (x²+1)(x+1).

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Answer: y = 65

Step-by-step explanation: PLEASE GIVE BRAINLIEST IT HELPS ALOT

Answer:

What is the question?! I don't understand, sry?!

Step-by-step explanation:

Answer:

-1/3>-1/2

Step-by-step explanation:

-1/3>-1/2

The leading coefficient of the polynomial is -2, and the degree of the polynomial is 3.

To identify the leading coefficient and degree of the polynomial, we need to consider the highest power of the variable in the polynomial expression.

In the given polynomial, -2y³ is the term with the highest power of y. The coefficient of this term, which is -2, is the leading coefficient of the polynomial. The degree of a polynomial is determined by the highest power of the variable. In this case, the highest power of y is 3 in the term -2y³. Therefore, the degree of the polynomial is 3.

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The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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The corresponding values of y so that each ordered pair is a solution of the equation y = 0.2x – 2 is,

Input    (x)    -6        -1       1  

Output (y)     -3.2  -2.2   -1.8

Function rule is the rule of writing the relationship between the two variables, one is dependent and another is independent.

The table given in the problem is;

Input    (x)    -6        -1       1  

Output (y)

We have given the equation as;

y = 0.2x – 2

Complete the table using the above function rule;

At (x) equal to -6,

y = 0.2x – 2

y = 0.2(-6) – 2

y = -3.2

At (x) equal to -1,

y = 0.2x – 2

y = 0.2(-1) – 2

y = -2.2

At (x) equal to 1,

y = 0.2x – 2

y = 0.2(1) – 2

y = -1.8

Hence,

Input    (x)    -6        -1       1  

Output (y)     -3.2  -2.2   -1.8

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Answer:

Step-by-step explanation:

The Bank discount and proceeds of the given information is:

$2365.27 and $47634.73 respectively.

Given the face value is $50,000

Discount rate = 13%

No.of term days = April 5 to August 14

= 131 days.

Bank discount = ?

Proceeds = ?

First calculate the bank discount using the formula:

Bank discount = face value × discount rate × time

Bank discount = $50,000 × 0.13 × 131/360

= 50,000×0.13×0.36388

= $2365.27

now calculate the proceeds using the formula :

Proceeds = face value - bank discount

= 50,000 - 2365.27

= $47634.73

Hence the bank discount and proceeds are $2365.27 and $47634.73 respectively.

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Answer:

Please elaborate more your question so I can actually give you a more accurate answer.

Step-by-step explanation:

The airplane will become balanced if we add a 100- pound weight to the baggage compartment.

An airplane is used to convey people and goods from one point to another by air. The airplane must be airlifted. This means that the airplane must be balanced while on air. If the airplane is not balanced, it may be difficult to control.

Looking at the situation of this airplane, the airplane will become balanced if we add a 100- pound weight to the baggage compartment.

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Answer:

A. 8fg + 3h

Step-by-step explanation:

\(4f × 2g + 3h \\ \\ = 4 \times 2 \times f \times g + 3h \\ \\ = 8fg + 3h\)

Step-by-step explanation:

\(4f \times 2g + 3h \\ = (4 \times 2)fg + 3h \\ = 8fg + 3h \\ \)

Answer:

The answer is 1.

Step-by-step explanation:

None.