Neck size, in inches, and number of teeth of 18 randomly selected puppies are compared. Which significance test should be used to see if neck size and number of teeth have a linear relationship? Assume all test conditions are met.

a
Two-sample z-test

b
Two-sample t-test

c
Two-proportion z-test

d
t-test for slope of regression line

e
One-proportion z-test

Answer:

125x³ − 150x²y + 60xy² − 8y³

Step-by-step explanation:

(5x − 2y)³

₃C₀ (5x)³ (-2y)⁰ + ₃C₁ (5x)² (-2y)¹ + ₃C₂ (5x)¹ (-2y)² + ₃C₃ (5x)⁰ (-2y)³

(1) (125x³) (1) + (3) (25x²) (-2y) + (3) (5x) (4y²) + (1) (1) (-8y³)

125x³ − 150x²y + 60xy² − 8y³

Answer:

5

Step-by-step explanation:

The given equation written in standard form is 8x - 14y = 26

From the question, we are to write the given linear equation is standard form.

From the given information, the given linear equation is

8x = 26 + 14y

The standard form of linear equation is given as

Ax + By = C

Where x and y are the variables

A, B, and C are the constants

Now, we will write the given equation in standard form

8x = 26 + 14y

Subtract 14y from both sides of the equation

8x - 14y = 26 + 14y - 14y

8x - 14y = 26

Hence, the equation is 8x - 14y = 26

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cos 6° + i sin 6° is a 15th root of i.

The value of cos 6° + I sin 6° raised to the power of 15, we can use De Moivre's theorem, which states that for any complex number z = cosθ + I sinθ and a positive integer n

zⁿ = (cos(nθ) + i sin(nθ))

In this case, we have z = cos 6° + i sin 6° and n = 15.

Using De Moivre's theorem

zⁿ = (cos(15 * 6°) + i sin(15 * 6°))

= (cos 90° + i sin 90°)

= i

Therefore, (cos 6° + i sin 6°)¹⁵ = i.

We have (cos 6° + I sin 6°) raised to the power of 15, which results in i. This means that (cos 6° + I sin 6°) is the 15th root of i.

So, cos 6° + I sin 6° is the 15th root of i.

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Answer: [-4,4]

Step-by-step explanation: Range is the set of y-values that are outputted by function f(x).

From the graph we see that our y-values span from -4 to 4. Since both are closed dot, they are included in the range:[-4, 4] or -4≤ y ≤ 4

rational equation using is D

Answer:

hmmm this is harder then i thought

Step-by-step explanation:

Therefore, Alvin's average paddling rate for a canoe trip to a campsite was 6 km/hr

Let's find out Alvin's average paddling rate for a canoe trip to a campsite.The distance Alvin paddled on the way to the campsite is the same as on the way back since he travelled to the same place and back to his initial location.

The rate at which Alvin paddled to the campsite is given by the relation;

r - 3 = (total distance)/(time taken to get to the campsite).

Where r is Alvin's average paddling rate, 3 is the speed of the river current, the total distance is D, and the time taken to get to the campsite is 9 hours.

On the way back, Alvin's rate of paddling is given by;

r + 3 = (total distance)/(time taken to get back from the campsite).

Where r is Alvin's average paddling rate, 3 is the speed of the river current, the total distance is D, and the time taken to get back from the campsite is 4 hours.Since the distance Alvin paddled to and from the campsite is the same, we can use D = rt.

Therefore, we can get an equation in r only:

r - 3 = D/9(r) + 3

r= D/4

Now, we need to solve for D. We can do this by setting both expressions equal to each other. That is:

r - 3 = r + 3D/9

r-3 = D/4(4)D/9

r-3= D/4

Multiplying both sides by 36 gives:

4D = 9D/4 * 36D

D= 81 km

Therefore, the distance of the campsite is 81 km.

Using D = rt,

we can find the average paddling rate r:

r = D/t

r = 81/(9 + 4) r

r = 6 km/hr.

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Answer:1 is b and 2 is d

Step-by-step explanation:

X = 23

Y = 129

Hope this is helpful!

Answer:

i think x = 23, y = 129

Step-by-step explanation:

5x+14+3x-18 = 180

8x-4 = 180

8x = 184

x = 23

3x-18+y = 180

3(23)-18+y = 180

69-18+y = 180

51+y = 180

y = 129

As per the concept of margin of error, the standard deviation increases as the margin of error increases.

The term margin of error is referred as the estimate of a small sample drawn from a relatively large population data.

Here the margin of error is usually governed by parameters such as standard deviation of population, sample size and desired confidence level.

Here we have given that for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.

And we need to find the missing term in the statement.

Here let us consider that the following values are represented the given situation,

=> σ = Standard deviation for population

=> m = Margin of error

=> Z = Empirical value of Z-score at a given confidence level

Then the minimum sample size for a given confidence level is written as

=> (Z x σ)²/m²

Here from the above given formula it can be inferred that the minimum sample size is directly related to the population standard deviation. Therefore, the minimum sample size required would increase with the increase in population standard deviation.

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Based on the given options, option b (n = 15 and SS = 190 for both samples) is the least likely to reject the null hypothesis in a test with the independent-measures t statistic.

We need to take into account the sample size (n) and the sum of squares (SS) for both samples in order to determine which set of data is least likely to reject the null hypothesis in a test using the independent-measures t statistic.

As a general rule, bigger example sizes will more often than not give more dependable evaluations of populace boundaries, coming about in smaller certainty stretches and lower standard blunders. In a similar vein, values of the sum of squares that are higher reveal a greater degree of data variability, which can result in higher standard errors and estimates that are less precise.

Given the choices:

a. n = 30 and SS = 190 for both samples; b. n = 15 and SS = 190 for both samples; c. n = 30 and SS = 375 for both samples; d. n = 15 and SS = 375 for both samples. Comparing options a and b, we can see that both samples have the same sum of squares; however, option a has a larger sample size (n = 30) than option b does ( Subsequently, choice an is bound to dismiss the invalid speculation.

The sample sizes of option c and d are identical, but option d has a larger sum of squares (SS = 375) than option c (SS = 190). In this way, choice d is bound to dismiss the invalid speculation.

In a test using the independent-measures t statistic, therefore, option b (n = 15 and SS = 190 for both samples) has the lowest probability of rejecting the null hypothesis.

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System of equations can be used to find each digit is option A.

An equation is a mathematical statement that shows that two expressions are equal to each other. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

Let's represent the hundreds, tens, and units digits as h, t, and u, respectively. Then we can use the given information to set up a system of equations:

A three-digit number has a digit sum of 13:

h + t + u = 13

One more than the hundreds digit (h) is the tens digit (t):

t = h + 1

The digit in the units, u, is 3 greater than the total of the digits in the tens and hundreds:

u = t + h + 3

Therefore, the correct system of equations is:

h + t + u = 13

t = h + 1

u = t + h + 3

Therefore, the answer is (A).

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Step-by-step explanation:

The americium is represented as 1. Every 432 years it decreases by 50%.

First half-life:

432 years.

\(1 \div 2 = 0.50\)

0.50 (1/2) of americium remains after 432 years.

Second half-life:

\(432 \times 2 = 864\)

\(0.5 \div 2 = 0.25\)

0.25 (1/4) of the americium remains.

Third half-life:

\(432 \times 3 = 1296\)

\(0.25 \div 2 = 0.125\)

0.125 (1/8) of the americium remains.

Last half-life:

\(432 \times 4 = 1728\)

\(0.125 \div 2 = 0.0625\)

0.0625 (1/16) of the americium remains.

Option B is correct.

Answer:

3 (4 x + 6): Each side length is 4 x + 6 units.

Step-by-step explanation:

Perimeter of equilateral triangle = 12x + 18 = 3(4x + 6) units

Answer:

B

Step-by-step explanation:

An equilateral triangle has a perimeter of 12 x + 18 units. Which expression can be used to show the length of one side of the triangle?

  6 (2 x + 3): Each side length is 2 x + 3 units.

✔3 (4 x + 6): Each side length is 4 x + 6 units.

  2 (6 x + 9): Each side length is 6 x + 9 units.

  x (12 + 18): Each side length is 12 + 18 units.

Answer:

A

Step-by-step explanation:

Using the formula y=mx+b we see the b (the y intercept) is at -1. Only answer choice A and B have a y intercept at -1. Now we check which one of those will correspond with the negative slope. A is negative and B is positive --> A is the correct answer choice.

Answer:

yes

Step-by-step explanation:

40 divided by 5 equals 8 and 120 divided by 14 equals 8.5. they are in the same number range.

Answer:

YES!

Step-by-step explanation:

UwU

Answer:Good luck bro

Step-by-step explanation:

10. Variable : x = 4.78

60(x)=287

11. x = 94

$6.90 - $1.25 = $5.65

6(x) = 5.65

Sorry I couldn't do all someone else can do the 2 others

Answer:

25 people

Step-by-step explanation:

c = 5p + 220

345 = 5p + 220

-220          -220

125 = 5p

/5       /5

25 = p

4. We start with the base case of \(5^0 = 1\) and recursively generate the next element in the set by multiplying the previous element by \(5\).

5. if a divides \(b\) and \(b\) divides \(a\), either a equals \(b\) or \(a\) equals negative \(b\).

4. The recursive definition of the set of positive integer powers of 5 can be expressed as follows:

Base case: \(5^0 = 1\) is in the set.

Recursive step: If n is in the set, then \(5^(n+1)\) is also in the set.

Using this definition, we start with the base case of \(5^0 = 1\)and recursively generate the next element in the set by multiplying the previous element by \(5\).

5. To prove that if a divides \(b\) and \(b\)divides \(a\), then a equals \(b\) or \(a\) equals negative \(b\), we can use the definition of divisibility.

Assume that \(a\) divides \(b\), denoted as \(a | b\) , and \(b\) divides \(a\), denoted as \(b | a.\)

By definition, if a divides b, there exists an integer k such that b = ak.

Similarly, if \(b\) divides \(a\), there exists an integer m such that \(a = bm.\)

Substituting the expression for\(b\) in terms of \(a\), we have \(bm = ak.\)

Dividing both sides by b (since b is nonzero), we get m = a/b.

Since \(m\) is an integer, \(a/b\) must be an integer, which means \(a\) is divisible by \(b\).

If \(a/b\)  is an integer, it implies that \(b/a\)is also an integer, which means \(b\) is divisible by \(a\).

Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), it follows that \(a/b\) and \(b/a\) are both integers.

If \(a/b = m\) and \(b/a = k\), then we have \(a = bm\) and\(b = ak.\)

\(If m = k = 1, then $a = b.\)

\(If m = k = -1, then a = -b.\)

Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), either \(a\) equals \(b\) or \(a\) equals negative \(b\).

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We can locate the positions of Q1, median, and Q3 on a box plot or a number line to visualize the data distribution and quartiles.

To identify the location of Q1, the first quartile, the median, and Q3, the third quartile, for the given salary data {29, 32, 34, 34, 34, 35, 35, 39, 43, 67, 185}, we need to sort the data in ascending order and then locate the corresponding positions.

First, let's sort the data in ascending order:

29, 32, 34, 34, 34, 35, 35, 39, 43, 67, 185.

The median, which represents the middle value of the sorted data, is found by locating the value at the center or the average of the two center values if the data has an even number of observations. In this case, since we have 11 observations, the median will be the 6th value when the data is sorted:

Median = 35.

Next, to find Q1 and Q3, we need to divide the data into lower and upper halves. Since we have an odd number of observations, the median is not included in either half.

The lower half of the data consists of the first five values:

29, 32, 34, 34, 34.

The upper half of the data consists of the last five values:

35, 35, 39, 43, 67.

To find Q1, we locate the median of the lower half, which is the 3rd value when the data is sorted:

Q1 = 34.

To find Q3, we locate the median of the upper half, which is the 3rd value when the data is sorted:

Q3 = 39.

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Answer:

true

Step-by-step explanation:

Answer:

The answer is C It takes Ted 16 hours to knit a scarf.

Step-by-step explanation:

I got it on Khan.

Answer:

c

Step-by-step explanation:

In the log linear model (WX, XY, YZ), W and Z are independent given alone or given Y alone or given both X and Y because they do not share any common factors. This means that the probability of W occurring does not affect the probability of Z occurring and vice versa, regardless of the presence or absence of Y or X.

W and Y are conditionally independent when the presence or absence of X makes no difference to their relationship. This means that the probability of W occurring given Y is the same whether or not X is present.

                        Similarly, X and Z are conditionally independent when the presence or absence of Y makes no difference to their relationship. This means that the probability of X occurring given Z is the same whether or not Y is present.
                                In summary, W and Z are always independent given any combination of X and Y, while W and Y are conditionally independent when X is irrelevant to their relationship and X and Z are conditionally independent when Y is irrelevant to their relationship. It's important to note that these independence assumptions are based on the log linear model and may not hold true in other models or contexts.

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Answer:

Step-by-step explanation:

Givens

Length = a

Width = a + 3

Formulas

P = 2L + 2w

Area = L * w

Solution

Perimeter

P = 2L +  2w

P = 2*a + 2(a + 3)             Remove the Brackets

p = 2a + 2a + 6                Combine

P = 4a + 6

Area

Area = L * w

Area = a (a + 3)

Area = a^2 + 3a

There is a 75.40% chance that the sample mean X will be more than 0.5 away from the population mean μ.

Let X be the random variable representing the sample mean of a random sample of size 36 selected from a population with mean μ=44 and standard deviation σ=8.

The Central Limit Theorem (CLT) states that, under certain conditions, the distribution of the sample mean X can be approximated by a normal distribution with mean μ and standard deviation σ/√(n), where n is the sample size. Since the sample size is 36, we can use this approximation.

The probability that X is more than 0.5 away from the population mean can be calculated as follows:

P(|X-μ| > 0.5) = P((X-μ)/ (σ/√(n)) > (0.5) / (σ/√(n))) + P((X-μ)/ (σ/√(n)) < (-0.5) / (σ/√(n)))

Using the standard normal distribution table, we can find the corresponding probabilities for each term on the right-hand side of the equation. We have:

P(Z > 0.3125) + P(Z < -0.3125)

where Z is a standard normal random variable with mean 0 and standard deviation 1.

Using the standard normal distribution table, we can find that P(Z > 0.3125) = 0.3770 and P(Z < -0.3125) = 0.3770.

Therefore, the approximate probability that X will be more than 0.5 away from the population mean is:

P(|X-μ| > 0.5) = 0.3770 + 0.3770 = 0.7540

In terms of percentage, we can rewrite it as,

P(|X-μ| > 0.5) = 0.7540*100 = 75.40%

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We can be 99.7% confident that the true proportion of individuals with schizophrenia in the population lies between 0.44 and 0.62.

In our schizophrenia model, the rough 99.7% certainty stretch can be determined utilizing the point gauge and standard blunder of the extent. With a point gauge of 0.53 and a standard blunder of 0.03, we can involve the equation for a certainty stretch, which is point gauge ± z* (standard mistake), where z* is the z-score related with the ideal certainty level.

For a 99.7% certainty stretch, the z-score is roughly 3. Consequently, the certainty span would be:

0.53 ± 3(0.03) = (0.44, 0.62)

This implies that we can be 99.7% certain that the genuine extent of people with schizophrenia in the populace lies somewhere in the range of 0.44 and 0.62.

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Answer:

(b) The distribution of the last digits of ID numbers in a sample of 100 college students

Step-by-step explanation:

Uniform Distribution Explanation

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely.

The only possibility here is the distribution of the last digits since the last digit can be 0 thru 9 and each is equally likely to appear in a random sample of 100 students

The others can be eliminated

Heights can vary depending on gender, ethnic background etc. In fact heights will follow a normal distribution

Scores can vary, most students will be scoring around the mean follows a  normal distribution

GPAs like scores can vary, most students will have GPAs close to the mean GPA so follows a normal distribution