5.
A number n is such that when it is divided by 27, 30, or 45, the remainder is alway
smallest value of n​

The "n" in the formula for calculating degrees of freedom for a correlation coefficient represents the sample size. The correct option is a.

Explanation: In statistics, the correlation coefficient measures the strength and direction of the linear relationship between two variables. When calculating the degrees of freedom for a correlation coefficient, the "n" represents the sample size. Degrees of freedom (df) refers to the number of independent observations in a statistical analysis. It represents the number of values that are free to vary after certain restrictions or conditions have been imposed.

In the context of correlation, the formula for degrees of freedom is given by (n - 2), where "n" is the sample size. The subtraction of 2 is because the calculation of the correlation coefficient involves estimating the parameters of the line that best fits the data, which requires two degrees of freedom. Subtracting 2 ensures that the degrees of freedom accurately reflect the number of independent observations available for analysis.

Therefore, the correct answer is (a) sample size. The larger the sample size, the greater the degrees of freedom, which generally improves the reliability and precision of the correlation coefficient estimate.

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Answer:

Suppose that we have a circle of radius R.

The total perimeter of this circle will be:

P = 2*pi*R

Where pi = 3.14159...

Now, if we have a section of this circle with an angle A, the "chord" of this section will be:

C = (A/360°)*2*pi*R.

Where you can see that if A = 360° (so the section is the whole circle) the chord is equal to the perimeter.

In this particular case, the chord is equal to the radius of the circle, then we get:

C = R =  (A/360°)*2*pi*R

We need to solve this for A.

R =  (A/360°)*2*pi*R

We can divide both sides by R to get:

1 =   (A/360°)*2*pi

Now we need to isolate A.

(360°/2*pi) = A = 57.3°

This would be the angle in the minor arc.

And the angle for the mayor arc would be the difference between the angle for a whole circle (360°) and the angle of this section (57.3°)

The angle for the major arc is:

A = 360° - 57.3° = 302.7°

The main difference between an area variance and a use variance is that area variance allows for an exception to zoning regulations related to the physical characteristics of a property, while use variance allows for an exception to regulations related to the intended use of a property.

An area variance is typically granted when a property owner is unable to comply with zoning regulations related to setbacks, building height, lot coverage, or other physical characteristics of a property.

In contrast, a use variance allows a property owner to use their property for a purpose that is not permitted under the current zoning regulations. This may include using a residential property for commercial purposes or using a commercial property for residential purposes.

Use variances are generally more difficult to obtain than area variances, as they require a showing of a unique hardship or practical difficulty that cannot be addressed through other means.

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Salutem City would need to build 275 more health centers to match the current city with the most health centers per capita.

What is capita?

In the context of the phrase "per capita", capita refers to the per person or per individual basis. It is a Latin term that means "by the head". When used in statistics or economics, per capita is a measure of a particular variable such as income, health centers, or any other quantity, that is divided by the total population of a given area or country. This measure provides a way to compare variables across different populations or regions, taking into account the differences in their sizes.

To determine how many more health centers Salutem City would need to build to claim the most health centers per capita, we can use the following steps:

Calculate the current number of health centers per capita in Salutem City:

Number of health centers per b = (215 centers / 10,000 people) = 0.0215 centers per person

Calculate the number of health centers needed to match the current leader's ratio:

Number of health centers needed = (0.0215 centers per person) * (250,000 people) = 5,375 centers

Calculate the number of additional health centers Salutem City would need to build:

Additional health centers needed = (5,375 centers) - (5,100 centers) = 275 centers

Therefore, Salutem City would need to build 275 more health centers to match the current city with the most health centers per capita.

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a. The class width for all intervals in this frequency distribution is 3.

b. Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

c. Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

The number of full oscillations that any wave element performs in one unit of time is how we determine the frequency of a sinusoidal wave.

To find the class width, class midpoints, and class boundaries for the given frequency distribution, let's analyze the temperature intervals and frequencies:

Temperature (°F)    Frequency

32-35                      1

36-39                      3

40-43                      5

44-47                      11

48-51                      7

52-55                      7

56-59                      1

(a) Class width:

The class width is the difference between the upper and lower boundaries of each temperature interval. In this case, all the intervals have the same width.

Class width = Upper boundary - Lower boundary

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class width = 35 - 32 = 3

The class width for all intervals in this frequency distribution is 3.

(b) Class midpoints:

The class midpoint is the average value of the upper and lower boundaries of each interval. It represents the central value of the interval.

Class midpoint = (Upper boundary + Lower boundary) / 2

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class midpoint = (35 + 32) / 2 = 33.5

Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

(c) Class boundaries:

The class boundaries are the values that separate each interval. They are calculated by adding or subtracting half of the class width from the upper and lower boundaries.

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35, and the class width is 3.

Lower class boundary = Lower boundary - (0.5 * class width) = 32 - (0.5 * 3) = 32 - 1.5 = 30.5

Upper class boundary = Upper boundary + (0.5 * class width) = 35 + (0.5 * 3) = 35 + 1.5 = 36.5

Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

Note: The class boundaries are inclusive of the lower boundary and exclusive of the upper boundary.

These are the calculations for the class width, class midpoints, and class boundaries for the given frequency distribution.

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To find the class width, subtract the lower class limit from the upper class limit. To find the class midpoints, add the lower and upper class limits and divide by 2. To find the class boundaries, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit.

(a) Class width:

To find the class width, we subtract the lower class limit from the upper class limit. For example, the class width for the first class interval (32-35) is 35 - 32 = 3.

(b) Class midpoints:

To find the class midpoints, we add the lower class limit and the upper class limit and divide the sum by 2. For example, the class midpoint for the first class interval (32-35) is (32 + 35) / 2 = 33.5.

(c) Class boundaries:

To find the class boundaries, we subtract 0.5 from the lower class limit and add 0.5 to the upper class limit. For example, the class boundaries for the first class interval (32-35) are (32 - 0.5) and (35 + 0.5).

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Our assumption that two consecutive elements of the Fibonacci sequence can be divisible by 13 is false, and the proposition is proved.

We begin with the fact that the Fibonacci sequence is an increasing sequence; that is, each element is greater than the one before it.

The sequence is defined as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, and so on.

Now, let us prove the proposition by contradiction. Assume that there are two consecutive elements of the Fibonacci sequence that are divisible by 13. Then there must be some integer n such that:

F(n) = 13m, andF(n + 1) = 13p,

where m and p are integers.

Since the Fibonacci sequence is defined recursively by F(n) = F(n-1) + F(n-2), we can obtain an expression for F(n-2) in terms of F(n) and F(n-1):

F(n-2) = F(n) - F(n-1)Since F(n) and F(n-1) are both divisible by 13, their difference must also be divisible by 13.

Therefore, F(n-2) is divisible by 13 as well. However, this contradicts the well-ordering principle, which states that every non-empty set of positive integers has a least element.

Since the Fibonacci sequence is an increasing sequence, there must be some least element k such that F(k) is divisible by 13 but F(k-1) is not. But this means that F(k-2) cannot be divisible by 13, which contradicts our assumption that both F(n) and F(n-1) are divisible by 13.

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Answer:

3x + 3y = x+ 7y is the equation and solutions are in bold below

subtract 3y from both sides

3x= x + 4y

subtract x from both sides

2x=4y

divide both sides by 2

x = 2y

Now we solve for y

3x + 3y = x+ 7y

2x=4y

0.5x = y

y = 0.5x or 1/2x

Step-by-step explanation:

Answer:

a. \(8x^{2} -14x-15\)

b. \((x+3)(x+2)\)

Step-by-step explanation:

A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)

For F, take the first terms of the 2 and multiply

\(4x*2x=8x^{2}\)

For O, take the outer terms and multiply

\(4x*-5=-20x\)

For I, take the inner terms and multiply

\(3*2x=6x\)

For L, take the last terms and multiply

\(3*-5=-15\)

After that, add all of them up

\(8x^{2} +(-20x)+6x+(-15)=8x^{2}-14x-15\)

B. Since the equation is in the form x^2+bx+c,

\((x+?)(x+?)\)

Now we need to find 2 numbers that will add up to 5 and multiply to 6.

Here are some of the combinations of numbers that multiply to 6

3*2

1*6

-3*-2

-1*-6

3 and 2 add up to 5 so:

\((x+3)(x+2)\)

Answer:

The answer is D

Step-by-step explanation:

I just did this

The figure which has rotational symmetry is figure A.

It is the property of a shape that it looks same after some rotation by a partial turn.

In the figure given first shape has equal length of sides at each direction which means that if we rotates this figure then we will get same looking figure.

In the second figure when we rotates the figure vertically the it will look like a tower.

When we rotates the third figure they also look different.

In the graph figure are shown after some rotation.

Hence among all the figures given first figure has rotational symmetry.

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The distance that the boat travel is 17.5 miles per hour.

A boat travels upstream on a Mississippi river for 3.5 hours and the return trip takes 2.5 hours

The boat travels 2 miles per hour faster downstream

Let y = the speed that was traveled upsteam.

This will be illustrated as

3.5y = 2.5(y + 2)

3.5y = 2.5y + 5

3.5y - 2.5y = 5

y = 5

Therefore the distance travelled by the boat upstream will be:

= 3.5 × 5

= 17.5 miles per hour

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The value of x is x = 9/4. The equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4

The equation 2xc = d and 2x + 1 = 9 are similar in that they are both linear equations and involve the variable x.

However, they are different in that they have different constants and coefficients.

How to use 2xc = d to solve 2x + 1 = 9? To use 2xc = d to solve 2x + 1 = 9, you first need to rewrite 2x + 1 = 9 in the form 2xc = d.

To do this, you need to isolate x on one side of the equation. 2x + 1 = 9

Subtract 1 from both sides2x = 8. Divide both sides by 2x = 4Now, we can write 2x + 1 = 9 as 2x * 1/2 = 9/2.

Therefore, we can see that this equation is similar to 2xc = d, where c = 1/2 and d = 9/2.

We can use this relationship to solve for x in the equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4 Therefore, x = 9/4.

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Answer:

−10x − 6y

Step-by-step explanation:

−2(5x+3y)

=(−2)(5x+3y)

=(−2)(5x)+(−2)(3y)

=−10x−6y

Answer:

just 150x2 = 300 minutes or just 150 minutes to cook

Step-by-step explanation:

The cooking time of a turkey depends on its weight, so a 16-pound turkey will take longer to cook than an 8-pound turkey. However, without additional information such as the cooking method, temperature, and the shape and size of the turkeys, it's not possible to determine the exact cooking time for the 16-pound turkey.

Answer:

14

Step-by-step explanation:

use order of operations (PEMDAS: Parenthesis, exponents, multiplication, division, addition, subtraction)

5 + 4 * 2 + 6 - 2 *2-1

5+ 8 + 6 -4 -1

13+6-4-1

19-4-1

15-1

14

The confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.

It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.

The formula for finding the MOE:

\(\rm MOE = Z\times{\sqrt \dfrac{p(1-p)}{n}\\\)

Where   Z is the z-score at the confidence interval

            p is the population proportion

            n is the number of samples.

We have p = 68% = 0.68

n = 115

Z score for 90% confidence interval = 1.64

\(\rm MOE = 1.64\times{\sqrt \dfrac{0.68(1-0.68)}{115}\\\)

MOE = 0.071

So the confidence interval will be:

= (0.68-0.071, 0.68+0.071)

= (0.609, 0.751)  or

= (60.9%, 75.1%)

Thus, the confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.

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The number of groups of three that the college can select is 56.

Total number of students = 8

Number of assistantships available = 3

Groups of three can be selected by the college means that out of the eight students three need to be selected at random and this can be done in ⁸\(C_{3}\) ways.

In this case, we use combination and not permutation because the order of selection of the students does not matter.

Now, we know

ⁿ\(C_{r}\) = ( n! )/( r! (n-r )!)

Here, n = 8 and r = 3

⁸\(C_{3}\)  = ( 8! )/( 3! (8-3)! )

⁸\(C_{3}\)  =  ( 8 × 7 × 6 × 5! )/ ( 3 × 2 × 1 × ( 5! ) )

⁸\(C_{3}\)  = ( 8 × 7 × 6 )/ ( 3 × 2 )

⁸\(C_{3}\)  = 56

The number of groups of three that the college can select is 56.

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Answer:

2x-1= p

Step-by-step explanation:

dude srsly

Answer:

42 84 106 148 170 252

Step-by-step explanation:

Answer:

Both sides that are parallel ( 6 inches I believe ) would be 12 in total for both sides. Then the top and bottom would be 3 inches ( I believe ) which would be 6. I think you need to do 6 times 12 until you get 360 and then see how many times you multiplied it and that is your answer. But I am not FULLY sure. Hope this helps somehow!

Step-by-step explanation:

Answer:

21/100

Step-by-step explanation:

there are 100 total people and 21 who have a dog but do not take walks. You can leave it like that because it cannot be simplified more.

Answer:

the answer is B

in radians it is 10 pi/3

Answer:

1) v_i = 2.78 m/s

v_f = 16.67 m/s

t = 5 s

Acceleration = 2.78 m/s²

2) a = 1.5 m/s²

Step-by-step explanation:

1) The car was running at 10 km/hr.

In m/s this is 2.78 m/s

Thus;

Initial velocity; v_i = 2.78 m/s

It increased its speed to 60 km/hr in 5 seconds.

Thus, final velocity is 60 km/hr

Converting to m/s gives; 16.67 m/s

Final velocity; v_f = 16.67 m/s

Time to reach final velocity; t = 5 seconds

From Newton's first equation of motion, we can find the acceleration;

a = (v_f - v_i)/t

a = (16.67 - 2.78)/5

a = 2.78 m/s²

2) started from test, so initial velocity;

v_i = 0 m/s

Reached a speed of 9 m/s in 6 seconds.

Final velocity; v_f = 9 m/s

Time; t = 6 s

Acceleration is calculated as;

a = (v_f - v_i)/t

a = (9 - 0)/6

a = 1.5 m/s²

Answer:

y=-7x+6

Step-by-step explanation:

-21 divided by 3x is- 7x . 18 divided by 3 is 6.

Answer:

D

Step-by-step explanation:

Convert all of the fractions' denominators so that they are 8. This is because 4,2, and 8's least common multiple is 8.

Remember that when multiplying the denominator, we must also multiply the numerator. So:

\(\frac{1}{2} * \frac{4}{4} = \frac{4}{8} \\\)

\(\frac{1}{4} *\frac{2}{2} =\frac{2}{8}\)

Since we are asked to add all of them, we can do that easily since all of the fractions now share a common denominator.

\(\frac{2}{8} +\frac{4}{8} + \frac{1}{8} = \frac{7}{8}\)

Therefore, the answer is D.

Answer: quantity of water added = 19.6 quarts

Step-by-step explanation:

Let x= quantity of water added

Then, Quantity of saline in 7 quarts solution  = 19% of 7 = 0.19 (7)=1.33 quarts [to remove % divide number by 100]

When x quarts water is added , the quantity of solution becomes = x+7

Quantity of saline in it= 5% of (x+7)= 0.05(x+7)

Now, quantity of saline remains same, so

\(1.33= 0.05(x+7)\\\\\Rightarrow\ 1.33x=0.05x+0.35\\\\\Rightarrow\ 1.33-0.35=0.05x\\\\\Rightarrow\ x=\dfrac{0.98}{0.05}=19.6\)

Hence,  quantity of water added = 19.6 quarts

Answer:what it is

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

Only 4 and 5 can be considered because 6 is not included, so the probability would be 2/4, or 50%.

Answer: 50%

Step-by-step explanation: It says if you pick a random card that is less than 6 or 4. That means that 4 and 5 are the ones you hope to get. 2/4 = 50%.

Answer:

Reflection

Step-by-step explanation: