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From the truth table, it can be observed that the ¬((¬(p ∩ q) → (p → q))) is unsatisfiable.

For each of the formulas below, let's state whether they are valid, unsatisfiable, or contingent as follows:-

(p V q) → q is valid because it is a tautology.

Let's prove it:

|p | q | ¬(p V q) | ¬(p V q) → q

||---|---|--------|-----------|

| T | T | F | T || T | F | F | T || F | T | F | T || F | F | T | T |

From the truth table, it can be seen that the conditional operator is always true.

Thus, (p V q) → q is valid.- (((p → q) → p) → p is contingent because it can be true or false based on the value of p and q.

Let's prove it:

|p | q | p → q | (p → q) → p | ((p → q) → p) → p

||---|---|--------|-------------|-----------------------|

| T | T | T | T | T || T | F | F | T | T || F | T | T | F | F || F | F | T | T | T |

From the truth table, it can be observed that the formula is sometimes true and sometimes false.

Thus, (((p → q) → p) → p is contingent.- ¬((¬(p ∩ q) → (p → q))) is unsatisfiable because it contradicts itself.

Let's prove it:

|p | q | ¬(p ∩ q) | ¬(p ∩ q) → (p → q) | ¬(¬(p ∩ q) → (p → q))

||---|---|-----------|-----------------------|-------------------------||

T | T | F | T | F || T | F | T | T | F || F | T | T | T | F || F | F | T | T | F |

From the truth table, it can be observed that the formula is always false.

Thus, ¬((¬(p ∩ q) → (p → q))) is unsatisfiable.

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Answer:

x^2 +6x -15

Step-by-step explanation:

(3x^2 +2x -8) - (2x^2 -4x+7)

Distribute the minus sign

(3x^2 +2x -8) - 2x^2 +4x-7

Combine like terms

x^2 +6x -15

Answer:

x²+6x-15

Step-by-step explanation:

We are given this expression:

\((3x^2+2x-8) - ( 2x^2-4x+7)\)

We want to simplify the expression. First, distribute the negative sign in front of the second set of parentheses. Multiply each term inside the parentheses by -1.

\((3x^2+2x-8) + (-1*2x^2) + (-1*-4x) + (-1*7)\)

\((3x^2+2x-8) -2x^2+ 4x -7\)

Next, combine like terms. The 2 terms with an x² can be combined, just like the two terms with an x, and the two terms without a variable.

\((3x^2-2x^2) + (2x+4x) + (-8-7)\)

\(x^2+(2x+4x)+(-8-7)\)

\(x^2+6x+(-8-7)\)

\(x^2+6x-15\)

The expression x²+6x-15 is equivalent to (3x²+2x-8)-(2x²-4x+7)

The given expression, \(d(n)d(n)d(n)\), represents the duration in seconds for Hailey to run her \(n^{th}\) lap. The specific values provided, 333, 777, 999, correspond to the durations of the 3rd, 7th, and 9th laps, respectively. The values 858585, 999999, and 110110110 are unrelated and do not provide any additional information about lap durations.

The expression \(d(n)d(n)d(n)\) suggests that each lap duration is represented by the function \(d(n)\), where \(n\) denotes the lap number. The specific values given (333, 777, 999) correspond to the 3rd, 7th, and 9th laps, respectively. However, the remaining values (858585, 999999, 110110110) do not appear to have a direct connection to the lap durations or the function \(d(n)\).

Without further information or a specific pattern, it is difficult to interpret the significance of the remaining values. It's important to note that more context or information about the pattern or relationship between the values would be necessary to provide a more detailed explanation or analysis.

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Best guess for the function is

\(\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}\)

By the ratio test, the series converges for

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1\)

When \(x=1\), \(f(x)\) is a convergent \(p\)-series.

When \(x=-1\), \(f(x)\) is a convergent alternating series.

So, the interval of convergence for \(f(x)\) is the closed interval \(\boxed{-1 \le x \le 1}\).

The derivative of \(f\) is the series

\(\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n\)

which also converges for \(|x|<1\) by the ratio test:

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1\)

When \(x=1\), \(f'(x)\) becomes the divergent harmonic series.

When \(x=-1\), \(f'(x)\) is a convergent alternating series.

The interval of convergence for \(f'(x)\) is then the closed-open interval \(\boxed{-1 \le x < 1}\).

Differentiating \(f\) once more gives the series

\(\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)\)

The first series is geometric and converges for \(|x|<1\), endpoints not included.

The second series is \(f'(x)\), which we know converges for \(-1\le x<1\).

Putting these intervals together, we see that \(f''(x)\) converges only on the open interval \(\boxed{-1 < x < 1}\).

Answer:

154 is the mean

Step-by-step explanation:

First you will add up all the numbers. Which will give you a total of 770, then you have to divide the AMOUNT OF NUMBERS, which is 5. So 770 ÷ 5 = 154.

Gloria's mean score is 154.

The simplest and most popular way to measure a mean or average is the arithmetic mean. It simply entails adding up a collection of numbers, then dividing that total by the total number of numbers in the series.

Formula: Arithmetic Mean

= (Sum of observation)/ Total number of observation

Given:

Gloria  scores were 110, 127, 206, 174, and 153.

Now, Arithmetic Mean

= (Sum of Gloria scores)/ Total number of games

So, Sum of Gloria score = 110+127 + 206+ 174 + 153 = 770

Total number of games = 5

Thus, Arithmetic Mean

= 770 /5

= 154

Hence, the Mean is 154.

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The forest fires in southern Mexico and Guatemala consumed forest land at a rate of 28,600 acres per week.

During May 1998, forest fires in southern Mexico and Guatemala were burning at a significant rate, resulting in the spread of smoke all the way to Austin. The fires were consuming forest land at a rate of 28,600 acres per week. This indicates the amount of forest area that was destroyed or affected by the fires within a span of one week.

The figure of 28,600 acres per week provides an understanding of the magnitude and impact of the forest fires. It highlights the rapid rate at which the fires were spreading and consuming the forested areas. Forest fires are known to have severe ecological and environmental consequences, including loss of biodiversity, destruction of habitats, and degradation of air quality due to the smoke generated. The fact that the smoke from these fires reached Austin suggests the vast distance covered by the smoke plume, indicating the scale and intensity of the fires.

Forest fires are a significant concern as they pose risks to both human lives and natural ecosystems. They can have long-lasting effects on the affected regions, requiring extensive recovery and rehabilitation efforts. Monitoring and managing forest fires, along with implementing preventive measures, are crucial for minimizing their impact and protecting valuable forest resources.

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Answer:

38cm

Step-by-step explanation:

4+2+2+4+13+13=38

The graph is plotted and Following observations are noted Do, 0.75 (x,y) = (0.75x, 0.75y) ,  LM is parallel to L'M' , and The vertices of the image are closer to the origin than those of the pre-image.

The complete question is

Triangle KLM was dilated according to the rule

Do,0.75 (x,y).

What is true about the image △K'L'M'? Check ALLl that apply.

- Do, 0.75 (x,y) = (0.75x, 0.75y)

- LM is parallel to L'M'.

- KM is shorter than K'M'.

- The vertices of the image are closer to the origin than those of the pre-image.

- The distance from M' to the origin is exactly half the distance from M to the origin.

Dilation is the stretching or compression of a figure by a factor known as Scale Factor.

The shape of the new image is same as the initial image.

The graph is plotted and Following observations are noted

A. Do, 0.75 (x,y) = (0.75x, 0.75y)

B. LM is parallel to L'M'.

C. The vertices of the image are closer to the origin than those of the pre-image.

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The simplified expressions are -6x²(x+7)³ + 21x(x+7)³ and 3x²(x+7)³. The expressions are simplified by factoring out the greatest common factor, which is

To simplify the expressions 3x(x+7)⁴ - 9x²(x+7)³ and 3x²(x+7)³, we can apply the factoring of the greatest common factor (GCF) and utilize the rules of exponents.

Let's simplify each expression step by step:

1. 3x(x+7)⁴ - 9x²(x+7)³:

First, we identify the GCF, which is x(x+7)³. We can factor out the GCF from both terms:

3x(x+7)⁴ - 9x²(x+7)³ = x(x+7)³(3(x+7) - 9x)

Next, we simplify the expression inside the parentheses:

= x(x+7)³(3x + 21 - 9x)

= x(x+7)³(-6x + 21)

Therefore, the simplified expression is -6x²(x+7)³ + 21x(x+7)³.

2. 3x²(x+7)³:

Similarly, we can factor out the GCF, which is x²(x+7)³:

3x²(x+7)³ = x²(x+7)³(3)

= 3x²(x+7)³

Therefore, the expression 3x²(x+7)³ is already simplified.

In conclusion, the simplified expressions are:

-6x²(x+7)³ + 21x(x+7)³ and 3x²(x+7)³.

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Answer:

Commutative property of multiplcation.

Step-by-step explanation:

An identifier for the property of multiplcation is by multiplying it by 1. Therefore the answer remains the same.

Answer:

Step-by-step explanation:

(a)  If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.

(b)  If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.

(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.

What is permutation of rearranging letters?

A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .

The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.

Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.

Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.

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a) 36, 35, 3, 1 ways; b) 126, 5, 6, 1 ways; c) total number of ways to reorder the letters in the word tennessee is 3780 for both a) and b).

(a)  If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.

(b)  If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.

(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.

What is permutation of rearranging letters?

A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .

The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.

Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.

Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.

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The length of the guy wire is 630 ft

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

If a and b are the legs of the triangle and c is the hypotenuse of the triangle, then,

c² = a² + b²

Pythagoras theorem is applicable to only right angled triangle.

Using Pythagorean theorem, the length of the guy wire

b² = 344000

a² = 52900

l =√ 344000 + 52,900

l = √ 396900

l = 630

The length of the guy wire 630 feet

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As per the given conditions function g(x) = [ 1 / (x- 3)] -5.

"The graph of y=f(x)+k (where k is a real number) is the same as the graph of y=f(x) only it's shifted up (when k>0) or down (when k<0). Similarly, the graph of y=f(x-h) (where h is a real number) is the same as the graph of y=f(x) only it's shifted to the right (when h>0) or to the left (when h<0)."

According to the question,

We have

Parent function f(x) = 1/x

Function f(x) shifted down = 3 units

Function f(x) shifted right = 5 units

The graph of reciprocal.

parent function f(x) = 1/x is shifted 3 units down then

f(x) = \(\frac{1}{x - 3}\)

5 units to the right to create the graph g(x)

g(x) =  \(\frac{1}{x - 3} - 5\)

Hence, option D is the correct answer.

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Answer:

a = 19.6 (rounded to the nearest tenth)

Step-by-step explanation:

a^2 + b^2 = c^2

Hypotenuse - 35 m, Legs - 29 m, x

a^2 +29^2 = 35^2

a^2 + 841 = 1225

Subtract 841 from both sides

a^2 = 384

Square root both sides

√a^2 = √384

a = 19.595

Answer:

A is correct

Step-by-step explanation:

b has a negative value cause it's before 0

but -b will become a positive value thus >0

example:

b is -1

-b = -(-1)

= 1

hope you understand

Answer:

⇨ Choice A.

Step-by-step explanation:

We'll consider three choices and compare the answers with the given number line and points.

⟺ Choice A

This is the correct answer and here is why.

\(-b>0\)

Solving Inequality is similar to solving equation. The difference is if the coefficient for the variable is in negative, moving to another side would swap the sign/operator of Inequality.

Thus, our new Inequality would be \(b<0\) which is true by the number line itself.

⟺ Choice B

The reason why choice B is not correct because the point a is lesser than the point b. It's obvious that point a cannot be greater than point b.

⟺ Choice C

The reason why choice C is not correct because if we solve the Inequality.

\(-b<-c\)

We can either solve for b-term or c-term, the outcome would be the same. I'll solve for both terms.

⇨ Solve for b-term

\(-b<-c\\b>\frac{-c}{-1}\\b>c\)

Also remember that moving a negative coefficient would swap the sign/operator of Inequality.

⇨ Solve for c-term

\(-b<-c\\\frac{-b}{-1}>c\\b>c\)

As b>c is not true in the number line. We notice that c point is greater than b point.

Thus, the clear answer is A choice.  

The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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The probability that a randomly selected American plans to stay home or travel by car over the next holiday weekend given the information that 9.35% of Americans plan to travel by car and 88.6% plan to stay home. The probability of staying home or traveling by car over the next holiday weekend is given by the addition of probabilities of these events.

P(stay home or travel by car) = P(stay home) + P(travel by car)P(stay home or travel by car) = 0.886 + 0.0935P(stay home or travel by car) = 0.9795Therefore, the probability that a randomly selected American plans to stay home or travel by car over the next holiday weekend is 0.9795.

The value of probability does not equal 1 because some Americans traveled by other means.

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Answer:

1. b⁵

2. +16m⁹

Step-by-step explanation:

1. Add exponents: b³⁺² = b⁵

2. Negative and Negative = positive

2*8 = 16

m⁴⁺⁵ = m⁹

Hence: + 16m⁹

Answer:

\(1) \: {b}^{5} \)

\(2) \: \: + 16 {m}^{9} \)

Step-by-step explanation:

\( {b}^{3} \times {b}^{2} = {b}^{3 + 2} = {b}^{5} \)

we know that

\(( - ) \times( - ) = ( + )\)

So

\( - 2 {m}^{4} \times - 8 {m}^{5} \\ = + 16 {m}^{9} \)

Answer:

745

Step-by-step explanation:

Step-by-step explanation:

Given :A pool is filled with 2,980 quarts of water.

To Find : How many gallons of water are in the pool?

Solution :

Amount of water in pool = 2980 quarts

1 quart = 0.25 gallon

2980 quarts =

So, There are 745 gallons of water in the pool .

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Sam is filling up his pool. The water hose filled the 441 gallon pool in 49 minutes. At what rate did the hose fill the pool in gallons per minute?

The solutions for the system of equations is the point (2, 2).

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given are two linear equations,

y = -x + 4 and

y = 2x - 2

First graph the lines.

For that, find two points on each equation and join them.

x = 0, then y = 4

y = 0, then x = 4

We have two points (0, 4) and (4, 0). Join these points to form the line.

x = 0, then y = -2

y = 0, then x = 1

We have two points (0, -2) and (1, 0). Join these points to form the line.

We have two equations, which are equal to each other.

-x + 4 = 2x - 2

-x - 2x = -2 - 4

-3x = -6

x = 2

y = -2 + 4 = 2

So the solution of the system of equations is the intersecting point of the two lines which is (2, 2).

Hence the solution of the system of equations is (2, 2).

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-π/2

(a) To evaluate this definite integral, we will use the u-substitution method. Let u = 1 + 4x^2, then du = 8x dx.

Therefore, the definite integral becomes:

∫^1_1 x/1 + 4x^2dx = ∫^1_1 (1/8) du = (1/8)(u|^1_1) = (1/8)(1 + 4x^2|^1_1) = (1/8)(1 - 1) = 0

(b) To evaluate this definite integral, we will use the u-substitution method. Let u = 2e^-x + 3, then du = -2e^-x dx.

Therefore, the definite integral becomes:

∫^1_0 e^-x(2e^-x+3)^9dx = ∫^1_0 (-1/2)u^9 du = (-1/2)(u^10|^1_0) = (-1/2)((2e^-x+3)^10|^1_0) = (-1/2)((2e^-x+3)^10 - 1)

(c) To evaluate this definite integral, we will use the u-substitution method. Let u = 1/x, then du = -1/x^2 dx.

Therefore, the definite integral becomes:

∫^4/pi_2/pi cos(1/x)/x^2dx = ∫^4/pi_2/pi (-1/u^2) du = (-1/u|^4/pi_2/pi) = (-1/(1/x|^4/pi_2/pi)) = (-1/(4/π - 2/π)) = (-1/(2/π)) = -π/2

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Answer:

$34.78

Step-by-step explanation:

...............

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: slope \:\: of \:\: line = \cfrac{3}{2}\)

____________________________________

\( \large \tt Solution \: : \)

The equation of line is written in slope - intercept form

\(\qquad \tt \rightarrow \: f(x) = \dfrac{3}{2} x - 4\)

if we compare it with general slope - intercept equation of line :

\(\qquad \tt \rightarrow \: f(x) = mx + c\)

[ m represents slope of line ]

\(\qquad \tt \rightarrow \: m = \dfrac{3}{2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

\(\frac32\)

Step-by-step explanation:

Hello!

An equation of a line is usually written in slope-intercept form.

Slope Intercept Form: \(y = mx + b\)

If we compare our given equation with the format:

This means that \(\frac32\) would be our slope for the line.

Answer:

2x^2+3x+3

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

STEP  1

The Equation at the end of step 1

 (3x2 +  5x) -  x2) -  2x) +  3

STEP  2

Trying to factor by splitting the middle term

2.1     Factoring  2x2+3x+3  

The first term is,  2x2  its coefficient is  2.

The middle term is,  +3x  its coefficient is  3.

The last term, "the constant", is  +3  

Step-1: Multiply the coefficient of the first term by the constant   2 • 3 = 6  

Step-2: Find two factors of  6  whose sum equals the coefficient of the middle term, which is   3.

     -6    +    -1    =    -7  

     -3    +    -2    =    -5  

     -2    +    -3    =    -5  

     -1    +    -6    =    -7  

     1    +    6    =    7  

     2    +    3    =    5  

     3    +    2    =    5  

     6    +    1    =    7  

Observation: No two such factors can be found !!

Conclusion: Trinomial can not be factored

Final result :

 2x^2 + 3x + 3

Hope this helps!

Brain-List?

The given statement about two variables is false. This is because to determine whether the respective two variables are related, we cannot compare two marginal distributions.

A correlation coefficient is used to assess the relationship between the two variables. The letter r is used to represent this coefficient. The r values range from -1 to  +1.

Based on this value, the correlation is classified into two types negative correlation and positive correlation. When the r value is -1, it is referred to as a perfect negative correlation. When the r value is +1, it is referred to as a perfect positive correlation. So to compare the relation of two variables, we require a correlation coefficient, not marginal distribution. Therefore, the given statement is false.

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Answer: (2x + 3y)^2; m = 2 n = 3

Step-by-step explanation:

another way to write (2x + 3y)^2 is

(2x+3y) (2x+3y) if you FOIL (First, Outsides, Insides, Lasts) you will get

4x^2 + 6xy + 6xy + 9y^2

= 4x^2 + 12xy + 9y^2

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are given a equation,

\(\longrightarrow (mx+ny)^2 = 4x^2+12xy+9y^2  \\\)

Consider the LHS ,

\(\longrightarrow (mx+ny)^2 \\\)

We can expand it using an indentity ,

Identity:-

\(\longrightarrow \boxed{ (a+b)^2=a^2+b^2+2ab}\\\)

So we have;

\(\longrightarrow (mx)^2+(ny)^2+2(mx)(ny) = 4x^2+12xy + 9y^2  \\\)

Simplify,

\(\longrightarrow  m^2(x^2) + n^2(y^2) + 2xy(mn) = 4x^2+12xy + 9y^2\\\)

On comparing the respective terms , we have;

Simplify and solve for m and n as ,

\(\longrightarrow m =\sqrt{4} =\boxed{2}\\\)

\(\longrightarrow n =\sqrt{9} =\boxed{3} \\\)

Hence the value of m is 2 and that of n is 3 .

The 95% confidence interval for the true population mean turtle weight is approximately 26.35 ounces to 35.65 ounces.

To construct a 95% confidence interval for the true population mean turtle weight, we can use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / √n)

Where:

- Sample mean: 31 ounces (given)

- Critical value: determined by the desired confidence level (95%) and the sample size

- Standard deviation: 12.4 ounces (given)

- n: number of observations (27)

The critical value can be obtained from the standard normal distribution table or a statistical software. For a 95% confidence level, the critical value is approximately 1.96.

Substituting the given values into the formula:

Confidence interval = 31 ± (1.96) * (12.4 / √27)

Calculating the standard error (standard deviation divided by the square root of the sample size):

Standard error = 12.4 / √27 ≈ 2.385

Now, we can substitute the standard error into the formula:

Confidence interval = 31 ± (1.96) * (2.385)

Calculating the values:

Lower bound = 31 - (1.96) * (2.385) ≈ 26.35

Upper bound = 31 + (1.96) * (2.385) ≈ 35.65

Therefore, the 95% confidence interval for the true population mean turtle weight is approximately 26.35 ounces to 35.65 ounces.

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Answer:

\(6n + 3 + 2n = 8n + 3\)

\(99-9-9 = 81\)

\(2p + 3p+ 6-p-3 = 4p + 3\)

\(2.25(14.3m + 6 + 2.7m) = 38.25m + 15.5\)