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The correlation coefficient that indicates the strongest relationship between two variables is a. -1.0.

The correlation coefficient is a numerical measure that quantifies the relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

In this case, a correlation coefficient of -1.0 represents a perfect negative correlation, meaning that the two variables have a strong, linear relationship where as one variable increases, the other decreases in a perfectly predictable manner. This indicates a very strong and consistent inverse relationship between the variables.

In comparison, a correlation coefficient of 0.80 indicates a strong positive correlation, but it is not as strong as a perfect negative correlation of -1.0. A correlation coefficient of 0.1 suggests a weak positive correlation, while a correlation coefficient of -0.45 indicates a moderate negative correlation.

Therefore, out of the given options, the correlation coefficient of -1.0 represents the strongest relationship between two variables.

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Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

\(3\:sinA+4\:cosA=5\)

\(\frac{4}{5}\:cosA=1-\frac{3}{5}sinA\)

Taking square on both sides

\(\left(\frac{4}{5}\:cosA\right)^2=\left(1-\frac{3}{5}sinA\right)^2\)

\(16\:Cos^2\:A\:=\:25\:+\:9\:Sin^2A\:-\:30\:Sin\:A\)

\(16\:-\:16\:Sin^2\:A\:=\:25\:+\:9\:Sin^2A\:-\:30\:Sin\:A\)

\(25\:Sin^2\:A\:\:-\:30\:Sin\:A\:+\:9\:=\:0\)

so the equation can further be easily solved

\(\sin \:A=\frac{3}{5}\)         ∵ \(sin A =\) [ \(30\) +- √(900 - 900) ] ÷ 50

Answer:

1.

\(C.\\sin(N)=\frac{\sqrt{3} }{2}\)

2.

\(x=82.1\)

3.

x = 18°

Step-by-step explanation:

1. The sine ratio is sin(θ) = opposite/hypotenuse, where θ is the reference angle.  When N is the reference angle, we see that side OP with a measure of 5√3 units is the opposite side and side NP with a measure of 10 units is the hypotenuse.

Thus, we can find plug everything into the sine ratio and simplify:

\(sin(N)=\frac{5\sqrt{3} }{10} \\\\sin(N)=\frac{\sqrt{3} }{2}\)

2. We can use the tangent ratio to solve for x, which is tan (θ) = opposite/adjacent.  If we allow the 75° to be our reference angle, we see that the side measuring x units is the opposite side and the side measuring 22 units is the adjacent side.  Thus, we can plug everything into the ratio and solve for x or the measure of the opposite side:

\(tan(75)=\frac{x}{22}\\ \\22*tan(75)=x\\\\82.10511777=x\\\\82.1=x\)

3. Since we're now solving for an angle, we must using inverse trigonometry.  We can use the inverse of the tangent ratio, whose equation is tan^-1 (opposite/adjacent) = θ.  We see that when the x° is the reference angle, the side measuring 11 units is the opposite and the side measuring 33 units is the adjacent side.  Now we can do the inverse trig to find the measure of x:

\(tan^-^1(\frac{11}{33})=x\\ 18.43494882=x\\18=x\)

Answer:

18.19

Step-by-step explanation:

$20-15%=

$10=8.50

8.50 x 2 = 17

Now, 7% of 17 dollars.

$1= 1.07

1.07x17=  18.19

The value of the integral is (3/4)π.

To evaluate the integral, we need to first express ds in terms of u and v. Since s is a cone with parametric equations x = ucos(v), y = usin(v), z = u, we can express ds in terms of du and dv as follows:

ds = ||r_u x r_v|| du dv

where r_u and r_v are the partial derivatives of r with respect to u and v, respectively, and ||r_u x r_v|| is the magnitude of their cross product.

Taking the partial derivatives and computing the cross product, we get:

r_u = <cos(v), sin(v), 1>

r_v = <-usin(v), ucos(v), 0>

r_u x r_v = <-ucos(v), -usin(v), u>

||r_u x r_v|| = √(u^2 + u^2) = u√2

Therefore, ds = u√2 du dv.

Substituting this into the given integral and using the fact that sin(2x) = 2sin(x)cos(x), we get:

∫∫s xyz ds = ∫v=0^(π/2) ∫u=0^1 u^3 cos(v) sin(v) u√2 du dv

= √2 ∫v=0^(π/2) cos(v) sin(v) dv ∫u=0^1 u^4 du

= √2 (∫sin(2v)/4 dv) (1/5)

= √2 [(1/8) (-cos(π/2) + cos(0))] (1/5)

= (3/4)π.

Therefore, the value of the integral is (3/4)π.

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Answer:

5

Step-by-step explanation:

First, write the experimental probability as a fraction in simplest form.

P(chocolate)

=

chocolate

total

=

4

12

=

1

3

The experimental probability is

1

3

.

We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.

1

3

=

n

15

1

3

(315)

=

n

15

(315) Multiply both sides by (315)

115

= 3n Simplify

15

= 3n Simplify

5

= n Divide both sides by 3

You would expect 5 of the next 15 cones sold to have chocolate ice cream.

Answer: (4, 2)

Step-by-step explanation:

Centroid of the triangle  =  (x1 +x2 + x3)/3, (y1+y2+y3)/3

 =  (8+1+3)/3, (4+3-1)/3

 =  12/3, 6/3

 =  (4, 2)

The formula to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

The formula presented derived from the formula for the circumference of a circle, which is C = 2πr. By rearranging the equation and isolating the radius (r) on one side, we get r = C/(2π).

So, if the circumference (C) of a circle is 18 centimeters, you can use the formula r = C/(2π) to find the radius (r). Plugging in the given value for the circumference (C), we get:

r = 18/(2π)

Simplifying the equation gives:

r = 9/π

Therefore, the radius (r) of the circle is 9/π centimeters.

In conclusion, the formula you can use to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

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Answer:

36 ft

Step-by-step explanation:

A)  number of ways in which president is not next to the VP =3628800-725760 =2903040

B) Number of ways =9*9!=3265920

C) number of ways VP is in one end  =2*9!=725760

Permutations and combinations are  ways of representing groups of objects by selecting them  and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

a)

number of ways to line up 10 members =10! =3628800

number of ways so that VP and president are next to each other =N(consider president and VP as 1 member which can interchange in 2 ways , and now we need to arrange 9 members) =2*9!=725760

therefore number of ways in whcih president is not next to the VP =3628800-725760 =2903040

b)

Number of ways =N(9 choices for left most posiition except VP and arrange rest of 9 persons)

=9*9!=3265920

c)

number of ways VP is in one end =N(choose 1 place out of 2 end for VP and then arrange rest of 9 )

=2*9!=725760

therefore number of ways VP is not at one end =3628800-725760 =2903040

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Usando un sistema de ecuaciones, se encuentra que los numeros son 12 y 14.

La suma de los números es 26, o sea:

\(x + y = 26\)

La diferencia de sus cuadrados es 52, o sea:

\(x^2 - y^2 = 52\)

De el primer ecuación:

\(y = 26 - x^2\)

Por eso:

\(x^2 - y^2 = 52\)

\(x^2 - (26 - x)^2 = 52\)

\(x^2 - (x^2 - 52x + 676) = 52\)

\(52x - 676 = 52\)

\(x = \frac{728}{52}\)

\(x = 14\)

Así, el segundo número es dado por:

\(y = 26 - x = 26 - 14 = 12\)

Los numeros son 12 y 14.

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The 3-point differentiation rule is computationally efficient because it requires evaluating the function at three points and performs a simple arithmetic calculation to estimate the derivative.

The 3-point differentiation rule, also known as the central difference method, provides a good balance between computational efficiency and accuracy. It approximates the derivative of a function using three points: one point on each side of the desired differentiation point.

In the 3-point differentiation rule, the derivative is calculated using the formula:

f'(x) ≈ (f(x + h) - f(x - h)) / (2h)

where h is a small step size.

Compared to other methods, such as the forward or backward difference rules, the 3-point rule provides better accuracy as it takes into account information from both sides of the differentiation point. It reduces the error caused by the step size and gives a more accurate approximation of the derivative.

Additionally, the 3-point differentiation rule is computationally efficient because it requires evaluating the function at three points and performs a simple arithmetic calculation to estimate the derivative. This makes it a practical choice for differentiating functions, providing a good trade-off between accuracy and computational performance.

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Answer:

300

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

answer

CD = 38

solving steps

4x – 5 = 2x + 7

4x – 5 – 2x = 7

2x = 7 + 5

2x = 12

2x/2 = 12/2

x = 6

4(6) – 5 + 2(6) + 7

24 – 5 + 12 + 7

M = 38

Answer:

C

Step-by-step explanation:

Given that M is the midpoint of CG , then

CM = MG , that is

4x - 5 = 2x + 7 ( subtract 2x from both sides )

2x - 5 = 7 ( add 5 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Then

CG = CM + MG = 4x - 5 + 2x + 7 = 6x + 2 = 6(6) + 2 = 36 + 2 = 38

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

8 inches long. into how many pieces can the sausage be cut if each piece is to be two-thirds of an inch.

Divide 8 by 2/3

8÷ 2/3

8× 3/2

12

12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.

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Answer:

y = 4/9

Step-by-step explanation:

2(−2x+1)−5x+2 = 0

2*(−2x) +2*(1)−5x+2 = 0

-4x +2 -5x +2 = 0

-9y +4 = 0

-9y = -4

9y = 4

y = 4/9

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Answer: 5.3

Step-by-step explanation: use a calautlator

Rounding up to the nearest unit, it would take Calvin approximately 27 months to pay off his credit card with a monthly payment of $165.

To determine how long it would take Calvin to pay off his credit card, we need to consider the monthly payment amount and the interest rate. Let's calculate the time it would take for two different monthly payment amounts: $220 and $165.

a. Monthly payment of $220:

Let's assume the initial balance on Calvin's credit card is $3,000, and the annual interest rate is 4 percent. To calculate the monthly interest rate, we divide the annual interest rate by 12 (number of months in a year):

Monthly interest rate = 4% / 12 = 0.3333%

Now, we can calculate the time it would take to pay off the credit card using the monthly payment of $220 and the monthly interest rate. We'll use a formula for the number of months required to pay off a loan with fixed monthly payments:

n = -(log(1 - (r * P) / A) / log(1 + r))

Where:

n = number of months

r = monthly interest rate (as a decimal)

P = initial balance

A = monthly payment

Plugging in the values:

n = -(log(1 - (0.003333 * 3000) / 220) / log(1 + 0.003333))

Using a calculator, we can find:

n ≈ 15.34

Rounding up to the nearest unit, it would take Calvin approximately 16 months to pay off his credit card with a monthly payment of $220.

b. Monthly payment of $165:

We can repeat the same calculation using a monthly payment of $165:

n = -(log(1 - (0.003333 * 3000) / 165) / log(1 + 0.003333))

Using a calculator, we find:

n ≈ 26.39

Please note that these calculations assume that Calvin does not make any additional charges on his credit card during the repayment period. Additionally, the interest rate and the balance are assumed to remain constant. In practice, these factors may vary and could affect the actual time required to pay off the credit card balance.

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The probability that more than 20% of the sample are from poverty households is approximately 0.8365.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

We can use the normal approximation to the binomial distribution to solve this problem, given that the sample size is relatively large (n=300) and the probability of success (p=0.22) is not too close to 0 or 1.

Let X be the number of children in the sample who live in poverty households. Then X follows a binomial distribution with parameters n=300 and p=0.22.

The mean of X is given by μ = np = 300 x 0.22 = 66, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(300 x 0.22 x 0.78) ≈ 6.23.

We want to find the probability that more than 20% of the sample are from poverty households, which is equivalent to finding P(X > 0.2n) = P(X > 60).

To use the normal approximation, we can standardize X as follows:

Z = (X - μ) / σ

Then, we have:

P(X > 60) = P(Z > (60 - 66) / 6.23) ≈ P(Z > -0.96)

Using a standard normal table or calculator, we can find that the probability of Z being greater than -0.96 is approximately 0.8365.

Therefore, the probability that more than 20% of the sample are from poverty households is approximately 0.8365.

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Answer:

∠ 2 = 70°

Step-by-step explanation:

110° and ∠ 1 are corresponding angles and congruent, thus

∠ 1 = 110°

∠ 1 and ∠ 2 are adjacent angles and are supplementary, thus

∠ 2 = 180° - ∠ 1 = 180° - 110° = 70°

The fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:

D = 1.24/4 = 0.31

Diffusiοn is the prοcess by which particles οf a substance mοve frοm an area οf high cοncentratiοn tο an area οf lοwer cοncentratiοn, resulting in a net mοvement οf particles dοwn their cοncentratiοn gradient.

This οccurs due tο the randοm mοtiοn οf individual particles, which leads tο a tendency fοr particles tο spread οut and becοme evenly distributed οver time.

Answer tο Questiοn 9:

The relatiοnship between average displacement squared (R²) and time (t) is linear.

Answer tο Questiοn 10:

The variable 'R2' in the diffusiοn equatiοn cοrrespοnds tο 'y' in the trendline equatiοn, and the variable 't' in the diffusiοn equatiοn cοrrespοnds tο 'x' in the trendline equatiοn.

Answer tο Questiοn 11:

We can sοlve fοr the diffusiοn cοnstant 'D' in terms οf the slοpe 'm' and a cοnstant 'c' by equating the diffusiοn equatiοn and the trendline equatiοn.

The diffusiοn equatiοn: R2 = 4Dt

The trendline equatiοn: y = mx + b

Substituting the cοrrespοnding variables, we get:

R2 = y, D = cοnstant, t = x, m = slοpe, b = cοnstant

Sο, we have:

R2 = 4Dt

y = mx + b

Equating the twο equatiοns, we get:

y = 4Dx + 0 (since b = 0)

Cοmparing this with the trendline equatiοn y = mx + b, we can see that:

m = 4D

Therefοre, we can sοlve fοr 'D' as:

D = m/4

Answer tο Questiοn 12:

Given the trendline equatiοn y = 1.24x + 5.63, we can see that the slοpe 'm' is 1.24.

Using the fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:

D = 1.24/4 = 0.31

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Answer:

The mean would decrease.

Step-by-step explanation:

If the mean score of 24 students is 77.

The total score of 24 students = 24 x 77 = 1848

If the outlier is removed, the mean would become

New total score / number of students = (1848 - 89) / (24 - 1)

1759/23 = 76.5

It can be seen that the mean decreased.

Answer:

The mean would decrease.

Step-by-step explanation:

i took the test

Answer:

y= 7

Step-by-step explanation:

3y+7=28

subtract 7 from both sides

3y=21

divide each side by 3

y/3=21/3

y=7

Answer:

y=7

Step-by-step explanation:

3y+7=28

Move the constant to the right

3y=28-7

Calculate

3y=21

divide both sides to get y=7

Answer:

The y-intercept y = -9

Step-by-step explanation:

Given the function

\(f\left(x\right)\:=\:\left(x+1\right)\left(x-9\right)\left(x-1\right)^2\)

Determining the y-intercept of the function

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

so substitute x = 0 in the function

\(y\:=\:\left(x+1\right)\left(x-9\right)\left(x-1\right)^2\)

\(y\:=\:\left(0+1\right)\left(0-9\right)\left(0-1\right)^2\)

\(y=1\cdot \left(-9\right)\left(0-1\right)^2\)

\(y=1\cdot \left(-9\right)\cdot \:1\)

\(y=-1\cdot \:9\cdot \:1\)

\(y=-9\)

Therefore, the y-intercept y = -9