WILL MARK AS BRAINLEIST!! ASAP PLEASE!!

The velocity function is
v(t)= -t² + 5t - 4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,6].

displacement =
distance traveled =

Area = 0.5 * |PQ x PR| = 0.5 * sqrt(12475) ≈ 55.93 square units.

To find the area of the parallelogram determined by these points, we need to find the cross product of the vectors formed by two adjacent sides of the parallelogram. Let's choose vectors PQ and PS:

Vector PQ = (-7 - 7, 2 - (-5), -2 - 5) = (-14, 7, -7)

Vector PS = (-4 - 7, 8 - (-5), -4 - 5) = (-11, 13, -9)

The cross product of these two vectors is:

(-7)(-9) - (-7)(13), (-2)(-9) - (-14)(-9), (-2)(13) - (-14)(-11)

= (-14, 126, -30)

The magnitude of this vector gives us the area of the parallelogram:

|(-14, 126, -30)| = sqrt(14^2 + 126^2 + (-30)^2) = sqrt(17308) ≈ 131.6

Therefore, the area of the parallelogram determined by the given points is approximately 131.6 square units.
To find the area of the parallelogram determined by the points P(7, -5, 5), Q(-7, 2, -2), R(10, 1, 3), and S(-4, 8, -4), we can use the cross product of the vectors PQ and PR.

First, let's find the vectors PQ and PR:
PQ = Q - P = (-7-7, 2-(-5), -2-5) = (-14, 7, -7)
PR = R - P = (10-7, 1-(-5), 3-5) = (3, 6, -2)

Next, find the cross product of PQ and PR:
PQ x PR = (7*(-7) - (-7)*6, (-14)*(-2) - 3*(-7), (-14)*6 - 7*3) = (-49+42, 28+21, -84-21) = (-7, 49, -105)

Now, calculate the magnitude of the cross product:
|PQ x PR| = sqrt((-7)^2 + 49^2 + (-105)^2) = sqrt(49 + 2401 + 11025) = sqrt(12475)

The area of the parallelogram is half the magnitude of the cross product:
Area = 0.5 * |PQ x PR| = 0.5 * sqrt(12475) ≈ 55.93 square units.

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I'm sorry, but I cannot provide an answer without more information about the value of "C3". Can you please provide that information?
To evaluate the given expression 34^C3, we need to find the number of combinations of choosing 3 items from a set of 34 items. This can be calculated using the formula:

C(n, r) = n! / (r!(n-r)!)

Here, n = 34 and r = 3. Plugging the values into the formula, we get:

34^C3 = C(34, 3) = 34! / (3!(34-3)!)

= 34! / (3! * 31!)

= (34 * 33 * 32) / (3 * 2 * 1)

= 5984

So, 34^C3 = 5984.

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The algebraic laws for the given expressions are Identity Law and Zero Law

The algebraic laws for the given expressions are:

A.1 = A: (Identity Law)

This law states that any variable or expression multiplied by 1 remains unchanged. In this case, A multiplied by 1 is still A.

A.0 = 0 (Zero Law)

This law states that any variable or expression multiplied by 0 equals 0. In this case, A multiplied by 0 equals 0.

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Answer: coordinates of the y-intercept is (0, -21)

Step-by-step explanation:

I'm assuming that you are asking for the coordinates of the y-intercept of the function

f(x)=(x-7)(x+3).

Well the y-intercept occurs when x=0, so plugging this value into f(x) yields f(0)=(-7)(3)=-21.

The answer is 0.64 or 64%. The Pearson correlation (r) measures the strength and direction of the relationship between two variables, in this case, X and Y.

To determine the proportion of variance in Y that is predicted by the relationship with X, you need to square the correlation coefficient (r²). In this case, r = 0.80, so r² = 0.80 * 0.80 = 0.64 or 64%. Therefore, 64% of the variance in the Y scores is predicted by the relationship with X. To calculate the amount of variance in Y scores predicted by the relationship with X, we need to square the correlation coefficient (r) which gives us the coefficient of determination (r²).
r² = 0.80² = 0.64
This means that 64% of the variance in Y scores is predicted by the relationship with X.

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Answer:

The answer is 0.64 or 64%. The Pearson correlation (r) measures the strength and direction of the relationship between two variables, in this case, X and Y.

To determine the proportion of variance in Y that is predicted by the relationship with X, you need to square the correlation coefficient (r²). In this case, r = 0.80, so r² = 0.80 * 0.80 = 0.64 or 64%. Therefore, 64% of the variance in the Y scores is predicted by the relationship with X. To calculate the amount of variance in Y scores predicted by the relationship with X, we need to square the correlation coefficient (r) which gives us the coefficient of determination (r²).

r² = 0.80² = 0.64

This means that 64% of the variance in Y scores is predicted by the relationship with X.

Step-by-step explanation:

Using Chebyshev's theorem, at least 96% of the data lies within five standard deviations of the mean.

Let's use Chebyshev's theorem for standard deviation to calculate the percentage of data that lie within five standard deviations of the mean.

Chebyshev's theorem states that at least [tex](1 - \frac{1}{k^2})[/tex] of the data will be within k standard deviations of the mean, where k is the number of standard deviations from the mean. In this case, k = 5.

Calculate the proportion using Chebyshev's theorem formula.
[tex](1 - \frac{1}{k^2}) = (1 - \frac{1}{5^2}) = (1 - \frac{1}{25})[/tex]

Simplify the expression to get the following:
(1 - 1/25) = 24/25

Convert the fraction to a percentage to get:
(24/25) × 100% = 96%

Using Chebyshev's theorem, at least 96% of the data lies within five standard deviations of the mean.

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Answer:

Step-by-step explanation:

The question is a little hard to interpret. I hope this is what you wanted.

Let the small number be [tex]x[/tex], so the greater number will be [tex](x+1)[/tex].

the smaller of two consecutive numbers is doubled and added to the greater gives:

                            [tex]2x+(x+1)=3x+1[/tex]

The total will be [tex]3x+1[/tex] if the smaller number is [tex]x[/tex].

Required true statements are f(6)=66, f(3)=10, f(5)=33.

What is recursive formula?

A recursive formula is a way of defining a sequence or function in terms of previous terms or values. In other words, the formula uses the output of the previous step to generate the input for the next step.

For example, the Fibonacci sequence is defined recursively as follows:

F(0) = 0

F(1) = 1

F(n) = F(n-1) + F(n-2) (for n ≥ 2)

Here, the value of each term in the sequence is defined in terms of the two previous terms. The first two terms (F(0) and F(1)) are defined directly, while subsequent terms are defined recursively by adding the two previous terms.

Another example of a recursive formula is the factorial function:

n! = n × (n-1)! (for n ≥ 1)

Here, the value of n! is defined in terms of (n-1)!, which is defined in turn in terms of (n-2)!, and so on until the base case of 0! is reached

We can use the recursive formula to calculate the values of the sequence:

f(1) = 3

f(2) = 2f(1) - 1 = 23 - 1 = 5

f(3) = 2f(2) - 1 = 25 - 1 = 9

f(4) = 2f(3) - 1 = 29 - 1 = 17

f(5) = 2f(4) - 1 = 217 - 1 = 33

f(6) = 2f(5) - 1 = 233 - 1 = 65

Therefore, statements 2 (f(4)=18) and 5 (f(2)=5) are false, and statements 1 (f(6)=66), 3 (f(3)=10), and 4 (f(5)=33) are true.

So the correct options are:

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The US government recommends low dose x-ray or dual-energy x-ray absorptiometry (DEXA) screening for women aged 65 years and older to check for osteoporosis. The suggested screening interval for low dose x-ray or DEXA for women aged 65 years and older is every two years.

The US government recommends low dose x-ray or dual-energy x-ray absorptiometry (DEXA) screening for women aged 65 years and older to check for osteoporosis. Osteoporosis is a condition that weakens bones, making them more likely to break. The suggested screening interval for low dose x-ray or DEXA is every two years. However, this may vary based on individual risk factors such as family history of osteoporosis, use of certain medications, and history of fractures.
Women who are at higher risk of developing osteoporosis may need more frequent screenings. For example, women with a history of fractures or those who have taken certain medications for a prolonged period may need more frequent screenings. It is important to discuss individual risk factors with a healthcare provider to determine the appropriate screening interval.
It is also important to note that while low dose x-ray or DEXA is recommended for women aged 65 years and older, women who are younger and have risk factors for osteoporosis may also need screening. Some of these risk factors include a family history of osteoporosis, low body weight, smoking, and certain medical conditions such as rheumatoid arthritis.
In summary, the suggested screening interval for low dose x-ray or DEXA for women aged 65 years and older is every two years. However, the screening interval may vary based on individual risk factors. It is important to discuss individual risk factors with a healthcare provider to determine the appropriate screening interval.

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The perimeter of the rhombus is 52 units.

A rhombus is a quadrilateral with equal sides in Euclidean plane geometry. A quadrilateral with equal-length sides is also referred to as a "equilateral triangle". A parallelogram has a different shape called a rhombus. A rhombus has equal and parallel opposing sides and angles. A rhombus has equal-length sides and a right angle that divides its diagonal in half.

Let's denote the diagonals of the rhombus as d₁ and d₂, and let's denote its side length as s. The area of the rhombus is given by the formula:

A = (d₁ x d₂) / 2

Since the area is given as 120 square units and one diagonal is 10 units, we can substitute these values into the formula and solve for the other diagonal:

120 = (10 x d₂) / 2

240 = 10 x d₂

d₂ = 24 units

Now we can use the Pythagorean theorem to find the length of the sides of the rhombus:

s = √[(d₁/2)² + (d₂/2)²]

s = √[(10/2)² + (24/2)²]

s = √[25 + 144]

s = 13 units

Since a rhombus has four congruent sides, the perimeter of the rhombus is:

P = 4s = 4 x 13 = 52 units

Therefore, the perimeter of the rhombus is 52 units.

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The statement with limit of function that [tex]\lim_{ x→ 2} f(x) = 5[/tex], implies or states that the limit of the function f at x=5 is two is a false statement.

Limit is a constant number that a function approaches. If the values of x approach some value, a , as the values of approach from both sides but can't necessarily equals to x= a , then we say the limit of f(x) as approaches L is equal to L . It is denoted as [tex]\lim_{ x→ a} f(x) = L[/tex]. We have a notation, [tex]\lim_{ x→ 2} f(x) = 5[/tex], also states that the limit of the function f at x=5 is 2. It is not correct formated statement and it does not implies that the limit of the function f at x=5 is 2. The correct notation is [tex]\lim_{ x→ 5} f(x) = 2[/tex], which states that the limit of the function f at x=5 is equals to 2. Hence, the provide notation of limits is a false one.

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Drawing every single square may not be necessary, as you can use the pattern of the previous figures to predict the placement of the squares in the final figure. This can save time and effort, while still achieving the desired outcome.

To answer your question, if you were to combine the first 100 figures, you would end up with a much larger figure consisting of 100 squares in each row and column, resulting in a total of 10,000 squares. However, you do not need to draw every square to sketch the final figure.
To sketch the final figure, you would start by drawing a square grid of 100 squares in each row and column, similar to the previous figures. Then, you would need to fill in the squares based on the pattern of the previous figures.
Assuming you drew each square in the previous figures, combining the first 100 figures would result in drawing a total of 100 x 100 x 100 squares, which equals 1,000,000 squares. This is because each figure consists of 100 squares, and there are 100 figures being combined.
However, drawing every single square may not be necessary, as you can use the pattern of the previous figures to predict the placement of the squares in the final figure. This can save time and effort, while still achieving the desired outcome.

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The Laplace transform of f(t) = te^(6t) is:

L{f(t)} = ∫[0, ∞] te^(6t) e^(-st) dt

Using integration by parts, we can write:

L{f(t)} = [t * (-1/6) * e^(6t) * e^(-st)]∣[0,∞] + ∫[0, ∞] (1/6) * e^(6t) * e^(-st) dt

Simplifying, we get:

L{f(t)} = [-t/6 + (1/6) * 1/(s-6)]∣[0,∞]

Since the limit as t approaches infinity of t/6 is infinity, the first term in the expression above does not converge. Therefore, we have:

L{f(t)} = (1/6) * 1/(s-6)    (for s > 6)

Given f(t) = te^(6t), we can use the definition of the Laplace transform to find L{f(t)}:

L{f(t)} = ∫(from 0 to ∞) f(t) * e^(-st) dt

In our case, f(t) = te^(6t), so the integral becomes:

L{f(t)} = ∫(from 0 to ∞) te^(6t) * e^(-st) dt

To solve this integral, we can combine the exponentials:

L{f(t)} = ∫(from 0 to ∞) te^(t(6-s)) dt

Now, we can use integration by parts to solve the integral:

Let u = t and dv = e^(t(6-s)) dt

Then, du = dt and v = ∫e^(t(6-s)) dt = (1/(6-s))e^(t(6-s))

Applying integration by parts:

L{f(t)} = uv |(from 0 to ∞) - ∫(from 0 to ∞) v du

L{f(t)} = (1/(6-s))te^(t(6-s)) |(from 0 to ∞) - (1/(6-s)) ∫(from 0 to ∞) e^(t(6-s)) dt

Now, we evaluate the limits and the integral:

L{f(t)} = (1/(6-s))[0 - (1/(6-s)) ∫(from 0 to ∞) e^(t(6-s)) dt]

The remaining integral is the Laplace transform of e^(t(6-s)), which is:

(1/(s-(6-s))) = (1/(2s-6))

So, L{f(t)} = (1/(6-s))[0 - (1/(2s-6))]

Finally, L{f(t)} = (1/((6-s)(2s-6)))

Thus, the Laplace transform of f(t) = te^(6t) is L{f(t)} = (1/((6-s)(2s-6))).

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4000 kg is equal to 4 metric tonnes or 4.4 short tons.

We need to convert 4000 kg to tonnes.
Identify the units you need to convert:

In this case, you want to convert 4000 kilograms (kg) to tonnes (t).
Determine the conversion factor:

To convert from kilograms to tonnes, you need to know the relationship between the two units.

1 tonne is equal to 1000 kilograms (1 t = 1000 kg).
Apply the conversion factor:

To convert 4000 kg to tonnes, divide the number of kilograms (4000 kg) by the conversion factor (1000 kg/t):
  4000 kg ÷ 1000 kg/t = 4 t
Write the final result:

4000 kg is equal to 4 tonnes.

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The probability that a random z-score will be greater than 1.33 given a standardized normal distribution is approximately 0.0918 or 9.18%.

To find the probability that a random z-score will be greater than 1.33 given a standardized normal distribution, you'll need to use a z-table or a calculator with a built-in z-table function.

1. Identify the given z-score: 1.33.

2. Look up the z-score in a z-table or use a calculator with a built-in z-table function. This will give you the area to the left of the z-score, also known as the cumulative probability.

3. For a z-score of 1.33, the cumulative probability is approximately 0.9082.

4. Since you want to find the probability that a random z-score will be greater than 1.33, you'll need to calculate the area to the right of the z-score.

5. To do this, subtract the cumulative probability from 1: 1 - 0.9082 = 0.0918.

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Answer:

[tex]\huge\boxed{\sf 63}[/tex]

Step-by-step explanation:

[tex]= x^2+10x + 24[/tex]

Put x = 3

= (3)² + 10(3) + 24

= 9 + 30 + 24

= 63

[tex]\rule[225]{225}{2}[/tex]

Answer:

Option D) 63 is the correct answer.

Step-by-step explanation:

where :

[tex] \quad\sf{\dashrightarrow{{x}^{2} + 10x + 24}}[/tex]

Substituting the value of x :

[tex] \quad\sf{\dashrightarrow{{(3)}^{2} + 10 \times 3 + 24}}[/tex]

[tex] \quad\sf{\dashrightarrow{(3 \times 3) + 30 + 24}}[/tex]

[tex] \quad\sf{\dashrightarrow{(9) + 54}}[/tex]

[tex] \quad\sf{\dashrightarrow{9 + 54}}[/tex]

[tex] \quad\sf{\dashrightarrow{63}}[/tex]

[tex]\quad{\star{\underline{\boxed{\sf{\pink{63}}}}}}[/tex]

Hence, the answer is 63.

We have shown that the argument is valid and ¬g, ¬k entails ¬(k ∨ g) using natural deduction.

Here's one possible proof using natural deduction:

Assume k ∨ g

Assume k
The premise ¬k, derive a contradiction: ⊥

Assume g

Derive a contradiction: ⊥

Conclude from above equations, ¬(k ∨ g) by negation introduction

From the premise ¬g and ¬(k ∨ g), conclude ¬(k ∨ g) by modus tollens (¬g → ¬(k ∨ g))

From the premise ¬k and ¬(k ∨ g), conclude ¬(k ∨ g) by modus tollens (¬k → ¬(k ∨ g))

Now, from above, conclude ¬(k ∨ g) by conjunction introduction (¬g ∧ ¬k → ¬(k ∨ g))

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The distribution of sample means (for a specific sample size) consists of all the sample means that could be obtained (for the specific sample size).

This distribution is created by taking multiple random samples from the population and calculating the mean for each sample. The resulting distribution shows the range of possible sample means and how often they are likely to occur. It does not include all the scores contained in the population or in any one particular sample.
The distribution of sample means (for a specific sample size) consists of c. All the sample means that could be obtained (for the specific sample size). This concept is also known as the sampling distribution of the mean, which represents the distribution of all possible sample means for a given sample size from a population.

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The best prediction for the number of times Jeremy will roll a number greater than 444 is 60060060.

Since the die is fair, each number between 1 and 666 is equally likely to show up on any given roll. The probability of rolling a number greater than 444 is:

(666-444)/666 = 222/666 = 1/3

This means that out of every 3 rolls, we expect one to be greater than 444. Therefore, out of 180180180 rolls, we expect:

180180180/3 = 60060060

rolls to be greater than 444. Therefore, the best prediction for the number of times Jeremy will roll a number greater than 444 is 60060060.

Since the die is fair, each number between 1 and 666 is equally likely to show up on any given roll. The probability of rolling a number greater than 444 is:

(666-444)/666 = 222/666 = 1/3

This means that out of every 3 rolls, we expect one to be greater than 444. Therefore, out of 180180180 rolls, we expect:

180180180/3 = 60060060

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The website gets, on average, 24 hits per hour.

To answer this question using a Poisson process, we first need to find the average rate of hits per hour. Given that the website gets 4 hits every 10 minutes, we can calculate the average hits per hour by multiplying the hits per 10 minutes by 6 (since there are six 10-minute intervals in an hour).

So, 4 hits/10 minutes * 6 = 24 hits per hour. The Poisson process allows us to model the number of hits as a random variable with an average rate of 24 hits per hour, making it suitable for predicting the number of hits in different time intervals.

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Answer:

The cylinder shown is sliced vertically through its center. What is the area of the c

The area of the cross-section of the cylinder is 142.5 in.sq.

What does mean by a cross-section of any shape?

 The cross-section is a mathematical depiction of an object's intersection with a plane along its axis. A cross-section is a shape that results from the cutting of a solid (such as a cone, cylinder, or sphere) by a plane.

 For instance, if the base of a cylinder-shaped item is cut by a plane, the resulting cross-section will be a circle. The object has to come into contact with one another. This idea may be used for two-dimensional forms as well as three-dimensional ones, therefore the item need not be in three dimensions.

Given:

The length and radius of a cylinder are 19 inches and 7.5 inches respectively.

Now, the vertical cross-section of a cylinder is a rectangle.

Length = 19 in; Breadth = 7.5 in

Area of cross-section (rectangle) = length * breadth

                                                       = 19 * 7.5  ⇒ 142.5 in.sq

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Answer:

First, we need to calculate the amount that the insurance company will pay for the hospital stay.

On the first two days, the insurance will pay 80% of the expenses, which is:

0.8 x ($360 + $492) = $698.40

On the remaining 4 days, the insurance will pay 100% of the expenses, which is:

4 x $840 x 0.8 = $2688

Therefore, the total amount that the insurance company will pay is:

$200 + $698.40 + $2688 = $3586.40

Now, we can calculate the amount that Melanie will pay. Her total expenses for the hospital stay were:

$360 + $492 + $298 + $980 + $1006 + $781 = $3917

The insurance company paid $3586.40, so Melanie is responsible for paying the difference:

$3917 - $3586.40 = $330.60

Therefore, the insurance company paid $3586.40, and Melanie paid $330.60.

Answer: $330.60.

Step-by-step explanation:

Answer: Y = 5X

Step-by-step explanation:

The given differential equation y'' - 5y' + 6y = 0 can be factored as (D-2)(D-3)y = 0, where D denotes the derivative operator. Hence, the general solution is y = c1*e^(2x) + c2*e^(3x), where c1 and c2 are constants that depend on the initial conditions.

Using the given initial conditions, we can find c1 and c2 as follows:

y(0) = c1 + c2 = 1
y'(0) = 2c1 + 3c2 = 2

Solving this system of equations, we get c1 = -1 and c2 = 2. Therefore, the particular solution that satisfies the given initial conditions is:

y = -e^(2x) + 2*e^(3x)

To find ln(y(1)), we substitute x = 1 in the above expression:

y(1) = -e^2 + 2*e^3

Taking natural logarithm on both sides, we get:

ln(y(1)) = ln(-e^2 + 2*e^3)

Note that this is an exact value, which cannot be simplified further.
To find the solution of the given differential equation y'' - 5y' + 6y = 0 with initial conditions y(0) = 1 and y'(0) = 2, we will first find the complementary function and then apply the initial conditions to determine the constants.

The given equation is a second-order linear homogeneous differential equation with constant coefficients. We will start by finding the characteristic equation:

r^2 - 5r + 6 = 0

This can be factored as:

(r - 2)(r - 3) = 0

This gives us two roots, r1 = 2 and r2 = 3. Now, we can write the general solution for the differential equation as:

y(x) = C1 * e^(2x) + C2 * e^(3x)

Now, let's apply the initial conditions:

1. y(0) = 1:
C1 * e^(2*0) + C2 * e^(3*0) = 1
C1 + C2 = 1

2. y'(0) = 2:
The derivative of y(x) is:
y'(x) = 2C1 * e^(2x) + 3C2 * e^(3x)
y'(0) = 2C1 * e^(2*0) + 3C2 * e^(3*0) = 2
2C1 + 3C2 = 2

Solving this system of linear equations for C1 and C2, we get:
C1 = 1
C2 = 0

So, the particular solution is:
y(x) = e^(2x)

Now we need to find ln(y(1)):
ln(y(1)) = ln(e^(2*1)) = ln(e^2) = 2

So, ln(y(1)) = 2.

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The measure of the angle FNM is ∠FNM = 73°

Here we want to find the measure of the angle FNM, and we know the measures of two angles, these are:

∠GNF = 60°

∠MNL = 47°

You can see that:

∠GNF + ∠FNM + ∠MNL  = ∠GNL

And GNL is a plane angle, so its measure is 180°, then we can write tehe quation:_

60° + ∠FNM + 47° = 180°

We can solve that to get.

∠FNM  = 180° - 60° - 47°

∠FNM = 73°

That is the measure of the angle.

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The index number indicates that the value in period 7 has increased by about 119.83% compared to the value in period 1.

Based on the information provided, we will calculate the simple index number for period 7 (i7) using the given values for y1 and y7.

The simple index number formula is:

i7 = (y7 / y1) × 100

Where y1 represents the value in period 1 (116) and y7 represents the value in period 7 (255).

Plugging in these values, we get: i7 = (255 / 116) × 100 i7 ≈ 219.83

Thus, the simple index number for period 7 (i7) is approximately 219.83.

This index number is a measure that compares the value of y7 to the value of y1, with y1 being the base period.

In this case, the index number indicates that the value in period 7 has increased by about 119.83% compared to the value in period 1.

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The vertices of the rectangle with maximum area are: (1, 0), (-1, 0), (1, 3), and (-1, 3). Let's see how,

Step:1. Recognize that the given curve is y = 6/(1 + x^2).
Step:2. Consider one vertex of the rectangle on the curve as (x, y) = (x, 6/(1 + x^2)).
Step:3. Since one side of the rectangle is on the x-axis, the length of that side will be y = 6/(1 + x^2).
Step:4. The other side of the rectangle will be parallel to the x-axis and have length 2x, since there are two equal halves with the origin as the midpoint.
Step:5. The area of the rectangle, A = length * width = 2x * (6/(1 + x^2)).
Step:6. To find the maximum area, differentiate A with respect to x and set the derivative to 0.
Let's differentiate A(x) = 12x / (1 + x^2):
dA/dx = [12(1 + x^2) - 12x(2x)] / (1 + x^2)^2 = (12 - 12x^2) / (1 + x^2)^2.
Set dA/dx = 0:
(12 - 12x^2) / (1 + x^2)^2 = 0.
Solve for x:
12x^2 = 12.
x^2 = 1.
x = ±1.
Now, find the corresponding y-values using y = 6/(1 + x^2):
For x = 1, y = 6/(1 + 1^2) = 6/2 = 3.
For x = -1, y = 6/(1 + (-1)^2) = 6/2 = 3.
Thus, the vertices of the rectangle with maximum area are: (1, 0), (-1, 0), (1, 3), and (-1, 3).

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Answer:

-4

Step-by-step explanation:

5x + 20 = 0

5x = -20 / : 5

x = -4

The sum of the infinite terms of a G.P. is (aᵣ / (1 - r))

A geometric progression (G.P.) is a sequence where each term is obtained by multiplying the preceding term by a constant ratio. The general term of a G.P. is given by the formula aₙ = aᵣ(r)^(n-1), where aᵣ is the first term and r is the common ratio.

The sum of infinite terms of a G.P. can be calculated using the formula Sₙ = a(1 - rⁿ) / (1 - r), where Sₙ is the sum of the first n terms of the G.P., a is the first term, and r is the common ratio.

As n approaches infinity, rⁿ approaches zero if the value of r is less than one. Hence, we can write the formula for the sum of infinite terms of a G.P. as S = a / (1 - r), provided that the value of r is less than one.

Therefore, the main answer can be written as the sum of the infinite terms of a G.P. is (aᵣ / (1 - r)), where aᵣ is the first term, and r is the common ratio.

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