Seating 8 students in 4 seats in the front row of the school auditorium.

Answer:

\(a_{n}\) = 2n - 3

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

given a₁ = - 1 and a₅ = 7 , then

a₁ + 4d = 7 , that is

- 1 + 4d = 7 ( add 1 to both sides )

4d = 8 ( divide both sides by 4 )

d = 2

then

\(a_{n}\) = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

\(a_{n}\) = 2n - 3

Answer: A = \(-\frac{13}{18} - \frac{9}{-14}\)

                  =>(x7) \(-\frac{13}{18} + \frac{9}{14}\)  (x9)

                  => \(\frac{-91+81}{126}\)

                  => \(\frac{-10}{126}\) (÷2)

                  => \(-\frac{5}{63}\)

B = \(-\frac{17}{28} + \frac{15}{36}\) (÷3)

   =>(x3) \(-\frac{17}{28} + \frac{5}{12}\) (x7)

   => \(-\frac{51}{84} + \frac{35}{84}\)

   => \(\frac{-51+35}{84}\)

   => \(\frac{-16}{84}\) (÷4)

   => \(-\frac{4}{21}\)

I have been working 1004 days at the job as a student

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the days from 08/21/2019 to 08/21/2022, we get:

Days 1 = (08/21/2022 - 08/21/2019) * (365 days/1 year)

Days 1 = 3 years * (365 days/1 year)

Days 1 = 1095 days

Calculating the days from 05/21/2019 to 08/21/2019, we get:

Days 2 = (08/21/2019 - 05/21/2019) * (30 days / 1 month)

Days 2 = 3 month * (30 days / 1 month)

Days 2 = 90 days

Calculating the days from 05/20/2019 to 05/21/2019, we get:

Days 3 = 05/21/2019 - 05/20/2019

Days 3 = 1 day

Calculating the total days from 08/21/2019 to 05/20/2022, we get:

Total days = Days 1 - days 2 - days 3

Total days = 1095 days - 90 days - 1 day

Total days = 1004 days

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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When every length in the cylinder is decreased by 60%, the volume of the cylinder decreases by approximately 85.6%.

Let's assume the original diameter and height of the cylinder are both represented by "d". The original volume of the cylinder can be calculated as V = π * (d/2)^2 * d.

When every length in the cylinder is decreased by 60%, the new diameter and height become 0.4d (40% of the original value). The new volume of the cylinder can be calculated as V' = π * (0.4d/2)^2 * (0.4d).

To find the percent decrease in volume, we can calculate (V - V') / V * 100.

Substituting the values, we have:

Percent decrease in volume = [(V - V') / V] * 100

Percent decrease in volume = [(π * (d/2)^2 * d - π * (0.4d/2)^2 * (0.4d)) / (π * (d/2)^2 * d)] * 100

Simplifying further, we get:

Percent decrease in volume = [(1 - 0.4^3) / 1] * 100

Evaluating the expression, we find:

Percent decrease in volume ≈ 85.6%

Therefore, the volume of the cylinder decreases by approximately 85.6% when every length is decreased by 60%.

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Answer: 601

              200

Step-by-step explanation: when you reduce 3.005 it is 601/200 and it is in its simpilist form

Answer:

3\frac{1}{200}

Step-by-step explanation:

Answer:

y = (x+5)(x+2)(4x-3)

Step-by-step explanation:

This is almost correct but the problem is that the signs should be flipped...

Why? If we solve for x-5=0 the answer we would get is 5, but the graph shows -5 as its zero so that doesn't match

The revised version would be the opposite signs

y = (x+5)(x+2)(4x-3)

The standard deviation of the critical path is 6.

To calculate the standard deviation of the critical path, we need to use the concept of variance and consider the activities on the critical path.

The variance of a project or critical path is the sum of the variances of the activities on that path.

Since the variances are given as the squares of the standard deviations, we can square the standard deviations of each activity and sum them to find the variance of the critical path. Finally, we take the square root of the variance to obtain the standard deviation.

Given the standard deviations of the activities on the critical path:

Activity 1: Standard deviation = 1 day

Activity 2: Standard deviation = 3 days

Activity 3: Standard deviation = 1 day

Activity 4: Standard deviation = 4 days

Activity 5: Standard deviation = 3 days

Calculating the variance of the critical path:

Variance = (1^2) + (3^2) + (1^2) + (4^2) + (3^2) = 1 + 9 + 1 + 16 + 9 = 36

Taking the square root of the variance, we find the standard deviation of the critical path:

Standard deviation = √(36) = 6

Therefore, the standard deviation of the critical path is 6.

The correct choice is A. 6.

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9514 1404 393

Answer:

  x = 0

Step-by-step explanation:

You can eliminate parentheses and subtract 50.

  5(2x +10) = 50

  10x +50 = 50 . . . . use the distributive property

  10x = 0 . . . . . . . . . subtract 50 from both sides

  x = 0 . . . . . . . . . . . divide by 10

__

Check

  5(2·0 +10) = 50

  5(10) = 50 . . . . true

The big-O estimate for the number of operations in this segment of the algorithm is O(n), where n represents the input size.

To give a big-O estimate for the number of operations used in a segment of an algorithm, we need more specific information about the segment and its complexity. Big-O notation provides an upper bound on the growth rate of the algorithm as the input size increases.

If the segment involves a loop that iterates n times, and each iteration performs a constant number of operations (additions or multiplications), then the complexity would be O(n). This means that the number of operations increases linearly with the input size.

However, without further details about the specific segment or the algorithm's overall structure, it is challenging to provide a more accurate estimation. The complexity analysis requires examining the code's control flow and considering factors such as nested loops or recursion.

In summary, the big-O estimate for the number of operations in this segment of the algorithm is O(n), where n represents the input size.

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Answer:

(5,7)



x = 5

y = 7

The area of the largest rectangle is 46.47 square root.

Consider a semi-circle with a rectangle ABCD inscribed in it.

Let, O = centre of the semi-circle

A and B lies on the base of the semi-circle

OA = OB = x

D and C lie on the semi-circle

BC = AD = y

AB = CD = 2x

By Pythagorean theorem,

CB² + OB² = OC²

⇒ y² + x² = (6)²

⇒ y² = 36 - x²

⇒ y = √(36 - x²)

Now, area of rectangle in terms of x,

Area, A = 2x × y

= 2x × √(36 - x²)

Differentiating,

A' = 2 × √(36 - x²) - 2x²/(36 - x²)

When x = 0, y = 6 and when x = 6, y = 0, area = 0.

It implies that area is maximum when the value of x lies between 0 and 6.

This will occur where A’ = 0.

⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0

⇒ 2 × √(36 - x²) = 2x²/(36 - x²)

On simplification, we get,

⇒ 2 × (36 - x²) = 2x²

⇒ 36 - x² = x²

⇒ 2x² = 36

⇒ x² = 36/2

⇒ x = √36/2

Now, y = √(36 - x²) becomes

⇒ y = √(36 - (√36/2)²)

⇒ y = √(36 - 36/2)

⇒ y = √(96 - 36)/2

⇒ y = √60/2

Maximum area = 2xy

= 2(√36/2)(√60/2)

= 46.47

Therefore, the area of the largest rectangle = 46.47 square units.

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Answer:

Jason runs faster then his friend.

Step-by-step explanation:

Jason's speed is represented by the equation y = 7x because he runs 7 miles in an hour. If his friend's speed is represented by y = 6x, then his friend runs a total of 6 miles in an hour.

Answer:

B.

Step-by-step explanation:

Just do it

Answer:

B. 2 círculos, 1 rectángulo

Answer:

10

Step-by-step explanation:

We cannot use the Pythagorean Theorem here because we only have one side length. However, we can use the fact that \(\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}\)

I decided to make the corner with the 60° as ∠A, the corner with the 30° as ∠B, and the corner with the right angle as ∠C. While then making side a as the unmarked side, side b as the side with 5, and the hypotenuse p as side c.

Since we do not need to solve for a in this equation to solve for p, we can simply use the sides and numbers we are given.

Manipulating two of our equations, preferably the equations with the variables b and c, we can get \(\frac{b}{sin(B)}=\frac{c}{sin(C)}\) and solving for c, which is p in this case, will give us \(c=\frac{bsin(C)}{sin(B)}\)

Plugging in the numbers we have gives us \(c=\frac{5sin(90)}{sin(30)}\) = 10 mi

Answer:B

count 2 and ~1/4 back and you get b

If two angles of triangle ∆DEF are fixed, the third angle is determined since the sum of the interior angles of a triangle is always 180 degrees.

Therefore, the shape of ∆DEF is fixed and cannot be changed without altering the angles.

Comparing ∆DEF to ∆ABC, we can say that they may have different shapes. If the third angle of ∆DEF is different from the corresponding angle of ∆ABC, then the triangles will not be congruent and will have different shapes. However, if the third angle of ∆DEF is the same as the corresponding angle of ∆ABC, then the triangles will be similar and have the same shape, but they may be scaled or rotated versions of each other.

In summary, if two angles of ∆DEF are fixed, we cannot determine the shape of ∆DEF relative to ∆ABC without additional information such as the lengths of the sides.

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The cost C (in dollars) for ordering and storing x units is C = 4x + 100,000 x. We can calculate it in the following manner.

The minimum cost of the order size can be obtained by differentiating the given expression of the cost C (in dollars) with respect to x and equating it to 0.

So, we have C(x) = 4x + 100,000/x

Differentiating both sides with respect to x, we get: C′(x) = 4 - 100,000/x²C′(x) = 0 for minimum C(x)∴ 4 - 100,000/x² = 0

Thus, we have x² = 100,000/4= 25,000

Order size x = ± 25,000

Taking positive value for the order size, we get:x = 25000

Therefore, the order size that will produce a minimum cost is 25,000. Answer: 25,000.
To find the minimum cost, we need to minimize the function C(x) = 4x + 100,000/x. To do this, we will find the critical points by taking the derivative of the function and setting it to zero.

dC/dx = 4 - 100,000/x^2

Now, set dC/dx = 0:

4 - 100,000/x^2 = 0

Add 100,000/x^2 to both sides:

4 = 100,000/x^2

Now, multiply both sides by x^2:

4x^2 = 100,000

Divide both sides by 4:

x^2 = 25,000

Take the square root of both sides:

x = sqrt(25,000)

x ≈ 158.11

Since we need to round to the nearest whole number, the order size that will produce a minimum cost is 158 units.

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Answer:

The values of x that solves the equation, which in this case is 2 + i and 2 - i.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

The answer is y=3/4+5 (C)

Step-by-step explanation:

You have to find two exact points on the line then calculate the rise/run (3/4). 3/4 is the slope. Now all that's left is to find the y- intercept (where the line crosses the y-axis) which is 5. Which leaves you with answer choice C.

The equation of the line of best fit that Waylan drew is y=3/4 x+5. Therefore, the correct answer is option C.

From the given graph, the coordinate points are (4, 8) and (16, 17).

Here, slope (m) = (y₂-y₁)/(x₂-x₁)

= (17-8)/(16-4)

= 9/12

= 3/4

Substitute m=3/4 and (x, y)=(4, 8) in y=mx+c, we get

8=3/4 ×4+c

8=3+c

c=5

Substitute m=3/4 and c=5 in y=mx+c, we get

y=3/4 x+5

Therefore, the correct answer is option C.

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The probability of rolling a 3 more than 31 times when rolling a die 126 times using the normal approximation is approximately 0.006 (or 0.6% when expressed as a percentage).

To find the probability of rolling a 3 more than 31 times when rolling a die 126 times, we can use the normal approximation to the binomial distribution. The normal approximation can be applied when the number of trials is large (126 in this case) and the probability of success (rolling a 3) is not extremely small or extremely large.

First, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the formula:

μ = n * p

σ = √(n * p * (1 - p))

In this case, the number of trials (n) is 126, and the probability of rolling a 3 (p) is 1/6 since there is one favorable outcome (rolling a 3) out of six possible outcomes (rolling a die).

μ = 126 * (1/6) ≈ 21

σ = √(126 * (1/6) * (5/6)) ≈ 4.18

Next, we can use the normal distribution to approximate the probability. We need to find the z-score corresponding to 31.5 (31 + 0.5, considering continuity correction). The z-score is calculated using the formula:

z = (x - μ) / σ

z = (31.5 - 21) / 4.18 ≈ 2.51

We can then consult a standard normal distribution table or use statistical software to find the probability associated with a z-score of 2.51. The probability can be obtained by subtracting the cumulative probability corresponding to 2.51 from 0.5 (to account for one tail).

Based on the calculation, the probability of rolling a 3 more than 31 times when rolling a die 126 times using the normal approximation is approximately 0.006 (or 0.6% when expressed as a percentage).

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Answer:

A,B

Step-by-step explanation:

As per the Pythagoras theorem, the ratio of the short side to the long side of this rectangle is (√5 - 1)/ 2

In math Pythagoras theorem is defined as the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

Here we have given that the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal.

And we need to find is the square of the ratio of the short side to the long side of this rectangle

While we looking into the given question we have identified that the short side of the rectangle be a and let the long side of the rectangle be b.

Therefore, the diagonal, according to the Pythagorean Theorem, is

√(a²+b²)

Now we can write the equation:

a / b = b /√ a² + b²

Then we have to find the square of the ratio of a to b.

Let us consider the answer, be k.

When we squaring the above equation,

a²/ b² = b² / a² + b² = k

When we solve this one then we get the value of  k = 1.

Now we have to Multiply each side of the equation by k,

=> k² = 1 - k.

And then adding each side by k,

k² + k − 1 = 0.

Now, we have to Solving for k using the Quadratic Formula,

= > k = -1 ± √[1² − 4(1)(−1)] / 2

=> k = -1±√5/2

As we know that the ratio of lengths and diagonals of a rectangle cannot be negative.

Therefore, the resulting value is √5 - 1/2

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The geometric average of -10%, 20%, and 40% is approximately -20.2%.

To find the geometric average of a set of numbers, you need to multiply them together and then take the nth root, where n is the number of values.

In this case, we have three values: -10%, 20%, and 40%.

Step 1: Convert the percentages to decimal form by dividing by 100.

-10% becomes -0.10

20% becomes 0.20

40% becomes 0.40

Step 2: Multiply the decimal values together.

-0.10 * 0.20 * 0.40 = -0.008

Step 3: Take the cube root (since we have three values) of the result.

∛(-0.008) ≈ -0.202

Step 4: Convert the result back to a percentage by multiplying by 100.

-0.202 * 100 ≈ -20.2%

Therefore, the geometric average of -10%, 20%, and 40% is approximately -20.2%.

None of the given options (11.2%, 14.8%, 20.3%, and 21.4%) matches the calculated value.

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Answer: \(527\ ft^2\)

Step-by-step explanation:

Given

Cost of paint is \(\$12.34\ \text{per gallon}\)

Dimension of room is \(11\times 13\times 8\ ft^3\)

There are five side of wall to be painted leaving only the floor

Area is given by

\(\Rightarrow 2[8\times 11+8\times 13]+11\times 13\\\Rightarrow 2\times 8[24]+143\\\Rightarrow 384+143\\\Rightarrow 527\ ft^2\)

Answer:

they do know true the callender

Answer:

49.50

Step-by-step explanation:

All you do is turn the fraction into a decimal so:

1/2 = .50

so the answer would be 49.50

Ace Carlos