Give an algorithm to calculate the sum of first n numbers. For example, if n = 5, then the ouput should be 1 + 2 + 3 + 4 + 5 = 15. Give three solutions for this problem. The first solution with a complexity O(1), the second solution with a complexity O(n), and the third solution with a complexity O(n2).
Question 2: [6 Marks]
Give an algorithm to calculate the sum of first n numbers. For example, if n = 5, then the ouput should be 1 + 2 + 3 + 4 + 5 = 15. Give three solutions for this problem. The first solution with a complexity O(1), the second solution with a complexity O(n), and the third solution with a complexity O(n²).
Solution 1:
Solution 2:

Answer:

17.52%

Step-by-step explanation:

65.35/11.45 = 0.1752

.1752 * 100

= 17.52

The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².

To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:

Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.

So, the integral for the area of the region is given by:

A = ∫a b [x₂(y) - x₁(y)] dy

Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10

So,

A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy

=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy

=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2

=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]

=> A = 174/3

Hence, the area of the region enclosed by the curves is 174/3 units².

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If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid

What is Function?

A function is a relationship between a number of inputs and outputs. A function is, to put it simply, an association between inputs where each input is linked to exactly one output. For each function, a domain, codomain, or range exists.

The values that are specified inside a function when the function is called are referred to as a "argument." However, the parameters are the variables that are defined when the function is declared.

true statement : all dogs have hair

true statement : clifford is a dog.

true statement : clifford has hair

Conclusion is true

If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid. Deductive Argument based on logic ie reasoning out to get a valid inference.

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Answer:

256 miles

Step-by-step explanation:

Divide 640 into 5 = 128

128 is 1/5 of the distance

128 x 2 = because she has driven 2/5 of the distance already.

128x2= 256 miles

:)

Answer:

no i do think so that dose not make sensens

in slope-intercept form, is y = (-2/3)x - 25/3. This equation represents a line that passes through the point (-5, -5) and is parallel to the line 2x + 3y + 6 = 0.

To find an equation of a line that is parallel to another line, we can use the fact that parallel lines have the same slope. Given the line 2x + 3y + 6 = 0, we need to find a line that has the same slope and passes through the point (-5, -5).

Here are the steps to find the equation of the line:

Step 1: Determine the slope of the given line:

Convert the given line to slope-intercept form (y = mx + b), where m represents the slope.

Rearrange the equation 2x + 3y + 6 = 0 to isolate y.

Subtract 2x and divide by 3: y = (-2/3)x - 2.

The slope of the given line is -2/3.

Step 2: Use the slope to find the equation of the parallel line:

Since the parallel line has the same slope, we know that the slope of the parallel line is also -2/3.

We can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Substitute the given point (-5, -5) and the slope -2/3 into the equation: y - (-5) = (-2/3)(x - (-5)).

Simplify the equation: y + 5 = (-2/3)(x + 5).

Step 3: Convert the equation to slope-intercept form:

Expand the right side of the equation: y + 5 = (-2/3)x - 10/3.

Rearrange the equation to isolate y: y = (-2/3)x - 25/3.

This is the equation of the line in slope-intercept form.

The final answer, in slope-intercept form, is y = (-2/3)x - 25/3. This equation represents a line that passes through the point (-5, -5) and is parallel to the line 2x + 3y + 6 = 0.

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Step-by-step explanation:

a 360/9 = 40

b 2/9 × 360 = 80

c similarly 160

d 400

Answer:

i think d and a. u welcome

Answer:

A

Step-by-step explanation:

The six main criteria to define normality and abnormality include statistical infrequency, personal distress, others' distress, unexpected behavior, highly consistent/inconsistent behavior, and maladaptiveness/disability.

1. Abnormality as statistical infrequency: This criterion defines abnormality based on behaviors or characteristics that deviate significantly from the statistical norm.

2. Abnormality as personal distress: This criterion focuses on the individual's subjective experience of distress or discomfort. It considers behaviors or experiences that cause significant emotional or psychological distress to the person as abnormal.

For instance, someone experiencing intense anxiety or depression may be considered abnormal based on personal distress.

3. Abnormality as others' distress: This criterion takes into account the impact of behavior on others. It considers behaviors that cause distress, harm, or disruption to others as abnormal.

For example, someone engaging in violent or aggressive behavior that harms others may be considered abnormal based on the distress caused to others.

4. Abnormality as unexpected behavior: This criterion defines abnormality based on behaviors that are considered atypical or unexpected in a given context or situation.

For instance, if someone starts laughing uncontrollably during a sad event, their behavior may be considered abnormal due to its unexpected nature.

5. Abnormality as highly consistent/inconsistent behavior: This criterion involves comparing an individual's behavior to both their own typical behavior and the behavior of others. Consistent or inconsistent patterns of behavior may be considered abnormal.

For example, if a person consistently engages in risky and impulsive behavior, it may be seen as abnormal compared to their own usually cautious behavior or the behavior of others in similar situations.

6. It considers behaviors that are maladaptive, causing difficulties in personal, social, or occupational areas. For instance, someone experiencing severe social anxiety that prevents them from forming relationships or attending school or work may be considered abnormal due to the disability it causes.

The medical model and classification systems used in physical illnesses have both value and limitations when applied to psychological disorders. They provide a structured framework for understanding and diagnosing psychological disorders, allowing for standardized assessment and treatment. However, they can oversimplify the complexity of psychological experiences and may lead to overpathologization or stigmatization.

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The equation that says the area of the picture itself is 800 square inches is option C: (40 - 2x)(32 - 2x) = 800.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The length of the bigger rectangle is = 32 inches

The width of the bigger rectangle is = 40 inches

The distance between bigger and smaller rectangle is x inches.

In terms of bigger rectangle -

The length of smaller rectangle = 32 - (x + x)

The length of smaller rectangle = (32 - 2x) inches

The width of the smaller rectangle = 40 - (x + x)

The width of the smaller rectangle = (40 - 2x) inches

The area of the smaller rectangle is 800 in².

The formula for the area of rectangle is -

Area = length × width

800 = (32 - 2x)(40 - 2x)

Therefore, the equation is obtained as 800 = (32 - 2x)(40 - 2x).

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ABCD can be square if the distance between all four points is the same.

A square is a two-dimensional closed shape with four equal sides and four corners. The opposite sides of the square are parallel to each other. A square is also a rectangle with equal length and width. A square is an equilateral quadrilateral with all four equal sides and all four equal angles. Square angles are right angles or 90 degrees. Also, the diagonals of the square are equal and bisect at 90 degrees. A square is just a quadrilateral with four equal sides. There are many rectangular objects around us.

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Answer:

The answer is 4/31

Step-by-step explanation:

Total=4+9+7+11=31

Probability =4/31

The value of x when y =4 is 2

An inverse proportion is represented as:

k = yx

Where

k represents the constant of proportion

When y = 2, x = 4.

So, we have:

k =2 * 4

k = 8

Substitute k = 8 in k = yx

So, we have:

yx = 8

When y = 4, we have:

4x = 8

Divide by 4

x = 2

Hence, the value of x when y =4 is 2

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a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

To calculate the amount you will repay and the annual interest rate charged by the loan company, we can follow these steps:

Step 1: Calculate the number of $500 increments for the loan amount:

Number of $500 increments = loan amount / $500

= $1,693 / $500

≈ 3.386

Since we can't have a fraction of an increment, we round up to 4.

Step 2: Calculate the daily payment:

Daily payment = 25 © * Number of $500 increments

= 25 © * 4

= $100

Step 3: Calculate the total repayment amount:

Total repayment amount = Daily payment * number of days

= $100 * 120

= $12,000

Step 4: Calculate the annual interest rate:

Annual interest rate = (Total repayment amount - Loan amount) / Loan amount * (360 / Number of days)

= ($12,000 - $1,693) / $1,693 * (360 / 120)

Now, let's perform the calculations:

Amount you repay ≈ $12,000

Annual interest rate ≈ (($12,000 - $1,693) / $1,693) * (360 / 120)

Calculating the annual interest rate:

Annual interest rate ≈ (($10,307) / $1,693) * 3

Rounding to four decimal places:

Annual interest rate ≈ (6.0905) * 3

≈ 18.2715

Therefore,

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

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Answer:

medium, extra large

Step-by-step explanation:

BRAINLIEST PLEASE

Answer:

1.25 kg

Step-by-step explanation:

1/4 = 0.25

0.25 of 5

0.25 × 5 = 1.25

The z-value of -2.88 would support the alternative hypothesis that the population mean is less than 0 (μ < 0).

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Answer:

True

Step-by-step explanation:

Consciousness means a state of mind in which one is aware of the surrounding and himself. The one who is aware of his mind, thoughts, and the environment near him is called a conscious person. In consciousness a person is fully aware of his desires, wishes and surrounding circumstances. Consciousness is more about thought, feelings, neuroscience psychology, cognitive development. If one needs to be civilized he must be aware of the disciplines and thought process he is living in. It is an exclusive part of civilizations as your mental health defines your social health.The altered state of consciousness is that person starts being uncivilized by consuming alcohol and drugs. We can say so that consciousness appears to be an exclusive feature of organisms that develop civilization.

For example, a boss scolding an employ also makes the employ angry but the employ politely accepts his mistake and apologize for the same in order to act in a civilized manner. So, in order to be civilized the person must act wisely with people present in his surrounding.

As a result, we can conclude that the statement: consciousness appears to be an exclusive feature of organisms that develop civilizations, is true.

Answer:

FALSE

Step-by-step explanation:

Answer:

Thinking Process

(i) Firstly, determine the factors of quadratic polynomial by splitting middle term.

(ii) The two different values of zeroes put in bioquadratic polynomial.

(iii) In both the case if remainder is zero, then bioquadratic polynomial is divisible by

quadratic polynomial.

Answer:

2x⁴ - 5x³ + 2x² - x + 2=

2x²(x²-3x+2) +x³-2x² -x +2=

2x²(x²-3x+2) + x(x²-3x+2) +x² -3x +2=

(x²-3x+2)(2x²+x+1)

since x²-3x+2 is the factor of the given polynomial, we can state the polynomial is divisible by x²-3x+2

-------------

note: x²+3x+2 is not the factor of the given polynomial

The specific weight of mercury is 133kN/m3.

The specific gravity of mercury is 13.6.The specific gravity of a substance is the ratio of its density to the density of water at 4°C (39.2°F), which is defined as 1 gram per milliliter (g/mL).

As a result, Specific gravity of substance = Density of substance/Density of water at 4°C

What is the specific weight? The specific weight, also known as the unit weight, of a substance is its weight per unit volume. The specific weight is represented by the symbol γ and is expressed in units of force per unit volume, such as newtons per cubic metre (N/m3) or pounds per cubic foot (lb/ft3).

What is the formula to find specific weight?The equation is given as W = γ V, where W is the weight, γ is the specific weight, and V is the volume. Therefore, the formula for specific weight is given as γ = W/V.

What is the specific weight of mercury? We can use the formula γ = ρ × g to compute the specific weight of mercury. Here's the calculation: Specific gravity of mercury = 13.6ρ of mercury = 13.6 × 1000 kg/m3 = 13,600 kg/m3The specific weight formula is γ = ρ × gγ = 13,600 × 9.81 N/m3γ = 133,416 N/m3γ = 133 kN/m3

Therefore, The specific weight of mercury is 133kN/m3.

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Answer:

---------------------------------------------------

Let the number be N.

If N is divided by 5 the remainder is 3:

Similarly:

We can observe N + 2 is divisible by both 5 and 6, then it can be represented as:

so

The left side is divisible by 3, then q = 3t:

The least m and t would be m = 5 and t = 7.

Then:

Proof:

(a) The points (4, 17), (5, 21), and (-1, -3) are collinear.

(b) The points (3, 16), (5, 22), and (-4, -17) are not collinear.

To determine whether three points are collinear, we can calculate the slopes of the line segments formed by the pairs of points and check if they are equal.

(a) For the points (4, 17), (5, 21), and (-1, -3):

The slope of the line segment between (4, 17) and (5, 21) is (21 - 17) / (5 - 4) = 4.

The slope of the line segment between (5, 21) and (-1, -3) is (-3 - 21) / (-1 - 5) = 4.

Since the slopes are equal, the points are collinear.

(b) For the points (3, 16), (5, 22), and (-4, -17):

The slope of the line segment between (3, 16) and (5, 22) is (22 - 16) / (5 - 3) = 3.

The slope of the line segment between (5, 22) and (-4, -17) is (-17 - 22) / (-4 - 5) = -4.

The slopes are not equal, indicating that the points are not collinear.

By calculating the slopes and comparing them, we can determine whether the given points lie on the same line (are collinear) or not.

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The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.

a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.

b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.

c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.

By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.

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x = 0.5

or

x = 6

just factorize it

If the explicit formula is in the form of Formula 2, we can consider p to be (35 + √(1213))^n and c to be (35 - √(1213))^n.

To find the explicit formula for the given recurrence relation, we need to solve the characteristic equation associated with the recurrence relation and determine the form of the explicit formula.

The given recurrence relation is:

an = 70n-1 - 12an-2

To find the characteristic equation, we assume the solution of the form an = r^n and substitute it into the recurrence relation:

r^n = 70(r^(n-1)) - 12(r^(n-2))

Dividing both sides by r^(n-2), we get:

r^2 = 70r - 12

This is the characteristic equation. We can rearrange it to:

r^2 - 70r + 12 = 0

To solve this quadratic equation, we can use the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 1, b = -70, and c = 12. Plugging in these values, we get:

r = (70 ± √(70^2 - 4*1*12)) / (2*1)

r = (70 ± √(4900 - 48)) / 2

r = (70 ± √(4852)) / 2

r = (70 ± √(4 * 1213)) / 2

r = (70 ± 2√(1213)) / 2

r = 35 ± √(1213)

So the roots of the characteristic equation are r1 = 35 + √(1213) and r2 = 35 - √(1213).

Now, we consider the explicit formula in the form of Formula 2: an = px^n + cy^n, where T and y are the roots of the characteristic equation.

Since the roots of the characteristic equation are r1 = 35 + √(1213) and r2 = 35 - √(1213), we have:

an = p(35 + √(1213))^n + c(35 - √(1213))^n

Note that the coefficients p and c depend on the initial conditions a1 = 17 and az = 59. We would need to use these initial conditions to determine the values of p and c.

Therefore, if the explicit formula is in the form of Formula 2, we can consider p to be (35 + √(1213))^n and c to be (35 - √(1213))^n.

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Answer:

To solve the inequality 7x - 1 <= -50, we'll start by isolating x on one side of the inequality.

Add 1 to both sides: 7x <= -49

Divide both sides by 7: x <= -7

So the solution to the inequality is x <= -7.

This means that x can be any value less than or equal to -7. For example, -7, -8, -9, -10, etc. It is also possible to express this as an interval notation, which is (-∞, -7].

To find the inverse Laplace transform of the function h(s) = as * b * (s - α)^2 / β^2, you can use the inverse Laplace transform formula and properties. Here's the result:
Inverse Laplace Transform{ h(s) } = L^(-1){ as * b * (s - α)^2 / β^2 }

The inverse Laplace transform of this function is a time-domain function represented as h(t). Keep in mind that the inverse Laplace transform is a unique process that transforms a function from the frequency (s) domain back to the time (t) domain. Unfortunately, without more information about the specific values of a, b, α, and β, I cannot provide a more precise answer.

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