According to the flood recurrence interval equation, a flood that occurs in 2021, after 149 years of record keeping, and is the third largest ever recorded has a recurrence interval of _______ years.

Answer:

Step-by-step explanation:

By taking the help of the standard deviation, the answer obtained is

n = 719

What is Standard Deviation?

At first it is important to know about Variance.

Variance is the sum of the square of deviation from the mean of the data.

On taking the square root of variance, Standard deviation is obtained.

The formula used for calculating the number of samples required is

\(n=\frac{Z^{2}_{\alpha /2}\times \sigma ^{2}}{e^{2}}\), \(\sigma\) is the standard deviation , e is the error,

Here,

\(\alpha\) = 1 - \(\frac{95}{100}\)

  = 1 - 0.95

  = 0.05

Critical values of Z = \(\pm\)1.96 [ From the table]

Standard deviation (\(\sigma\)) = 9.3

error (e) = $0.68

On putting  the value,

n = \(\frac{1.96^2 \times 9.3^2}{0.68^2}\)

n = 718.5

n = 719

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In greedy method, A locally optimal of solution is generated

Greedy algorithms

Greedy algorithms construct a solution piece by piece, selecting the next portion in such a way that it provides an immediate benefit.

This method never reconsiders earlier decisions. This method is most commonly used to tackle optimization problems. Greedy algorithms employ a problem-solving procedure to progressively build candidate solutions, to approximate the global optimum, by obtaining better and better locally optimal solutions at each stage.

The property states that the globally optimum solution may be determined by first determining the locally optimal solution (Greedy). A Greedy algorithm's decision may be influenced by previous decisions but not by future ones.

Globally Optimal Solution

A globally optimal solution is one where there are no other feasible solutions with better objective function values. A locally optimal solution is one where there are no other feasible solutions in the vicinity with better objective function values.

It makes one Greedy decision after another iteratively, reducing the given problem to a smaller one.

Greedy is an algorithmic paradigm that assembles a solution piece by piece, constantly selecting the next component that provides the greatest evident and immediate advantage.

In greedy method, A locally optimal of solution is generated

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Answer:

$3100 is invested at 9%

$4900 is invested at 11%

Step-by-step explanation:

Let's take "x" be the amount invested at 9%.

(x + 1800) is invested in another account at 11%.

The interest amount earned by the two accounts is $818.

Here we can use the simple interest formula and find the amount invested in each account.

Simple interest (I) = , where P- is the principal , N is the number of years and R is the interest rate.

Simple interest =

0.09x + 0.11(x+1800) = 818

Now we have to simplify and find the value of x .

Use the distributive property and simplify the second term.

0.09x + 0.11x + 198 = 818

0.2x + 198 = 818  

0.2x =818 - 198

0.2x = 620

x = 620/0.2

x = 3100.

So $3100 is invested at 9%

x + 1800 = 3100 + 1800

= $4900

$4900 is invested at 11%

Hope this helped.

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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Answer:

y = -x+8

Step-by-step explanation:

Abbie and Ben would not be able to buy locally-grown corn in Rhode Island until late October.

Amount is an indefinite quantity of something, typically money, that is to be paid or received. It is often used in the context of a purchase, loan, or other financial transaction. Amounts can be expressed as a numerical value, such as a dollar amount, or as a percentage of the total transaction. In accounting, the term "amount" is used to refer to the total amount of money that is owed or received.

Abbie and Ben could not buy locally-grown corn in May or June in Rhode Island because the growing season for corn in Rhode Island runs from late June through late October. This is the typical growing season for corn in the Northeastern United States and is largely dependent on the region's climate. Corn is a warm-season crop, meaning it requires temperatures of at least 50 degrees Fahrenheit for germination and growth. In early spring, most of Rhode Island is still too cold for corn to be planted. This means that the earliest corn grown in Rhode Island is planted in late June, and it is not harvested until late October. Thus, Abbie and Ben would not be able to buy locally-grown corn in Rhode Island until late October.

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Answer: 192

Step-by-step explanation:

Use algebra

x + 3x + x + 3x = 64 (perimeter)

Combine Like Terms

8x = 64

x = 8

8 + 24 + 8 + 24 = 64

24/8 = 3

Answer:

B

Step-by-step explanation:

To apply the next law from the right in the given formula, we first identify the next logical law from the right that can be applied, which is the double negation elimination rule.

We apply this rule to the first term in the formula, (s→¬¬n), which gives us (s→n).

The next law from the right to apply would be the law of double negation again, which simplifies the first term even further by giving us (¬s∨n) instead of (¬s∨¬¬n).

We then apply the implication law to convert the implication in the formula to a disjunction, giving us (¬s∨n)∧(¬(n∨F)∨s).

Finally, we apply De Morgan's law to distribute the negation in the formula, giving us the final answer of (¬s∨n)∧((¬n∧¬F)∨s).

Step-by-step explanation:

Identify the next logical law from the right that can be applied to the given formula. In this case, it is the double negation elimination rule.

Apply the double negation elimination rule to the given formula: (s→¬¬n)∧((n∨F)→s) becomes (s→n)∧((n∨F)→s)

Continue applying relevant logical laws from the right: (s→n)∧((n∨F)→s) becomes (¬s∨n)∧((n∨F)→s)

Apply the implication law to convert the implication in the formula to a disjunction: (¬s∨n)∧((n∨F)→s) becomes (¬s∨n)∧(¬(n∨F)∨s)

Apply De Morgan's law to distribute the negation in the formula: (¬s∨n)∧(¬(n∨F)∨s) becomes (¬s∨n)∧((¬n∧¬F)∨s)

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Answer:

bother = 6 years ; sister = 12 years

Step-by-step explanation:

s = sister

b = brother

s - b =  6

s * b = 4(s+b)

s = b + 6

b(b+6) = 4(b+6 + b)

b² + 6b = 4(2b + 6)

b² + 6b = 8b + 24

b² + 6b - 8b - 24 = 0

b² - 2b - 24 = 0

(b-6)(b+4) = 0

b = 6

b = -4 (impossible because an age can’t be negative)

s = 6 + 6

s = 12

Answer:

1. y = 3/2z

Step-by-step explanation:

1. ,2y-3z + 3z =0 + 3z ,2y=3z, 2y/2 =3z/2=3/2z

Therefore, the due date of the note is August 9 adding the number of days in the note's term to the note's date adding the number of days in the note's term to the note's date.

To determine the due date of the note, we need to add the number of days in the note's term to the note's date.

Given:

Note term: 120 days

Note date: April 9

To find the due date, we add 120 days to April 9.

April has 30 days, so we can calculate the due date as follows:

April 9 + 120 days = April 9 + 4 months = August 9

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Answer:

\(180 - 35 - 72 = 73\)

The equation that represents the total cost is  C(x)=13x +95​. (option d)

The problem tells us that it costs $95 to rent the cafeteria, which is a fixed cost that doesn't change based on the number of people attending. However, the cost per person is $13. So, if we have x number of people attending the banquet, the total cost would be $95 (for the cafeteria rental) plus $13x (for each person attending).

Now, we need to represent this relationship using an equation. An equation is a mathematical statement that shows the relationship between two quantities. In this case, the two quantities are the total cost and the number of people attending the banquet.

Using the third equation, C(x) = 95x + 13, we get:

C(0) = 95(0) + 13 = 13

This makes sense, because if there are 0 people attending, the total cost should just be the rental fee of $95.

Now, let's try the last equation, C(x) = 13x + 95:

C(0) = 13(0) + 95 = 95

This gives us the correct rental fee of $95, but it doesn't take into account the cost per person. This equation takes into account the rental fee of $95 as well as the $13 cost per person attending the banquet.

Hence the correct option is (d).

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The bubble sort algorithm applied to the list of 6, 2, 3, 1, 5, 4 is as follows:

Step 1: 6, 2, 3, 1, 5, 4

Step 2: 2, 6, 3, 1, 5, 4

Step 3: 2, 3, 6, 1, 5, 4

Step 4: 2, 3, 1, 6, 5, 4

Step 5: 2, 3, 1, 5, 6, 4

Step 6: 2, 3, 1, 5, 4, 6

Bubble Sort is an algorithm that consists of repeatedly swapping adjacent elements if they are in wrong order. This algorithm is also known as Sinking Sort.

Bubble Sort works by comparing each element of the list with the adjacent element and swapping them if they are in wrong order. The algorithm continues this process until the list is sorted.

The bubble sort algorithm applied to the list of 6, 2, 3, 1, 5, 4 is as follows:

Step 1: 6, 2, 3, 1, 5, 4

Step 2: 2, 6, 3, 1, 5, 4

Step 3: 2, 3, 6, 1, 5, 4

Step 4: 2, 3, 1, 6, 5, 4

Step 5: 2, 3, 1, 5, 6, 4

Step 6: 2, 3, 1, 5, 4, 6

After the first pass, the largest element will be at the end of the list. After the second pass, the second largest element will be at the end of the list, and so on.

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Answer:

The slope of the line passing through the points (-3,3) and (5,9) is 3/4

3/2 is the second one

1 ) y = - 1 / 3 x + 2

2 ) y = 0x - 7

To find the slope of the line you can use the equation.

m = y2 - y1 / x2 -x1 = tan(Ф)

Answer:

1 ) y = - 1 / 3 x + 2

2 ) y = 0x - 7

Step-by-step explanation:

To find the slope of the line you can use the equation...

m = y2 - y1 / x2 -x1 = tan(Ф)

Hope this helps! :)

The statement: If ∠F is a 60° angle, then cos (F) = sin (F), is never true.

Two of the six trigonometric functions used to connect angles to the sides of a right triangle are sine and cosine. The length of the opposite side of an angle divided by the length of the hypotenuse of a right triangle is known as the sine function. The length of the adjacent side of an angle divided by the length of the hypotenuse of a right triangle is known as the cosine function.

We know that,

If angle F is 60 degrees, then the value of cos F = 1/2 and sin F = sqrt(3)/2.

Therefore, cos F is not equal to sin F and the statement is never true.

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Answer: No

Step-by-step explanation: Because not all lines can have to end ponits some needs to go on forever like infinte and not be stop by the end points Hope this is the answer your looking for :).

Answer:

180

Step-by-step explanation:

the missing angle is 90 because anges in tri add to 180

xo that means that x=90(2)=180

Answer:

For a day VFR flight in a Piper Archer, you would need a fuel reserve of approximately 5 gallons.

Step-by-step explanation:

The amount of fuel reserve that must be carried on a day VFR (Visual Flight Rules) flight, the FAA requires a minimum fuel reserve of 30 minutes at cruising speed for day VFR flights. To calculate the gallons needed for a Piper Archer, follow these steps:

1. Determine the fuel consumption rate of the Piper Archer at cruising speed, which is typically around 10 gallons per hour (GPH).
2. Divide the required fuel reserve minutes (30) by the minutes in an hour (60): 30 / 60 = 0.5 hours.
3. Multiply the fuel consumption rate (10 GPH) by the required fuel reserve time in hours (0.5 hours): 10 * 0.5 = 5 gallons.

Therefore, for a day VFR flight in a Piper Archer, you would need a fuel reserve of approximately 5 gallons.

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Answer:

1000ml

Step-by-step explanation:

4 days she drank ½ of the bottle

so she drank ⅛ l of juice everyday

so

1000ml is the answer

(-9, 2)

Note that the coordinates of the center of a line are given by the formulae:

The center of the line (a, b) = (-4, 2)

The first point on the line (x₁, y₁) = (1, 2)

The other end of the line = (x₂, y₂)

The point also located on the circle W is (-9, 2)

Answer:

For this problem, we need to add to the price of the phone (50 $) the cost of the data usage (which is 0.20 $ per minute).

If he spends on average 200 minutes, we can calculate what that costs by multiplying the number of minutes by the cost of each one: 200 * 0.2 = $40

And we can now add to the $50 the $40: 50 + 40 = $90

Answer:

$40

Step-by-step explanation:

$.20×200=$40

it's pretty simple

Answer:

LCM (k, n) = 10 and HCF(k, n) = 2

Step-by-step explanation:

The given parameters are;

The time after which Keshav takes  a break = k hours

The value of k = The first smallest prime natural number

Therefore, by mathematical definition, k = 2

The time after which Noel takes a break = n hours

The value of n = The fifth smallest composite natural number

The first five composite numbers are given as follows;

4, 6, 8, 9, and 10

Therefore, the fifth smallest composite natural number = 10 = n

The LCM (k, n) = LCM (2, 10) = Least common multiple of 2 and 10 is given as follows;

Dividing by 2, we get;

2/2 = 1,  10/2 = 5

Dividing the result by 5, we get;

5/5 = 1

Multiplying the devisors together gives;

5 × 2 = 10

Therefore, the LCM of 2 and 10 = 10

LCM(2, 10) = LCM (k, n) = 10

The HCF(k, n) = HCF of 2 and 10 = The highest common factor that divides both 2 and 10 is given as follows;

Dividing 2 and 10 by 2 gives;

2/2 = 1 and 10/2 = 5

Therefore, HCF(k, n) = The highest common factor of 2 and 10 = HCF(2, 10) = 2

The five-card hand is dealt at random from a standard 52-card deck. the probability of having exactly 2 kings and the ace of spades given that you have at least one ace is 2.9%.

        To find the probability of having exactly 2 kings and the ace of spades given that you have at least one ace

        When a five-card hand is dealt at random from a standard 52-card deck is as follows:

        There are 52 cards in a standard deck. Therefore, there are 4 Kings and 1 Ace of Spades. The number of ways in which we can select 2 Kings from 4 Kings is:

                             ₄C₂ = \((4 * 3)/(2 * 1)\)

                                    = 6

           The number of ways in which we can select the Ace of Spades from 1 Ace is:

                              ₁C₁ = 1

            The remaining 2 cards are non-Kings and non-Ace of Spades cards. So, there are 44 such cards. The number of ways in which we can select 2 cards from 44 cards is:

                           ₄₄C₂ = \((44 * 43)/(2 * 1)\)

                                   = 946

      Therefore, the total number of ways in which we can select 2 Kings and 1 Ace of Spades and 2 non-Kings and non-Ace of Spades cards is:

                        \(6 * 1 * 946\) = 5676

      There are 4 Aces in a standard deck. The number of ways in which we can select at least one Ace from 4 Aces is:

                 ₄C₁ + ₄C₂ + ₄C₃ + ₄C₄ = 4 + 6 + 4 + 1

                                                    = 15

       Therefore, the probability of having exactly 2 kings and the ace of spades given that you have at least one ace when a five-card hand is dealt at random from a standard 52-card deck is:

P(exactly 2 Kings and the Ace of Spades | at least one Ace) = (Number of ways in which we can select 2 Kings and 1 Ace of Spades and 2 non-Kings and non-Ace of Spades cards) / (Number of ways in which we can select at least one Ace)

                         = 5676/15

                         = 378.4 or 0.029 or 2.9%.

   Therefore, the required probability is 0.029 or 2.9%.

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