Let an = 5+1+1. Prove that an = O(1). 6.7.15.

Answer:

  d - 2 < -1

Step-by-step explanation:

Replace the words with corresponding math symbols.

  d minus 2 is less than -1

  d  - 2  < -1

Answer:

75.609

Step-by-step explanation:

75 would be before the decimal, since it's a whole number.

609/1000 would be 0.609

609/1000 =  .609

75 + 0.609 =  75.609

So, '75 609/1000 as a decimal' would be 75.609.

Answer:

75 .609

Step-by-step explanation:

75 is the whole number

609/1000 as a decimal is .609

75 .609

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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The point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the points at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j, we need to find the gradient vector of the function and equate it to the given direction vector.

The gradient vector of the function f(x, y) is given by:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

Taking partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x - 2

∂f/∂y = 2y - 6

Setting the gradient vector equal to the given direction vector i + j:

[2x - 2, 2y - 6] = [1, 1]

Equating the corresponding components, we have:

2x - 2 = 1

2y - 6 = 1

Solving these equations, we get:

2x = 3  =>  x = 3/2

2y = 7  =>  y = 7/2

Therefore, the point at which the direction of fastest change of the function f(x, y) = x² + y² - 2x - 6y is in the direction of vector i + j is (3/2, 7/2).

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the number is 3.

Have a great day!!

Brainliest??<3

Answer:

3 is missing from the diamond.

Step-by-step explanation:

The pattern shown is that the bottom three numbers, when added together, equal the top number. 4+4+2 =10. 7+2+3=12. 2+8+5=15. 3+2+?=8. So, 3+2=5 and 8-5=3. The missing number is 3.

Answer:

Step-by-step explanation:

when x = 5

x² + 8

= (5)² + 8

= 25 + 8

= 33

Answer:

33

Step-by-step explanation:

Plug the 5 in the x so it would be 5^2 + 8

The Analyst can use COALESCE function to eliminate the null values from the results.

The SQL Coalesce functions is used to handle NULL values. During the expression evaluation process the NULL values are replaced with the user-defined value. It  returns the first non-NULL value from a series of expressions.

The SQL Coalesce function evaluates the arguments in order and always returns first non-null value from the defined argument list.

Few Properties of COALESCE Function

SYNTAX -

COALESCE ( expression [ ,...n ] )  

Hence, the analyst can use COALESCE function to eliminate the null values from the results.

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Answer:

\(\huge\boxed{Answer\hookleftarrow}\)

Given,

Length of the rectangle (l) = 6

Width of the rectangle (w) = 5

Perimeter of the rectangle (p) = ?

\(p = 2(l + w) \\ p = 2(6 + 5) \\p = 2(11) \\ p = 2 \times 11 \\ p = 22 \: \: units\)

⎆ The perimeter of the rectangle (p) is 22 units.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

The difference between the largest and the smallest of these three numbers is 95.

in mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Let the common multiple of ratio be x.

then, according to given condition, the ratio of three numbers is 7 : 3 : 2 and these three numbers have a sum of 228. i.e.

7x + 3 x + 2x = 228

12x = 228

x = 19

so, the largest number is

= 7x

= 7 × 19

= 133

and the smallest number is

= 2x

= 2 × 19

= 38

so, the Difference between the largest and  the smallest number is

= 133 - 38

= 95

Therefore, the difference between the largest and the smallest of these three numbers is 95.

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The value of CPI will be 178.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Now,

Since, In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Hence, The value of CPI will be;

CPI = 118.10 × 100 / 66.35

      = 11810 / 66.35

       = 178

Thus, The value of CPI will be 178.

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Answer:

x=24/13

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

times both sides by 8

x = 24/13

24/13 = 1.8

The particle crosses the origin at a time of 2.346 seconds.

To find the time at which the particle crosses the origin, we need to determine the value of t when x(t) is equal to zero, since the particle will be at the origin when its position is zero.

Using the given position function x(t) = 5.42 m - 2.31 m/s t, we can set x(t) equal to zero and solve for t:

x(t) = 0

5.42 m - 2.31 m/s t = 0

Subtracting 5.42 m from both sides, we get:

-2.31 m/s t = -5.42 m

Dividing both sides by -2.31 m/s, we get:

t = 5.42 m / 2.31 m/s

t = 2.346 s

Therefore, the particle crosses the origin at a time of 2.346 seconds.

In summary, we find the time at which the particle crosses the origin by setting the position function equal to zero and solving for the corresponding value of t. This method works for any one-dimensional motion along a straight line.

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Answer:

   ∠e = 32°

   ∠d = 69°

   ∠f = 79°

Step-by-step explanation:

       Angle e and 32° are vertical angles, so this means that ∠e = 32° because vertical angles are congruent.

       Next, a straight line is equal to 180°, and angle e is equal to 32°, so we can write the following equation to solve for angle f:

69° + e + f = 180° ➜ 69° + 32° + f = 180° ➜ 101° + f = 180° ➜ f = 79°

       Lastly, angle d and 69° are also vertical angles, so this means that ∠d = 69° because vertical angles are congruent.

The distance between the two planes after 4 hours is approximately 150 km.

to find out how far apart the planes are after 4 hours, we can use the concept of vectors.

Let's start by finding the positions of the two planes after 4 hours.

The first plane flies at a speed of 110 km/h in a direction of 280°. To find its position after 4 hours, we can use the formula: distance = speed × time. So, the distance traveled by the first plane is 110 km/h × 4 hours = 440 km.

To determine the position of the first plane, we need to convert the direction (280°) into components. The x-component is given by: cos(280°) × distance = cos(280°) × 440 km. The y-component is given by: sin(280°) × distance = sin(280°) × 440 km.

Similarly, for the second plane, which flies at a speed of 250 km/h in a direction of 200°, the distance traveled after 4 hours is 250 km/h × 4 hours = 1000 km. To determine its position, we need to convert the direction (200°) into components. The x-component is given by: cos(200°) × distance = cos(200°) × 1000 km. The y-component is given by: sin(200°) × distance = sin(200°) × 1000 km.

Now, let's calculate the x and y components for both planes:

For the first plane:
x-component = cos(280°) × 440 km
y-component = sin(280°) × 440 km

For the second plane:
x-component = cos(200°) × 1000 km
y-component = sin(200°) × 1000 km

the distance between the two planes, we can use the distance formula, which is given by: distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the positions of the first and second planes respectively.

Now, substitute the values we calculated into the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((cos(200°) × 1000 km - cos(280°) × 440 km)^2 + (sin(200°) × 1000 km - sin(280°) × 440 km)^2)

After evaluating the above expression, the distance between the two planes after 4 hours is approximately 150 km.

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Answer:

x component / y component

Answer:

This is the formula

Step-by-step explanation:

Y2-Y1

----------

X2-X2

Answers to Question 6: m∠1 = 92, m∠2 = 88

    The sum of a linear pair's angles is 180°, so we will set up an equation to solve.

(x + 67) + (3x + 13) = 180

4x + 80 = 180

4x = 100

x = 25

    -

(x + 67) ➜ (25 + 67) ➜ 92

(3x + 13) ➜ (3(25) + 13) ➜ 88

Answer to Question 7: m∠2 = 56

    Vertical angles are congruent, or equal, so we can set up an equation to solve.

(5x + 16) = (4x + 24)

x = 8

    -

(5x + 16) ➜ (5(8) + 16) ➜ 56

(4x + 24) ➜ (4(8) + 24) ➜ 56

Answer:

10 fish left

7 fish alive

Step-by-step explanation:

Answer:

It is 7

Step-by-step explanation:

If you have 10 fish and 3 drown so you go down 3 fish. 9,8,7

C(76.1) represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

The function C(F) = (5/9)(F - 32) is used to convert temperatures from degrees Fahrenheit to degrees Celsius. In this case, the input of the function is 76.1, which represents the temperature in degrees Fahrenheit. By substituting this value into the function, we can calculate the corresponding temperature in degrees Celsius.

To convert 76.1 degrees Fahrenheit to degrees Celsius, we plug it into the function: C(76.1) = (5/9)(76.1 - 32). By performing the necessary calculations, we can find the value of C(76.1), which represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. Therefore, the correct answer is the first option: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.


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The value of the line integral ∫cf⋅dr is (-2 + y) * sqrt(3).

To evaluate the line integral ∫cf⋅dr using Stokes' theorem, we first need to find the curl of the vector field f. The curl of f is given by ∇ × f, where ∇ is the del operator.

Calculating the curl of f:

\(∇ × f = (∂/∂y)(xz) - (∂/∂z)(2y) + (∂/∂z)(xy) - (∂/∂x)(xy) + (∂/∂x)(2y) - (∂/∂y)(2y)\)

\(= x - 2 - x + 2y - y\\= -2 + y\).

Now, let's find the area of triangle C using the vertices given. The triangle with vertices (2,0,0), (0,2,0), and (0,0,2) forms an equilateral triangle in the xy-plane with side length 2.

The area of an equilateral triangle is given by\((sqrt(3)/4) * (side length)^2\), so the area of this triangle is \((sqrt(3)/4) * (2)^2 = sqrt(3)\).

Since we have the curl of f as -2 + y and the area of the triangle as sqrt(3), we can now evaluate the line integral using Stokes' theorem:

∫cf⋅dr = ∬S (∇ × f) ⋅ dS

= ∬S (-2 + y) ⋅ dS

= (-2 + y) ∬S dS

= (-2 + y) * sqrt(3).

Therefore, the value of the line integral ∫cf⋅dr is (-2 + y) * sqrt(3).

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Answer:

98,100,A

Plz mark me brainliest.

Step-by-step explanation:

Answer:

1170

Step-by-step explanation:

45 times 26

Answer:

1170

45x26=1170

Answer:

23 (rounded) (You can't overflow a fish take Or what would be the point of the tank.)

Step-by-step explanation:

The unrounded answer is 23.376623376623376623376623376623.

The probability shows sample mean differ from the true mean by less than 5.91 liters is equal to 0.9864.

Standard deviation = 24 liters

sample size = 100

The standard error of the mean is,

Standard error = σ / √(n)

where σ is the population standard deviation, n is the sample size.

Substituting the given values, we get,

Standard error

= 24 / √(100)

= 2.4

Probability that the sample mean would differ from the true mean by less than 5.91 liters,  standardize the difference using the standard error,

z = (X - μ) / (SE)

where X is the sample mean,

μ is the true population mean,

and SE is the standard error of the mean.

Substituting the given values, we get,

z = (5.91) / 2.4

  = 2.4625

Probability corresponding to this z-score,

Use a standard normal distribution attached table

The probability of the sample mean differing from the true mean by less than 5.91 liters is the probability of getting a z-score between -2.4625 and 2.4625.

This can be found by taking the difference between the cumulative probabilities corresponding to these two z-scores.

Using a standard normal distribution attached table ,

Probability of getting a z-score less than -2.4625 is 0.0068,

Probability of getting a z-score less than 2.4625 is 0.9932.

Probability of getting a z-score between -2.4625 and 2.4625 is  

0.9932 - 0.0068 = 0.9864 (Rounding to four decimal places)

Therefore, the probability that the sample mean would differ from the true mean by less than 5.91 liters is 0.9864.

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Answer:

z = 103

x = 20

Step-by-step explanation:

See photo for steps. You got this… don’t give up. I believe you can do this. Comment if u need me to explain more :)

The solution of the equation in the interval [0, 2π] is π or 180.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given the equation;

Sinx = cosx + 1

Then Square both sides of the equation;

Sin²x = (cos x + 1)²

Sin²x = cos²x + 2cos x + 1

Since Sin²x = 1 - cos²x

1 - cos²x = cos²x + 2cos x + 1

Collect like terms;

1-1-cos²x-cos²x-2cos x  = 0

-2cos²x-2cos x = 0

-2cos²x = 2cos x

-cosx = 1

cos x = -1

x = 180 degrees

Hence, the value of x = π

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Answer:

8 1/4x

Step-by-step explanation:

I'm good at math.

Answer: 3

Step-by-step explanation:

6x + 4 = 9x - 5

6x - 9x = -5 - 4

-3x = -9

x = 3

\(\\ \sf\longmapsto 6x+4=9x-5\)

\(\\ \sf\longmapsto 9x-6x=4+5\)

\(\\ \sf\longmapsto 3x=9\)

\(\\ \sf\longmapsto x=\dfrac{9}{3}\)

\(\\ \sf\longmapsto x=3\)

Answer:

option c

Step-by-step explanation:

hope it helps you

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