Write the statements “If you take away 6 from 6 time a number, you get 60”in the form of equations:.

To prove that 1^k + 2^k + 3^k + ... + n^k is O(n^(k+1)), we need to find a constant c and a positive integer N such that for all n ≥ N:

1^k + 2^k + 3^k + ... + n^k ≤ c * n^(k+1)

We can start by using the inequality (n/2)^k ≤ 1^k + 2^k + ... + n^k ≤ n^k to obtain an upper bound on the sum.

Using this inequality, we get:

(n/2)^k * n ≤ 1^k + 2^k + ... + n^k ≤ n^k * n

Multiplying through by n, we get:

(n/2)^k * n^2 ≤ 1^k + 2^k + ... + n^k ≤ n^(k+1) * n

Simplifying and rearranging, we get:

n^(k+1)/2^k ≤ 1^k + 2^k + ... + n^k ≤ n^(k+1)

Therefore, we can take c = 2^(k+1) and N = 1 to complete the proof:

For all n ≥ N = 1,

1^k + 2^k + ... + n^k ≤ n^(k+1) ≤ c * n^(k+1)

1^k + 2^k + ... + n^k is O(n^(k+1)) for k, n ∈ ℕ and k, n ≥ 1.

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Answer:

d = 14

43.96/3.14 = 14

hope that helps

Answer:

The diameter of the pizza should be 14.

Answer:28

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

The area of a sector of a circle is given by:

\(A = \frac{\alpha }{360} * \pi r^2\)

where α = central angle of sector in degrees

r = radius of circle.

The radius of the circle is 15 cm and the area of the sector is 235.62 cm^2. Therefore:

\(235.62 = \frac{\alpha }{360} * \pi * 15^2\\\\84823.2 = 706.86 * \alpha \\\\=> \alpha = 84823.2 / 706.86\\\\\alpha = 120^o\)

The central angle of the sector is 120°

Answer:

An exponential function is a function of the form

f(x)=bx

where b≠1 is a positive real number. The domain of an exponential function is (−∞,∞) and the range is (0,∞).

Solve the equation: 52x−3=752x−3=7.

Since we can’t easily rewrite both sides as exponentials with the same base, we’ll use logarithms instead. Above we said that logb(x)=ylogb⁡(x)=y means that by=xby=x. That statement means that each exponential equation has an equivalent logarithmic form and vice-versa. We’ll convert to a logarithmic equation and solve from there.

52x−3log

⎛⎝⎜

⎞⎠⎟=7=2x−352x−3=7log5

⁡(7

)=2x−3

From here, we can solve for xx directly.

2xx=log5(7)+3=log5(7)+32

A logarithmic function is a function defined as follows

logb(x)=ymeans thatby=xlogb⁡(x)=ymeans thatby=x

where b≠1b≠1 is a positive real number. The domain of a logarithmic function is (0,∞)(0,∞) and the range is (−∞,∞)(−∞,∞).

Solve the equation:

log3(2x+1)=1−log3(x+2).log3⁡(2x+1)=1−log3⁡(x+2).

With more than one logarithm, we’ll typically try to use the properties of logarithms to combine them into a single term.

log3(2x+1)log3(2x+1)+log3(x+2)log3((2x+1)(x+2))log3(2x2+5x+2)2x2+5x+22x2+5x−1=1−log3(x+2)=1=1=1=3=0log3⁡(2x+1)=1−log3⁡(x+2)log3⁡(2x+1)+log3⁡(x+2)=1log3⁡((2x+1)(x+2))=1log3⁡(2x2+5x+2)=12x2+5x+2=32x2+5x−1=0

Let’s use quadratic formula to solve this.

x=−5±52−4⋅2⋅−1−−−−−−−−−−−√2⋅2=−5±

−−−−−−−−⎷4.x=−5±52−4⋅2⋅−12⋅2=−5±33

4.

What happens if we try to plug x=

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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Answer: 232.05 meters

Answer:

line a and b are perpendicular as well as c and b

i think if not then none of them are because its hard to tell since they are sideways

Step-by-step explanation:

Answer:

Frame 1 to Frame 2:

Translation (x,y) to (x,-y)

Frame 2 to Frame 3:

Rotation R₉₀

Frame 3 to Frame 4:

Translation (x,-y) to (x,y)

Step-by-step explanation:

I know this very well :)

Answer:

425 ml.

Step-by-step explanation:

into ratio units of (5+3), you can find out how many times 8 goes into 680. Multiply by 5.

If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.

Then the perimeter of the preimage, the original triangle, before its

dilation will be

Let c be the perimeter of the original triangle.

Then we have

\(\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67\)

Then the perimeter of the original triangle is 66.67 units.

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Answer:

não sei nam mano foi mal ai

vei kskksksksk

Step-by-step explanation:

Answer:

Step-by-step explanation:

7: Area=77km^2

8: Not sure I think Area=77cm^2

9: Area=56m^2

10: Area=43.51km^2

Im not too sure of this problem but I hope this helps

Explaination:

Put a dot where all 4 lines meet (the + in the center). Go down one cube from there, then go right two (put a dot at the place you stop on). Now, go back to the center of the graph. Go up one, and then left two (make another dot here at the place yo ended on). Then, make a straight line that touches the two points nicely, and going straight through the center. Put arrows at each end of the line. I hope this helped!

The total number of possible trains that can be formed by connecting 3, 4, or 5 passenger cars chosen from the available 7 cars is 35 + 35 + 21 = 91

To determine the number of possible trains that can be formed, we need to consider the number of ways we can select 3, 4, or 5 passenger cars from the available 7 cars.

To calculate this, we can use the concept of combinations. The number of combinations of selecting k items from a set of n items is given by the binomial coefficient, denoted as C(n, k), which can be calculated using the formula:

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

For selecting 3 passenger cars from 7, the number of combinations is:

C(7, 3) = 7! / (3!(7-3)!) = 7! / (3!4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35

For selecting 4 passenger cars from 7, the number of combinations is:

C(7, 4) = 7! / (4!(7-4)!) = 7! / (4!3!) = (7 * 6 * 5 * 4) / (4 * 3 * 2 * 1) = 35

For selecting 5 passenger cars from 7, the number of combinations is:

C(7, 5) = 7! / (5!(7-5)!) = 7! / (5!2!) = (7 * 6) / (2 * 1) = 21

Therefore, the total number of possible trains that can be formed by connecting 3, 4, or 5 passenger cars chosen from the available 7 cars is:

35 + 35 + 21 = 91

Hence, there are 91 possible trains that could be formed.

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The standard deviation of f$ ar{x},f$ is usually called the "sample standard deviation".

This is a commonly used statistical measure that represents the amount of variation or dispersion within a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The sample standard deviation is often used to compare the variability of different sets of data and to determine the significance of differences between them. Financial contracts known as derivatives are those entered into by two or more parties and whose value is derived from an underlying asset,

collection of assets, or benchmark. A derivative may be traded over-the-counter or on an exchange. Derivative prices are based on changes in the underlying asset.

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\(\tt Step-by-step~explanation:\)

\(\tt Solve~for~y:\)

To solve for y, we have to move all of the terms that do not equal to y on one side, and let y be on the other side alone. Do this by subtracting 3x on both sides to cancel it out from the left side and bring it to the right.

\(\tt 3x-3x+y=-5-3x\\y=-5-3x\\y=-3x-5\)

\(\tt Solve~for~x:\)

To solve for x, we will do the same thing we did to solve for y: move all the terms that do not equal to x to one side, and leave x on another side of the equation. We can do this by first subtracting y from both sides.

\(\tt3x+y-y=-5-y\\3x=-y-5\)

Then, we divide all terms by 3 to isolate the x.

\(\tt \frac{3x}{3}=x\\\\ \frac{-y}{3}=\frac{-y}{3} \\\\\frac{-5}{3}=\frac{-5}{3}\)

\(\tt x=-\frac{y}{3} -\frac{5}{3}\)

\(\lare\boxed{\tt Our~final~answer:~y=-3x=5,~x=-\frac{y}{3}-\frac{5}{3} }\)

Definitions:

A number, x, is even if it satisfies: x = 2n for some integer n

A number, x, is odd if it satisfies: x = 2k+1 for some integer k

Rewriting the Question:

In this case the question is asking if there is a number, x, that is has the following property:

x = 2n for some integer n AND x = 2k+1 for some integer k

Proof:

We can set these two equations equal:

2n = x = 2k + 1

2n = 2k + 1

2n - 2k = 1

2(n - k) = 1

Let number y = n - k. Note that since n and k are integers, n-k (and therefore, y) must also be an integer.

2y = 1

You can see on the left side (2y) that this becomes the definition of an even number! So the left side is an even number and the right side is 1. Since we know by definition that 1 is not an even number and k must be an integer (not 0.5), this equation becomes false.

As a result, there are NO numbers that can be both even AND odd.

For a continuous random variable x, the probability of x taking on a specific value a is zero. This is due to the infinite number of possible values that x can take on within its range.

In the case of a continuous random variable, the probability density function (PDF) describes the likelihood of x taking on different values. Unlike discrete random variables, which can only take on specific values with non-zero probabilities, a continuous random variable can take on an infinite number of values within a given range. Therefore, the probability of x being equal to any specific value, such as a, is infinitesimally small, or mathematically speaking, it is equal to zero.

To understand this concept, consider a simple example of a continuous random variable like the height of individuals in a population. The height can take on any value within a certain range, such as between 150 cm and 200 cm. The probability of an individual having exactly a height of, say, 175 cm is extremely low, as there are infinitely many possible heights between 150 cm and 200 cm.

Instead, the probability is associated with ranges or intervals of values. For example, the probability of an individual's height being between 170 cm and 180 cm might be nonzero and can be calculated using integration over that interval. However, the probability of having an exact height of 175 cm, as a single point on the continuous scale, is zero.

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Answer:

One

Step-by-step explanation:

It is given that,

y = 3x-5 ....(1)

y = -x+4 .....(2)

We can solve the above equations using substitution method. Put the value of y from equation (1) to equation (2) such that,

\(3x-5 = -x+4\\\\3x+x = 5+4\\\\4x = 9\\\\x=\dfrac{9}{4}\)

Put the value of x in equation (1) we get :

\(y = 3x-5\\\\y = 3\times \dfrac{9}{4}-5\\\\y=\dfrac{7}{4}\)

It means that the value of x is \(\dfrac{9}{4}\) and the value of y is \(\dfrac{7}{4}\). Hence, the given equations has only one solution.

Answer:

1

Step-by-step explanation:

Answer:

It travels for 2 hours, then stops for 1 hour, and finally travels again for 5 hours.

Step-by-step explanation:

Answer:

It travels for 3 hours, then stops for 1 hour, and finally travels again for 1 hour.

Step-by-step explanation:

Sorry I'm late

(I got it right on my FLVS test)

Answer:

42/6

Each color blocks have 6 each, and they're 7 groups of them. Simple.

The value of g is g = w² - 14w + 49, according to the question.

What do you mean by formula?

A truth or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more values. When you are aware of the value of one quantity, you can use the formula to determine the value of the other. It facilitates speedy question resolution. Formulas are used in algebra, geometry, and other subjects to speed up and simplify the process of arriving at the result.

According to the given question,

We have :

w = 7 - √g

Firstly isolate the g,

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides,,

w (-7) = -√g + 7 (-7)

w - 7 = -√g

Now, multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g

-1w + 7 = √g

To get rid of the square root, you must square both sides,

Note: -1w is the same as -w.

Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²

g = (-w + 7)²

g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or                                            g = (-w + 7)²    )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²

(-w)(7) = -7w

(7)(-w) = -7w

(7)(7) = 49

g = w² - 7w - 7w + 49

Then, simplify (combine all like terms):

g =w² - 7w - 7w + 49

g = w² - 14w + 49

Therefore, the value of g = w² - 14w + 49 .

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The inequality that show how  many of each bike model must be sold so the

company avoids losing money is 75x + 90y ≥ $1350

Let x represent the number of model A bikes produced and y represent the number of model B bikes produced.

Since A local bicycle shop makes $75 on each  Model A bike and $90 on each Model B bike, hence:

Revenue = 75x + 90y

The overhead cost is $1350, hence to make profit:

Revenue ≥ cost

75x + 90y ≥ $1350

The inequality that show how  many of each bike model must be sold so the

company avoids losing money is 75x + 90y ≥ $1350

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Solving for D & C

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

(3c + d) + (-d) = 60 + (-d)

3c + d - d = 60 - d

3c= -d + 60

3c/3 =-d+60/3

c= -d+60/3

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

(3c+d)+(-3c)=60+(-3c)

d = -3c + 60

Answer:

Step-by-step explanation:

no of days                                                   no of men

30                                                                         20

24                                                                             20

30/24=x/20

24 x=30*20

24x=600

x=600/24

x=25

therefore  5 more men are needed to complete the work in 24 days                

Answer:

Not a solution.

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

y = -2x + 5

Solution (-4, 15)

Step 2: Check

Here we see that 15 is NOT equal to 13. Therefore, it is NOT a solution to the equation.