A class has 36 students in it and 25% of the students wore hats to school.What fraction of the students wore hats?

Answer:

x=-15

y= 65

Step-by-step explanation:

I explain the answer of the question in the photo

Rewrite the factorial parts of the summand as

[tex]\dfrac{(2n+1)!}{n!(n+2)!} = \dfrac{(2n+1)(2n!)}{(n+2)(n+1)(n!)^2} = \dfrac{2n+1}{(n+2)(n+1)} \dbinom{2n}n[/tex]

where [tex]\binom nk[/tex] is the binomial coefficient, and [tex]\binom{2n}n[/tex] are the so-called central binomial coefficients.

Expand the rational expression into partial fractions:

[tex]\dfrac{2n+1}{(n+2)(n+1)} = \dfrac3{n+2} - \dfrac1{n+1}[/tex]

Pull out a constant factor and collect the exponential terms.

[tex]\dfrac{(-1)^{n+1}}{4^{2n+3}} = -\dfrac1{64} \left(-\dfrac1{16}\right)^n[/tex]

The sum we want is now

[tex]\displaystyle \frac{13}8 - \frac1{64} \sum_{n=0}^\infty \binom{2n}n \left(\frac3{n+2} - \frac1{n+1}\right) \left(-\frac1{16}\right)^n[/tex]

Let f(x) and g(x) be functions with power series expansions

[tex]\displaystyle f(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+1}[/tex]

[tex]\displaystyle g(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+2}[/tex]

and recall the well-known binomial series

[tex]\displaystyle \dfrac1{\sqrt{1-4x}} = \sum_{n=0}^\infty \binom{2n}n x^n[/tex]

which converges for |x| < 1/4.

Integrating both sides yields

[tex]\displaystyle \int \frac{dx}{\sqrt{1-4x}} = \int \sum_{n=0}^\infty \binom{2n}n x^n \, dx[/tex]

[tex]\displaystyle -\frac12 \sqrt{1-4x} = C_1 + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+1}}{n+1}[/tex]

Taking x = 0 on both sides, it follows that C₁ = -1/2. We then see that

[tex]\displaystyle f(x) = \frac{1-\sqrt{1-4x}}{2x}[/tex]

Step back and multiply both sides of the binomial series identity by x, then integrate. This yields

[tex]\displaystyle \int \frac x{\sqrt{1-4x}} \, dx = \int \sum_{n=0}^\infty \binom{2n}n x^{n+1} \, dx[/tex]

[tex]\displaystyle -\frac1{12} \sqrt{1-4x} (1 + 2x) = C_2 + C_1 x + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+2}}{n+2}[/tex]

Taking x = 0 again points to C₂ = -1/12. Hence

[tex]\displaystyle g(x) = \frac{1 - \sqrt{1-4x}(1+2x)}{12x^2}[/tex]

Then the value of the sum we want is

[tex]\displaystyle \frac{13}8 - \frac1{64} \left(3g\left(-\frac1{16}\right) - f\left(\frac1{16}\right)\right) = \frac{1+\sqrt5}2 = \boxed{\phi}[/tex]

where ɸ ≈ 1.618 is the golden ratio.

==========================================

Work Shown:

[tex]\displaystyle S_n = \sum_{k=1}^{n} \frac{1}{k}\\\\\\\displaystyle S_4 = \sum_{k=1}^{4} \frac{1}{k}\\\\\\\displaystyle S_4 = \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\\\\\\\displaystyle S_4 = \frac{12}{12}+\frac{6}{12}+\frac{4}{12}+\frac{3}{12}\\\\\\\displaystyle S_4 = \frac{12+6+4+3}{12}\\\\\\\displaystyle S_4 = \frac{25}{12}\\\\[/tex]

Note: in step 3, I'm adding terms in the form 1/k where k ranges from k = 1 to k = 4 (k being an integer)

9514 1404 393

Answer:

  255

Step-by-step explanation:

If the sum of digits is 12, the number is divisible by 3. If the number ends in 0 or 5, it is divisible by 5. So, we're looking for ...

  2x0 . . . where x is a digit and 2+x+0 = 12 . . . . . . not possible

  2x5 . . . where x is a digit and 2+x+5 = 12 . . . . true for x=5

The number is 255.

Answer:

I belive the correct answers are 8 and 12

Step-by-step explanation:

Answer:

the correct answer should be 500,000 hope this helps

4000 is 0.8% of 500000.

Answer:

The measure of the angles are 61° and 119°

Step-by-step explanation:

Let the first angle = x°

let the second angle = y°

The sum of two supplementary angles = 180°

x° + y° = 180° ----- equation (1)

based on the given question; "the difference of two supplementary angles is 58 degrees."

x° - y° = 58° ------- equation (2)

from equation (2), x° = 58° + y°

Substitute the value of x into equation (1)

(58° + y°) + y° = 180°

58 + 2y = 180

2y = 180 -58

2y = 122

y = 122 / 2

y = 61°

The second angle is given by;

x° = 58° + y°

x = 58° + 61°

x = 119°

Thus, the measure of the angles are 61° and 119°

[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =75 \end{cases}\implies s=\cfrac{(75)\pi (7)}{180}\implies s=\cfrac{35\pi }{12}\implies s\approx 9.2[/tex]

Answer:

=3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

602 r. 2

Step-by-step explanation:

Step-by-step explanation:

John ran 3 miles this week.

Jane ran 10 times as far as John this week :

10×3 = 30 miles

but she ran this week 8 fewer miles than last week. in other words, last week she ran 8 miles more than this week :

30 + 8 = 38 miles.

so, last week she ran 38 miles.

Answer:

34

Step-by-step explanation:

cause you had to doit the simple math problem

are you trying to prank on this problem

the answer is 5 because I got it correct on a quiz

Answer:

C

Step-by-step explanation:

Hello!

In the equation y=a cos bx, we can learn alot about the cosine graph.

a is the amplitude, or how 'long' the cosine graph is.

b is the period, which is how 'wide' one cycle of a cosine period can be. The higher the period, the wider the cycle is.

In this equation, we are focused on finding the period; so any choices that contain amplitude is not a correct answer choice for this problem, which leaves out B and C.

To find the period, we can plug b into [tex]\frac{2\pi }{b}[/tex] , which in a way converts the b value to a period.

For B) y= cos3x

[tex]\frac{2\pi }{3}[/tex]= it does not equal 3 [tex]\pi[/tex]

For C) y=cos [tex]\frac{2}{3}[/tex]x

[tex]\frac{2\pi }{\frac{2}{3}}[/tex]= equals 3 [tex]\pi[/tex] when simplified

Since C equals 3 [tex]\pi[/tex] as a period, C is the only logical answer.

Answer:

(y-84) (y+78

Step-by-step explanation:

7/16 - 7/12 ?

common multiple of 16 and 12 = 48   ((3x16 and 12x4)

7/16 - 7/12 = (7x3) / (16x3) - (7x4) / (12x4) = 21/48 - 28/48 = - 7/48

Answer:

1020 m

Step-by-step explanation:

340 x 3 = 1020

Answer:

6800

Step-by-step explanation:

Answer:

1

Inconclusive

Step-by-step explanation:

aₙ = (-1)ⁿ / (n + 6)

aₙ₊₁ = (-1)ⁿ⁺¹ / (n + 1 + 6)

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 1 + 6)] / [(-1)ⁿ / (n + 6)]│

lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 7)] × [(n + 6) / (-1)ⁿ]│

lim(n→∞)│[(-1)ⁿ⁺¹ / (-1)ⁿ] × [(n + 6) / (n + 7)]│

lim(n→∞)│-1 × [(n + 6) / (n + 7)]│

lim(n→∞) [(n + 6) / (n + 7)]

1

The limit equals 1, so the ratio test is inconclusive.

Answer:

a)8x+6y

b)4x+2y

Step-by-step explanation:

a)5x+3x+2y+4y

5x+3x=8x

2y+4y=6y

=8x+6y

b)6x-2x+8y-6y

6x-2x=4x

8y-6y=2y

=4x+2y

Answer:

a) x = -0.75y

b) x = -0.5y

Step-by-step explanation:

Simplifying

5x + 3x + 2y + 4y = 0

Combine like terms: 5x + 3x = 8x

8x + 2y + 4y = 0

Combine like terms: 2y + 4y = 6y

8x + 6y = 0

Solving

8x + 6y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6y' to each side of the equation.

8x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0

8x + 0 = 0 + -6y

8x = 0 + -6y

Remove the zero:

8x = -6y

Divide each side by '8'.

x = -0.75y

Simplifying

x = -0.75y

Simplifying

6x + -2x + 8y + -6y = 0

Combine like terms: 6x + -2x = 4x

4x + 8y + -6y = 0

Combine like terms: 8y + -6y = 2y

4x + 2y = 0

Solving

4x + 2y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.

4x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0

4x + 0 = 0 + -2y

4x = 0 + -2y

Remove the zero:

4x = -2y

Divide each side by '4'.

x = -0.5y

Simplifying

x = -0.5y

Ese mes se le dedujeron $4774, y cobró un sueldo de $19,092.

Dado que el empleado de una compañía tiene un sueldo mensual de L. 23, 865,00, y en el mes de marzo del 2019 se le hizo una rebaja del 20% por llegadas tarde al trabajo, para determinar cuánto se le dedujo y qué sueldo neto sacó ese mes se debe realizar el siguiente cálculo:

Por lo tanto, ese mes se le dedujeron $4774, y cobró un sueldo de $19,092.

Aprende más acerca de cálculos de cantidades en https://brainly.com/question/14342345

Answer:

Step-by-step explanation:

Use below compound interest formula and the given data.

F- future amount, P- invested amount, r - interest rate, n - number of compounds, t- time

Given:

Find the amount after 3 years:

Answer:

○ -1

Step-by-step explanation:

Looking closely at this piecewise function, when the line on the left-hand side intersects at -3 = y, x is -1.

i hope this work for you

Answer:

first term = 3

Step-by-step explanation:

The n th term of a GP is

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here r = 3 and a₅ = 243 , thus

a₁ × [tex]3^{4}[/tex] = 243

a₁ × 81 = 243 ( divide both sides by 81 )

a₁ = 3

Answers:

A. y = -2x + 11

B. y = 1/2x + 5

C. y = -1/2x + 5

D. y = -1/2x + 5

E. y = 2x + 2

F. y = -1/2x + 11/2

Hope this helped! (brainliest please)

Answer:

24 (not sure)

Step-by-step explanation:

36 - 8 = 24

im not sure if this is what the question is asking for.