[tex] \rm\sum_{n = 0}^ \infty \bigg( - \frac{1}2 \bigg)^{n} \frac{ \Gamma ( \frac{1 + n}{2} )}{ \Gamma(1 + \frac{n}2) } \\ [/tex]​

Answers

Answer 1

Let [tex]S[/tex] be the sum. Introduce a factor of [tex]\Gamma\left(\frac12\right)=\sqrt\pi[/tex] to rewrite the summand as a beta function integral. Then in the sum, interchange it with the integral, and [tex]S[/tex] reduces to a simple integral.

[tex]\displaystyle S = \sum_{n=0}^\infty \left(-\frac12\right)^n \frac{\Gamma\left(\frac{n+1}2\right)}{\Gamma\left(\frac n2+1\right)}[/tex]

[tex]\displaystyle . ~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \, \mathrm{B}\left(\frac n2+\frac12, \frac12\right) \\\\ ~~~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \int_0^1 \frac{t^{n/2}}{\sqrt t \sqrt{1-t}} \, dt \\\\ ~~~~ = \frac1{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t \sqrt{1-t}} \sum_{n=0}^\infty \left(-\frac{\sqrt t}2\right)^n \\\\ ~~~~ = \frac2{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t\sqrt{1-t}\left(\sqrt t+2\right)}[/tex]

Substitute [tex]u=\sqrt t+2[/tex] and [tex]du=\frac{dt}{2\sqrt t}[/tex].

[tex]\displaystyle S = \frac4{\sqrt\pi} \int_2^3 \frac{du}{u\sqrt{-(u-1)(u-3)}}[/tex]

Now substitute [tex]u=1+\frac2{1+t^2}[/tex] and [tex]du=-\frac{4t}{(1+t^2)^2}\,dt[/tex] - this comes from an Euler substitution of the form [tex]\sqrt{a(x-\alpha)(x-\beta)}=(x-\alpha)t[/tex]. [tex]S[/tex] reduces drastically to a trivial arctangent integral.

[tex]\displaystyle S = \frac8{\sqrt\pi} \int_0^1 \frac{dt}{t^2+3} \\\\ ~~~~ = \frac8{\sqrt\pi} \cdot \frac\pi{6\sqrt3} = \boxed{\frac43\sqrt{\frac\pi3}}[/tex]


Related Questions

Полоску бумаги разрезали на 7 частей. После этого самую большую
из полученных частей снова разрезали на 7 частей. Затем снова самую большую
из полученных частей разрезали на 7 частей. Так поступили много раз: на
каждом шаге самую большую часть разрезали на 7 частей. Могло ли в итоге
получиться 500 частей?

Answers

Answer:

2556285=68358556

Step-by-step explanation:

+58385-5838688(68589)8999=9858288

hans bought three books at a bookstore. Here are the prices(in dollars). 6,19.1,6.97 what is the total amount Hans paid at the bookstore

Answers

Answer:

$32.07

Step-by-step explanation:

Just add them together.

One state has a 6% sales tax on clothing items priced at $75 or higher, and no sales tax on clothing items priced under $75. What is the total tax on the items in the table above?​

Answers

Hello! It seems that we need a table to answer this question, but it is not given to me in your question. I will help to guide your way, though!
For percentages, we turn it into a decimal (move it 2 places to the left) and then multiply by the number. Let’s use the example of 75 dollars. To find its tax, we would multiply $75 by .06. This equals $4.5. This means that the tax is equal to $4.5. Now we need to add this tax to our $75. 75 + 4.5 = $79.5. Our total price for this piece of clothing would be $79.5.

Let’s use another random price as an example - $84.95. $84.95 times .06 = $5.097. Now we add the tax. We would get a total of $90.047 (or $90.05, since we round to our nearest tenth in money).

For your table, you would find the tax for every individual clothing above $75. Your table says to add the total tax (NOT the totals of the prices) together. So, using the numbers I did, we would add $4.5 + $5.097. This equals $9.597, or $9.60 total tax for these items. (Note: You can just ignore items under $75)

A plumber has a 20Foot

Answers

Answer:

14

Step-by-step explanation:

I think the question is whether: "a plumber has a 20-foot piece of PVC pipe. how many 7/5 foot pieces can be cut from the 20-foot piece?"

Graph the line with a slope of 1/3 passing through point (-1, -1)

Answers

Considering the expression of a line, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

Definition of line

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Knowing the value of slope m, substituting this value and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Line in this case

In this case, you know:

The line has a slope of 1/3The line passes through point (x,y)=(-1, -1)

Substituting the value of the slope m:

y= 1/3x +b

Substituting the point to calculate the value of b:

-1= 1/3×(-1) + b

-1= -1/3 + b

-1 + 1/3= b

-2/3= b

Finally, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

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help please rn please help

Answers

Answer: the answer is MO=5

Step-by-step explanation:

5 1/2 x 1 1/4
put in simplest form

Answers

Answer:

6 7/8

Step-by-step explanation:

First we would need to turn the 5 1/2 into a improper fraction. Then, do the same for the 1 1/4 as well. To do this, multiply the denominator by the whole number and then add the numerator. Once you get those values, you simply multiply across, meaning the numerators get multiplied together and the denominators get multiplied together. The value you get is the improper fraction form of the simplest form. Then you can convert it back to a mixed fraction if that is the form you need. To do this divide the numerator by the denominator. Now we have a value of 11/2 x 5/4 = 55/8. So divide 55 by 8 and leave the remainder in fraction form. Therefore the answer should be 6 7/8, after it is reduced.

I hope this helps, have a blessed day! :)

what is the domain and range of the question below
domain=
range =

Answers

The Domain is   [-4, -2] U  [-1, 1)  and range is [4, 0)

What is Domain and Range?

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

Given:

The left piece has its other endpoint at x = -2.

So, the interval for the domain is [-4, -2] and the other part is [-1, 1)

So, the domain is [-4, -2] U  [-1, 1)

and the range is the vertical range of the right part.

So, range is [4, 0)

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Tom bought a pencil case for $60 and sold it to gain a profit of 20% on his cost price.
(a) How much money did he gain? (b) How much money did he sell the pencil case for?

Answers

$60 x 1.20 = $72 - $60 = $12 profit

a. $12
b. $72

two complementary angles are X + 4 degree and 2 x - 7 degree find the value of x​

Answers

Answer:

x+4+2x-7=180

3x-3=180

3x=183

x=61

The radius of a circle is 12 inches. What is
the diameter?

Answers

Answer:

diameter is 24 inches

Step-by-step explanation:

diameter is basically two times the radius

finding the common difference

5,11,____ , 23,29,____…

Answers

Answer:

5,11 , 17, 23, 29, 35

Step-by-step explanation:

Answer:

5, 11, 17, 23, 29, 36

Step-by-step explanation:

To get from 5 to 11, we add 6. Similarly, to get from 11 to _, we add 6, and get 17. This also works with 29 to _. We get 36.

The sum of three consecutive odd numbers is 177. Find the number. Step by step please

Answers

X=57 is the required answer and 57 59 and 61 are the required numbers

Answer:

57, 59 and 61

Step-by-step explanation:

Let the first odd number be n The next consecutive odd number is n + 2 and the next one after that is n + 4
(consecutive odd numbers have difference of 2 between them. For example if 7 is the first odd number next one is 9(7+2) and the next one is 11(7+4)

We are given that the sum of the numbers is 177. So we have the following equation:

n + (n + 2) + (n +4) = 177

Simplifying gives

n + n + 2 + n + 4  = 177

Collect like terms:

n + n + n + 2 + 4 = 177
3n + 6 = 177

Subtract 6 from both sides
==> 3n = 177 - 6
==> 3n = 171

Divide by 3 both sides
3n/3 = 171/3

n = 57 and this is the first of the odd numbers

The next odd number is 57+ 2 = 59

and the next one after that is 59 + 2 = 61 (same as 57 + 4)

[tex] \rm \int_{0}^1 \int_{0}^1x \bigg \{ \frac{1}{1 - xy} \bigg \}dydx \\ [/tex]​

Answers

The fractional part vanishes when the argument is an integer; in this case, for

[tex]\left\{\dfrac1{1-xy}\right\} = 0 \iff \dfrac1{1-xy} = n \iff xy = \dfrac{n-1}n[/tex]

which are hyperbolas in the [tex](x,y)[/tex]-plane.

Observe that between neighboring hyperbolas, we have

[tex]\dfrac{n-1}n < xy < \dfrac n{n+1} \\\\ ~~~~ \implies \dfrac1{n+1} < 1-xy < \dfrac1n \\\\ ~~~~ \implies n < \dfrac1{1-xy} < n+1 \\\\ ~~~~ \implies \left\{\dfrac1{1-xy}\right\} = \dfrac1{1-xy} - \left\lfloor\dfrac1{1-xy}\right\rfloor = \dfrac1{1-xy} - n[/tex]

Split up the integral over [tex][0,1)^2[/tex] along the curves [tex]xy=\frac{n-1}n[/tex]. The subregions somewhat resemble the layers or scales of an onion (see attached plot with the first 5 "scales").

Let [tex]S_n[/tex] denote the [tex]n[/tex]-th ([tex]n\in\Bbb N[/tex]) "scale", starting from the blue region closest to the origin and counting diagonally upward in the direction of (1, 1).

In Cartesian coordinates, the integral over [tex]n[/tex]-th "scale" is

[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx \\\\\\ ~~~~~~~~= \int_{(n-1)/n}^{n/(n+1)} \int_{(n-1)/(nx)}^1 x \left(\frac1{1-xy} - n\right) \, dy dx \\\\\\ ~~~~~~~~~~~~~ + \int_{n/(n+1)}^1 \int_{(n-1)/(nx)}^{n/((n+1)x)} x \left(\frac1{1-xy} - n\right) \, dx[/tex]

(see attached plot of the 2nd "scale" for reference)

The integral is trivial, so I'll leave it to you to confirm that it drastically reduces to

[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx = \frac1{2n (n+1)^2} = \frac12 \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right)[/tex]

Now we recover the original integral by summing over [tex]\Bbb N[/tex].

[tex]\displaystyle \int_0^1 \int_0^1 x \left\{\frac1{1-xy}\right\} \, dy \, dx = \frac12 \sum_{n=1}^\infty \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right) \\\\ ~~~~~~~~ = \frac12 \left(\left(1-\frac12\right)+\left(\frac12-\frac13\right)+\left(\frac13-\frac14\right)+\cdots\right) - \frac12 \sum_{n=2}^\infty \frac1{n^2} \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\sum_{n=1}^\infty \frac1{n^2} - 1\right) \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\frac{\pi^2}6 - 1\right) = \boxed{1 - \frac{\pi^2}{12}}[/tex]

Calculate (multiply (1-2i)(6+5i)

Answers

Answer:

-7 i + 16

Step-by-step explanation:

Simplify the following:

(-2 i + 1) (5 i + 6)

(1 - 2 i) (6 + 5 i) = (1) (6) + (1) (5 i) + (-2 i) (6) + (-2 i) (5 i):

6 + 5 i - 2 i×6 - 2 i×5 i

-2×6 = -12:

6 + 5 i + -12 i - 2 i×5 i

-2 i×5 i = -2 i^2 5:

6 + 5 i - 12 i + -2 i^2×5

i^2 = -1:

6 + 5 i - 12 i - 2-1×5

-2 (-5) = 10:

6 + 5 i - 12 i + 10

6 + 5 i - 12 i + 10 = (6 + 10) + (5 i - 12 i) = 16 - 7 i:

Answer:  -7 i + 16

Answer: your answer to this question would be 16-7i

Step-by-step explanation:

20 points!!!What is a two step problem with variables on each side equal 20? (Please help)

Answers

5x • (2 +2) = (5-3) • 10x
5x • 4 = 2 • 10x
20x = 20x

5x-15=5+4x

    +15 +5

   5x=20+4x

  -4x       -4x

     x= 20

Step-by-step explanation:

I need help to find x and y

Answers

The system of nonlinear equations have two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).

What is the solution of a system of nonlinear equations?

In this problem we find a system of two nonlinear equations involving radical expressions. We proceed to resolve the system of nonlinear equations by algebra properties:

(2 · x - 1)² + 8√(2 · x · y) = 4

8√(2 · x · y) = 4 - (2 · x - 1)²

8√(2 · x · y) = 4 - 4 · x² + 4 · x - 1

8√(2 · x · y) = 4 · x - 4 · x² + 3

64 · (2 · x · y) = [(4 · x + 3) - 4 · x²]²

128 · x · y = (4 · x + 3)² - 8 · (4 · x + 3) · x² + 64 · x⁴

128 · x · y = 16 · x² + 24 · x + 9 - 32 · x³ - 24 · x² + 64 · x⁴            (1)

4 · y - √(8 · x · y - 1) = 1

4 · y - 1 = √(8 · x · y - 1)

(4 · y - 1)² = 8 · x · y - 1

16 · y² - 8 · y + 2 = 8 · x · y                                                             (2)

Now we plot two equations on a graphing tool and find that the system has the following two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).

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Solve the equation by the zero factor property
b^2-8b+15=0

Answers

Answer:

(b-5)(b-3)

Step-by-step explanation:

To factor this equation we have to find 2 numbers that combine to equal -8 and multiply together to equal 15

these numbers would be -3 and -5

after that you just put them in an equation like so:

(b-5)(b-3)

you can check your work by just multiplying those back together

If you want future explanation on how to do this just ask

hope this helps :D

Make a conjecture about each pattern. Then write the next two items. 4. 1, 2, 2, 4, 8, 32, . . .​

Answers

Answer:

256, 8192

{This is an educated guess}

Step-by-step explanation:

The problem seems to be a variation of the Fibonacci sequence: 1, 1, 2, 3, 5, 8...

1 ⇒ 2: 1*2

2 ⇒ 2: 2*1

2 ⇒ 4: 2*2

4⇒8:4*2

8⇒32:8*4

32⇒256: 32*8

256*32 = 8192

At Keller's Bike Rentals, it costs $15 to rent a bike for 4 hours.
How many dollars does it cost per hour of bike use?

Answers

Answer:

3.75

Step-by-step explanation:

15/4=3.75

Answer:

12 1/3

Step-by-step explanation:

because when you find the total cost plus divide it gives u the answer

Express 88 kilometers per hour in miles per hour.
mi/hr
(Round to the nearest hundredth as needed.)

Answers

88 kilometers per hour in miles per hour is 54.68 mi/hr

Converting kilometers per hour to miles per hour

Note that:

1 km = 0.6214 miles

The measurement to convert is 88 kilometers per hour

Multiply 88 kilometers per hour by 0.6214 to convert to miles per hour

88 kilometers per hour = 88 x 0.6214 miles per hour

88 kilometers per hour = 54.6832 miles per hour

88 kilometers per hour =  54.68 mi/hr

Therefore, 88 kilometers per hour in miles per hour is 54.68 mi/hr

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Given the graphs of f(x) and g(z) below, find the composition of functions f(g(-1)).

Answers

The composition of the functions, f(g(-1)) = 2.

How to Find the Composition of Functions?

To find the composition of the functions, f(g(-1)), first, find the function, g(-1) by tracing the value of y that will give an x-value of -1 on the function graph.

The next step is to use the value you get in the first step to trace which value of y will give an x-value equivalent to what you got in the first step on the second function graph.

Thus, from the graph of g(x), g(-1) = 0. Using the graph of f(x), the value of y when x = 0 is 2.

Therefore, the composition of the functions, f(g(-1)) = 2.

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Solve.
3z +2y-z = 8
2z+22=-4
z+3y=4

Answers

Answer:

(1, 1,-3)

Step-by-step explanation:

EASY QUESTION 20 POINTS

Answers

Answer:(7/9)^12

Step-by-step explanation:

Answer:

C. (7/9)^12

Step-by-step explanation:

(49/81)^6 = (7^2/9^2)^6 = (7/9)^(2x6) = (7/9)^12

Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level.
Then they climb the opposite of -8 meters to return to ground level.
How many meters did they climb in all? Enter your answer in the box

Answers

Answer:

16 meters is the answer of this question

One side of a rectangle is 4 m longer than four times another side. The area of the rectangle is 224 m².
Find the length of the shorter side.
m

Answers

Let the another side be x m.

Therefore, the longer side = (4 + 4x) m.

Now,

[tex]{\sf{→x \times (4 + 4x) = 224 \\ →4x + 4x {}^{2} - 224 = 0 \\→ x {}^{2} + x - 56 = 0 \\ →x {}^{2} + 8x - 7x - 56 = 0 \\ →x(x + 8) - 7(x + 8) = 0 \\ →(x - 7)(x +8 ) = 0 \\ →x = 7 \: or \: x = - 8 \\ \\ length \: cannot \: be \: negative \\ possible \: solution \: (x) = 7}}[/tex]

Length of shorter side = x = 7 metres.

[tex]{\sf{answer\: \\ss}}[/tex]

For the piecewise​ function, find the values ​g(​-6), ​g(1​), and ​g(8​).

Answers

The output values of ​g(​-6), ​g(1​), and ​g(8​) in the given piecewise function are -1, 6 and -6 respectively.

What are the output values of g(​-6), ​g(1​), and ​g(8​) in the given piecewise function?

Given the piecewise function in the question;

                   x + 5, for x ≤ 1

g(x) = {

                   2 - x, for x > 1

g(​-6) = ?​g(1​) = ?​g(8​) = ?

Determine the output value of g(-6), -6 falls in the domain of x ≤ 1,

Hence;

g(x) = x + 5

g(-6) = -6 + 5

g(-6) = -1

Determine the output value of g(1), 1 falls in the domain of x ≤ 1,

Hence;

g(x) = x + 5

g(1) = 1 + 5

g(1) = 6

Determine the output value of g(8), 8 falls in the domain of x > 1,

Hence;

g(x) = 2 - x

g(8) = 2 - 8

g(8) = -6

Therefore the output values of ​g(​-6), ​g(1​), and ​g(8​) in the given piecewise function are -1, 6 and -6 respectively.

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Rewrite using an exponent.

Answers

Answer:

2[tex] {}^{5} [/tex]

Step-by-step explanation:

2×2×2×2×2 = 2[tex] {}^{5} [/tex]

Kenneth measured a hotel and made a scale drawing. The scale he used was 1 inch = 4 feet. The actual length of a room in the hotel is 20 feet. How long is the room in the drawing ​

Answers

Answer:

The room is 5 inches in the drawing.

Step-by-step explanation:

If the room is 20 feet and each inch in his drawing measures 4 feet what you need to do is see how many times 4 goes into 20.

4 times 5 = 20

So the answer would be 5

Hope it helps! =D

For the function
f(x) = x + 10/6x + 4, consider the following.
(a)Find the vertical and horizontal asymptotes for the graph of f.
Vertical:
Horizontal:

b)Find f^ −1.
f^ −1(x) =

c)Find the vertical and horizontal asymptotes for the graph of
f^ −1
Vertical:
Horizontal:

Show all steps.

Answers

Using the concepts of asymptotes and inverse function, we have that:

a) For f, the vertical asymptote is x = -2/3 and the horizontal asymptote is y = 1/6.

b) The inverse function is: [tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

c) For the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

What are the asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

For this problem, the function is given by:

[tex]f(x) = \frac{x + 10}{6x + 4}[/tex]

The zero of the denominator is:

6x + 4 = 0

6x = -4

x = -4/6 = -2/3.

Hence the vertical asymptote is x = -2/3.

The horizontal asymptote is given as follows:

[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{x + 10}{6x + 4} = \lim_{x \rightarrow \infty} \frac{x}{6x} = \lim_{x \rightarrow \infty} \frac{1}{6} = \frac{1}{6}[/tex]

How to find the inverse function?

To find the inverse function of a function y = f(x), we exchange x and y then isolate y.

Exchanging x and y, we have that:

[tex]x = \frac{y + 10}{6y + 4}[/tex]

Applying cross multiplication:

x(6y + 4) = y + 10

6xy - y = 10 - 4x

y - 6xy = 4x - 10

y(1 - 6x) = 4x - 10

[tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

Applying the same procedure, for the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

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b. rational, self-interested government officials seeking more funding for mass transit through higher taxes should consider Which of the following uses commas clearly?A. Late to the party were, my two sisters, Bob and Frank.B. Late to the party were my two sisters Bob and Frank.C. Late to the party were my two sisters, Bob, and Frank.D. Late to the party were my two sisters, Bob and Frank. Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form. i have already answered this question but got it wrong but really interested on the right answer what might an organism do if there is a change to its ecosystem????? A: Move B: DieC: surviveD: All of theseI NEED HELP if both the ram air input and drain hole of the pitot system become blocked, the indicated airspeed will what roles do facts and opinion play in deciding whether something is an injustice? Which graph shows the solution to the system of linear inequalities?x 4y < 4y < x + 1On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded. On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded. students look out a window for 5 min. they record the number of vehicles that pass, the type of vehicle (car, pickup, truck, motorcycle, and so on) and the color of the venhicle. what are the students doing? A. concluding B. experimenting C. predicting D. observing ,and explain the more heterogeneous an audience is, the harder it is to construct a speech for them. true or false the most abundant protein in the human body is (fill in the blank) ; it provides (fill in the blank). quizlet Determine the constant rate of change When will you say a body is in Uniform acceleration and Non Uniform acceleration? Prepare a frequency table of the following scores obtained by 40 students in atest:24,16,17,30,28,20,15,24,16,18,18,15,16,20,25,24,25,20,16,15,18,25,20,18,28,27,25,24,24,18,18,25,20,16,25,20,27,28,28,16.This contains 20 points please help me quick What happens to the interference pattern that results from the diffraction of electrons passing through two closely spaced slits if the rate of electrons going through the slits is decreased to one electron per hour?. question 5(multiple choice worth 1 points) (02.06 lc) what was one way in which african americans helped the revolutionary war effort? they convinced native americans to join the army. they joined with women's groups to write petitions. they protested the war outside british parliament. they raised and contributed food for the army. If you roll a 6-sided die 66 times, what is the best prediction possible for the number of times you will roll an even number? Can someone help me with this? How do you add this expression? -1/2 + 2/7 Which is the closest synonym for the word mentor?A. censorB. tutorC. employD. compensate