Evaluate the exponential function f(x) = (1/2)x

Х 4, -1 ,0 ,1 ,3
f(x) 16, ?, 1, 1/2, 1/8

Which value completes this table?
A. 12
B. 8
C. 4
D. 2

Answer: Convergent; converges to 9/5 = 1.8

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Explanation:

The expression 8/(n^2-1) is the same as 8/( (n+1)(n-1) )

Use partial fraction decomposition to get

8/( (n+1)(n-1) ) = A/(n+1) + B/(n-1)

8 = (n+1)(n-1)*( A/(n+1) + B/(n-1) )

8 = A(n-1) + B(n+1)

8 = An-A + Bn+B

0n + 8 = (A+B)n + (-A+B)

We can see that

[tex]\begin{cases}A+B = 0\\-A+B = 8\end{cases}[/tex]

Use elimination to get 2B = 8 which leads to B = 4

Plug B = 4 into either equation of that system to solve for A getting A = -4

Therefore,

8/( (n+1)(n-1) ) = A/(n+1) + B/(n-1)

8/( (n+1)(n-1) ) = -4/(n+1) + 4/(n-1)

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Why do all this? Because it'll be helpful to set up the telescoping sum

Let's plug in a few values of n. Let's say from n = 5 to n = 10

If we do so, then we have...

 -4/(5+1)+4/(5-1)   =    -4/6 + 4/4

 -4/(6+1)+4/(6-1)   =    -4/7 + 4/5

 -4/(7+1)+4/(7-1)   =    -4/8 + 4/6

 -4/(8+1)+4/(8-1)   =    -4/9 + 4/7

 -4/(9+1)+4/(9-1)   =    -4/10 + 4/8

 -4/(10+1)+4/(10-1) =    -4/11 + 4/9

I'm not evaluating or simplifying further because we'll have cancellations as shown in the diagram below. The left panel is what you see before cancelling happens, and the right hand panel is what happens after the terms pair up and cancel (since those pairs add to 0).

Note the color coding so you can see what terms pair up and cancel. The only stuff left is the 4/4 and the 4/5

So,

4/4 + 4/5 = 1 + 4/5 = 5/5+4/5 = 9/5 = 1.8

is what the infinite sum converges to. You can use a tool like wolfram alpha to confirm this answer.

Answer:

C) x=1.5

Step-by-step explanation:

Hope This Helps!

Answer:

it is c!

Step-by-step explanation:

top one is correct

Answer:

The auditorium has a total of 5,300 seats

Step-by-step explanation:

The seats for kids can be calculated by multiplying the number of rows by the number of seats per row:

Seats for kids=39*53 =2,067 seats

The seats for adults are calculated in a similar way:

Seats for adults = 61*53= 3,233 seats

Total seats: 2,067+3,233 = 5,300

The auditorium has a total of 5,300 seats

Answer:

3-√11  must also be a root of f(x)

Step-by-step explanation:

Answer:

They can make 49 hamburgers

Step-by-step explanation:

Answer:

They can make 49 hamburgers

Step-by-step explanation:

Answer:

Exact Form:

x

=29/20

Decimal Form:

x=1.45

Mixed Number Form:

x=1 9/20

Step-by-step explanation:

I did that before trust me I know

When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

Answer:

If x equals -1 or anything less than -1, then the inequality statement is false

Step-by-step explanation:

So to find the number x has to be for the statement to be false, we have to find what number x would be to make it so both sides equal the same thing. So in this case, it would be -1 because 5-3 equals 2 and -2x=2 only if x=-1. So anything greater than -1 would make the statement true.

I hope this helped.

Answer:

Step-by-step explanation:

Inequality

As per above, the graph covers all numbers to the right from the point -1

The graph is attached

Answer:

41.25 minutes i think sorry if its wrong

Answer:

I think it's 1/3

Step-by-step explanation:

because yo can see that in y-1, x=1 then in y0, x=1.3 and it keep going

Answer:

0.96

Step-by-step explanation:

0.12 x 8 = 0.96

9514 1404 393

Answer:

  W = P/2 -L

Step-by-step explanation:

Divide by 2 and subtract L.

  P = 2L +2W

  P/2 = L +W

  P/2 -L = W

The width is ...

  W = P/2 -L

Answer:$3.50

Step-by-step explanation:

14/4 =3.5. To check answer multiply 3.5 by 4. You get 14

Answer: -1/8                                                                                                                            

Step-by-step explanation:

Answer:

4) x=110º

5) x=90º (so does y)

6) x=109

7) x=15º and y=5º

8) x=7

9) x=95

10) x=33

Step-by-step explanation:

4), 5) and 6) were a little hard to read but they were mostly simple to solve from what I saw. Using the verticle angles theorem and corresponding theorem you can easily find the values.

7) I plugged in the two first equations to solve x which is (3x+60)=(6x+15)

and for y I had to plug in x to find one of the angles' values to plug in with 15y and then created a second equation which should look like this 105+15y=180º (Since they should be supplementary angles)

8) This one's similar to 7) and even a little simpler. The equation should look like this 4x=3x+7

9) The equation to solve it that I used is x + (x-10)=180º

10) The equation to solve it that I used is (4x+5)=137

Hope this was helpful and (to other people too) if I made any mistakes or didn't explain properly feel free to let me know! :)

Answer:

a

The  null hypothesis is   [tex]H_o  :  \mu =  32.48[/tex]          

The alternative  hypothesis is   [tex]H_a  :  \mu  <  32.48[/tex]

b

  [tex]t  =  -1.504[/tex]

c

There is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

Step-by-step explanation:

From the question we are told that

   The mean price of   is  [tex]\mu = \$ 32.48[/tex]

   The  sample size is n  =  56  

    The sample mean is  [tex]\=  x  =  \$30.15[/tex]

     The standard deviation is  [tex]\sigma =  \$12[/tex]

The  null hypothesis is   [tex]H_o  :  \mu =  32.48[/tex]          

The alternative  hypothesis is   [tex]H_a  :  \mu  <  32.48[/tex]

Generally the test statistic is mathematically represented as

       [tex]t =  \frac{\= x  - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]

=>    [tex]t =  \frac{30.15  - 32.48 }{\frac{12 }{\sqrt{60} } }[/tex]

=>    [tex]t  =  -1.504[/tex]

Generally the p-value  is mathematically represented as

      [tex]p-value  =  P (t < -1.504 )[/tex]

From the z-table  

    [tex]P(t <  -1.504) =   0.066291[/tex]

So  

    [tex]p-value  = 0.066291 [/tex]

From the value we obtain we see that  

    [tex]p -value  >  \alpha[/tex]

Then we fail to reject the null hypothesis  

   Hence there is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

Answer:

B

Step-by-step explanation:

7 x 4 = 28

12 x 4 = 48

The higher numbers might be higher on the line but still in the same line :)

Answer:

A

Yes, because they are similar triangles

Step-by-step explanation:

Each angle increases by four

Triangle one is 7 and 12

Triangle two is 28 and 48

7 x 4 = 28

12 x 4 = 48

Answer:

there's no S .X=1 ,Xc=9.So 91

Answer:

Last option; 5/2+ i5/2

Answer:

your right

Step-by-step explanation:

Answer:

Answer 3

Step-by-step explanation:

Answer:

A. 27

Step-by-step explanation:

trust me

Answer:

im guessing b.4

Step-by-step explanation:

It is not possible to have a) 1 as one f the third side of the triangle

It defines the relationship between the sides `of a triangle .

The triangle inequality theorem states that sum of length of two sides of a triangle is greater than the length of the third side .

a + b > c

correct answer option a) 1

it is not possible to make a triangle if one side is 1 because triangle inequality theorem will be violated

1 + 4 = 5 and not greater than 5

hence , not possible

learn more about triangle inequality theorem

https://brainly.com/question/1163433?referrer=searchResults

#SPJ2

Hello! Your answer to this question is Yes!

Step-by-step explanation:

About 90% of babies born with a certain ailment recover fully. A hospital is caring for sixsix babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment.

Answer:

-5

Step-by-step explanation:

Answer:

GIVEN x=4 and y=-2

So, in (9x-2y)/xy when we apply x=4 and y=-2​

{9(4)-2(-2)}/(4)(-2)

36+4/-8

40/-8

-5/1

=-5

Answer:

Ok sorry but I have a very strong feeling that this isn't a college question because I am in an 8th grader taking Algebra 1 and this is sooooo simple.

Step-by-step explanation:

the answer is

8=m

Answer:

$36

Step-by-step explanation:

i dont know how to explain it but heres the number answer

Answer:

well 3÷13= 4.33 and 4.33×12=52

Answer:

[tex] 25\frac{1}{2} [/tex]

Step-by-step explanation:

[tex]5 \frac{2}{3} \times 4 \frac{1}{2} \\ \\ = \frac{5 \times 3 + 2}{3} \times \frac{4 \times 2 + 1}{2} \\ \\ = \frac{15 + 2}{3} \times \frac{8 + 1}{2} \\ \\ = \frac{17}{3} \times \frac{9}{2} \\ \\ = \frac{17}{1} \times \frac{3}{2} \\ \\ = \frac{51}{2} \\ \\ = 25 \frac{1}{2} [/tex]