Please solve this question

Given:

Number of mice and frequency

Mean = 7

To find:

The value of x.

Solution:

Number of mice = X

Frequency = Y

XY = Multiply X and Y values.

X         Y            XY

5         4            20

6         13           78

7         16           112

8          x            8x

9          6            54

Sum of Y = 4 + 13 + 16 + x + 6

               = 39 + x

Sum of XY = 20 + 78 + 112 + 8x + 54

                  = 8x + 264

Mean formula:

Do cross multiplication.

Subtract 264 from both sides, we get

Subtract 7x from both sides, we get

The value of x is 9.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}