Sanjeet paid $32.85 for a file and 3 identical pens.Leon paid $83.50 for 2 such files and 8 such pens.Find the cost of 1 pen.

x = 3

-2 | 2.2(3) - 3.3 | = -6.6

-2 | 6.6 - 3.3 | = -6.6

-2 | 3.3 | = -6.6

-2 * 3.3 = -6.6

-6.6 = -6.6

Answer: The correct choice is (C) A = {1, 2, 3, 4, 5, 7, 8}.

Step-by-step explanation: We have eight identical slips of paper, each numbered from one to eight, which have been mixed inside a bag.

The sample space, S is as follows:

S = {1, 2, 3, 4, 5, 6, 7, 8}.

Subset A consists of the complement of the event where the number 6 is drawn.

Let 'B' denote the event of drawing the number 6.

Thus, B = {6}.

Since 'A' represents the complement of 'B', it will include all elements in the sample space 'S' that are not part of set 'B'.

Therefore,

A = B' = {1, 2, 3, 4, 5, 7, 8}

So, A = {1, 2, 3, 4, 5, 7, 8}.

Consequently, (C) is the correct choice.

The correct option is the first one - refer to the image for the solution:

Answer:

Answer and Explanation:

We have:

Population mean,

μ

=

3

,

000

hours

Population standard deviation,

σ

=

696

hours

Sample size,

n

=

36

1) The standard deviation for the sampling distribution:

σ

¯

x

=

σ

√

n

=

696

√

36

=

116

2) By the central limit theorem, the sampling distribution's expected value matches the population mean.

Thus:

The expected value of the sampling distribution equals the population mean,

μ

¯

x

=

μ

=

3

,

000

The standard deviation of the sampling distribution,

σ

¯

x

=

116

The sampling distribution of

¯

x

is roughly normal due to a sample size greater than

30

.

3) The likelihood that the average lifespan of the sample falls between

2670.56

and

2809.76

hours:

P

(

2670.56

<

x

<

2809.76

)

=

P

(

2670.56

−

3000

116

<

z

<

2809.76

−

3000

116

)

=

P

(

−

2.84

<

z

<

−

1.64

)

=

P

(

z

<

−

1.64

)

−

P

(

z

<

−

2.84

)

=

0.0482

In Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)

4) The probability of the average life in the sample exceeding

3219.24

hours:

P

(

x

>

3219.24

)

=

P

(

z

>

3219.24

−

3000

116

)

=

P

(

z

>

1.89

)

=

0.0294

In Excel: =NORMSDIST(-1.89)

5) The likelihood that the sample's average life is lower than

3180.96

hours:

P

(

x

<

3180.96

)

=

P

(

z

<

3180.96

−

3000

116

)

=

P

(

z

<

1.56

)

=

0.9406

Let’s define x as the amount invested by Sam in the first year.
Here are the corresponding expressions derived from the provided descriptions for Sam's investments.

For Sam:
2nd year: investment = 5x/2 - 2000
3rd year: investment = x/5 + 1000

The total Sam invested is:
x + (5x/2 - 2000) + (x/5 + 1000)

Next, we can form the expressions for Sally’s investments.
For Sally
1st year: investment = 3x/2 - 1000
2nd year: investment = 2x - 1500
3rd year: investment = x/4 + 1400

Thus, Sally's total investment is,
total = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)

Setting both totals equal gives us:
(x) + (5x/2 - 2000) + (x/5 + 1000) = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)

Solving for x,
x = 2000
For Sally's investment for the third year:
investment = x/4 + 1400 = (2000/4 + 1400) = 1900

RESULTS:
Sam's first year = $2000
Sally's third year = $1900