What is the maximum number of times two planes can intersect? What is the minimum number of times they can intersect?

Answer:

At least 315

Step-by-step explanation:

A journalist intends to find the average annual salary of CEOs within the S&P 1,500. Due to time constraints, a sample is used.

Standard deviation of the sample (s) = 449300

Sample size = n

Permissible margin of error = 50000

Z critical value = 1.96

Thus, 1.96 times the standard error equals 50000.

Standard error equals 25510.20

Standard deviation divided by the square root of n = 25510.20

By simplifying, we can derive:

Thus, the minimum sample size required is 315.

Manny's assertion is flawed; his reasoning lacks adequate support for his claim.

Answer:

Step-by-step explanation:

The probability distribution for the random variable X is provided.

X 4 5 6 7 Total

P 0.2 0.4 0.3 0.1 1

x*p 0.8 2 1.8 0.7 5.3

x^2*p 3.2 10 10.8 4.9 28.9

a) The expected value E(X), representing the mean of X, equates to 5.3.

Standard deviation is the square root of the variance, which amounts to 0.9.

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b) For the mean of the sample, we find:

Mean = 5.3

Variance = var(x)/n =

c)

Answer:

The highest number of long-sleeved shirts that can be ordered is 8

and

The lowest number of long-sleeved shirts that can be acquired is 0

Step-by-step breakdown:

Let y denote the quantity of short sleeves and x indicate the quantity of long sleeves.

According to the stipulated conditions:

Members of a school club are purchasing coordinating shirts. They understand that a minimum of 25 members will opt for a shirt.

therefore, we have;

               or

....[1]

Given that long-sleeved shirts are priced at $10 each and short-sleeved shirts at $5 each.

Thus;

The total expense for long sleeves amounts to 10x and

Moreover; the club has a budget that does not exceed $165

therefore;

......[2]

By plotting the inequality functions:

Graphing equations [1] and [2] produces a maximum at the coordinates (8, 17)

thus, x= 8.

Taking the minimum value of x =0 results in y falling between 25 and 33.

consequently, the solution space is situated between the intersecting lines to the left.

In conclusion, a maximum of 8 long-sleeved shirts can be obtained, while the minimum number of long-sleeved shirts that can be bought is 0