Arectangular box is constructed in 3-space with one corner at the origin and other vertices at (1, 0, 0), (0, 4, 0), (0, 0, 2). find the length of the diagonal of the box.

The space diagonal will have length ...

... d = √(1² +4² +2²) = √(1 +16 +4) = √21

This can be found using the Pythagorean theorem. A drawing can help. Find the length of any face diagonal, then use that length as the leg of a right triangle whose hypotenuse is the space diagonal and whose other leg is the edge length not used in the first calculation.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

493 would be the correct answer

step-by-step explanation: