What is a rectangular prism with a surface area of 96 square meters

Mathematics

2 answers:

goldenfox [79]3 years ago

8 0

If you're asking for the measurements, they are...

Length (l) = 4 ft.
Width (w) = 4 ft.
Height (h) = 4 ft.

mrs_skeptik [129]3 years ago

5 0

Answer:

Rectangular prism is a square prism with side = 4 meters

Step-by-step explanation:

A rectangular prism with a surface area = 96 square meters

Means 2(length×width + height×width + length×height) = 96

One possible solution is when length = width = height

2×3×side² = 96

6 × side² = 96

side² = 96/6 = 16

side = 4

Therefore length = width = height = 4 meters.

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A computer is used to generate passwords made up of numbers 0 through 9 and lowercase letters. The computer generates 400 passwo

tamaranim1 [39]

The prediction for the number of passwords in which the first character is a vowel is 56 passwords.

<h3>How to find that a given condition can be modelled by binomial distribution?</h3>

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

$X \sim B(n,p)$

The probability that out of n trials, there'd be x successes is given by

$P(X =x) = \: ^nC_xp^x(1-p)^{n-x}$

The expected value and variance of X are:

$E(X) = np\\$

Given that the characters that can be used are numbers 0 through 9 and lowercase letters. Therefore, a total of 36 different characters are available.

Since we need to know the passwords made with vowels, therefore, the probability of a password in which the first character will be a, e, i, o, u is (5/36).

Now as the computer produces 400 passwords, therefore, the predicted value can be written as,

$E = np = 400 \times \dfrac{5}{36} = 55.5556 \approx 56$