Find the odds of each outcome if a computer randomly picks a letter in the name: THE UNITED STATES OF AMERICA a) The letter A
b) The letter M
c) a Vowel
d) a consonant
e) Vowel and Letter T

a) 0.125

b) 0.041

c) 0.458

d) 0.541

e) 0.0763

Step-by-step explanation:

The number of letters in the name THE UNITED STATES OF AMERICA = 24

The probability of a particular outcome occurring = (The number of required outcome)/(The number of possible outcome)

The number of possible letters the computer can pick = 24, therefore the number of possible outcome = 24

a) The number of As in the name = 3 As

The number of required outcome = 3

Therefore, the probability the probability that the letter is an A = 3/24 = 1/8 = 0.125

b) The number of Ms in the name = 1 M

Which gives the number of required outcome = 1

Therefore, the probability the probability that the letter is a M = 1/24 = 1/24 = 0.041

c) The vowels in the name are E, U, I, E, A, E, O, A, E, I, A which are 11 in number

Which gives the number of required outcome = 11

Therefore, the probability the probability that the computer picks a vowel = 11/24 = 0.458

d) The number of consonants = The number of letters in the name - The number of vowels

∴ The number of consonants = 24 - 11 = 13 consonants

Which gives the number of required outcome = 13

Therefore, the probability the probability that the computer picks a consonant = 13/24 = 0.541

e) The number of letter Ts in the name are 4 Ts

The probability that the computer picks a letter T = 4/24 = 1/6

The probability that the computer picks a vowel and a letter T is given by the product of the two probabilities as follows

P(Vowel and Letter T) = P(Vowel) × P(Letter T) = 11/24 × 1/6 = 11/144 = 0.0763.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)