Select from the drop-down menus to correctly complete the proof. to prove that 3√5 is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0. isolating the radical gives √5= a/3b (all one fraction). the right side of the equation is [rational or irational]. because the left side of the equation is [rational or irational], this is a contradiction. therefore, the assumption is wrong, and the number is [rational or irational].

1. rational

2. irrational

3. irrational

Rational; irrational; irrational.

Step-by-step explanation:

a/3b is a rational number, as it is represented by a fraction and b ≠ 0.  This means the first blank is "rational."

√5 is an irrational number.  This means the second blank is "irrational."

Since we have an irrational number set equal to a rational number, this is a contradiction.  This means our original assumption is wrong, and the number is irrational.  This is the third blank.

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;