5.) a gardener wants to divide a square piece of lawn in half diagonally. what is the length of the diagonal side of the square is 8 fr. leave your answer in simplest radical form.

diagonal ^2 = 8^2 + 8^2

diagonal ^2 = 64 + 64

diagonal ^2 = 128

diagonal ^2 = 64 * 2

diagonal ^2 = 8 * sq root (2)

Diagonal of a square = SqrRoot (2 * side^2)

Diagonal = SqrRoot (2 * 8^2)

Diagonal = SqrRoot (128)

SqrRoot (128) = SqrRoot (2 * 64) = SqrRoot (2) * 8

DIAGONAL = SqrRoot (2) * 8

The length of the diagonal side can be calculated by using Pythagoras theorem.

The length of the diagonal side is 8√2

Pythagoras theorem:

diagonal ² = opposite ² + adjacent ²

= 8² + 8²

= 64 + 64

diagonal ² = 128

find the square root of both sides

√diagonal ² = √128

diagonal = √2×64

= √2 × √64

= √2 × 8

= 8√2

Therefore, the length of the diagonal side is 8√2

Learn more about the Pythagoras theorem:

link

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

e^-kt = n/n0 = 0.79  

-kt = ln 0.79  

t = - ln 0.79/0.0001  

= 2357 years

step-by-step explanation: