This is a right angle triangle and you use the Pythagorean theorem to solve for the hypotenuse (the diagonal)

A^2 + B^2 = C^2
8^2 + 8^2 = C^2
64 + 64 = C^2
128 = C^2
C = square_root (128)
C = 11 (to the nearest whole number)

The diagonal is 11 feet (to the nearest whole number)

7 0

3 years ago

X<br> For f(x)=0.01(2) , find the average rate of change from x=3 to x=8.

NikAS [45]

Answer:

Option b. 0.496

Step-by-step explanation:

we know that

f(x)=0.01(2^{x})

The average rate of change is equal to

\frac{f(b)-f(a)}{b-a}

where

a=3

b=8

f(a)=f(3)=0.01(2^{3})=0.08

f(b)=f(8)=0.01(2^{8})=2.56

Substitute

\frac{2.56-0.08}{8-3}

\frac{2.48}{5}

0.496

3 0

2 years ago

A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots.

andriy [413]

Answer:

$ 1.96

Step-by-step explanation:

Number of spots with outcome of $1 = 9

Number of spots with outcome of $2 = 18

Number of spots with outcome of $10 = 1

Total number of spots = 28

Probability that ball will land on $1 = $\frac{9}{28}$

Probability that ball will land on $2 = $\frac{18}{28}$

Probability that ball will land on $10 = $\frac{1}{28}$

The amount that player should expect to win on average in equal to expected value of the game. Expected value is calculated as the summation of product of probabilities with their respective outcomes.

i.e. for this case:

Expected Value will be:

$(1 \times \frac{9}{28})+(2 \times \frac{18}{28})+(10 \times \frac{1}{28})\\\\ =1.96$