Answer:
120
Step-by-step explanation:
Using factorial, we can calculate the total possible number of combinations to line up.
5! = 120.
5! is another way of saying 5 × 4 × 3 × 2 × 1
The given path can be illustrated in the following diagram:
She has only 30 miles worth of gas, if she comes back through the same path then the total distance is:
Therefore, she has not enough gas to go back using the same path.
Now, the total distance traveled in a straight path (SP) can be found using the Pythagorean theorem, we get:
![\begin{gathered} SP=\sqrt[]{13^2+24^2} \\ SP=\sqrt[]{745} \\ SP=27.3\text{ miles} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20SP%3D%5Csqrt%5B%5D%7B13%5E2%2B24%5E2%7D%20%5C%5C%20SP%3D%5Csqrt%5B%5D%7B745%7D%20%5C%5C%20SP%3D27.3%5Ctext%7B%20miles%7D%20%5Cend%7Bgathered%7D)
Therefore, she needs to take a straight path.
Answer: 3c
Step-by-step explanation: add 4 to 1 and take away 2.
Answer:
C
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (8, - 14), thus
y = a(x - 8)² - 14
To find a substitute (5, 13) into the equation
13 = a(5 - 8)² - 14
13 = a(- 3)² - 14
13 = 9a - 14 ( add 14 to both sides )
27 = 9a ( divide both sides by 9 )
a = 3
Thus
y = 3(x - 8)² - 14 → C
Well, 3^9 is the same thing as
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3
So 3^9 is equal to 19,683
