Answer:
0.33696
Step-by-step explanation:
Given that:
Probability of showing up head (p) = 0.6
Number of flips = number of trials = 5
Probability of getting more than 3 heads
P(x = x) = nCx * p^x * (1 - p)^(n-x)
P(x> 3) = p(4) + p(5)
P(x = 4) = 5C4 * 0.6^4 * 0.4^1 = 0.2592
P(x = 5) = 5C5 * 0.6^5 * 0.4^0 = 0.07776
Hence,
0.2592 + 0.07776
= 0.33696
Answer:
$7.2
Step-by-step explanation:
56 * .75 = 42
42+ 56 = 98
Answer is 98
Answer:
See below
Step-by-step explanation:
We first have to understand the parts of a y=mx+b equation
y=mx+b
m: Is the slope
b: Is the y-intercept
x: is the x part of (x,y)
y: is the y part of(x,y)
So...
if we use an example ordered pair like (1,3)
and a slope of 2
We can plug everything into y=mx+b to get
1=2*3+b which simplifies to b= -5
Now, you can use this concept to fill in the blanks below:
Use the two ordered pairs to find the slope, (m).
Then substitute the slope, and (one set of ordered pairs) into y=mx+b to solve for (b).
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
