Let Jean's speed while running = x mph
Then Jean's speed while riding will be = x+9 mph
Distance covered by running = 8 miles
Distance covered by riding = 11 miles
Total time taken to complete the race = 1.5 hours
As, 
So, time for running= 
And time for riding= 
Equation becomes:
Now, multiply every term by 2x(x+9) to clear denominators:
Simplifying it we get
Solve the quadratic equation using formula
putting a=3 , b= -11, c= -144
we get (x - 9)(3x + 16) = 0
where x=9 and x=
Neglect the negative answer as speed cannot be negative, so x = 9 mph
Hence, Jean's running speed is 9 mph and riding speed is x+9 = 9+9 = 18 mph
Between the probability of union and intersection, it's not clear what you're supposed to compute. (I would guess it's the probability of union.) But we do know that
For parts (a) and (b), you're given everything you need to determine
.
For part (c), if
and
are mutually exclusive, then
, so
. If the given probability is
, then you can find
. But if this given probability is for the intersection, finding
is impossible.
For part (d), if
and
are independent, then
.
Answer:
Step-by-step explanation:
Use consistent units. The length of the roller is 2.8 m. The diameter is 168 cm = 1.68 m
Circumference of roller = 1.68π m
Contact area of roller = 1.68π × 2.8 = 4.704π m²
Each rotation levels 4.704π m² of the playground.
Area of playground = 750 rotations × (4.704π m²)/rotation
= 3528π m²
≈ 11,084 m²
Answer:
5 amperes will produce the maximum power
Step-by-step explanation:
The power generated by an electrical circuit (in watts) as a function of its current c (in amperes) is modeled by: P(c)= -12c^2 + 120c.
To find out the maximum power we need to find the vertex
formula to find x -coordinate of vertex is 
P(c)= -12c^2 + 120c is given in the form of y=ax^2+bx+c
a= -12, b = 120
c= 5 amperes will produce the maximum power
Answer:
The ratio for the boys is 24:40 and the girls is 16:40 so the girls and boys is 16:24
Step-by-step explanation:
