Answer:
(5 - y) ^3 = 125 - 75y + 15y^2 - y^3
Step-by-step explanation:
Binomial expression
1
1. 1
1. 2. 1
1. 3. 3. 1 --------power of 3
( 5 - y) ^3
( 5 - y) (5 - y) (5 - y)
( a + b) ^3 = a^3 + 3a^2b + 3ab^2 + b^3
a = 5
b = -y
( 5 - y) ^2 = ( 5 - y) (5 - y)
= 5( 5 - y) - y(5 - y)
= 25 - 5y - 5y + y^2
=(25-10y+y^2)
( 25 - 10y + y^2)( 5 - y)
= 5(25 - 10y + y^2) - y( 25 - 10y + y^2)
= 125 - 50y + 5y^2 - 25y + 10y^2 - y^3
Collect the like terms
= 125 - 50y - 25y + 5y^2 + 10y^2 - y^3
= 125 - 75y + 15y^2 - y^3
Answer:
This function represents a direct variation because it passes through the origin and has a constant rate
Answer:
45 km/h
Step-by-step explanation:
In the first part of the trip, he already covered 30 km so we can subtract that from the total distance
45 - 30 = 15
This means he has 15 km to go
He also took an hour, or 60 minutes, to get to school. We subtract the time spent of the first part and time spent talking to a friend from the 60 minutes
60 - 35 = 25
25 - 5 = 20
He took 20 minutes to cover the second part of the journey
Speed = distance/time
15/20 = 0.75
He covered 0.75 km per MINUTE
to find it in km/h, we just multiply the number by 60
0.75 x 60 = 45
Answer:
c. 3.6 and 10.4 hrs
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviations of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean 7, standard deviation 1.7.
For about 95% of students, nightly amount of sleep is between
7 - 2*1.7 = 7 - 3.4 = 3.6 hours
7 + 2*1.7 = 7 + 3.4 = 10.4 hours
So the correct answer is:
c. 3.6 and 10.4 hrs
Answer:
6.84
Step-by-step explanation:
