Answer:
70√2 units²
Step-by-step explanation:
(see attached for reference notes on parallelograms)
we are given ABCD is a parallelogram where
Short Length, AB = 10 units
Long Length, BC = 14 units
Angle A = 45°
The area of the parallelogram is hence,
= AB x BC sin 45°
= 10 x 14 x sin 45
= 140 sin 45° (recall from special angles, that sin 45° = 1/√2)
= 140/√2 (remove radical from denominator by multiplying by √2/√2)
= (140/√2) x (√2/√2)
=70√2 units²
Answer:
The null hypothesis is:
The alternative hypothesis is:
Step-by-step explanation:
Consider the provided information.
It is given that the average air pressure in footballs used by the Patriots was significantly less than the allowable limit of 12.5 psi.
The null hypothesis indicates that there is no substantial difference between given populations, due to sampling or experimental error, any observed difference.
Therefore, the null hypothesis is:
The required alternative hypothesis is:
Answer:
The average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ] are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.
Step-by-step explanation:
The given function is
where, P(t) is population after t years.
At t=5,
At t=6,
At t=7,
At t=8,
At t=9,
At t=10,
The rate of change of P(t) on the interval is
Using the above formula, the average rate of change of the population on the intervals [ 5 , 10 ] is
The average rate of change of the population on the intervals [ 5 , 9 ] is
The average rate of change of the population on the intervals [ 5 , 8 ] is
The average rate of change of the population on the intervals [ 5 , 7 ] is
The average rate of change of the population on the intervals [ 5 , 6 ] is
Therefore the average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ] are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.