Answer:
see explanation
Step-by-step explanation:
f(g(2)) = f(0) = -2
g(f(1)) = g(0) = 0
I was originally going to graph the two equations, but I don't have graph paper so I set the equations equal to each other.
so Mr.Reeds equation is: y=70x+4.5 and Mrs.Reeds equation is: y=85x
so if I set these equal to each other I would minus the 70x from both sides leaving me with 15x = 4.5. Now since that's done I would divide everything by 15 which will cause me to get a fraction. So once that's done I would be left with x=3/10. I hope this helped!
Answer:
7 minutes 48 seconds.
Step-by-step explanation:
Average speed for the whole journey is
distance / time, so
105 = (2*80)/ (t + t2)
where t is the time when it is moving and t2 is the time it stays at town Q.
Time for journey P to Q
= distance / speed
= 80 /120
= 2/3 hours,
Time for journey Q to P
= 80/110
= 8/11 hours
So t = 2/3 + 8/11
= 46/33 hours.
- and substituting in the equation for the whole journey:
160 / (46/33 + t2) = 105
105*46/33 + 105*t2 = 160
105 t2 = 160 - (105*46)/33
= 160 - 146.364
= 13.636
t2 = 13.636/105 = 0.1299 hours.
= 7 minutes 48 seconds.
Answer: the width of the uniform path is 9 meters.
Step-by-step explanation:
Let x represent the width of the uniform path.
A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. It means that the combined length of the pool and the uniform path is (18 + 2x) meters and the combined width of the pool and the uniform path is (22 + 2x) meters.
If the area of the pool and the path combined is 1440 square meters, it means that
(18 + 2x)(22 + 2x) = 1440
396 + 36x + 44x + 4x² = 1440
4x² + 80x + 396 - 1440 = 0
4x² + 80x - 1044 = 0
Dividing both sides of the equation by 4, it becomes
x² + 20x - 261 = 0
x² + 29x - 9x - 261 = 0
x(x + 29) - 9(x + 29) = 0
x - 9 = 0 or x + 29 = 0
x = 9 or x = 29
Since the width cannot be negative, then x = 9 meters
Answer:
The appropriate probability model for X is a Binomial distribution,
X 
Bin (<em>n</em> = 5, <em>p</em> = 1/33).
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of American births resulting in a defect.
The proportion of American births that result in a birth defect is approximately <em>p</em> = 1/33.
A random sample of <em>n</em> = 5 American births are selected.
It is assumed that the births are independent, i.e. a birth can be defective or not is independent of the other births.
In this experiment the success is defined as a defective birth.
The random variable <em>X</em> satisfies all criteria of a Binomial distribution.
The criteria are:
- Number of observations is constant
- Independent trials
- Each trial has only two outcomes: Success and Failure
- Same probability of success for each trial
Thus, the appropriate probability model for X is a Binomial distribution, Bin (<em>n</em> = 5, <em>p</em> = 1/33).
