Answer:
The simplification for the expression is given as =( 7 + 2(a-3))/(a-3)
Step-by-step explanation:
To simplify the expression we will first convert the words to values in numbers and alphabets.
StartFraction 5 Over a minus 3 EndFraction minus 4 divided by 2 + StartFraction 1 Over a minus 3 EndFraction
= 5/(a-3) -4/2 + 2/(a-3)
Having done that, let's move on and simplify the expression.
5/(a-3) -4/2 + 2/(a-3)
= 5/(a-3) -2+ 2/(a-3)
= 5/(a-3) + 2/(a-3) -2
= 7/(a-3) -2
=( 7 + 2(a-3))/(a-3)
- Make an equation representing the number of vehicles needed.
We have six drivers so
x + y ≤ 6
That's not really an equation; it's an inequality. We want to use all our drivers so we can use the small vans, so
x + y = 6
- Make an equation representing the total number of seats in vehicles for the orchestra members.
s = 25x + 12y
That's how many seats total; it has to be at least 111 so again an inequality,
25x + 12y ≥ 111
We solve it like a system of equations.
x + y = 6
y = 6 - x
111 = 25x + 12y = 25x + 12(6-x)
111 = 25x + 72 - 12x
111 - 72 = 13 x
39 = 13 x
x = 3
Look at that, it worked out exactly. It didn't have to.
y = 6 - x = 3
Answer: 3 buses, 3 vans
Answer:
We need a sample size of at least 719
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
How large a sample size is required to vary population mean within 0.30 seat of the sample mean with 95% confidence interval?
This is at least n, in which n is found when 
. So
Rouding up
We need a sample size of at least 719
A beam of light (travelling at the speed of light) would take 65 years to go and 65 years to come back from aldebaran, i.e. 130 years. You can send and receive a radio message (travelling at the speed of light, being electromagnetic radiation) taking so 130 years.
