Step-by-step explanation:
Lets look at each of the options one by one:
Price System: In this system markets allocate resources through the price mechanism. An increase in demand raises price and encourages businesses to use more resources into the production of that good or service. In this system the government limits itself to protecting property rights of people and businesses using the legal system and protecting the value of money or the value of a currency.
Authoritarian System: In this system it is associated with a communist system. The scarce resources are owned by the government. The state allocates resources, and sets production targets and growth rates according to its own view of people's wants. They have their own idea of demand.
By comparing two systems it can be seen that Price System automatically moves resources to where they are most needed. So, price system is more efficient than authoritarian means.
Answer: 2/3 is the simplest form
X=amount of canned juice with 25% of orange juice
y=amount of other canned juice with 10% of orange juice.
25%=25/100=1/4
10%=10/100=1/10
17%=17/100
We can suggest this system of equations:
(1) x+y=15
(2) (x/4+y/10) / (x+y)=17/100 ⇒100(x/4 + y/10)=17(x+y) ⇒25x+10y=17x+17y ⇒8x-7y=0
Finally, we have this system of equations:
x+y=15
8x-7y=0
We can solve this system by substitution method.
x+y=15 ⇒ y=15-x
8x-7(15-x)=0
8x-105+7x=0
15x=105
x=105/15
x=7
y=15-x=15-7=8
answer: we should mix 7 liters of juice (with 25% orange juice) and 8 liters of juice (with 10% orange juice).
It is known
and
(if you want to determine cosine of 30° you should draw the perpendicular line to the x-axis and find the point of intersection, the value of x-coordinate is the cosine of 30°).
The angle
and
(see image).
The angle
and
(see image).
