TheThe area of the shaded region if the radius of the outer circle is 4 and the radius of the inner circle is 2 is 12π.
<h3>Area of the shaded region</h3>
Area of a circle = πr²
r =radius of the circle
Area of the outer circle:
Area of the outer circle = π(4)²
Area of the outer circle = 16π
Area of the inner circle:
Area of the inner circle = π (2)²
Area of the inner circle = 4 π
Area of the shaded Region :
Area of the shaded Region = 16π - 4 π
Area of the shaded Region = 12π
Therefore the area of the shaded region if the radius of the outer circle is 4 and the radius of the inner circle is 2 is 12π.
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The question is incomplete. Here is the complete question.
The football team needed to buy Gatorade for Saturday's big game. They have two options. The first option is they can buy it pre-made in 48 ounces bottles for $3.84 for each bottle. Or they can buy packets and mix with water. Each packet makes 64 ounces and will cost $4.80.
a) Find the cost per ounce of each.
b) Which size costs less?
c) The team will need to buy 192 ounces of Gatorade. How much do you save using the choice from answer b?
Answer: a) Pre-made: $0.08 cost per ounce; Packet: $0.075 cost per ounce
b) Packets
c) Save $0.96.
Step-by-step explanation:
a) Cost per ounce:
<u>Pre-made:</u>
= 0.08
<u>Packet:</u>
<u />
= 0.075
b) Comparing costs per ounce, packets costs less than pre-made.
c) Buying packets, the cost will be:
0.075*192 = $14.4
Buying pre-made:
0.08*192 = $15.36
Comparing costs, pre-made is 0.96 more than packets, so <u>they will save </u><u>96 cents</u>.
Answer
a) k=7, h=9, the unique solution of the system is 
b) If k=6 and h=8 the system has infinite solutions.
c)If k=6 and h=9 the system has no solutions.
Step-by-step explanation:
I am assuming that the system is x1+3x2=4; 2x1+kx2=h
The augmented matrix of the system is ![\left[\begin{array}{ccc}1&3&4\\2&k&h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%264%5C%5C2%26k%26h%5Cend%7Barray%7D%5Cright%5D)
. If two times the row 1 is subtracted to row 2 we get the following matrix![\left[\begin{array}{ccc}1&3&4\\0&k-6&h-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%264%5C%5C0%26k-6%26h-8%5Cend%7Barray%7D%5Cright%5D)
.
Then
a) If k=7 and h=9, the unique solution of the system is 
and solviong for 
,
Then the solution is
b) If k=6 and h=8 the system has infinite solutions because the echelon form of the matrix has a free variable.
c)If k=6 and h=9 the system has no solutions because the last equation of the system of the echelon form of the matrix is 
Q1
Divide each distance by its time to find the speed for each driver.
T: 380 km / 4 hr = 95 km/h
M: 530 km / 5 hr = 106 km/h
Martine's average speed was greater.
Q2
Bronze to aluminum is 25:2
The alloy is bronze plus aluminum, so by adding 25 + 2 you get 27.
Bronze to total is 25:27
25 is 27 as x is to 55
25/27 = x/55
27x = 25 * 55
x = 50.926
Answer: 50.926 kg of bronze
Q3
Manipulative toys to art toys is 30:40
Total toys = 30 + 40 = 70
manipulative toys are 30 out of 70
30/70 * 100 = 42.9%
It takes Tom <u>90 minutes</u> to reach at the work.
Given,
Total time taken by paul = 45 minutes
Time taken by tom = x
According to the question,
the equation will be -
45 = (1/3)x + 15
On solving,
45 - 15 = (1/3)x
30 = (1/3)x
x = 90 minutes
So, it takes, tom 90 minutes to reach
<h3>What is a linear equation?</h3>
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
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