Select the correct answer from each drop-down menu. The options are: The ratio of the heights is 1 : 2.5 1 : 5 1 : 10 1 : 25 The
ratio of the surface areas is 1 : 5 1 : 10 1 : 25 1 : 125 The ratio of the volumes is 1 : 5 1 : 10 1 : 25 1 : 125.
1 answer:
Using proportions, it is found that:
- The ratio of heights is of 1:5.
- The ratio of surface areas is of 1:25.
- The ratio of volumes is of 1:125.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The heights are measured in units, hence the ratio is:
The surface areas are measured in units squared, hence the ratio is:
(1:5)² = 1:25.
The volumes are measured in cubic units, hence the ratio is:
(1:5)³ = 1:125.
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Answer:
a) w+c = 5 ____equation(1) and w = c ____equation (2)
b) 2.5 lb walnuts and 2.5 lb cashews
Step-by-step explanation:
Let w pounds be the weight of walnuts required and c pounds be the weight of cashews required to make the new mixture.
Total weight of the new mixture = 5 lb
So,
Weight of walnuts + Weight of cashews = Total weight of the new mixture
w+c = 5 ____equation (1)
Now,
60% of walnuts +40% of cashews = 20% of walnuts + 80% of cashews
0.60w+0.40c = 0.20w+0.80c
Subtracting 0.20w from both the sides of the equation, we get
0.60w+0.40c-0.20w = 0.20w+0.80c-0.20w
Cancelling out the 0.20w and -0.20w from the right side, we have
0.60w-0.20w+0.40c = 0.80c
=> 0.40w+0.40c=0.80c
Subtracting 0.40c from both sides, we get
0.40w+0.40c-0.40c=0.80c-0.40c
Cancelling out 0.40c and -0.40 c form the left side, we get
0.40w = 0.40c
Dividing both sides by 0.40, we have
Cancelling out the 0.40's from the top and bottom, we get
w = c ____equation (2)
Plugging in w=c into the equation 1, we get
w+c = 5
=> c+c =5
=> 2c = 5
Dividing both sides by 2, we get
Cancelling out the 2's from the left, we get
c = 2.5
Plugging in c=2.5 into the equation 1, we get
w+c = 5
=> w + 2.5 = 5
Subtracting 2.5 from both sides, we get
w+ 2.5 -2.5 = 5 - 2.5
Cancelling out the +2.5 and -2.5 from the left side, we get
w = 2.5
So, we need 2.5 lb walnuts and 2.5 lb cashews to make the new mixture.
Answer: Expression as a power of the number a is given as
Explanation:
Since we have given that
First we use the exponential law i.e.
So, our expression becomes,
Now, we'll use the exponential law i.e.
So, it becomes,
Now, we'll use the exponential law i.e.
Hence, our expression becomes,