Answer:
B.
Step-by-step explanation:
The ratio of Claire's songs to her mother's songs = 3 : 2
A.
3 : 2 = 3/2
9 : 6 = 9/6 = 3/2
12 : 10 = 12/10 = 6/5
B.
3 : 2 = 3/2
6 : 4 = 6/4 = 3/2
15 : 10 = 15/10 = 3/2
C.
3 : 2 = 3/2
4 : 3 = 4/3
5 : 4 = 5/4
D.
3 : 2 = 3/2
4 : 6 = 4/6 = 2/3
20 : 30 = 20/30 = 2/3
The table which shows the correct ratio and two equivalent ratios is B
Answer:
The viscosity at 140°C is predicted to be 7.2
Step-by-step explanation:
The function that model the relationship between viscosity and temperature = Quadratic model
The general form of a quadratic equation is y = a·x² + b·x + c
Therefore, we have;
When y = 10.8, x = 110, which gives;
10.8 = a·110² + b·110 + c = 12100·a + 110·b + c
10.8 = 12100·a + 110·b + c
When y =8.2, x = 130
8.2 = a· 130² + b· 130 + c = 16900·a + 130·b + c
8.2 = 16900·a + 130·b + c
When y = 160, x = 5.8
5.8 = a·160² + b·160 + c = 25600·a + 160·b + c
5.8 = 25600·a + 160·b + c
The three equations above can be listed as follows;
10.8 = 12100·a + 110·b + c
8.2 = 16900·a + 130·b + c
5.8 = 25600·a + 160·b + c
Solving using matrices gives;
From which we have;
a = 0.001, b = -0.37, c = 39.4
Substituting gives;
y = 0.001·x² - 0.37·x + 39.4
When x = 140
y = 0.962·140² - 0.37·140 + 39.4= 7.2
The viscosity at 140°C = 7.2.
The percentage of change in the area of the rectangle is -25% ⇒ B
Step-by-step explanation:
The given is:
We need to find the percentage change in the <em>AREA</em> of the rectangle
Assume that the length of AB ans DC is x units, and the length of AD and BC is y units
∵ The length of the sides AB and DC increased by 50%
∵ The length of AB and CD = x
- That means x will increase by 50% of x
∵ 50% of x = (50 ÷ 100) × x = 0.5 x
∴ The length is increased by 0.5 x
∴ The new length of AB and CD = x + 0.5 x = 1.5 x units
∵ The length of the sides BC and AD decreased by 50%
∵ The length of BC and AD = y
- That means y will decrease by 50% of y
∵ 50% of y = (50 ÷ 100) × y = 0.5 y
∴ The length is decreased by 0.5 y
∴ The new length of BC and AD = y - 0.5 y = 0.5 y units
∵ The area before the change = x × y = xy units²
∵ The area after the change = 1.5 x × 0.5 y = 0.75 xy units²
∵ The new area is less than the old area
∴ The area is decreased
- To find the the percentage of change in the area subtract the
new area from the old area and divide the difference by the
old area and then multiply the quotient by 100%
∴ The percentage of the change = × 100%
∴ The percentage of the change = × 100%
∴ The percentage of the change = 0.25 × 100%
∴ The percentage of the change = 25%
∴ The area of the rectangle is decreased by 25% ⇒ (-25%)
The percentage of change in the area of the rectangle is -25%
Learn more:
You can learn more about the percentage in brainly.com/question/12960754
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