Using the compound interest formula,
572.86=287,50(1+i)^8
(1+i)^8=572.86/287.50=1.992557
1+i=(1.992557)^(1/8)=1.0899996
=>
i=1.0899996-1=9%
Note: This problem can also be solved in the head using the rule of 72.
Since after 8 years, the amount is roughly doubled, we can say that the interest rate is approximately 72/8=9%
Answer:
Step-by-step explanation:
Let's convert this statement into a system of two equations
3 * (cost of a liter of milk) + 5 * (cost of a loaf of bread) = $11
4 * (cost of a liter of milk) + 5 * (cost of a loaf of bread) = $10
cost of a liter of milk = x
cost of a loaf of bread = y
3x + 5y = 11
4x + 4y = 10
You can now solve this using either substitution or elimination
I'll use elimination. Let's say I want to get rid of the x first. I need to choose numbers to multiply by the top and bottom equations to eliminat the x's. The easiest way to do this is to multiply them by each other. So we'll multiply the top by 4 and the bottom by 3. We'll need to make sure the signs are opposite as well so I'll make that a negative 3 on the bottom.
4 * (3x + 5y = 11)
-3 * (4x + 4y = 10)
12x + 20y = 44
-12x - 12y = -30
Now add straight down
0x + 8y = 14
8y = 14
y = 14/8 = $1.75
Now we can plug this back in to either equation to find the x. I'll choose the second equation
4x + 4*(1.75) = 10
4x + 7 = 10
4x = 3
x = 3/4 = $0.75
So, cost of a liter of milk = x = $0.75
and cost of a loaf of bread = y = $1.75
Answer:
Step-by-step explanation:
Q17
For Q18 and Q19.
If ΔABC ≅ ΔSRT (congruent), then
Q20
Answer:
The linear model will give a good approximation if the new value is within or close to the values we used to construct the linear model.
Step-by-step explanation:
A linear model gives reasonable approximations under these two conditions:
- If the value for which we need to use the approximation is within the range of values we used to construct the linear model
- If the value for which we need to use the approximation is close to the values which we used to construct the linear model.
For the given model, heights of children aged 5 to 9 were recorded. Here, age is the independent variable and height will be the independent variable. Heights of 30 children from age 5 to 9 were recorded and a linear model was constructed. Now, we need to tell which value of age can be made an input of this function to find the approximate height.
Using the above two principles, the linear model will give a good approximate if:
- The age of the child is between 5 and 9 years. In this situation, the value approximated by the model will be closer to the actual height in majority of the cases. For example, the model will give good approximations for children of ages 6, 6.5, 7, 7.75 etc
- The age of child is close to 5 and 9 years old but outside the range. In this case, the model will also give good approximations. For example. for a child of age 4.5 years or 10 years, the model will still give a good and reasonable approximations.
