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.
Answer:
7/9 ÷ 1/3 = 21/9 as simplified as 7/3 in fraction form. 7/9 ÷ 1/3 = 2.3333 in decimal form.
Answer: The measure of each exterior angle is 6.4°.
Step-by-step explanation:
Since we have given that
Number of sides = 56
We have to find the measure of each exterior angles:
As we know the formula :
Hence, the measure of each exterior angle is 6.4°.
Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)
Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches
Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.
The answer is 1.85
To figure this out, think about what we want. We want our original number plus 85% of the original number. The 1 part will give you back your original number, and the 0.85 part will add 85%.
