9. √105 is irrational (105 is not the square of an integer) Its value is near +10.
-4 is an integer (and rational)
4/3 is a rational number
Smallest to largest, these are -4, 4/3, √105.
10. The nearest square less than 14 is 9 = 3×3. The nearest square greater than 14 is 16 = 4×4. 14 is closer to 16 than to 9, so we expect 4 to be the integer closest to its square root. (√14 ≈ 3.74, closer to 4 than to 3.)
11. The numbers are in the same order; only the location of parentheses has changed. The property that lets you do that with addition is the associative property.
Answer:
See below.
Step-by-step explanation:
1.
2a + 3 * (1 + 2) = 2a + 9: Yes. Expression is equivalent.
2.
33v = (3 * v) * 11: Yes. Expression is equivalent.
3.
3b - 19 + 2b = 3b + 19 - 2b: No. Both expressions are different answers.
4.
4(3c - 4) = 2(6c - 8): No. expressions are not equivalent.
There are 22lbs of kernels available for the second batch
Answer: 800pi inches
=======================================
Explanation:
The formula to find the circumference of a circle is
C = pi*d
where
C = distance around the circle (aka circumference)
pi = 3.14 approximately
d = diameter
We know that the diameter of the wheel is d = 8, so
C = pi*d
C = pi*8
C = 8pi
is the circumference of the wheel
One full rotation will have the wheel cover a distance of 8pi inches. Imagine that wet paint is on the outer surface of the wheel. If the wheel is rolled out in a straight line, then the wet paint would cover a linear distance of 8pi inches along the flat ground. This is one full rotation, so 100 rotations covers 100*8pi = 800pi inches
Note: if we use pi = 3.14 as the approximation, then the hamster ran approximately 800*pi = 800*3.14 = 2512 inches if the wheel could move
