The empirical rule says that approximately 68% of a normal distribution falls within one standard deviation of the mean. In this case, this would include all values of the variable in the interval
![(19-7,19+7)=(12,26)](https://tex.z-dn.net/?f=%2819-7%2C19%2B7%29%3D%2812%2C26%29)
.
Answer:
The right answer is approximately 210.031 cubic inches. (Answer: E)
Step-by-step explanation:
First, we need to convert the diameter (
), in inches, of the round balloon to an entirely decimal mode:
![D = 7\,in + \frac{3}{8}\,in](https://tex.z-dn.net/?f=D%20%3D%207%5C%2Cin%20%2B%20%5Cfrac%7B3%7D%7B8%7D%5C%2Cin)
![D = \frac{56 + 3}{8}\,in](https://tex.z-dn.net/?f=D%20%3D%20%5Cfrac%7B56%20%2B%203%7D%7B8%7D%5C%2Cin)
![D = \frac{59}{8}\,in](https://tex.z-dn.net/?f=D%20%3D%20%5Cfrac%7B59%7D%7B8%7D%5C%2Cin)
![D \approx 7.375\,in](https://tex.z-dn.net/?f=D%20%5Capprox%207.375%5C%2Cin)
The volume of the balloon is modelled after the volume function of a sphere (
), in cubic inches:
(1)
If we know that
, then the volume of the round balloon is:
![V = \frac{\pi}{6}\cdot D^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B%5Cpi%7D%7B6%7D%5Ccdot%20D%5E%7B3%7D)
![V = \frac{\pi}{6} \cdot (7.375\,in)^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%5Ccdot%20%287.375%5C%2Cin%29%5E%7B3%7D)
![V \approx 210.031\,in^{3}](https://tex.z-dn.net/?f=V%20%5Capprox%20210.031%5C%2Cin%5E%7B3%7D)
Hence, the right answer is approximately 210.031 cubic inches.
Answer:
A reasonable estimate is [tex]1,900 * 300 = 570,000[tex]
Step-by-step explanation:
This is because 1,900 is the closest multiple of 100 for 1,912, and 300 is the closest multiple of 100 for 305. And [tex]1,900 * 300[tex] is [tex]19 * 3 * 10,000[tex].
Answer:
3
Step-by-step explanation:
In this problem we need to kind of write the picture into an equation so the first thing we see are 4 xs on the far left-hand side this is representing "4x" then we see 5 - blocks on the right which represents "-5" because we have 5 minuses then on the other side we see 7 + blocks which represent just "7". After we identify everything in the picture we can write an equation so 4x -5 = 7. Then we solve so we need to separate x on one side and all the other numbers to the other to do that we can move the -5 to the side the 7 is on and because of math when we move a number to another side of the equation we have to switch the sign it has so if it was -5 then on the other side it would be 5 then we add 7 to 5 which would equal 12. Then we are left with 4x = 12 and to keep x on its own side we need to divide 4 from the other side because it is multiplying on the x side and again we need to switch the sign. then we are left with x=3. Hope this helps!
Answer:
3
Step-by-step explanation
So, you need to find 10% of 30
10/100 (fraction form of 10%) x 30
of = multiply
10/100 x 30 = 300/100 = 3