Answer:
a) The volume of the water is approximately 678.6 cm³.
b) The volume of the sphere is approximately 113.1 cm³.
c) The new height of the water is approximately 7 cm, one cm higher than before.
Step-by-step explanation:
To solve this problem we first need to calculate the volume of the water, which is given by the cylinder volume, since it's stored in a cylindrical container.
![\text{water volume} = \pi*r^2*h\\\text{water volume} = \pi*(6)^2*6\\\text{water volume} = \pi*36*6\\\text{water volume} = 678.584 \text{ }cm^3\\](https://tex.z-dn.net/?f=%5Ctext%7Bwater%20volume%7D%20%3D%20%5Cpi%2Ar%5E2%2Ah%5C%5C%5Ctext%7Bwater%20volume%7D%20%3D%20%5Cpi%2A%286%29%5E2%2A6%5C%5C%5Ctext%7Bwater%20volume%7D%20%3D%20%5Cpi%2A36%2A6%5C%5C%5Ctext%7Bwater%20volume%7D%20%3D%20678.584%20%5Ctext%7B%20%7Dcm%5E3%5C%5C)
We now need to calculate the volume of the sphere, by using the appropriate formula:
![\text{volume sphere} = \frac{4}{3}\pi*r^3\\\text{volume sphere} = \frac{4}{3}\pi*(3^3)\\\text{volume sphere} = \frac{4}{3}\pi*27\\\text{volume sphere} = 113.09 \text{ } cm^3](https://tex.z-dn.net/?f=%5Ctext%7Bvolume%20sphere%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%2Ar%5E3%5C%5C%5Ctext%7Bvolume%20sphere%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%2A%283%5E3%29%5C%5C%5Ctext%7Bvolume%20sphere%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%2A27%5C%5C%5Ctext%7Bvolume%20sphere%7D%20%3D%20113.09%20%5Ctext%7B%20%7D%20cm%5E3)
When the sphere is inserted into the cylinder the volume of the things that are inside of the container are added up, so the volume would be the volume of the water plus the volume of the sphere, we can use this information to calculate the height of the water as shown below:
![\text{total volume} = \text{water volume} + \text{sphere volume}\\\text{total volume} = 678.6 + 113.1 = 791.7\\\text{total volume} = \pi*r^2*h_{new}\\791.7 = \pi*(6)^2*h_{new}\\h_{new} = \frac{791.7}{\pi*36} = 7.00016\text{ } cm](https://tex.z-dn.net/?f=%5Ctext%7Btotal%20volume%7D%20%3D%20%5Ctext%7Bwater%20volume%7D%20%2B%20%5Ctext%7Bsphere%20volume%7D%5C%5C%5Ctext%7Btotal%20volume%7D%20%3D%20678.6%20%2B%20113.1%20%3D%20791.7%5C%5C%5Ctext%7Btotal%20volume%7D%20%3D%20%5Cpi%2Ar%5E2%2Ah_%7Bnew%7D%5C%5C791.7%20%3D%20%5Cpi%2A%286%29%5E2%2Ah_%7Bnew%7D%5C%5Ch_%7Bnew%7D%20%3D%20%5Cfrac%7B791.7%7D%7B%5Cpi%2A36%7D%20%3D%207.00016%5Ctext%7B%20%7D%20cm)
a) The volume of the water is approximately 678.6 cm³.
b) The volume of the sphere is approximately 113.1 cm³.
c) The new height of the water is approximately 7 cm, one cm higher than before.
For 3 the sides are going to be equal since the angles are equal, I’ll explain the comments
Answer:
C. -4 = 16x
Step-by-step explanation:
That is the graph i got when I typed -4 = 16x.
Brainliest Please!!!
- Hermionia
A = person is female
B = person holds a managerial position
A) explain what P(A)= 0.47 means in context = of the population, 47% is composed of females.
<span>B) explain what P(B|A)= 0.34 means in context = 34% is the probability that the person chosen is a female manager
</span>
<span>C) what is the probability that a randomly chosen employed person is a male? 53%</span>
<span>D) what is the probability that a randomly chosen employed person is a female manager? 34% </span>
<span>E) what is the probability that a randomly chosen employed female is not a manager? 72%
</span>
Answer:
or (depends on what your curriculum requires)
Step-by-step explanation:
This question is asking for how many shares this person can buy when they have $2000 and each share costs $237.68
So how many 237.68s go into 2000? Well 2000 divided by 237.68 is roughly 8.14. However, you can not buy .14 of a share, so you round down to 8 full shares.
Now its time to write the inequality. Lets assign "x" as the amount of shares the character can buy. We know that they can buy as much as 8 shares, but remember that they can actually buy less than that, so anything below 8 shares and 8 shares would be x
8, indicating that x, the number of shares, can be 8 and anything less than that.
If you want to be really accurate, you could also add that x
0, since you cant buy 0 amount of shares. So then your answer would be
, meaning that they can buy between 0 and 8 shares, including 0 and 8
Lmk if this helped, was incorrect, or if you wanted me to clarify anything :)