Answer:
Height: 8.471
Volume: 2245.641cm3
Step-by-step explanation:
To solve this problem we need to find the volume of the cone, then the volume of the semi sphere, and then, sum all together.
To obtain the volume of the cone, we need to focus our attention in the triangle that already was given to us, since its height is the same as the height of the cone.
We can use the tan(26,7) since it relates the radius of the cone, and its height.
This gives us. h=9/tan(27,9)= 8.471 cm
The volume of the cone is then. 718.629cm3
The volume of the spehere is 1527.012 cm3
FInally the volumen of the toy is the sum of both volumes previously obtained:
2245.641cm3.
Refer the attached picture for a more detailed procedure.
Answer:
- $12,000 at 4%
- $9,000 at 2%
Step-by-step explanation:
If x represents the amount invested at 4%, then the total interest earned is ...
0.04x + 0.02(21000 -x) = 660
0.02x = 240 . . . . . . . . . . . simplify, subtract 420
x= 240/0.02 = 12,000 . . . . amount invested at 4%
21,000 -x = 9,000 . . . . . . . . amount invested at 2%
The amount invested at 2% is $9,000.
The amount invested at 4% is $12,000.
_____
<em>Comment on method of solution</em>
These problems can usually be solved using one variable for the amount associated with the highest contribution to the mix. Here, that is the amount getting 4% interest. This keeps the numbers in the solution positive, helping to minimize errors. As you can see, the solution develops in about 2 or 3 steps. Other methods can take longer.
Answer: 0.4402
Step-by-step explanation:
Given : The proportion of the registered voters in a country are Republican = P=0.50
Sample space = 36
The test statistic for proportion :-
![z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bp-P%7D%7B%5Csqrt%7B%5Cdfrac%7BP%281-P%29%7D%7Bn%7D%7D%7D)
For p= 0.477
![z=\dfrac{0.477-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{36}}}\approx-0.276](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.477-0.50%7D%7B%5Csqrt%7B%5Cdfrac%7B0.50%281-0.50%29%7D%7B36%7D%7D%7D%5Capprox-0.276)
For p= 0.58
![z=\dfrac{0.58-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{36}}}\approx0.96](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.58-0.50%7D%7B%5Csqrt%7B%5Cdfrac%7B0.50%281-0.50%29%7D%7B36%7D%7D%7D%5Capprox0.96)
Now, the probability that the proportion of freshmen in the sample is between 0.477 and 0.58 (by using the standard normal distribution table):-
![P(0.477](https://tex.z-dn.net/?f=P%280.477%3Cx%3C0.58%29%3DP%28-0.276%3Cz%3C0.96%29%5C%5C%5C%5C%3DP%28z%3C0.96%29-P%28z%3C-0.276%29%5C%5C%5C%5C%3D0.8314724-%200.391274%3D0.4401984%5Capprox0.4402)
Hence, the probability that the proportion of freshmen in the sample is between 0.477 and 0.580 = 0.4402