1). $2,700 is (2,700/6,000) = 45% of 6,000.
It took 6 years to earn it, so it earned (45%/6) = 7.5% each year.
That's the simple-interest rate.
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2). The investment earns 4.5% each year, so it earned 9% in 2 years.
The $1,150.65 is the 9% of the original investment. Call it V.
1150.65 = 0.09 x V .
Divide each side by 0.09 :
V = 1150.65 / 0.09 = $12,785 .
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3). There are 18 marbles in the bag all together.
a). 8 of them are green. If you close your eyes and pull out 1 marble,
the probability that it's a green one is
8/18 = 4/9 = 44.4% .
b). If it was a red marble, and you put it in your pocket, then
there are only 17 in the bag now, and 8 of them are still green.
If you pull another one, the probability that it's green is
8/17 = 47.1% .
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5). There are 10 marbles in the bag all together.
(The second sentence doesn't say anything, and doesn't mean anything.)
If you pull out a silver marble and put it in your pocket, then
there are 9 marbles in the bag, and 2 of them are orange.
The probability of pulling an orange marble now is
2/9 = 22.2% .
Answer:
So, the volume is:
Step-by-step explanation:
We get the limits of integration:
We use the spherical coordinates and we calculate a triple integral:
![V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}\int_0^4 \rho^2 \sin \varphi \, d\rho\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \left[\frac{\rho^3}{3}\right]_0^4\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \cdot \frac{64}{3} \, d\varphi\, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} [-\cos \varphi]_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} \sqrt{2} \, d\theta\\\\](https://tex.z-dn.net/?f=V%3D%5Cint_0%5E%7B2%5Cpi%7D%5Cint_%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%5E%7B%5Cfrac%7B3%5Cpi%7D%7B4%7D%7D%5Cint_0%5E4%20%20%5Crho%5E2%20%5Csin%20%5Cvarphi%20%5C%2C%20d%5Crho%5C%2C%20d%5Cvarphi%5C%2C%20d%5Ctheta%5C%5C%5C%5CV%3D%5Cint_0%5E%7B2%5Cpi%7D%5Cint_%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%5E%7B%5Cfrac%7B3%5Cpi%7D%7B4%7D%7D%20%5Csin%20%5Cvarphi%20%5Cleft%5B%5Cfrac%7B%5Crho%5E3%7D%7B3%7D%5Cright%5D_0%5E4%5C%2C%20d%5Cvarphi%5C%2C%20d%5Ctheta%5C%5C%5C%5CV%3D%5Cint_0%5E%7B2%5Cpi%7D%5Cint_%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%5E%7B%5Cfrac%7B3%5Cpi%7D%7B4%7D%7D%20%5Csin%20%5Cvarphi%20%5Ccdot%20%5Cfrac%7B64%7D%7B3%7D%20%5C%2C%20d%5Cvarphi%5C%2C%20d%5Ctheta%5C%5C%5C%5CV%3D%5Cfrac%7B64%7D%7B3%7D%20%5Cint_0%5E%7B2%5Cpi%7D%20%5B-%5Ccos%20%5Cvarphi%5D_%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%5E%7B%5Cfrac%7B3%5Cpi%7D%7B4%7D%7D%20%20%5C%2C%20d%5Ctheta%5C%5C%5C%5CV%3D%5Cfrac%7B64%7D%7B3%7D%20%5Cint_0%5E%7B2%5Cpi%7D%20%5Csqrt%7B2%7D%20%5C%2C%20d%5Ctheta%5C%5C%5C%5C)
we get:
![V=\frac{64}{3} \int_0^{2\pi} \sqrt{2} \, d\theta\\\\V=\frac{64\sqrt{2}}{3}\cdot[\theta]_0^{2\pi}\\\\V=\frac{128\sqrt{2}\pi}{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B64%7D%7B3%7D%20%5Cint_0%5E%7B2%5Cpi%7D%20%5Csqrt%7B2%7D%20%5C%2C%20d%5Ctheta%5C%5C%5C%5CV%3D%5Cfrac%7B64%5Csqrt%7B2%7D%7D%7B3%7D%5Ccdot%5B%5Ctheta%5D_0%5E%7B2%5Cpi%7D%5C%5C%5C%5CV%3D%5Cfrac%7B128%5Csqrt%7B2%7D%5Cpi%7D%7B3%7D)
So, the volume is:
Answer: -3.3%
By not knowing how i did it, means you will still not know how to do it next time you encounter a similar problem.
Knowing how to solve a problem is just as important or even more important than just knowing the solution.
First we have to find the median
The median is 19 when we cross off all the numbers
Now we have 11 12 15 16 and 17 in the first quartile
Cross 11 and 12 and cross 16 and 17, off which leaves you with 15
Answer is option d
13. Supplementary angles are two angles that add up to 180 degrees.
3x + x = 180
Combine like terms:
4x = 180
4x divided by 4 = x
180 divided by 4 = 45
x = 45
Equation:
3(45) + 45 = 180
135 + 45 = 180 (TRUE STATEMENT)
Angle A = 135 degrees
Angle B = 45 degrees
This is correct as 135 + 45 adds up to 180 (making it a supplementary angle) AND 135 is 3 times bigger than 45 so it fits the answer’s standard.
Ima do number 14 in the comments as I don’t want to take too long to show number 13.
