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galben [10]
3 years ago
14

Volume of sphere with radius of 6

Mathematics
2 answers:
viktelen [127]3 years ago
8 0

Answer is provided in the image attached.

Solnce55 [7]3 years ago
5 0

Answer:

904.8  cm rounded (904.78 cm^3) to the nearest tenth.

Step-by-step explanation:

V= 904.8  cm rounded (904.78 cm^3) to the nearest tenth.


Step-by-step explanation:


The volume of a sphere is given as  4/3πr^3

There is only one variable, the radius, which we are given in the problem.

since the radius is 6 cm, we can plug that in to the formula

4/3π6^3


Put this into the calculator, and we see that the volume is  

904.8  cm rounded (904.78 cm^3) to the nearest tenth.



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Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams):
Tpy6a [65]

Answer:

98% confidence interval for the difference μX−μY = [ 0.697 , 7.303 ] .

Step-by-step explanation:

We are give the data of Measurements of the sodium content in samples of two brands of chocolate bar (in grams) below;

Brand A : 34.36, 31.26, 37.36, 28.52, 33.14, 32.74, 34.34, 34.33, 29.95

Brand B : 41.08, 38.22, 39.59, 38.82, 36.24, 37.73, 35.03, 39.22, 34.13, 34.33, 34.98, 29.64, 40.60

Also, \mu_X represent the population mean for Brand B and let \mu_Y represent the population mean for Brand A.

Since, we know nothing about the population standard deviation so the pivotal quantity used here for finding confidence interval is;

        P.Q. = \frac{(Xbar -Ybar) -(\mu_X-\mu_Y)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}  } } ~ t_n__1+n_2-2

where, Xbar = Sample mean for Brand B data = 36.9

            Ybar = Sample mean for Brand A data = 32.9

              n_1  = Sample size for Brand B data = 13

              n_2 = Sample size for Brand A data = 9

              s_p = \sqrt{\frac{(n_1-1)s_X^{2}+(n_2-1)s_Y^{2}  }{n_1+n_2-2} } = \sqrt{\frac{(13-1)*10.4+(9-1)*7.1 }{13+9-2} } = 3.013

Here, s^{2}_X and s^{2} _Y are sample variance of Brand B and Brand A data respectively.

So, 98% confidence interval for the difference μX−μY is given by;

P(-2.528 < t_2_0 < 2.528) = 0.98

P(-2.528 < \frac{(Xbar -Ybar) -(\mu_X-\mu_Y)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}  } } < 2.528) = 0.98

P(-2.528 * s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} < (Xbar -Ybar) -(\mu_X-\mu_Y) < 2.528 * s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} ) = 0.98

P( (Xbar - Ybar) - 2.528 * s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} < (\mu_X-\mu_Y) < (Xbar - Ybar) + 2.528 * s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} ) = 0.98

98% Confidence interval for μX−μY =

[ (Xbar - Ybar) - 2.528 * s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} , (Xbar - Ybar) + 2.528 * s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} ]

[ (36.9 - 32.9)-2.528*3.013\sqrt{\frac{1}{13} +\frac{1}{9} , (36.9 - 32.9)+2.528*3.013\sqrt{\frac{1}{13} +\frac{1}{9} ]

[ 0.697 , 7.303 ]

Therefore, 98% confidence interval for the difference μX−μY is [ 0.697 , 7.303 ] .

                     

4 0
3 years ago
This table shows the size, in acres, of four large water parks.
Korvikt [17]
The answer is 65, hope this helps
6 0
3 years ago
Read 2 more answers
Consider a civilization broadcasting a signal with a power of 2.0×104 watts. The Arecibo radio telescope, which is about 300 met
Vitek1552 [10]

For light: Inverse Square Law 

<span>
The signal is weaken by the inverse square of the difference of distances this means that one over the square of the difference. </span>

<span>
</span>

Therefore, 70000LY / 141 LY =496.45 and that squared =246462.602 times less signal, or 1/246462.602.


 2 For a circular telescope like the Arecibo radio telescope that equals Pi times the radius squared. Sensitivity of the telescope depends on its area.<span>
The new telescope needs 246462.60 times that area to have enough sensitivity </span>

<span>
<span>(150 x 150 x Pi) = 70 685 sq m area for the Arecibo telescope and that times 246462.60
= 1.74212 x 10^10</span></span>

<span><span>
</span></span>

What is the diameter of a circle with that area?

 <span>
<span>1. Divide the area by Pi = 5.548156 x 10^9
2. Take the square root of the result to find the radius = 74485.94293</span></span>

3. Multiply by 2 to find the diameter = <span>148971.886</span>

7 0
3 years ago
14 ten thousand + 12 thousand in place value chart
quester [9]
14,0000 srry if it is wrong I am really good at math
6 0
3 years ago
What is the inverse of the function f(x) = x – 12?
SashulF [63]
y=x-12\\&#10;x=y+12\\&#10;f^{-1}(x)=x+12
7 0
3 years ago
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