24X16.9= 405.6oz is the weight
Answer:
c) 6x - 5y = 15
Step-by-step explanation:
Slope-intercept form of a linear equation: ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
(where m is the slope and b is the y-intercept)
Maria's line: ![y=-\dfrac{5}{6}x+8](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B5%7D%7B6%7Dx%2B8)
Therefore, the slope of Maria's line is ![-\frac{5}{6}](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B6%7D)
If two lines are perpendicular to each other, the product of their slopes will be -1.
Therefore, the slope of Nate's line (m) is:
![\begin{aligned}\implies m \times -\dfrac{5}{6} &=-1\\m & =\dfrac{6}{5}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20m%20%5Ctimes%20-%5Cdfrac%7B5%7D%7B6%7D%20%26%3D-1%5C%5Cm%20%26%20%3D%5Cdfrac%7B6%7D%7B5%7D%5Cend%7Baligned%7D)
Therefore, the linear equation of Nate's line is:
![y=\dfrac{6}{5}x+b\quad\textsf{(where b is some constant)}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B6%7D%7B5%7Dx%2Bb%5Cquad%5Ctextsf%7B%28where%20b%20is%20some%20constant%29%7D)
Rearranging this to standard form:
![\implies y=\dfrac{6}{5}x+b](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Cdfrac%7B6%7D%7B5%7Dx%2Bb)
![\implies 5y=6x+5b](https://tex.z-dn.net/?f=%5Cimplies%205y%3D6x%2B5b)
![\implies 6x-5y=-5b](https://tex.z-dn.net/?f=%5Cimplies%206x-5y%3D-5b)
Therefore, <u>option c</u> could be an equation for Nate's line.
Either a histogram or a Dot plot.
The radius of can is 2 inches
<em><u>Solution:</u></em>
Given that, Can has a volume of 62.8 cubic inches
Height of can is 5 inches
To find: Radius of can
The can is of shape cylinder
<em><u>The volume of a cylinder can be found using the formula:</u></em>
![V = \pi {r}^{2} h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
Where, "r" is the radius and "h" is the height of cylinder
Substituting the values we get,
![62.8 = 3.14 \times r^2 \times 5\\\\62.8 = r^2 \times 15.7\\\\r^2 = \frac{62.8}{15.7}\\\\r^2 = 4\\\\\text{Take square root on both sides }\\\\r = 2](https://tex.z-dn.net/?f=62.8%20%3D%203.14%20%5Ctimes%20r%5E2%20%5Ctimes%205%5C%5C%5C%5C62.8%20%3D%20r%5E2%20%5Ctimes%2015.7%5C%5C%5C%5Cr%5E2%20%3D%20%5Cfrac%7B62.8%7D%7B15.7%7D%5C%5C%5C%5Cr%5E2%20%3D%204%5C%5C%5C%5C%5Ctext%7BTake%20square%20root%20on%20both%20sides%20%7D%5C%5C%5C%5Cr%20%3D%202)
Thus the radius of can is 2 inches
Step-by-step explanation:
a probability is always
desired cases / total possible cases.
there is the theoretical probability in such cases, where we simply assume that all sides of such a die (or solid) truly have the same probability.
and then we have experimental probability, where we use only the actual data we got in the experiments to calculate the probability of that particular die (with all its actual internal imperfections) to roll certain results.
so, in our experiments how many total cases do we have ?
200.
how many desired cases (a number greater than 10, that means 11 or 12 as result) do we have ?
well, the sum of all appearances of 11s and 12s :
16 + 18 = 34
that means our experimental probability to get a number greater than 10 is
34/200 = 17/100 = 0.17
FYI
while the theoretical probability with an ideal die is
total cases : 12 (1 .. 12)
desired cases : 2 (11, 12)
the probability is
2/12 = 1/6 = 0.166666666...
it is actually a tiny little bit lower than what we observed in the experiments.