Answer:
The numbers are 11 and 49.
Step-by-step explanation:
<em>x = 5y - 6 </em> This is just the first sentence written as an equation.
<em>x + y = 60</em> This is just the second sentence written as an equation.
<em>5y - 6 + y = 60</em> Substitute x for what you know it is equal to
<em>6y - 6 = 60</em> Collect like terms
<em>6y = 66</em> Add 6 to each side
<em>y = 11</em> Divide each side by 6
<em>x = 5 × 11 - 6 </em> Substitute y for what you know it is
<em>x = 55 - 6</em> Simplify by working out 5 × 11 = 55
<em>x = 49</em> Subtract 6 from 55 to get 49
Answer:
surface area of the smaller figure ≈ 1474.64 m²
Step-by-step explanation:
The figures are similar base on the question . The surface area and the volume of the larger figure is given while only the figure of the smaller figure is given.
To find the surface area of the smaller figure we simply use the ratios. That is the scale factors.
Therefore, they are similar figure the scale factor can be represented as a:b.
The scale factor for volume is cubed.
volume of larger figure/volume of the small figure = a³/b³
4536/2625 = a³/b³
a/b = 16.5535451/13.7946209
Note that for two similar solid with scale factor a:b the surface area ratio is a²: b² (the scale factor is square)
16.55²/13.79² = 2124/x
273.9025/190.1641 = 2124/x
cross multiply
273.9025x = 403908.54840
x = 403908.54840/273.9025
x = 1474.6435261
x ≈ 1474.64 m²
Answer:
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the population, we have that:
Mean = 0.5
Standard deviaiton = 0.289
Sample of 12
By the Central Limit Theorem
Mean = 0.5
Standard deviation 
The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.
