<span>Mean = 270
Standard deviation = 10
x = 255
Formula for z-score, z = (x - mean)/SD
z = (255 - 270) / 10
=> z = -15 / 10 => z = -1.5
So by referring to z-table, -1.5 correlates to 0.0668 that implies to 0.07
So 7% of the boxes of Apples weight less than 255oz.
The percentage of boxes is in the range of 255 oz and 270 oz,
Now calculating the requiring percentage 50% - 7% = 43%</span>
The situation can be modeled by a geometric sequence with an initial term of 284. The student population will be 104% of the prior year, so the common ratio is 1.04.
Let \displaystyle PP be the student population and \displaystyle nn be the number of years after 2013. Using the explicit formula for a geometric sequence we get
{P}_{n} =284\cdot {1.04}^{n}P
n
=284⋅1.04
n
We can find the number of years since 2013 by subtracting.
\displaystyle 2020 - 2013=72020−2013=7
We are looking for the population after 7 years. We can substitute 7 for \displaystyle nn to estimate the population in 2020.
\displaystyle {P}_{7}=284\cdot {1.04}^{7}\approx 374P
7
=284⋅1.04
7
≈374
The student population will be about 374 in 2020.
Answer:4^2-(8x1)=8
Step-by-step explanation:
B. Angle B= Angle E
As this would only prove the AAA Similarity theorem, but not any Congruence Rule
Let 
be the dimensions of the rectangle. We know the equations for both area and perimeter:
So, we have the following system:
From the second equation, we can deduce
Plug this in the first equation to get
Refactor as
And solve with the usual quadratic formula to get
Both solutions are feasible, because they're both positive.
If we chose the positive solution, we have
If we choose the negative solution, we have
So, we're just swapping the role of 
and 
. The two dimensions of the rectangle are 
and 
