Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 In which section of the graph does the actual solution
to the system lie? 1 2 3 4
2 answers:
Answer:
The section shows below represents the solution of the system.
Step-by-step explanation:
Given system of inequalities,
y ≤ -0.75x,
y ≤ 3x - 2
Graphing y ≤ -0.75x :
Since, the related equation of y ≤ -0.75x is y = 0.75x
If x = 0, 1,
y = 0, 0.75,
Thus, join the points (0, 0) and (1, 0.75) in coordinate plane,
0 ≤ -0.75(0) ( true )
So, the shaded region will be contain the origin.
Graphing y ≤ 3x - 2 :
Since, the related equation of y ≤ 3x - 2 is y = 3x - 2
x = 0, y = - 2
y = 0, x = 2/3,
Thus, join the points (0, -2) and (2/3, 0) in coordinate plane,
0 ≤ 3(0) - 2 ( false )
So, the shaded region won't contain the origin.
Also, ' ≤ ' represents the solid line,
By the above explanation we can make the feasible region that shows the solution of the system ( shown below )
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The summation indicates the sum from n = 1 to n = 3 of the expression 2(n+5).
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42
Answer:
1
The probability is
2
The probability is
Step-by-step explanation:
From the question we are told that
The population mean is
The standard deviation is
The sample size is
Generally the standard error for the sample mean is mathematically evaluated as
substituting values
Apply central limit theorem[CLT] we have that
substituting values
From the z-table we have that
For the second question
Apply central limit theorem[CLT] we have that
substituting values
From the z-table we have that
Thus
Answer:
- Keisha’s experimental probability is 1/50.
- When the inventory is 4000 clocks, the prediction is that 3920 clocks will work.
- Keisha will have more than 97% of the products working.
Step-by-step explanation:
These are three prediction that Keisha can make based on the report that said 6 of 300 clocks tested weren't working.
Base on that information, Keisha can calculate an experimental probability, dividing <em>clocks that don't work properly </em>by <em>the total amount of clocks</em><em>:</em>
<em></em>
Therefore, the probability of success is 100% - 2% = 98%.
This means that Keisha has a probability of having 98% of all clocks functioning properly. So, she can make the prediction:<em> from 4000 clocks, 3920 will work. </em>Also, she can predict that she will actually have more than 97% working, because the experimental probability is higher than that.