A 95% confidence interval for a population mean is determined to be 100 to 120. if the confidence coefficient is reduced to 0.90
1 answer:
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ANSWER
(3,-1)
EXPLANATION
The given system of equations is :
5x+y=14
2x-y=7
For the first equation when x=0,
5(0)+y=14
y=14
The y-intercept is (0,14).
When y=0, 5x+0=14
The x-intercept is (2.8,0).
We plot the intercepts and draw a straight line through them to obtain the graph of 5x+y=14 as shown in the attachment.
We repeat the same process for the second equation 2x-y=7.
The intercepts are (0,-7) and (3.5,0)
The solution to the system is the point of intersection of the two straight lines.
The two straight lines intersected at
(3,-1)
Hence x=2, y=-1
(3,-1)
EXPLANATION
The given system of equations is :
5x+y=14
2x-y=7
For the first equation when x=0,
5(0)+y=14
y=14
The y-intercept is (0,14).
When y=0, 5x+0=14
The x-intercept is (2.8,0).
We plot the intercepts and draw a straight line through them to obtain the graph of 5x+y=14 as shown in the attachment.
We repeat the same process for the second equation 2x-y=7.
The intercepts are (0,-7) and (3.5,0)
The solution to the system is the point of intersection of the two straight lines.
The two straight lines intersected at
(3,-1)
Hence x=2, y=-1
Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25.
