Sin x + 22 degrees equals cos 2x - 7 degrees
2 answers:
sin22 = 0.375
cos7 = 0.993
cos2x = 1 - 2sin^2x
solve like a regular quadratic by completing the square: 2sin^2x + sinx = 0.632
2sin^2x + sinx - 1 = 0.632 - 1
(2sinx - 1)(sinx + 1) = -0.368
2 possible solutions:
1) 2sinx - 1 = -0.368
2sinx - 1 +1 = -0.368+1
2sinx = 0.632
2sinx/2 = 0.632/2
sinx = 0.316
x = sin^-1 (0.316) = 18.42
2) sinx + 1 = -0.368
sinx + 1 -1 = -0.368-1
sinx = -1.368
x = sin^-1 (-1.368) = UNDEFINED
Therefore x = 18.42
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Answer:
a
The point estimate of the population mean is
b
The 80% confidence level is
c
There is 80% confidence that the true population mean lies within the confidence interval.
Step-by-step explanation:
From the question we are told that
The sample size is n = 18
The standard deviation is
The sample mean is
Generally the point estimate of the population mean is equivalent to the sample mean whose value is
Given that the confidence interval is 80% then the level of significance is mathematically represented as
Next we obtain the critical value of from the normal distribution table
The value is
Generally the margin of error is mathematically evaluated as
=>
=>
Generally the 80% confidence interval is mathematically represented as
=>
=>
The interpretation is that there is 80% confidence that the true population mean lies within the limit
Given:
A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8).
To find:
The corresponding quadratic expression.
Solution:
If graph of a function intersect the x-axis at c, then (x-c) is a factor of the function.
A quadratic function has x-intercepts 2 and 6. It means (x-2) and (x-6) are two factors of the required quadratic function.
The function is defined as:
...(i)
Where, a is a constant.
The vertex of the quadratic function is (4,8). It means the point (4,8) will satisfy the function.
Substituting x=4 and P(x)=8 in (i).
Divide both sides by -4.
Putting in (i), we get
Therefore, the correct option is B.