Answer:
The z statistic is 0.23.
Step-by-step explanation:
Test statistic (z) = (sample mean - population mean) ÷ sd/√n
sample mean = 104 mg
population mean (mu) = 100 mg
sd = 55 mg
n = 10
z = (104 - 100) ÷ 55/√10 = 4 ÷ 17.393 = 0.23
Answer:
you're not doing anything wrong
Step-by-step explanation:
In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.
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Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.
As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.
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This is a good one to discuss with your teacher.
Answer:

Step-by-step explanation:
Hi there!
In
, m is the slope of the line and b is the y-intercept (the value of y when x is 0). y and x remain the same but m and b are replaced with numbers.
Given that the slope is -5, plug it into
:

Now, to solve for b, plug in the given point (-2,4):

Subtract 10 from both sides to isolate b:

Therefore, the y-intercept of this line is -6. Plug this back into
as b:

I hope this helps!