Answer:
Step-by-step explanation:
a) We want to prove that 
. Then, we can do that proving that every element of 
is an element of 
too.
Then, suppose that 
. From the definition of inverse image we know that 
, which is equivalent to 
and 
. But, as 
we can affirm that 
and, because we have 
.
Therefore, 
.
b) We want to prove that 
. Here we will follow the same strategy of the above exercise.
Assume that 
. Then, there exists 
such that 
. But, as we know that 
and 
. From this, we deduce 
and 
. Therefore, 
.
c) Consider the constant function 
for every real number 
. Take the sets 
and 
.
Notice that 
=Ø, so 
=Ø. But 
and 
, so 
.
The sample of students required to estimate the mean weekly earnings of students at one college is of size 96.04.
For the population mean (μ) , we have the (1 - α)% confidence interval as:
X ± Zₐ / 2 + I / √n
margin of error = MOE = Zₐ / 2 ×I / √n
We are given:
σ = $10
MOE = $2
The critical value of z for 95% confidence level is
Zₐ / 2 = Zₓ = 1.96 ( for x as 0.025)
n = (1.96 (10))²
n = 96.04
Thus, the sample of students required to estimate the mean weekly earnings of students at one college is of size, 96.04.
Learn more about estimation here:
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The quotient is simply a fancy would for the remainder.
We then need to divide the numbers as usual:
3216/8 = 1608/4 = 804/2 = 402
As this is a whole number there is no remainder and the quotient is 0.
Answer:
(x, y) = (4, -3)
Step-by-step explanation:
Relative to straight east with angles measured CCW, the vector is ...
5∠-36.9° = 5(cos(-36.9°), sin(-36.9°)) = 5(0.8, -0.6) = (4, -3)
