Answer:
see the explanation and the attached figure
Step-by-step explanation:
we have
----> given
Divide by -2 both sides
----> by Division Property of Equality
Simplifying

Subtract 1 both sides
----> by Subtraction Property of Equality
Simplifying

10) because of the alternative exterior angle theorem angle 2 is the same as angle 8 and because of the vertical angles congruence theorem angles 2 and 4 are also the same so if angle 2 is the same as both 4 and 8,
then x=5 because 4x+57 =77
subtract 57 from both sides and 4x=20
divide both sides by 4 and x equals 5
Answer:
40 student 110 adult
this is using desmos
but to smash the equation you can go like basically we have to cancel out each variable to solve for the other
3x + 8y = 1000
x + y < =150
-3(x + y <= 150)
-3x -3y = -450
3x + 8y = 1000
5y = 550
y= 110
3x + 8 y = 1000
-8(x+y<=150) = -8x - 8y <= -1200
-5x = -200


x= 40
40 kids 110 adults
Answer:
A sample size of 128 is needed.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so 
Now, find the margin of error M as such

In which
is the standard deviation of the population(square root of the variance) and n is the size of the sample.
How large should a sample be if the margin of error is 1 minute for a 93% confidence interval
We need a sample size of n, which is found when
. We have that
. So





Rounding up
A sample size of 128 is needed.