Answer:
a
The 95% confidence interval is 
b
The sample proportion is 
c
The critical value is 
d
The standard error is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is 
The alternative hypothesis is 
Generally the sample proportion is mathematically evaluated as
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
Next we obtain the critical value of 
from the normal distribution table, the value is
Generally the standard of error is mathematically represented as
substituting values
The margin of error is
=> 
=> 
The 95% confidence interval is mathematically represented as
=> 
=>
Answer:
Step-by-step explanation:
given that tonya charges 20$ monthly fee and 3$ per mile of her dog-walking service.
and beth does not charge any monthly fee but charges 5$ per mile of the dog walked in.
let x be the number of miles dog has walked in a month.
the amount tonya will charge on x miles = fixed monthly fee + number of miles * charge per mile = 20+3x
and the amount beth will charge on x miles = 0+ 5*x = 5x.
we are asked to find the x-value for which beth chargeable amount = tonya chargeable amount
that is 5x = 20+3x
5x-2x = 20
2x=20
x=
hence number of miles for which tonya and beth will charge the same amount is 10.
Louise wants to factorize completely the given polynomial 
Grouping first, second terms together and third, fourth terms together
=
Taking 
common from first and second terms of the given expression and taking 5 common from the third and fourth terms.
=
Taking (x+3) common from the given expression,
=
is the completely factored form.
