We have:
Thus:
Adding
gives:
Factoring gives:
Thus, we have:
or
.
Note that because
, there will be no solutions
of the form
for positive integer
and solution
. So we find the basic values of
giving
.
For
with positive
,
(this can be seen easily from the unit circle. But
, a contradiction. So we examine the case in which
.
In this case,
. So this is the only solution to this equation.
Substituting this back in, we have
, as desired. So this is a valid solution.
Thus,
.
Answer:
The answer would be 6.8 I believe.
Step-by-step explanation:
Step 1: You would have to find which side is the opposite , hypotenuse and adjacent to the degree. 8 is adjacent and x is the hypotenuse. Then you can use a strategy I like which is called SOH CAH TOA to find if you need to use sin, cosine, or tangent. It tells you in the acronym too how to set up the equation.
Step 2: In this case we need cosine since it is adjacent over hypotenuse (<u>C in the acronym is for cosine A is for adjacent and H is for hypotenuse)</u> so the equation would be Cos32= 8/x
Step 3: Then solve the equation, so you would do
8cos32=x
Put that into the calculator (I'm using a TI-84) and make sure it is in degree mode and you would get 6.78 but round that up to 6.8.
I hope this helps and that I did it right!!
-27 1/3 + x = 10
-27 1/3 (+27 1/3) + x = 10 (+27 1/3)
x = 37 1/3 yards
Answer:
A 95% confidence interval estimate of the population mean (average) daily balance of all the checking accounts is $274.32 to $331.68
Step-by-step explanation:
Consider the provided information.
A random sample of 21 checking accounts at the bank are chosen,
That means n=21
df = n-1
df = 21-1=20
We need to Construct and interpret a 95% confidence interval.
Determine t critical value for 95% confidence interval.
0.95=1-α
α=0.05
The sample size is small and it is a two tailed test.
From the t value table confidence interval is 2.086
An average daily balance is $303 and a standard deviation of $63.
Substitute the respective values.
A 95% confidence interval estimate of the population mean (average) daily balance of all the checking accounts is $274.32 to $331.68