The blue diamond company advertises that their nut mix contains (by weight) 40% cashews, 15% brazil nuts, 20% almonds and only 25% peanuts. the truth-in-advertising investigators took a random sample (of size 20 lbs) of the nut mix and found the distribution to be as follows:
5 lbs of cashews,
6 lbs of brazil nuts,
6 lbs of almonds and 3 lbs of peanuts.
a. at the 0.05 level of significance, is the claim made by blue diamond true?

At the 0.05 level of significance,  the claim made by Blue Diamond is true

Step-by-step explanation:

Given that the Blue Diamond Company advertises that their nut mix contains (by weight) 40% cashews, 15% Brazil nuts, 20% almonds and only 25% peanuts.

(Two tailed chi square test at 5% significance level)

Chi square is calculated as (Obs_exp)^2/Expected

CashewsBrazil nutsAlmondsPeanutsTotal

Observed566320

Expected  40%15%20%25%1

Expected  834520

Chi square1.125310.85.925

df = 3

p value = 0.1153

Since p value >0.0 we accept null hypothesis.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

arc length = radius * x ( in radians)

6 * pi = 18 * x

divide by 18 on each side

6 pi / 18 = x

pi/3 = x

the angle is pi / 3 radians

or   60 degrees