Answer:
Step-by-step explanation:
a) Sample statistics are used to estimate population value. Since 48% is a sample proportion, therefore, it is a sample statistic.
b) For 95% confidence level, z* = 1.96.
\hat{p}\pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}= 0.61\pm 0.61\sqrt{\frac{0.61(1-0.61)}{1578}}=0.61\pm 0.024 \ or (0.586, 0.634).
We are 95% confident that the true proportion of US residents who think marijuana should be made legal lies between 58.6% and 63.4%.
c)
\\np=1578(0.61)=962.58
\\n(1-p)=1578(1-0.61)=615.42
Since both np and n(1-p), are at least 10, the normal model is a good approximation for these data.
d) As the lower limit of confidence interval is less than 0.5, less than 50% population is also a plausible value of true proportion. This means the statement "Majority of Americans think marijuana should be legalized" is not justified.
Answer:
See explanation
Step-by-step explanation:
Triangles ΔABC and ΔBAD are congruent. So,
- AB ≅ BA;
- AC ≅ BD;
- BC ≅ AD;
- ∠ABC ≅ ∠BAD;
- ∠BCA ≅ ∠ADB;
- ∠CAB ≅ ∠DBA.
Consider triangles AEC and BED. In these triangles,
- AC ≅ BD;
- ∠EAC ≅ ∠EBD (because ∠CBA ≅ ∠BAD);
- ∠AEC ≅ ∠BED (as vertical angles).
So, ΔAEC ≅ ΔBED. Thus,
AE ≅ EB.
This means that segment CD bisects segment AD.
Answer:
Answer C: Becky is 27; John is 31
Step-by-step explanation:
1. John is 4 years older than Becky--27(Becky's age)+ 4=31(John's age)
2. Sum of their ages is 58--27(Becky's age)+31(John's age)=58
So, the correct answer is Answer C.
Given that PQ and RS intersect to form four right angles, then they form an angle of 90 degrees, this implies that:
if the meet at point O,
then;
∠POR=∠POS=∠QOS=∠ROQ=90°
Therefore the correct statement is:
PQ is perpendicular to RS
that is to mean:
PQ⊥RS
The answer is C.
When we say an amount increased by some percentage, we usually mean that percentage is added to the original amount. In symbols, if there were V visitors in 2003, then in 2005 there were
V + 200%×V = 3V
visitors. And in 2007 (after 2 more years), there were
3(3V) = 9V
visitors. This represents an increase of
(9V -V)/V × 100% = 800%
The number of daily visitors in 2007 was 800% more than in 2003.
