Answer:
The appropriate null hypothesis is 
The appropriate alternative hypothesis is 
Step-by-step explanation:
Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.
At the null hypothesis, we test if the proportion is still the same, that is, of 
. So
We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.
Decreased, so at the alternative hypothesis, it is tested if the proportion is less than 0.25, that is:
Answer:
- <em>convert </em>the mixed fractions to improper fractions (where the numerator is greater than or equal to the denominator): multiply the whole number part by the fraction's denominator, add that to the numerator, write the result on top of the denominator.
- if the denominators are not the same, work out the common denominator and <em>rewrite </em>the fractions with the same denominators
- subtract by subtracting the numerators and writing the result over the denominator
- convert back to mixed fractions by dividing the numerator by the denominator, write down the whole number answer, write down the remainder above the denominator.
Example
convert to improper fractions:
common denominator = 3 × 5 = 15, so:
subtract:
convert back to mixed fractions:
Answer: C. Definition of an Altitude
Step-by-step explanation:
Given: In triangle MNO shown below, segment NP is an altitude from the right angle.
Let ∠MNP=x
Then ∠PNO=90°-x
Therefore in triangle MNO,
∠MPN=∠NPO =90° [by definition of Altitude]
[Definition of altitude : A line which passes through a vertex of a triangle, and joins the opposite side forming right angles. ]
Now using angle sum property in ΔMNP
∠MNP+∠MPN+∠PMN=180°
⇒x+90°+∠PMN=180°
⇒∠PMN=180°-90°-x
⇒∠PMN=90°-x
Now, in ΔMNO and ΔPNO
∠PMN=∠PNO=90°-x
and ∠MPN=∠NPO =90° [by definition of altitude]
Therefore by AA similarity postulate, we have
ΔMNO ≈ ΔPNO
Answer:
- 3
Step-by-step explanation:
let n be the number , then
3n + 4 = n - 2 ( subtract n from both sides )
2n + 4 = - 2 ( subtract 4 from both sides )
2n = - 6 ( divide both sides by 2 )
n = - 3
The number is - 3
Answer:
91
Step-by-step explanation:
Mean is calculated as
mean = 
let x be his test score of his last test , then
= 85 ( multiply both sides by 7 )
504 + x = 595 ( subtract 504 from both sides )
x = 91
