Answer:
$( 51x^2 + x + 29).
Step-by-step explanation:
Amount she had left = original amount - amount spent on the gloves
= 62x^2 + x - 4 - (11x^2 - 33) (note we place the amount spent on gloves in parentheses because we have to subtract the whole amount)
Now we distribute the negative over the parentheses:
= 62x^2 + x - 4 - 11x^2 + 33 ( note - 33 becomes -33*-1 = +33)
Now simplifying like terms:
= 51x^2 + x + 29 (answer).
Answer:
Given:
and
.
Prove: 
Since
, By the definition of perpendicular lines angles 1, 2, 3 and 4 are 90 degree. similarly
, it means angles 5, 6, 7 and 8 are 90 degree.
We can say that,
,
,
and 
From figure it is noticed that the angle 1 and 5 are corresponding angles.
If two parallel lines are intersected by a transversal, then the corresponding angles are equal.
Since corresponding angles are congruent, therefore the line must be parallel to each other.
Hence proved that
.
Answer:
Step-by-step explanation:
Given that a researcher is trying to decide how many people to survey.
We have confidence intervals are intervals with middle value as the mean and on either side margin of error.
Confidence interval = Mean ± Margin of error
Thus confidence interval width depends on margin of error.
Margin of error = 
Thus for the same confidence level and std deviation we find margin of error is inversely proportional to square root of sample size.
Hence for small n we get wide intervals.
So if sample size = 300, the researcher will get wider confidence interval
Answer:
Step-by-step explanation:
35/4 = 8.75 or 8 3/4