We have been given that in a circle an arc length 10 is intercepted by a central angle of 2/3. We are supposed to find the radius of the circle.
We will use arc-length formula to solve our given problem.
, where,
= Arc length,
= Radius,
= Central angle corresponding to arc length.
Upon substituting our given values in arc-length formula, we will get:
Therefore, the radius of the given circle would be 15 units.
Answer:
She will earn $16.50.
Step-by-step explanation:
M = ($6/hr)h
If Crystal works 2 hrs 45 min, she will earn
M(2 3/4 hrs) = ($6/hr)(2 3/4 hrs), or
= $66/4 = $16.50
Answer: A and D
Step-by-step explanation:
1) Road Trip: Let’s say two friends are meeting at a playground. Mary is already at the park but her friend Bob needs to get there taking the shortest path possible. Bob has two way he can go - he can follow the roads getting to the park - first heading south 3 miles, then heading west four miles. The total distance covered following the roads will be 7 miles. The other way he can get there is by cutting through some open fields and walk directly to the park. If we apply Pythagoras's theorem to calculate the distance you will get:
(3)<span>2 </span>+ (4)2 =
9 + 16 = C2
√25 = C
5 Miles. = C
Walking through the field will be 2 miles shorter than walking along the roads. .
2) Painting on a Wall: Painters use ladders to paint on high buildings and often use the help of Pythagoras' theorem to complete their work. The painter needs to determine how tall a ladder needs to be in order to safely place the base away from the wall so it won't tip over. In this case the ladder itself will be the hypotenuse. Take for example a painter who has to paint a wall which is about 3 m high. The painter has to put the base of the ladder 2 m away from the wall to ensure it won't tip. What will be the length of the ladder required by the painter to complete his work? You can calculate it using Pythagoras' theorem:
(5)<span>2 </span>+ (2)2 =
25 + 4 = C2
√100 = C
5.3 m. = C
Thus, the painter will need a ladder about 5 meters high.
3) Buying a Suitcase: Mr. Harry wants to purchase a suitcase. The shopkeeper tells Mr. Harry that he has a 30 inch of suitcase available at present and the height of the suitcase is 18 inches. Calculate the actual length of the suitcase for Mr. Harry using Pythagoras' theorem. It is calculated this way:
(18)<span>2 </span>+ (b)2 = (30)2
324 + b2 = 900
B2 = 900 – 324
b= √576
= 24 inches
Remember that the difference between census and a sample survey is that in a census you take all the people of population in consideration in the study, and in the sample survey you take a part of that population in consideration to survey.
SO here if you check the problem it says that "in a recent poll, Pew reserchers found that 47% OF AMERICAN ADULT RESPONDENTS"
that is the population of the study that you want to focus, but there are a billion of american adult in US right? so its impossible that this company Pow Research made a census if you consider that a billion of people in US is almost infinite number for a company with a finite number of employees.
Also remember that a company has a budget to consider every month or every year, so to make a census or a sample survey it takes time and money, just to survey 10 people in a streeth of US cost money so if you want to reduce cost you might need to do a sample survey instead of a census.
