What is the simplified form of the following expression? 2sqrt 18 +3 sqrt 2 + sqrt 162
1 answer:
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Answer:
The number of ways the batting line up can be made is 3,851,971,200 ways.
Step-by-step explanation:
The coach of the baseball team needs to choose 9 players for the batting lineup.
He can choose from a total of 4 freshmen, 4 sophomores, 5 juniors and 4 seniors for the team.
He has to choose the team so that there at most 2 juniors on the lineup.
The total number of available player who are not juniors is 4 + 4 + 4 = 12
i) If the coach selects no juniors then there are 9 positions to fill up and
since the batting order is not specific so these 9 players can be selected
from 12 players = = 220 ways
ii) If the coach selects one junior then there are other 8 other positions to
fill up from 12 players and one junior is to be selected from 5 juniors
=
iii) If the coach selects two juniors then there are other 7 other positions to
fill up from 12 players and two juniors are to be selected from 5 juniors
=
So the ways of selecting the players is = 220 + 2475 + 7920 = 10615 ways
Since there is no specific order to the batting line up the number of ways the batting line up can be made = 9! × 10615 = 3,851,971,200 ways.
Answer:
The correct option is;
B. 50 km/h
Step-by-step explanation:
The information given in the question are;
The distance between the two cities = 140 km
The direction of motion of the first car = From A to B (left)
The direction of motion of the second car = From B to A
The time after which both cars meet = 1 hour
The time duration it takes after both cars meet for the second car to reach A = 35 minutes
The total time taken by the second car from city B to city A = The time it takes to meet the first car + The time it takes after meeting the first car to reach city A
∴ The total time taken by the second car from city B to city A = 1 hour + 35 minutes = 60 minutes + 35 minutes = 95 minutes
95 minutes = 95/60 hours = 1⁷/₁₂ hours = 1.58 hours
The speed of the second car = Distance/Time = 140 km/(1.58 hours) ≈ 88.42 km/h
Therefore, let the distance from A of the point the first car meet the second car = x
Therefore, we have;
The distance from B of the point both cars meet = (140 - x) km
Given that both cars meet after one hour, we have;
The distance travelled by the second car coming from city B, after one hour = (140 - x) km = Speed of the second car × 1 hour
88.42 km/h × 1 hour = 88.42 km = (140 - x) km
x = 140 - 88.42 ≈ 51.58 km
The distance from A of the point the first car meet the second car = x = 51.58 km
The speed of car A = (The distance from A of the point the first car meet the second car)/(Time it takes both cars to meet)
∴ The speed of the first car = 51.58 km/(1 hour)
The speed of the first car = 51.58 km/h ≈ 50 km/h (Rounding up to the nearest 10th).
Answer:
15cm
Step-by-step explanation:
Let x be the arc circumference.
The circumference of a circle usually subtends to 360°, that is, one complete revolution is 360°.
#Given the arc angle as 45° and the circumference as 120cm, the arc circumference can be obtained as:
#Apply proportions to find x:
Hence, the arc circumference is 15cm