Answer:
6 feet in the distance
Step-by-step explanation:
Answer:
The distance between the two airplanes (to the nearest mile) is 1058 miles.
Step-by-step explanation:
An airplane A is at a location 800 miles due west of city X. So AX = 800 miles.
Another airplane is at a distance of 1,200 miles southwest of city X. So BX = 1200 miles.
The angle at city X created by the paths of the two planes moving away from city X measures 60°. So angle ∠AXB = 60°.
In triangle ΔAXB, AX = 800 miles, BX = 1200 miles, ∠AXB = 60°.
Using law of cosines:-
AB² = AX² + BX² - 2 * AX * BX * cos(∠AXB).
AB² = 800² + 1200² - 2 * 800 * 1200 * cos(60°).
AB² = 640000 + 1440000 - 2 * 960000 * 1/2
AB² = 2080000 - 960000
AB² = 1120000
AB = √(1120000) = 1058.300524
Hence, the distance between the two airplanes (to the nearest mile) is 1058 miles.
Answer:
The probability that a person with restless leg syndrome has fibromyalgia is 0.183.
Step-by-step explanation:
Denote the events as follows:
<em>F</em> = a person with fibromyalgia
<em>R</em> = a person having restless leg syndrome
The information provided is as follows:
P (R | F) = 0.33
P (R | F') = 0.03
P (F) = 0.02
Consider the tree diagram attached below.
Compute the probability that a person with restless leg syndrome has fibromyalgia as follows:
Thus, the probability that a person with restless leg syndrome has fibromyalgia is 0.183.
The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
Given,
18th term of an arithmetic sequence = 8.1
Common difference = d = 0.25.
<h3>What is an arithmetic sequence?</h3>
The sequence in which the difference between the consecutive term is constant.
The nth term is denoted by:
a_n = a + ( n - 1 ) d
The sum of an arithmetic sequence:
S_n = n/2 [ 2a + ( n - 1 ) d ]
Find the 18th term of the sequence.
18th term = 8.1
d = 0.25
8.1 = a + ( 18 - 1 ) 0.25
8.1 = a + 17 x 0.25
8.1 = a + 4.25
a = 8.1 - 4.25
a = 3.85
Find the sum of 20 terms.
S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]
= 10 [ 7.7 + 19 x 0.25 ]
= 10 [ 7.7 + 4.75 ]
= 10 x 12.45
= 124.5
Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
Learn more about arithmetic sequence here:
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Answer:
The second and the last options.
Step-by-step explanation:
15/ 2/9 =67.5 Solve the original problem
15*2/9 =3.33333333333
15*9/2 =67.5
(15* 1/9) /2=0.833333333333333
15*9* 1/2 =67.5
