Answer:
A darts player practices throwing a dart at the bull’s eye on a dart board. Her probability of hitting the bull’s eye for each throw is 0.2.
(a) Find the probability that she is successful for the first time on the third throw:
The number F of unsuccessful throws till the first bull’s eye follows a geometric
distribution with probability of success q = 0.2 and probability of failure p = 0.8.
If the first bull’s eye is on the third throw, there must be two failures:
P(F = 2) = p
2
q = (0.8)2
(0.2) = 0.128.
(b) Find the probability that she will have at least three failures before her first
success.
We want the probability of F ≥ 3. This can be found in two ways:
P(F ≥ 3) = P(F = 3) + P(F = 4) + P(F = 5) + P(F = 6) + . . .
= p
3
q + p
4
q + p
5
q + p
6
q + . . . (geometric series with ratio p)
=
p
3
q
1 − p
=
(0.8)3
(0.2)
1 − 0.8
= (0.8)3 = 0.512.
Alternatively,
P(F ≥ 3) = 1 − (P(F = 0) + P(F = 1) + P(F = 2))
= 1 − (q + pq + p
2
q)
= 1 − (0.2)(1 + 0.8 + (0.8)2
)
= 1 − 0.488 = 0.512.
(c) How many throws on average will fail before she hits bull’s eye?
Since p = 0.8 and q = 0.2, the expected number of failures before the first success
is
E[F] = p
q
=
0.8
0.2
= 4.
Answer:
Area = 209.5 ft² (nearest tenth)
Cost = $505 (approximated)
Step-by-step explanation:
Step 1: convert the inches to be in feet by dividing length in inches by 12.
17 feet 10 inches => 
11 feet 9 inches => 
Step 2: Find the area of the floor of the dinning room
Area = 17.83*11.75 = 209.5 ft² (nearest tenth)
Step 3: Find the cost of the work.
Cost = 209.5 ft² × $2.41 = $505 (approximated)
Answer:
3.98 x 10^7
Step-by-step explanation:
Answer:
7) 1/4, 1/2, 5/8, 3/4, 7/8. This is in the right order.
Answer: a) 2:1. b) 3. c) Perimeter of ΔEFG=36 Perimeter of ΔHIJ=18. d) 2:1
Step-by-step explanation:
a) Find the ratio of GF and JI. 16:8. Simplify by dividing both by 8 to get 2:1.
b) Set up this equation: 6/16=x/8. Cross-multiply. 6*8=48. Divide by 16. 48/16=3.
c) First find the length of one half of GF by dividing 16 by 2. 16/2=8. Set up the Pythagorean theorem. 8^2+6^2=c^2. Square 8 and 6. 64+36=c^2. Add 64 and 36. 100=c^2. Find the square root of 100. c=10.
EF and EG both measure 10 since they are shown to be congruent. 10+10+16=36.
Next find the length of one half of JI by dividing 8 by 2. 8/2=4. Set up the Pythagorean theorem. Since we know x=3, it will be 4^2+3^2=c^2. Square both 4 and 3. 16+9=c^2. Add 16 and 9. 25=c^2. Find the square root of 25. c=5.
HJ and HI both measure 5 since they are congruent. 5+5+8=18.
d) Find the ratio of the perimeters of ΔEFG and ΔHIJ. 36:18. Simplify by dividing both by 6 to get 6:3. Simplify further by dividing both by 3 to get 2:1.
