Answer:
The probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375
Step-by-step explanation:
Let E be a random variable denoting the event that an artist makes a craft item with satisfactory level.
Then the random variable E follows a Geometric distribution.
A Geometric distribution is defined as the number of failures (<em>k</em>) before the first success.
The probability function of Geometric distribution is:
, <em>p</em> = Probability of success and <em>k</em> = 0, 1, 2, 3...
The probability of success is, <em>p</em> = 0.5 and the number of failures is, <em>k</em> = 3.
Compute the probability of at most 3 attempts before the first success is:
![P(X\leq 3) =P(X=3)+P(X = 2)+P(X=1) +P(X = 0)\\=[(1-0.5)^{0}*0.5]+[(1-0.5)^{1}*0.5]+[(1-0.5)^{2}*0.5]+[(1-0.5)^{3}*0.5]\\=0.9375](https://tex.z-dn.net/?f=P%28X%5Cleq%203%29%20%3DP%28X%3D3%29%2BP%28X%20%3D%202%29%2BP%28X%3D1%29%20%2BP%28X%20%3D%200%29%5C%5C%3D%5B%281-0.5%29%5E%7B0%7D%2A0.5%5D%2B%5B%281-0.5%29%5E%7B1%7D%2A0.5%5D%2B%5B%281-0.5%29%5E%7B2%7D%2A0.5%5D%2B%5B%281-0.5%29%5E%7B3%7D%2A0.5%5D%5C%5C%3D0.9375)
Therefore, the probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375.
Answer:
(a) 12π in
(b) 53.5 in
(c) 96 grams
Step-by-step explanation:
In the figure attached, the ornament is shown
(a) four three-quarter circles is equivalent to 4*3/4 = 3 circles. The perimeter of a circle is the total length of the circular portions.
Perimeter of each circle: 2*π*r
The radius is 2 in long, then for 3 circles:
Perimeter = 3*2*π*2 = 12π in
(b) Perimeter of square: 4*side length
The side length of the square is 4 in, then:
Total length of wire needed = 4*4 + 12π = 53.5 in
(c) The wire weighs 1.8 grams per inch, then:
total weight of the ornament = 1.8 grams/in * 53.5 in = 96 grams
Synthetic division yields
-3 | 1 5 4 -6
. | -3 -6 6
- - - - - - - - - - - - -
. | 1 2 -2 0
which translates to
with remainder 0. Now by the quadratic formula,
and so
Answer: The /\ is 6. The number is 6.
Explanation: 678564 ÷ 9 = 75396
∠ ABD = 5(2X+1)
∠ DBC = 3X+6
∠ EBC = Y +135/2
∠ ABD and ∠ DBC are linear pairs
∴ ∠ ABD +∠ DBC = 180
∴ 5(2X+1) + 3X+6 =180
solve for x
∴ x = 13
∴∠ ABD = 5(2X+1) = 5(2*13+1) = 135
∠ DBC = 3x+6 = 3*13+6 = 45
∠ ABD and ∠ EBC are vertical angles
∴ ∠ ABD = ∠ EBC = 135
∴ y +135/2 = 135
∴ y = 135/2
The <span>statements that are true:
--------------------------------------</span><span>
C.) x=13
E.)measure of angle EBC =135
F.) angle DBC and angle EBC are linear pairs
</span>
