The binomial distribution is given by,
P(X=x) =
q = probability of failure = 1-0.2 = 0.8
n = 100
They have asked to find the probability <span>of obtaining a score less than or equal to 12.
</span>∴ P(X≤12) =
where, x = 0,1,2,3,4,5,6,7,8,9,10,11,12
∴ P(X≤12) =
+
+
+
+
+
+
Evaluating each term and adding them you will get,
P(X≤12) = 0.02532833572
This is the required probability.
Answer:
Option 4 is the image of the given figure.
Step-by-step explanation:
We are given that,
The shape EFGHCD is transformed to form another shape.
From the options, we see that,
Figure 2 and 3 does not have the same vertices as that of the figure.
So, they are discarded.
Since, after transforming a figure, we get a new figure.
So, the vertices cannot have same name as that of the original figure.
So, option 1 is discarded.
Thus, we get,
Option 4 is the image of the given figure after transformation as shown below.
It costs $3.63 more for the gold die than the gold plated die.
The volume of each half of the die is given by the formula
V=1/3s³.
This means the total volume is V = 2(1/3s³) = 2(1/3(2³)) = 16/3 = 5.33 mm³.
For the solid gold die, we know that it weighs 0.02g per mm³:
5.33(0.02) = 0.1066g
Gold costs $40.38 per gram:
40.38(0.1066) = $4.30
For the plastic die, plastic weighs 0.01 g per mm³:
0.01(5.33) = 0.0533g
Plastic costs $10 per gram:
0.0533(10) = 0.533 ≈ $0.54.
We also need to find the surface area, as it will be painted. Each face is an equilateral triangle; the area of a triangle is given by the formula
A = 1/2bh
We need to use the Pythagorean theorem to find the height. The height will be one leg and 1/2 of the base will be the other; the slanted side will be the hypotenuse:
h² + (1/2(2))² = 2²
h² + 1² = 2²
h² + 1 = 4
h² = 3
h = √3
The area of the triangle would then be A = 1/2bh = 1/2(2)(√3) = √3. There are 8 such faces on the die, so the total surface area would be 8√3 = 13.86mm².
Paint costs $0.01 per mm²:
13.86(0.01) = 0.1386 ≈ $0.14
Together the cost for the plastic is 0.14+0.53 = $0.67.
The difference between it and the cost for the gold die is 4.30 - 0.67 = $3.63.
y = -8
y = mx + b, where m is the slope and b is the y intercept
since m = 0, the term mx = 0
since the line passes throug (7, -8) then y = -8
If you mean half as in 1/2, then yes, 0.31 is less than half because 1/2 as a decimal is 0.50.
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