Answer:
Step-by-step explanation:
the product of the two fractions are 3/32
first find common denominator then multiply then simplify
Given:
p = 90% = 0.9, the probability that an adult has had chickenpox by age 50.
Therefore,
q = 1 - p = 0.1, the probability that an adult has not had chickenpox by age 50.
Part (a)
Because there are only two answers: "Yes" or "No" to whether an adult has had chickenpox by age 50, the use of the binomial distribution is justified.
Part (b):
Calculate the probability that exactly 97 out of 100 sampled adults have had chickenpox.
The probability is
P₁ = ₁₀₀C₉₇ (0.9)⁹⁷ (0.1)³ = 0.0059
Answer: 0.006 or 0.6%
Part (c)
Calculate the probability that exactly 3 adults have not had chickenpox.
Theis probability is equal to
P₂ = 1 - P₁ = 1 - 0.006 = 0.994
Answer: 0.994 or 99.4%
Part (d)
Calculate the probability that at least 1 out of 10 randomly selected adults have had chickenpox.
The probability is
P₃ = ₁₀C₀ (0.9)⁰ (0.1)¹⁰ + ₁₀C₁ (0.9)¹ (0.1)⁹ = 10⁻¹⁰ + 10⁻⁹ = 10⁻⁹ ≈ 0
Answer: 0
Part (e)
Calculate the probability that at most 3 out of 10 randomly selected adults have not had chickenpox.
The probability is
P₄ = 1 - [₁₀C₀ (0.9)⁰(0.1)¹⁰ + ₁₀C₁ (0.9)¹(0.1)⁹ + ₁₀C₂ (0.9)²(0.1)⁸ + ₁₀C₃ (0.9)³(0.1)⁷]
= 1 - (10⁻¹⁰ + 9 x 10⁻⁹ + 3.645 x 10⁻⁷ + 8.748 x 10⁻⁶)
= 1
Answer: 1.0 or 100%
Answer: B, C, E
Step-by-step explanation:
For us to know if the options are correct, we just have to multiply the length the rope was cut into by the number of pieces and check if it equals 504 centimeter.
A. 12 pieces of 42.3 centimeter long rope.
= 12 × 42.3
= 507.6
This is wrong
B. 15 pieces of 33.6 centimeter long rope
= 15 × 33.6
= 504cm
This is correct
C. 16 pieces of 31.5 centimeter long rope
= 16 × 31.5
= 504cm
This is correct
D. 20 pieces of 25 centimeter long rope
= 20 × 25
= 500cm
This is incorrect
E. 35 pieces of 14.4 centimeter long rope
= 35 × 14.4
= 504cm
This is correct
Therefore, the correct option are B, C and E.
We know that
the equation of a parabola is of the form
y=a*(x-h)²+k--------> is a vertical parabola
(h,k) is the vertex
y=−14x²<span>+4x−19
</span><span>Factor the
leading coefficient </span>
y=-14*(x²-4/14x)-19
y=-14*(x²-2/7x)-19
<span>Complete
the square Remember to balance the equation </span>
y=-14*(x²-2/7x+(1/49)-(1/49))-19
y=-14*(x²-2/7x+(1/49))-19+14/49
<span>Rewrite as perfect squares</span>
y=-14*(x-1/7)²-917/49
the vertex of the parabola is
h=(1/7)-----> 0.1429
k=(-917/49)----> -18.7143
the vertex of the parabola is(0.1429, -18.7143)
see the attached figure
