How many lines of symmetry does a circle have? What point do all lines of symmetry for a given circle have in common?
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Answer:
Probability that ten or more homeowners would state a preference for either brand A or brand B = 0.302
Step-by-step explanation:
Given - A manufacturer of floor wax has developed two new brands, A and B, which she wishes to subject to homeowners’ evaluation to determine which of the two is superior. Both waxes, A and B, are applied to floor surfaces in each of 15 homes. Assume that there is actually no difference in the quality of the brands.
To find - What is the probability that ten or more homeowners would state a preference for either brand A or brand B?
Proof -
Given that,
There is actually no difference in the quality of the brands.
⇒P(A) = = 0.5
P(B) = = 0.5
Now,
We know that,
Binomial distribution is equals to
B(n, x) = ⁿCₓ (p)ˣ (1 - p)ⁿ⁻ˣ
Now,
P(X(A) ≥ 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)
= ¹⁵C₁₀ (0.5)¹⁰ (0.5)⁵ + ¹⁵C₁₁ (0.5)¹¹ (0.5)⁴ + ¹⁵C₁₂ (0.5)¹² (0.5)³ + ¹⁵C₁₃ (0.5)¹³ (0.5)² + ¹⁵C₁₄ (0.5)¹⁴ (0.5)¹ + ¹⁵C₁₅ (0.5)¹⁵ (0.5)⁰
= 0.092 + 0.042 + 0.014 + 0.003 + 0.0005 + 0.00005
= 0.151
⇒P(X(A) ≥ 10) = 0.151
As given Quality of both brands are same ,
So, the probability of both the brands are equal
⇒P(X(B) ≥ 10) = 0.151
Now,
Probability that ten or more homeowners would state a preference for either brand A or brand B = P(X(A) ≥ 10) + P(X(A) ≥ 10)
= 0.151 + 0.151
= 0.302
∴ we get
Probability that ten or more homeowners would state a preference for either brand A or brand B = 0.302
The function is not treated as linear because whenever we throw the thing in the air it traces the path of the parabola which is quadratic. Then the quadratic equation is y = -1.25x² + 7.35x + 3.2.
<h3>What is a quadratic equation?</h3>It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The following scatter plot represents the height of a basketball in seconds during a free throw shot.
(a) A student chose to model the data with the function, y = 0.9286x + 9.0571 . Then the function is not treated as linear because whenever we throw the thing in the air it traces the path of the parabola which is quadratic.
(b) Write a function
We know that the quadratic equation is given as ax² + bx + c = y
This will pass through the points (1, 9.3), (2, 12.9), and (3, 14). Then we have
On solving the equations 1, 2, and 3. Then we have
a = -1.25, b = 7.35, and c = 3.2
Then the quadratic equation will be
y = -1.25x² + 7.35x + 3.2
More about the quadratic equation link is given below.
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