Answer:
0.0064
0.00032
Step-by-step explanation:
Given the details:
P(X > 3), n = 5, p = 0.2
The binomial distribution is related using the formula:
P(x = x) = nCx * p^x * q^(n-x)
q = 1 - p = 1 - 0.2 = 0.8
P(X > 3) = p(x = 4) + p(x = 5)
P(x = 4) = 5C4 * 0.2^4 * 0.8^1 = 5 * 0.2^4 * 0.8^1 = 0.0064
P(x = 5) = 5C5 * 0.2^5 * 0.8^0 = 1 * 0.2^5 * 0.8^0 = 0.00032
The rate of change of the size of the diagonal is; 25.2 ft/s
By Pythagoras theorem;
The length, l of a diagonal of a rectangle whose sides have lengths x and y is;
In essence; the length of the diagonal is dependent on the length, x and y of the sides.
Therefore;
(dl/dt)² = (dx/dt)² + (dy/dt)²
where;
- (dx/dt) = 19 ft/s
- (dy/dt) = -15 ft/s
Therefore,
(dl/dt)² = 19² + (-15)²
(dl/dt)² = 361 + 225
dl/dt = √586
dl/dt = 25.2
Therefore, the size of the diagonal is changing at a rate of; 25.2 ft/s.
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Answer:
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Step-by-step explanation:
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Answer:
(5, 0 )
Step-by-step explanation:
Given the 2 equations
y = x² - 2x - 15 → (1)
y = 8x - 40 → (2)
Substitute y = x² - 2x - 15 into (2)
x² - 2x - 15 = 8x - 40 ( subtract 8x - 40 from both sides )
x² - 10x + 25 = 0 ← in standard form
(x - 5)² = 0 ← in factored form, thus
x - 5 = 0 ⇒ x = 5
Substitute x = 5 into (2) for corresponding value of y
y = 8(5) - 40 = 40 - 40 = 0
Solution is (5, 0 )
Answer: C,D
Step-by-step explanation:
