Mutually exclusive means that the intersection of the events is empty: P(S and T) = 0.
P(S or T) = P(S) + P(T) = 29% + 49% = 78%
If events S, T are not mutually exclusive, then P(S or T) = P(S) + P(T) - P(S and T)
value of x = 20 and value of y=16
Solution set=(20,16)
Step-by-step explanation:
We need to solve system of equations:
Let:
Simplifying equation 2:
Taking LCM on left side:
Adding eq(1) and eq(3)
Putting value of x in eq(1) and finding y:
So, value of x = 20 and value of y=16
Solution set=(20,16)
Keywords: System of equations
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36 is the y intercept
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Answer:
Step-by-step explanation:
<h3>Polynomial:</h3>
p(x) = ax³ + bx + x
Let g(x) = x² + kx + 1 .
g(x) is a factor of p(x). So, p(x) is divided by g(x), the remainder will be 0.
Divide p(x) by g(x) using long division method. {attached as an image}.
By doing long division, we get the remainder.
Remainder = bx - ax + k²ax + ka + c
= (b - a + k²a)x+ [ka + c]
Remainder = 0
b - a + k²a = 0 and ka + c = 0
ka + c = 0
ka = -c
k = -c/a ----------------(I)
b - a + k²a = 0
ab = a² - c²
Hence, proved.
Answer:
c. 112 ft
Step-by-step explanation:
the diagonal of a rectangle creates a right-angled triangle with a length and a width of the rectangle (the diagonal is the Hypotenuse or baseline).
and this means we can use Pythagoras :
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle).
diagonal² = 100² + 50² = 10000 + 2500 = 12500
diagonal = sqrt(12500) = 111.8033989... ft ≈ 112 ft