Answer:
event A and B are independent because P(A and B) = P(A) x P(B) = 0.15
Step-by-step explanation:
When two events are independent, the probability of both occurring is the product of their separate probabilities, as expressed below;
P(A and B) = P(A) x P(B)
Given;
P(A) = 0.25
P(B) = 0.60
P(A and B) = 0.15
Now, let's check if P(A and B) will be equal to P(A) x P(B)
P(A) x P(B) = 0.25 x 0.60 = 0.15
P(A and B) = P(A) x P(B), thus event A and B are independent.
Y = -2.1 , x = 3.5 the first line will be horizontal and the other will be vertical
The answer: The 3 (three) consecutive odd integers are: -3, -1, 1.
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Explanation:
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To represent 3 (three consecutive odd integers):
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Let "x" be the first odd integer.
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Let "(x+2)" be next consecutive odd integer.
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Let "(x+4") be the third odd integer.
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The sum of these three consecutive odd integers:
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x + (x + 2) + (x + 4) = x + x + 2 + x + 4 = 3x + 6 ;
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Six ("6") times the sum of these 3 (three) consecutive odd integers =
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6*(3x+6) = 6(3x + 6) = -18 (as given in the problem).
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Given: 6(3x + 6) = -18 ; We can divide EACH SIDE of the equation by "6", to cancel the "6" on the left-hand side into a "1";
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{6(3x + 6) } / 6 = -18 / 6 ; to get:
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3x + 6 = -3 ; Now, we can subtract "6" from EACH SIDE of the equation:
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3x + 6 - 6 = -3 - 6 ; to get:
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3x = -9 ; Now, we can divide EACH SIDE of the equation by "3"; to isolate "x" on one side of the question; and solve for "x" ;
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3x / 3 = -9 / 3 ; x = - 3 ;
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Remember, from above:
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Let "x" be the first odd integer. We know that "x = -3".
Is this an odd integer? Yes!
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Let "(x+2)" be next consecutive odd integer. So (x+2) = (-3+2) = -1.
Is this an odd integer? Yes! Is this "{-1}" the next consecutive odd integer with respect to "{-3}"? Yes!
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Let "(x+4") be the third odd integer. So (x+4) = (-3+4) = 1.
Is this an odd integer? Yes! Is this "{1"} the next consecutive odd integer with respect to "{-1}"? Yes!
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So, our 3 (three) consecutive odd integers are: -3, -1, 1.
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To check our work: Is 6 times the sum of our 3 consecutive odd integers, equal to "(-18)" ?
The sum of our 3 consecutive odd integers = -3 + (-1) + 1 = -3 - 1 + 1 = -3.
6 * -3 = ? -18? Yes!
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Answer:
Step-by-step explanation:
Actually, when dividing fractions, you always flip the second fraction and multiply, no matter the size of the numerator or denominator.
Answer:
Step-by-step explanation:
We have been given that Niu has decorated x cards. He started with 24 stickers and he used 4 stickers per card. So stickers used in x cards will be 4x.
As initial number of stickers was 24, so we can find number of stickers left after decorating x cards by subtracting number of stickers used in x cards from 24.
Therefore, the expression will represent the number of stickers that Niu has left after decorating x cards.
