6;15; x; 45;....... is a quadratic number pattern (sequence). Determine the value of x.
1 answer:
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Looking at the problem, you can come up with an equation for the consecutive numbers.
If we expand the second term:
Combine like terms:
You can reduce this by dividing both sides of the equation by two:
And we transpose 170 to get a standard quadratic form that the right side will be zero:
Then factor the left side:
Find out the values of x that makes each factor = 0
x + 14 = 0
x = -14
We can eliminate the negative symbol because the problem is asking for positive even integers.
and;
x - 12 = 0
x = 12
Now we can say that the first positive integer is 12 and the second one is 14
If we expand the second term:
Combine like terms:
You can reduce this by dividing both sides of the equation by two:
And we transpose 170 to get a standard quadratic form that the right side will be zero:
Then factor the left side:
Find out the values of x that makes each factor = 0
x + 14 = 0
x = -14
We can eliminate the negative symbol because the problem is asking for positive even integers.
and;
x - 12 = 0
x = 12
Now we can say that the first positive integer is 12 and the second one is 14
Answer:
The probability of driving to the store is 0.969
Step-by-step explanation:
The remaining part of the question is attached
Solution
There are only two possible ways –
a) Route comprising of bridges 123
b) Route comprising of bridge 45
Probability of success while traveling through Route 123 = P(Bridge 1 open) x P(Bridge 2 open) x P(Bridge 3 open)
= 0.9 x 0.92 x 0.91
= 0.75348
P(Route 123 is closed) = 1 - 0.75348 = 0.24652
Probability of success while traveling through Route 45 =
P(Bridge 4 open) x P(Bridge 5 open)
= 0.94 x 0.93
= 0.8742
P(Route 45 is closed) = 1 - 0.8742 = 0.1258
To travel to store, atleast one route from 123 and 45 should be open.
Probability that you can drive to store :
= P(atleast one route from 123 and 45 is open)
= 1 - P(Both routes 123 and 45 are closed)
= 1 - P(123 is closed)*P(45 is closed)
= 1 - 0.24652*0.1258
= 1 - 0.031012216
= 0.968987784
~ 0.969
