Answer: If the initial term of an arithmetic sequence is a 1 and the common difference of successive members is d, then the nth term of the sequence is given by: a n = a 1 + (n - 1)d The sum of the first n terms S n of an arithmetic sequence is calculated by the following formula: S n = n (a 1 + a n)/2 = n [2a 1 + (n - 1)d]/2
Answer:
<u>The correct answer is B. 1/729</u>
Step-by-step explanation:
1. Probability of any of the nine words would be randomly cited.
Using the Laplace Rule, we calculate that probability is 1/9
2. Now let's calculate the probability of any two - word phrase in specific order from those nine in the dictionary. We should remember that the probability of occurrence of two or more statistically independent events is equal to the product of their individual probabilities. So,
1/9 * 1/9 = 1/81
3. Using the same Multiplication Rule, we can calculate the probability of a random generation of the phrase "three blind mice", in that specific order. Because there are other phrases that could be generated with those three words, but in different order. The question was specific about the order.
1/9 * 1/9 * 1/9 = 1/729
<u>The probability of randomly generating the phrase "three blind mice" is 1/729 or 0.137%</u>
9514 1404 393
Answer:
Step-by-step explanation:
There are a couple of ways to work a problem like this. You have probably been taught to write equations for each of the payment amounts as a function of time, then equate those values to solve for the time that makes them equal.
at dealer 1, the total amount paid (y) will be a function of months (x):
y = 2500 +150x
at dealer 2, the corresponding equation is ...
y = 3000 +125x
These are equal when ...
y = y
2500 +150x = 3000 +125x
25x = 500 . . . . . . . . . subtract 125x +2500 from both sides
x = 500/25 = 20
The total paid will be the same after 20 months.
That amount is ...
y = 2500 +150(20) = 5500
$5500 will be paid to either dealer after 20 months.
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The other way to work the problem is to "cut to the chase". The difference in down payment is made up at the rate of difference in monthly payments. So The number of monthly payments (x) required to equal the difference in down payments is ...
25x = 500 . . . . . . . . . you may recognize this equation from above
x = 500/25 = 20
Answer:
The perimeter of the triangle can be expressed as 5x + 18.
Step-by-step explanation:
Perimeter of an object is the sum of the length of its sides.
For the required triangle, we have;
length of the base = x
length of the second side = 3x + 9
length of the third side = x + 9
Perimeter of the triangle = length of the base + length of the second side + length of the third side
= x + (3x + 9) + (x + 9)
= x + 3x + 9 + x + 9
= 5x + 18
The perimeter of the triangle can be expressed as 5x + 18.
Answer:
Step-by-step explanation:
2x^2-10x+7 A=1, B=-10. C=7
-(-10)±√-10^2-4(1)(7)
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2(1)
10±√100-28
----------------
2
10±√72
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2
<u>10±8.485281374</u>
2
<u>10+8.485281374 </u>=9.24
2
<u>10-8.485281374</u> =0.76
2