Answer:
925
Step-by-step explanation:
In order to solve this summation formula, you need to first understand what it means. The summation symbol is tell you to add the terms in a sequence. Below the summation sign, there is a variable and number; the variable n is the index of summation and the number 1 is the lower limit of summation or the first value of the sequence. The number 25 above the summation sign is the upper limit (so there would be 25 terms, with the first being 1). The polynomial to the right of the summation symbol represents the explicit function for each term. For example, using this, the first term would be (3(1) - 2) and the second (3(2) - 2) and so on. This means the value of that equation is:
(3(1) - 2) + (3(2) - 2) + (3(3) - 2)... + (3(25) - 2)
One way to solve this is to write all 25 of the terms and add them, but since that's tedious, you can solve this by first doing the basic summation of 1 to 25 and then inputting that into the equation:
1 + 2 + 3... + 25 = (25 × 26)/2 (when the first number is one and the rate of change is 1, the sum of the terms in a sequence is (n*(n+1))/2)
= 325
Now, that you know what the sum of the sequence of terms 1 to 25 are, you can multiply this by the constant since if you break up the equation you would be multiplying 3 by 1 then 3 by 2 and so on until 25, or 3 × (1 + 2 + 3... + 25):
3 × 325 = 975
At this point, you just need to add (-2) × 25. You do this because since there are 25 terms, if you subtracted 2 each time, you would subtract 2 twenty-five times:
975 + ((-2) × 25)
= 975 - 50
= 925
Answer:
-9^5
Step-by-step explanation:
(-9)*(-9)*... is -9^5
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Isolate the x. Do the opposite of PEMDAS.
−4 ≤ 11 −3x
First, subtract 11 from both sides
-4 (-11) ≤ 11 (-11) - 3x
-4 (-11) ≤ - 3x
-15 ≤ - 3x
Isolate the x. Divide -3 from both sides. Remember to flip the sign.
(-15)/-3 ≤ (-3x)/-3
-15/-3 ≤ x
5 ≥ x
x≤5 is your answer
hope this helps
Answer:
1650 families
Step-by-step explanation:
In a survey of his neighborhood, Timothy found out that 3 families out of 7 have a dog for a pet.
The given ratio = 3:7
When written as a fraction = 3/7
The number of families that would have a pet dog in a town with about 3,850 families is given as:
3/7 × 3,850
= 1650 families
Therefore, 1650 families would have a pet dog in town.
4x + 2 = -24
subtract 2 from both sides
divide -26 by 4
your answer is -6.5
