An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seat
2 answers:
Answer:
1170
Step-by-step explanation:
<em>hey there,</em>
(the other person just calculated each number themselves then added them up which i guess is okay but not in the long term for when you're taking a test for example or your teacher asks you this kind of question so it's better to memorize a formula.)
< There are two types of sequences: arithmetic and geometric. So also two formulas for finding sums of each. This situation is an arithmetic sequence.
Formula for the sum of an arithmetic sequence:
We know there are 30 total rows so <em>n</em> = 30. <em>a1 </em>is the very first term of a sequence so this is 10 in this situation. Before we fill in the formula, we should find what <em>an</em> is equal to.
For this, we will use the basic formula you learned previously:
<em>d</em> (the common difference) = a2-a1 = 12-10=2
<em>c </em>(the common ratio) = a1-d = 10-2 = 8
an = dn + c = 2(30) + 8 = 68
Now that we have found what a_n is equal to, we can plug everything into the sum equation.
So 1170 is your final answer. >
<u>Hope this helped! Feel free to ask anything else.</u>
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Answer:
57.8125% or approx. 57.8%
Step-by-step explanation:
There is a 1/4, or 25%, or 0.25 chance that an egg has salmonella.
Thus, there is a 75%, or 0.75 chance that an egg DOESN'T contain salmonella.
Let's find the probability that all 3 of Larry's eggs are free from salmonella. Larry would have to hit that 75% chance 3 times in a row. The chance of that happening is:
0.75 * 0.75 * 0.75 = = 0.421875
From this, we can deduce that if there is a 0.421875 (42.1875%) chance that all eggs are safe to eat, there must be a...
1 - 0.421875 = 0.578125
...0.578125 (57.8125%) chance that 1 or more of Larry's eggs do have salmonella.
Answer: approx. 57.8% or 57.8125%
Answer:
Width: 7
Length: 14
Step-by-step explanation:
The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let represent the width.
Since the length is 7 feet longer, we can represent the length by .
Now that we have our values for the length and the width we can multiply them together to find our area.
Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.
And multiply our area by 3.
set these equal to each other to find your new equation.
Now you need to solve for . To do this first muliply
and
.
Then multiply
Now you can begin solving for .
Subtract from both sides.
Subtract from both sides.
Divide by 2.
And finally take the sqaure root of both sides.
Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.
Now that we have the value of , we can plug it into our original values.
For width we simply get 7.
For length we get 7+7=14
To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.