Round 593,204 to the nearest million
1 answer:
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Answer:
If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit P can be expressed as:
The restriction for cloth can be written as:
The restriction for metal can be written as:
The restriction for wood can be written as:
The condition for S and H to be positive is:
Step-by-step explanation:
We have an objective function that, in this case, we want ot maximize.
This function is the Profit (P).
If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit can be expressed as:
We have 3 restrictions, plus the condition that both S and H are positive.
The restriction for cloth can be written as:
The restriction for metal can be written as:
The restriction for wood can be written as:
The condition for S and H to be positive is:
The chairs in the auditorium illustrates an arithmetic sequence
- The recursive rule is: an = an-1 + 8; a1 = 26
- The explicit rule is: an = 18 + 8n
- There are 74 seats in the 7th row
- 840 chairs can fit the auditorium
From the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
<h3>The explicit rule</h3>In (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
<h3>The number of seats in the row 7</h3>This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
<h3>The sigma notation</h3>We have the maximum number of rows to be 12.
So, the sigma notation would be:
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
Read more about arithmetic sequence at:
Answer:
0.006% probability that the final vote count is unanimous.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Random voting:
So 50% of voting yes, 50% no, so
15 members:
This means that
What is the probability that the final vote count is unanimous?
Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So
In which
So
0.006% probability that the final vote count is unanimous.