Answer:
7/4
Step-by-step explanation:
35 divided by 5
20 divided by 5
Answer:
<u>51.2</u> is 40% of 128
Step-by-step explanation:
One JOB = 1 and 2 hours = 120 min
Tyler Rate per minute: 1/120 (in 1 minute he performes 1/120 of the job)
Dakota<span> Rate per minute: 1/90 (in 1 minute he performes 1/90 of the job)
Tyler's + Dakota's rate per 1 minute = 1/120 + 1/90 = 7/360 (Job/minutes)
7/360 of the job was performed in 1 minute
</span>a complete JOB =1 to be performed in x minutes (Rule of three)
x = 1x1/(7/360) that equals to 360/7 and x (time of both) = 51 min 42
Part A
Answer: The common ratio is -2
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Explanation:
To get the common ratio r, we divide any term by the previous one
One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2
Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time
Side Note: each term is multiplied by -2 to get the next term
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Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
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Explanation:
Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio
The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)
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Part C
Answer: The next three terms are 16, -32, 64
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Explanation:
We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms
-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64
showing that the next three terms are 16, -32, and 64
An alternative is to use the formula found in part B
Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier
Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier
Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier
while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
first one: 1200/1.5 = 800, second one: 20,000/10= 2000, third one: 400/20 = 20, fourth one: 266.6, fifth one: 33.3, sixth one: 1000. You're welcome!!
