Answer:
33.33%
Step-by-step explanation:
We need to calculate the <u>unit selling price and cost of each cosmetics.</u>
If a person bought some cosmetics from wholesale market at the rate of Rs 360 per dozen., then for 1 cosmetics, we will say;
x = 1 cosmetic
since 360 = 12 cosmetic
cross multiply
12x = 360
x = 360/12
x = 30
Hence the unit cost price of the cosmetics will be Rs. 30
Similarly, if he sells it at Rs 80 a pair, then he sold one cosmetic at 80/2 = Rs. 40 (a pair is 2 cosmetics)
Selling price per unit = Rs. 40
Cost price per unit = Rs. 30
percent gain = SP-CP/CP * 100%
percent gain = 40-30/30 * 100
percent gain = 10/30 * 100
percent gain = 100/3
percent gain = 33.33%
Hence the percentage gain is 33.33%
So just add 1/8 and 2/8. add 1 plus 2 and the denominator (bottom number) stays the same so you get 3/8 then subtract 8/8 minus 3/8 so just 8 minus 3 is 5 and the denominator stays the same so you end up with 5/8 so 5/8 of the book remains unread
78.00 = 59.99+0.10x
10.01=0.10x
x= 180.1 so she can send 180 texts plus the 100 free ones for a total of 280 texts
double check: 180 x 0.10 = 18.00 + 59.99 = 77.99
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)
Answer:
(4, 7)
Step-by-step explanation:
The midpoint formula is (((x1 + x2)/2), ((y1+y2)/2)))
x1 +x2 = 1 +7 = 8
8/2 = 4
y1 + y2 = 10 + 4 = 14
14/2 = 7
(4, 7) is the midpoint
