Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Part a)
Given the table
Year Value ($)
1 18,000
2 15,300
3 13,005
Let us check the sequence
18000, 15300, 13005,...
Let us find the common ratio 'r' of all the adjacent terms to check whether the sequence represents the geometric sequence or not, using the formula such as:
[tex]\:r=\frac{a_{n+1}}{a_n}[/tex]
[tex]\frac{15300}{18000}=\frac{17}{20},\:\quad \frac{13005}{15300}=\frac{17}{20}[/tex]
As the ratio of all the adjacent terms is the same, so
[tex]r=\frac{17}{20}[/tex]
Therefore, the given sequence is a geometric sequence
Part b)
Given the sequence
18000, 15300, 13005,...
The nth term of the geometric sequence is
[tex]a_n=a_1\cdot r^{n-1}[/tex]
here
[tex]a_1=18000[/tex]
[tex]r=\frac{17}{20}[/tex]
so
[tex]a_n=18000\left(\frac{17}{20}\right)^{n-1}[/tex]
In order to determine the car worth in the 15th year, substitute n = 15
[tex]a_{15}=18000\left(\frac{17}{20}\right)^{15-1}[/tex]
[tex]a_{15}=18000\frac{17^{14}}{20^{14}}[/tex]
[tex]a_{15}=18000\times \:\:0.10276[/tex]
[tex]a_{15}=1850[/tex] $
Therefore, the worth of a car in the 15th year will be: $1850
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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x1 = -3, y = -2
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Step-by-step explanation:
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Answer:
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Answers
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The temperature in a chemical reactor was measured every half hour under the same conditions. The results were 78.1°C, 79.2°C, 78,9°C, 80.2°C, 78.3°C, 78.8°C. 79.4°C.
the mean ?
Answers
Answer:
72.2
Step-by-step explanation:
The mean of the data is 78.98.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
For example,
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Answer:
1. Steve's age is 18 and Anne's age is 8.
2. Max's age is 17 and Bert's age is 11.
3. Sury's age is 19 and Billy's age is 9.
4. The man's age is 30 and his son's age is 10.
Step-by-step explanation:
1. Let us assume that:
S = Steve's age now
A = Anne's age now
Therefore, in four years, we have:
S + 4 = (A + 4)2 - 2
S + 4 = 2A + 8 - 2
S + 4 = 2A + 6 .................. (1)
Three years ago, we have:
S - 3 = (A - 3)3
S - 3 = 3A - 9 ................................ (2)
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S = 3A - 9 + 3
S = 3A – 6 …………. (3)
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3A – 6 + 4 = 2A + 6
3A – 2A = 6 + 6 – 4
A = 8
Substitute A = 8 into equation (3), we have:
S = (3 * 8) – 6
S = 24 – 6
S = 18
Therefore, Steve's age is 18 while Anne's age is 8.
2. Let us assume that:
M = Max's age now
B = Bert's age now
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M - 5 = (B - 5)2
M - 5 = 2B - 10 .......................... (4)
A year from now, we have:
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M + 1 + B + 1 = 30
M + B + 2 = 30 .......................... (5)
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M = 30 – 2 – B
M = 28 – B …………………… (6)
Substitute M from equation (6) into equation (4) and solve for B, we have:
28 – B – 5 = 2B – 10
28 – 5 + 10 = 2B + B
33 = 3B
B = 33 / 3
B = 11
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M = 28 – 11
M = 17
Therefore, Max's age is 17 while Bert's age is 11.
3. Let us assume that:
S = Sury's age now
B = Billy's age now
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S = B + 10 ................................ (7)
Next year, we have:
S + 1 = (B + 1)2
S + 1 = 2B + 2 .......................... (8)
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B + 10 + 1 = 2B + 2
10 + 1 – 2 = 2B – B
B = 9
Substituting B = 9 into equation (7), we have:
S = 9 + 10
S = 19
Therefore, Sury's age is 19 while Billy's age is 9.
4. Let us assume that:
M = The man's age now
S = His son's age now
Therefore, now, we have:
M = 3S ................................... (9)
Five years ago, we have:
M - 5 = (S - 5)5
M - 5 = 5S - 25 ................ (10)
Substituting M from equation (9) into equation (10) and solve for S, we have:
3S - 5 = 5S – 25
3S – 5S = - 25 + 5
-2S = - 20
S = -20 / -2
S = 10
Substituting S = 10 into equation (9), we have:
M = 3 * 10
M = 30
Therefore, the man's age is 30 and his son's age is 10.
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A. $2.55
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C. $1.55
D. $2.75
Answers
Answer:
A
Step-by-step explanation:
you just need to divide $7.65 by 3
Answer: The answer is A
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Given to us,
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Number of blue pens box contains = 28,
[tex]\bold{Ratio\ between\ the\ black\ and\ blue\ pens = \dfrac{Number\ of\ black\ pens\ box\ contains}{Number\ of\ blue\ pens\ box\ contain} }[/tex]
Putting in the values we get,
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O True
False
Answers
Answer:
True
Step-by-step explanation:
The slope intercept form of an equation is
y = mx+b where m is the slope and b is the y intercept
y = 3x+7 where the slope is 3 and the y intercept is 7
This is in slope intercept form
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Step-by-step explanation:
Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.
What’s 1/4 +2/3 or 3/4+2/3
Answers
Answer:
1/4+2/3=11/12
3/4+2/3=17/12
Step-by-step explanation:
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Answers
Answer:
b > 100
Step-by-step explanation:
1. If 12 kg of sugar cost $ 250, calculate the cost of 20 kg of sugar.
Answers
Answer: 416.7
250/12 = 20.8
20.8 x 20 = 416.7
5 to the negative 3rd power
Answers
Answer:
1/125
Step-by-step explanation:
[tex](5)^{-3}\\\\=\frac{1}{5^3}\\\\=\frac{1}{125}[/tex]
The intercepts 9x^2+4y^2=36
Answers
Answer:
Step-by-step explanation:
a linear function contains the following points (0,-1) (3,8)
Answers
to find the slope you can do y2-y1/x2-x1
8-(-1)/3-0= 9/3 or 3
you can then put one of the points into the slope intercept form y=mx+b or 8=3(3)+b
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I need to Determine which two whole numbers each problem lies between. The number is 10/3
Answers
Answer:
I am not sure.
Step-by-step explanation:
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Answers
Answer:
true
Step-by-step explanation:
if you have a line LP and midpoint M means M divides LP in to two equal parts ie LM and MP
Which of the following statements about photocopier A1 is correct compared to the other photocopiers?
Answers
Answer:
Option 2
Step-by-step explanation:
Number of breakdowns of the photocopiers in year 2011,
A1 = 15
A2 = 21
B1 = 34
B2 = 32
B3 = 23
Option (1)
A1 had just under a half the number of breakdowns compared to photocopier B3.
Half of B3 = 12
And A1 = 15
Therefore, A1 > B3
So the statement is False.
Option (2)
A1 had just under 50% of the breakdowns compared to photocopier B2
50% of the breakdowns of B2 = 16
A1 = 15
So, A1 < 50% of B2
Statement (2) is True.
Option (3)
A1 had more than 25 extra breakdowns compared to B1.
A1= 15
B1 = 34
A1 < B1
Therefore, statement is False.
Option (4)
A1 had 6% less breakdowns than photocopier A2.
A1 = 15
A2 = 21
A2 - A1 = 21 - 15 = 6
Percentage less breakdowns = [tex]\frac{6}{21}\times 100[/tex] = 28.6%
So this Option is False.
Therefore, Option (2) is the correct option.