Please Help!!? Leah is solving the equation using properties of exponents? 2^2x-3=(1/6)^3x+9
1 answer:
HERE IS HOW TO SOLVE:
Simplify {2}^{2}2
2
to 44
4x-3={(\frac{1}{6})}^{3}x+94x−3=(
6
1
)
3
x+9
2 Use Division Distributive Property: {(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}(
y
x
)
a
=
y
a
x
a
4x-3=\frac{1}{{6}^{3}}x+94x−3=
6
3
1
x+9
3 Simplify {6}^{3}6
3
to 216216
4x-3=\frac{1}{216}x+94x−3=
216
1
x+9
4 Simplify \frac{1}{216}x
216
1
x to \frac{x}{216}
216
x
4x-3=\frac{x}{216}+94x−3=
216
x
+9
5 Multiply both sides by 216216
864x-648=x+1944864x−648=x+1944
6 Add 648648 to both sides
864x=x+1944+648864x=x+1944+648
7 Simplify x+1944+648x+1944+648 to x+2592x+2592
864x=x+2592864x=x+2592
8 Subtract xx from both sides
864x-x=2592864x−x=2592
9 Simplify 864x-x864x−x to 863x863x
863x=2592863x=2592
10 Divide both sides by 863863
ANSWER: x= 2592 over 863
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The obtained answers for the given frequency distribution are:
(a) The formula for the mean in sigma notation is where n is the number of observations;
are the n observations.
The mean for the given monthly plan price is $16.1.
(b) The frequency distribution for given data is {$9.99 - 2; $10 - 5; $12 - 1; $12.75 - 2; $14.99 - 6; $20 - 4; $25 - 5}
(c) The formula for the mean using the frequency distribution table is where
and on applying this formula for the given data, the mean is $16.1.
(d) The median for the given data is , and the mode for the given data is $14.99
The frequency distribution has sample observations and frequencies
.
Then, the mean is calculated by
Where (Sum of frequencies)
The median is calculated by
The mode is calculated by
Mode = highest frequency value
<h3>Calculation:</h3>The given list of data is
{$14.99, $12.75, $14.99, $14.99, $9.99, $25, $25, $10, $14.99, $10, $20, $10, $20, $14.99, $10, $25, $20, $12, $14.99, $25, $25, $20, $12.75, $10, $9.99}
(a) Formula for the mean using sigma notation and use it to calculate the mean:
The formula for the mean is
Where n = 25; - n observations
On substituting,
Mean
=1/25(14.99+12.75+14.99+14.99+9.99+25+25+10+14.99+10+20+10+20+14.99+10+25+20+12+14.99+25+25+20+12.75+10+9.99)
= 1/25(402.42)
= 16.09 ≅ 16.1
(b) Constructing a frequency distribution for the data:
Cost - frequency - cumulative frequency
$9.99 - 2 - 2
$10 - 5 - 7
$12 - 1 - 8
$12.75 - 2 - 10
$14.99 - 6 - 16
$20 - 4 - 20
$25 - 5 - 25
Sum of frequencies N = 25;
(c) Using frequency distribution, calculating the mean:
The formula for finding the mean using frequency distribution is
Where N = 25;
On substituting,
<em> </em>= 1/25 (2 × 9.99 + 5 × 10 + 1 × 12 + 2 × 12.75 + 6 × 14.99 + 4 × 20 + 5 × 25)
= 1/25 (402.42)
= 16.09 ≅ 16.1
Therefore, the mean is the same as the mean obtained in option (a).
(d) Calculating the median and the mode:
Since N = 25(odd) i.e., 2· 12 + 1; k = (12 + 1)th term = 13th term
So, the median = 14.99. (frequency at 13th term)
Since the highest frequency is 6 occurred by the cost is $14.99,
Mode = 14.99
Learn more about frequency distribution here:
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