If asking to simplify 2d + 18
The given formula is f(x) = 20(1.2)^x
The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.
A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)
B) the original amount is $20
C) for 2 weeks, replace x with 2 and solve:
20(1.2)^2
20(1.44) = $28.80
After 2 weeks the coupon is $28.80
D) To solve for the number of weeks (x) set the equation equal to $100:
100 = 20(1.2)^x
Divide both sides by 20:
5 = 1.2^x
Take the natural logarithm of both sides:
ln(5) = ln(1.2^x)
Use the logarithm rule to remove the exponent:
ln(5) = x ln(1.2)
Divide both sides by ln(1.2)
x = ln(5) / ln(1.2)
Divide:
X = 8.83
At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100
The answer is 9 weeks.
The margin of error of a given statistic is an amount that is allowed for in case of miscalculation or change of circumstances.
It is usually the radius or half of the width of the confidence interval of that statistic.
Given that a<span>
survey of the students in Lance’s school found that 58% of the
respondents want the school year lengthened, while 42% think it should
remain the same. The margin of error of the survey is ±10%.
This means that 58% </span><span>± 10% of the </span>respondents want the school year lengthened, while 42% <span><span>± 10% think it should
remain the same.</span>
Thus, from 48% to 68% </span><span><span>of the respondents want the school year lengthened, while from 32% to 52% <span>think it should
remain the same.</span> </span>
Therefore, according to
the survey data, at least 32% of students want the duration of the school
year to remain unchanged, and at least 48% want the school year to be
lengthened.</span>
The answer is <em>B. 6 ÷ D</em>
