Answer:
15 divided by 2 1/2
Step-by-step explanation:
$6 per yard.
Answer:
Step-by-step explanation:
Give the rate of change of sales revenue of a store modeled by the equation
. The Total sales revenue function S(t) can be gotten by integrating the function given as shown;
![\int\limits {S'(t)} \, dt = \int\limits ({-30t^{2}+420t }) \, dt \\S(t) = \frac{-30t^{3} }{3}+\frac{420t^{2} }{2}\\ S(t)= -10t^{3} +210t^{2} \\](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7BS%27%28t%29%7D%20%5C%2C%20dt%20%3D%20%5Cint%5Climits%20%28%7B-30t%5E%7B2%7D%2B420t%20%7D%29%20%5C%2C%20dt%20%5C%5CS%28t%29%20%3D%20%5Cfrac%7B-30t%5E%7B3%7D%20%7D%7B3%7D%2B%5Cfrac%7B420t%5E%7B2%7D%20%7D%7B2%7D%5C%5C%20%20S%28t%29%3D%20-10t%5E%7B3%7D%20%2B210t%5E%7B2%7D%20%5C%5C)
a) The total sales for the first week after the campaign ends (t = 0 to t = 7) is expressed as shown;
![Given\ S(t) = -10t^{3} + 210t^{2}](https://tex.z-dn.net/?f=Given%5C%20S%28t%29%20%3D%20-10t%5E%7B3%7D%20%2B%20210t%5E%7B2%7D)
![S(0) = -10(0)^{3} + 210(0)^{2}\\S(0) = 0\\S(7) = -10(7)^{3} + 210(7)^{2}\\S(7) = -3430+10,290\\S(7) = 6,860](https://tex.z-dn.net/?f=S%280%29%20%3D%20-10%280%29%5E%7B3%7D%20%2B%20210%280%29%5E%7B2%7D%5C%5CS%280%29%20%3D%200%5C%5CS%287%29%20%3D%20-10%287%29%5E%7B3%7D%20%2B%20210%287%29%5E%7B2%7D%5C%5CS%287%29%20%3D%20-3430%2B10%2C290%5C%5CS%287%29%20%3D%206%2C860)
Total sales = S(7) - S(0)
= 6,860 - 0
Total sales for the first week = $6,860
b) The total sales for the secondweek after the campaign ends (t = 7 to t = 14) is expressed as shown;
Total sales for the second week = S(14)-S(7)
Given S(7) = 6,860
To get S(14);
![S(14) = -10(14)^{3} + 210(14)^{2}\\S(14) = -27,440+41,160\\S(14) = 13,720](https://tex.z-dn.net/?f=S%2814%29%20%3D%20-10%2814%29%5E%7B3%7D%20%2B%20210%2814%29%5E%7B2%7D%5C%5CS%2814%29%20%3D%20-27%2C440%2B41%2C160%5C%5CS%2814%29%20%3D%2013%2C720)
The total sales for the second week after campaign ends = 13,720 - 6,860
= $6,860
Answer:
6 is the integer which is equivalent to 9 and 3 halves
Step-by-step explanation:
we have to find the integer which is equivalent to 9 and 3 halves
Rule of halves means the restatement of meaning of median. Therefore, we have to find the median of these two integers 9 and 3.
Median of 9 and 3 is ![\frac{9+3}{2}=\frac{12}{2}=6](https://tex.z-dn.net/?f=%5Cfrac%7B9%2B3%7D%7B2%7D%3D%5Cfrac%7B12%7D%7B2%7D%3D6)
Hence, 6 is the integer which is equivalent to 9 and 3 halves
9⁹ ÷ 9⁶.
The expression 9³ is equivalent to 9⁹ ÷ 9⁶.
Using the law of exponents aⁿ÷aˣ = aⁿ⁻ˣ
9⁹÷9⁶= 9⁹⁻⁶ = 9³