Check the picture below.
![\bf \stackrel{area}{A}=length\cdot width\implies A(w)=(1000-2w)w \\\\\\ \boxed{A(w)=1000w-2w^2} \\\\\\ \cfrac{dA}{dw}=1000-4w\implies 0=1000-4w\implies 4w=1000 \\\\\\ w=\cfrac{1000}{4}\implies \boxed{w=\stackrel{width}{250}} \\\\\\\ [1000-2(250)]\implies 1000-500\implies \boxed{l=\stackrel{length}{500}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Barea%7D%7BA%7D%3Dlength%5Ccdot%20width%5Cimplies%20A%28w%29%3D%281000-2w%29w%0A%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BA%28w%29%3D1000w-2w%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BdA%7D%7Bdw%7D%3D1000-4w%5Cimplies%200%3D1000-4w%5Cimplies%204w%3D1000%0A%5C%5C%5C%5C%5C%5C%0Aw%3D%5Ccfrac%7B1000%7D%7B4%7D%5Cimplies%20%5Cboxed%7Bw%3D%5Cstackrel%7Bwidth%7D%7B250%7D%7D%0A%5C%5C%5C%5C%5C%5C%5C%0A%5B1000-2%28250%29%5D%5Cimplies%201000-500%5Cimplies%20%5Cboxed%7Bl%3D%5Cstackrel%7Blength%7D%7B500%7D%7D)
and if you run a first-derivative test on say x = 249 and x = 251, you'll notice the slope is positive and negative respectively, meaning, is a maximum.
Answer:
3796.65
Step-by-step explanation:
I = $ 3,106.35
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 3.9%/100 = 0.039 per year,
then, solving our equation
I = 17700 × 0.039 × 4.5 = 3106.35
I = $ 3,106.35
The simple interest accumulated
on a principal of $ 17,700.00
at a rate of 3.9% per year
for 4.5 years is $ 3,106.35.
$ 6,903.00 - 3,106.35 = 3796.65
Answer:
15 Blue Jays
Step-by-step explanation:
Number of Blue Jays tagged = 22
Number of Blue jays captured = 550
Estimate of the Blue Jay population = 825
We need to find out how many Blue Jays out of 550 were tagged ones. Remember that in the beginning there were no tagged Blue Jays and Marley tagged 22 of them. This means total number of tagged Blue Jays in the entire population is 22. Rest of the blue Jays are not tagged. Marley calculated the estimated Blue Jay population using the proportions.
Assume that from 550, x Blue Jays were tagged. Out of 825 Blue Jays, 22 are tagged. The proportion of tagged Blue Jays in 550 must be equal to the proportion of tagged Blue Jays in entire population. i.e.
Since, the number of Blue Jays cannot be in decimal, we round it up to the nearest integer 15.This means, out of 550 trapped 15 Blue Jays were the tagged ones. Based on this Marley estimated the Blue Jays Population size.
Answer:
Step-by-step explanation:
Hello,
This question requires us to convert numbers from standard form to scientific form. This can easily be done using a calculator or just writing the number down then put a decimal point after the first digit and count the rest which would be raised to the power of that number.
Budget = 69.1 billion
Converting this to scientific form = 6.91×10¹⁰
Population = 11.67 million
Converting this to scientific form = 1.167×10⁷
Budget per capita refers to budget allocated to each individual in the population.
Budget per capita is used to compare economic indices or indicators of various countries with different population sizes.
Budget per capita = budget / total population
Budget per capita = 6.91×10¹⁰ / 1.169×⁷
Budget per capita = 5911.03
What this implies is that for each individual living in the state of Ohio, the amount budgeted for that particular period (mostly in a given year) is 5911.03
