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Lilit [14]
2 years ago
13

15 scouts can sell all of their troop's cookies in 24 days. How many days would it take to sell the cookies if 18 scouts sell at

the same rate?
Mathematics
2 answers:
Ksenya-84 [330]2 years ago
7 0

Answer:

  20 days

Step-by-step explanation:

If we assume the effort is constant (15·24 = 360 scout·days), then increasing the number of scouts will decrease the number of days.

  (360 scout·days)/(18 scouts) = 20 days

If 18 scouts sell at the same rate, it would take 20 days to sell the cookies.

Lunna [17]2 years ago
5 0

Answer:

k

Step-by-step explanation:

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Students voted on a school trip. 56 voted for the museum, 86 for the nature center, 172 for the state capital, and 116 for other
OLga [1]

Answer:

a = state capital

b = nature center

c =  museum

d = other

Step-by-step explanation:

3 0
2 years ago
A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.
Artist 52 [7]

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}

6 0
2 years ago
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p)
Nimfa-mama [501]

Answer:

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is 202500 swordfishes.

Step-by-step explanation:

Let be f(p) = -0.01\cdot p^{2}+9\cdot p, the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)

First Derivative Test

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Let equalize the resulting expression to zero and solve afterwards:

-0.02\cdot p + 9 = 0

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Second Derivative Test

f''(p) = -0.02

This means that result on previous part leads to an absolute maximum.

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is:

f(450) = -0.01\cdot (450)^{2}+9\cdot (450)

f(450) =2025

The maximum sustainable yield is 202500 swordfishes.

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Step-by-step explanation:

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