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3 years ago

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1 answer:

Vilka [71]3 years ago

5 0

-7/10 divided by 2/5 is -35/20 or -7/4 in the simplest form

-1/4 times (-4/3) is 4/12 or 1/3 in the simplest form

-3 1/3 or -10/3 times by -2 7/10 or -27/10 is 270/30 or 9

-10 2/7 or -72/7 divided by -4 4/11 or -48/11 is 792/336 or 33/14 in the simplest from

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Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

3 years ago

(IF CORRECT WILL MARK BRAINLIEST!)Which of the following equations has exactly one real solution?

telo118 [61]

A
explanation:
2x+10=-6-30
8x+40=0
x=-5

5 0

3 years ago

In order to take honors-level math, Lisa must have an average of 85 on her math tests. Her scores so far are 85, 70, and 98. Wha

Mila [183]

Answer:

d) 87

Step-by-step explanation:

to solve this lets set up the equation

$\frac{85+70+98+x}{4} =85\\\frac{253+x}{4} =85$

then we multiply 4 on both sides

253+x=340

and subtract 253 on both sides

x=87

to double check take the averages

(87+85+70+98)/4=85

5 0

3 years ago

A sample of 140 Vopstra customers have had their annual phone charge recorded for the previous calendar year. The data were used

taurus [48]

Answer:

Correct option: (a)

Step-by-step explanation:

A confidence interval is an interval estimate of the parameter value.

A (1 - <em>α</em>)% confidence interval implies that the confidence interval has a (1 - <em>α</em>)% probability of consisting the true parameter value.

OR

If 100 such confidence intervals are made then (1 - <em>α</em>) of these intervals would consist the true parameter value.

The 92% confidence interval for the mean annual phone charge of all Vopstra customers is:

$\$470\pm \$65=(\$405, \$535)$

This confidence interval implies that true mean annual phone charge of all Vopstra customers is contained in the interval ($405, $535) with 0.92 probability.

Thus, the correct option is (a).

6 0

3 years ago

11(2x + 1) = 4x - 7 <br> show work

Harlamova29_29 [7]

Answer:

0.22

Step-by-step explanation:

22x + 11 = 4x - 7

22x - 4x = -7 + 11

18x = 4

x = 4/18

x = 0.22

<em><u>Please mark as brainliest.</u></em>

8 0

3 years ago

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