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3 years ago

Please help me on 12 and 13 thanks :)

Mathematics

2 answers:

Advocard [28]3 years ago

4 0

Number 12 is 15 that was easy for me

Crank3 years ago

4 0

Problem 12 is an increase. The percent of change is +21%.

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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

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What is

Rufina [12.5K]

Answer:

Probability that a randomly selected bill will be at least $39.10 is 0.03216.

Step-by-step explanation:

We are given that the daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.

Let X = daily dinner bills in a local restaurant

So, X ~ N( $\mu=28,\sigma^{2} =6^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{ X -\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean amount = $28

$\sigma$ = standard deviation = $6

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, the probability that a randomly selected bill will be at least $39.10 is given by = P(X $\geq$ $39.10)

P(X $\geq$ $39.10) = P( $\frac{ X -\mu}{\sigma}$ $\geq$ $\frac{ 39.10-28}{6}$ ) = P(Z $\geq$ 1.85) = 1 - P(Z < 1.85)

= 1 - 0.96784 = 0.03216

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.85 in the z table which has an area of 0.96784.

Hence, the probability that a randomly selected bill will be at least $39.10 is 0.03216.

7 0

4 years ago

Please help , I’ve been stuck on it for ages , really appreciate it. , thanks

Shalnov [3]

it is delivered with the help of short note or a clear outline

5 0

3 years ago

Read 2 more answers

SOMEONE PUT AN ANSWER SO IT DOESNT GET DELETED!!!

Nadusha1986 [10]

Answer:

The height of the cylinder is 4x units.

Step-by-step explanation:

volume of a cylinder = nr^2h

n = 22/7

r = radius = x/2

Let illustrate with an example. If the diameter of a cylinder is 6 and the volume is 6^3 = 216. The radius = 6/2 = 3

n3^2 x h = 216

h = 216/9 = 24

so the height is 4 times the diameter

Area of the base = nr^2

1/2^2 x x = 1/4 pi x^2

3 0

3 years ago

Need help please ..

Strike441 [17]

Answer:

x = -11

Step-by-step explanation:

I'm assuming it's an isosceles triangle so 32 + 2x = 10;

subtract 32 from both sides;

2x = -22

x = -11

3 0

3 years ago