If a and b are odd integers,then a-b is an even integer identify the conclusion

The rate of change (dP/dt), of the number of people on an ocean beach is modeled by a logistic differential equation. The maximu

Kazeer [188]

Answer:

$\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})$

Step-by-step explanation:

The logistic differential equation is as follows:

$\frac{dP}{dt} = rP(1 - \frac{P}{K})$

In this problem, we have that:

$K = 1200$ , which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.

At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.

This means that $\frac{dP}{dt} = 400$ when $P = 200$ . With this, we can find r, that is, the growth rate,

So

$\frac{dP}{dt} = rP(1 - \frac{P}{K})$

$400 = 200r(1 - \frac{200}{1200})$

$166.67r = 400$

$r = 2.4$

So the differential equation is:

$\frac{dP}{dt} = rP(1 - \frac{P}{K})$

$\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})$

3 0

3 years ago

BRAINLIEST, help, thank youu!!

mihalych1998 [28]

Answer: B - 15/40

Step-by-step explanation: You can simplify the answer from

3/8 x 5 = 15/40

Hope this helps ty if you do give brainliest. means alot.

6 0

2 years ago

Read 2 more answers

Evaluate

lora16 [44]

Answer:

8

Step-by-step explanation:

the top part with the variables filled in is 0 + (2x4) + (3x4x2) which is 32

the bottom part would be (3x0) + 4 which is 4

7 0

3 years ago

Elizabeth has $10, $5, and $1 bills worth $101. she has five more five dollar bills than ten dollar bills and 4 times more 1 dol

vesna_86 [32]

Let x be number of $10 dollar bills

Let y be number of $5 dollar bills

Let z be number of $1 dollar bills

From the question, we can come up with three equations (so we can find the values of x, y & z) :

10x + 5y + z = 101
y - x = 5
z = 4x

The first equation comes from finding the total money Elizabeth has, which is $101.

The second equation comes from value of y (number of $5 bills) is more than value of x (number of $10 bills) by 5 dollars.

The third equation comes from the value of z (number of $1 bills) being 4 times more than the value of x (number of $10 bills).

Now, we will begin to find the value of x, y & z.

From the first equation,

10x + 5y + z = 101

Substitute the third equation (z = 4x) into z:

10x + 5y + 4x = 101

Simplify this and you get,

14x + 5y = 101

Now, we use the second equation. The second equation is y - x = 5. If we try to make y as the subject, it becomes y = 5 + x.

Now, substitute this into the value of y of the last working we did:

14x + 5(5+x) = 101

Simplify that and it becomes:

x = 4

Then, substitute this value of x into the second and third equations to find y and z.

y - x = 5

y - 4 = 5

y = 9

z = 4x

z = 4(4)

z = 16

Finally, let's check these answers by substituting them into the first equation to try and see if the total value is <em>really</em> $101.

10x + 5y + z = 10(4) + 5(9) + 16

10x + 5y + z = 40 + 45 + 16

10x + 5y + z = 101

Thus, our answers are correct. Elizabeth has FOUR $10 bills, NINE $5 bills and SIXTEEN $1 bills.

6 0

3 years ago

Read 2 more answers

The Genetics & IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceivi

Reika [66]

Answer: The test statistic needed to test this claim= 10.92

Step-by-step explanation:

We know that the probability of giving birth to a boy : p= 0.5

i..e The population proportion of giving birth to a boy = 0.5

As per given , we have

Null hypothesis : $H_0: p\leq0.5$

Alternative hypothesis : $H_a: p>0.5$

Since $H_a$ is right-tailed , so the hypothesis test is a right-tailed z-test.

Also, it is given that , the sample size : n= 291

Sample proportion: $\hat{p}=\dfrac{239}{291}\approx0.82$

Test statistic : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$ , where n is sample size , $\hat{p}$ is sample proportion and p is the population proportion.

$\Rightarrow\ z=\dfrac{0.82-0.5}{\sqrt{\dfrac{0.5(1-0.5)}{291}}}\approx10.92$

i.e. the test statistic needed to test this claim= 10.92

Critical value ( one-tailed) for 0.01 significance level = $z_{0.01}=2.326$

Decision : Since Test statistic value (10.92)> Critical value (2.326), so we reject the null hypothesis .

[When test statistic value is greater than the critical value , then we reject the null hypothesis.]

Thus , we concluded that we have enough evidence at 0.01 significance level to support the claim that the YSORT method is effective in increasing the likelihood that a baby will be a boy.

7 0

3 years ago