Simplify the expression. 1−(sec2x−tan2x)

Suppose a population grows according to the logistic equation but is subject to a constant total harvest rate of H. If N(t) is t

Elenna [48]

Answer:

a) Equilibrium point : [ 947, 53 ]

b) N = 947 is stable equilibrium, N = 53 is unstable equilibrium

c) N0, the population will not go extinct

Step-by-step explanation:

a)

Given that;

r = 2, k = 1000, H = 100

dN/dT = R(1 - N/k)N - H

so we substitute

dN/dt = 2( 1 - N/1000)N - 100

now for equilibrium solution, dN/dt = 0

so

2( 1 - N/1000)N - 100 = 0

((1000 - N)/1000)N = 50

N^2 - 1000N + 50000 = 0

N = 1000 ± √(-1000)² - 4(1)(50000)) / 2(1)

N = 947.213 OR 52.786

approximately

N = 947 OR 53

Therefore Equilibrium point : [ 947, 53 ]

b)

g(N) = 2( 1 - N/1000)N - 100

= 2N - N²/500 - 100

g'(N) = 2 - N/250

SO AT 947

g'(N) = g'(947) = 2 - 947/250 = -1.788 which is less than (<) 0

so N = 947 is stable equilibrium

now AT 53

g'(N) = g"(53) = 2 - 53/250 = 1.788 which is greater than (>) 0

so N = 53 is unstable equilibrium

The capacity k=1000

If the population is less than 53 then the population will become extinct but since the capacity is equal to 1000 then the population will not go extinct.

6 0

4 years ago

g A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is cha

leva [86]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=410$ represent the number of people indicating that their financial security was more than fair for the recent year

$X_{2}=245$ represent the number of people indicating that their financial security was more than fair for the year before

$n_{1}=1000$ sample 1 selected

$n_{2}=700$ sample 2 selected

$p_{1}=\frac{410}{1000}=0.410$ represent the proportion estimated of indicating that their financial security was more than fair this year

$p_{2}=\frac{245}{700}=0.35$ represent the proportion estimated of indicating that their financial security was more than fair the year before

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+245}{1000+700}=0.385$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

7 0

3 years ago

Where were the two cars in relation to each other when they began traveling?

Elza [17]

Answer:

The answer is A.

Step-by-step explanation:

As can be seen in the graph, car B starts at the "20" mark on the vertical axis, signifying that it starts 20 miles east of car A.

Hope this helped!

3 0

3 years ago

It cost $200 to rent a room at an event center. The event center charges an additional $13 per person for food. Write an algebra

nydimaria [60]

Answer:13n=200

Step-by-step explanation$13 for pood per person. n is the number of people. 13 times n equals 200

8 0

3 years ago

At the Kennel, the ratio of dogs to cats is 2:1. If there are 10 dogs, how many cats are there

beks73 [17]

Answer:

10 dogs, 5 cats

Step-by-step explanation:

2:1 = whole to half

5 0

3 years ago