If y varies directly with x and y = 2 when x = 10, then what is the value of y when x = 40? A. 8 B. 45 C. 200 D. 320

Solve the following differential equation: (1− 5 y +x) dy/dx +y= 5/x −1 .<br><br> C=

Ganezh [65]

Answer:

$y(1+x)+x-5\ln xy=C$

Step-by-step explanation:

Consider the given differential equation is

$(1-\frac{5}{y}+x)\frac{dy}{dx}+y=\frac{5}{x}-1$

$(1-\frac{5}{y}+x)\frac{dy}{dx}=\frac{5}{x}-1-y$

$(1-\frac{5}{y}+x)dy=(\frac{5}{x}-1-y)dx$

Taking all variables on right sides.

$(1-\frac{5}{y}+x)dy-(\frac{5}{x}-1-y)dx=0$

$(-\frac{5}{x}+1+y)dx+(1-\frac{5}{y}+x)dy=0$

Let as assume,

$M=-\frac{5}{x}+1+y$ and $N=1-\frac{5}{y}+x$

Find partial derivatives $\frac{\partial M}{\partial y}$ and $\frac{\partial N}{\partial x}$

$\frac{\partial M}{\partial y}=1$ and $\frac{\partial N}{\partial x}=1$

Since $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$ , therefore the given differential equation is exact.

The solution of the exact differential equation is

$\int Mdx+\int N(\text{without x)}dy=C$

$\int (-\frac{5}{x}+1+y)dx+\int (1-\frac{5}{y})dy=C$

$yx-5\ln x+x+y-5\ln y=C$

$y+x+xy-5\ln x-5\ln y=C$

$y(1+x)+x-5(\ln x+\ln y)=C$

$y(1+x)+x-5\ln xy=C$

7 0

3 years ago

riangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be less than 90°. greater than 90°. congruent

Softa [21]

Angle A must be less than 90<span>°</span>

5 0

3 years ago

How do you answer the question

Alex Ar [27]

14/4
Multiply the denominator and the whole number - 4*3=12
Add the numerator - 12+2=14
Put the answer over the denominator 14/4

7 0

2 years ago

Read 2 more answers

According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100:114 (46.7%

mojhsa [17]

Answer:

$z=\frac{0.42 -0.467}{\sqrt{\frac{0.467(1-0.467)}{150}}}=-1.154$

$p_v =2*P(z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of girls born is not significantly different from 0.467

Step-by-step explanation:

Data given and notation

n=150 represent the random sample taken

X=63 represent the number of girls born

$\hat p=\frac{63}{150}=0.42$ estimated proportion of girls born

$p_o=0.467$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion if girls is 0.467.:

Null hypothesis: $p=0.467$

Alternative hypothesis: $p \neq 0.467$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.42 -0.467}{\sqrt{\frac{0.467(1-0.467)}{150}}}=-1.154$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of girls born is not significantly different from 0.467

3 0

3 years ago

Thanks who ever helped

NeTakaya

Answer:

60 × 50 = 3000

7 × 50 = 350

60 × 4 = 240

7 × 4 = 28

3000 + 350 + 240 + 28 =3618

54 × 67 = 3618

3 0

2 years ago