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3 years ago

Select the correct answer.

Mathematics

1 answer:

IceJOKER [234]3 years ago

4 0

Answer: Option D. y+2x=3

Solution

If a line with a slope of -2:

Slope: m=-2

crosses the y-axis at (0,3):

(0,3)=(0,b)→b=3

What is the equation of the line?

y=mx+b

Replacing the known values:

y=-2x+3

Adding 2x both sides of the equation:

y+2x=-2x+3+2x

y+2x=3

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Suppose that you work for the child social services agency in your county. Your job is to investigate instances of possible chil

True [87]

Answer:

Null hypothesis: ∪ = No possible child abuse or neglect

Alternative hypothesis: Uₐ = Possible child abuse or neglect

Step-by-step explanation:

Null hypothesis: ∪ = No possible child abuse or neglect

Alternative hypothesis: Uₐ = Possible child abuse or neglect

A type I error occurs when you reject the null hypothesis when it is true. In this situation, a type I error occurs when you conclude on possible child neglect or abuse and place the child in protective custody

A type II error occurs when you accept the null hypothesis when it is false. In this instance, a type II error occurs when you conclude on no possible child abuse or neglect when there is and fail to remove the child from the home.

In this case, the type II error is the more serious error. Failure to remove the child when there is possible child abuse or neglect will lead to more detrimental effect. Although, the type I error is also serious, it is not so detrimental as the type II error.

5 0

3 years ago

First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

7 0

3 years ago

Which of the following is a correct equation for the line passing through the

11Alexandr11 [23.1K]

Answer:

Step-by-step explanation:

m = -3

y = mx +b

y = -3x + b

Plugin x = -1 and y = 4

4 = -3*(-1) +b

4 = 3 + b

4-3 = b

b = 1

y = -3x + 1

6 0

2 years ago

Read 2 more answers

Can’t figure this out need help

Morgarella [4.7K]

i think D hope it helps

Step-by-step explanation:

1 7/8 the least because it farther from the line than 0

8 0

3 years ago

Read 2 more answers

A van travels from Town A to Town B. It uses 1 gallon of gas for every 24 miles traveled. A) How many gallons of gas does the va

Setler79 [48]

Answer:

A) $\frac{x}{8}$ gallons

B) Distance between Town A and Town B is $48y$ miles

Step-by-step explanation:

We know, number of gallons = $\frac{DistanceTravelled}{MilesPerGallon}$

if miles per gallon (mpg) is given as 24 & total distance travelled is 3x miles, then, using formula we have:

Number of Gallons = $\frac{DistanceTravelled}{MilesPerGallon}=\frac{3x}{24}=\frac{x}{8}$

Now, given is number of gallons = 2y & we know mpg is 24; <em>so what is the distance?</em>

We use the same formula and solve for distance (let distance between A and B be "D"):

$NumberOfGallons=\frac{DistanceTravelled}{MilesPerGallon}\\2y=\frac{D}{24}\\D=2y*24\\D=48y$

7 0

2 years ago