Which ones are correct?

Step-by-step explanation:

[tex]y' + y = y^2[/tex]

We can rewrite the differential equation above as

[tex]\dfrac{dy}{dx} + y = y^2[/tex]

[tex]dy = (y^2 - y)dx[/tex]

or

[tex]\dfrac{dy}{y^2 -y} = dx[/tex]

We can rewrite the left side of the equation above as

[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]

We can the easily integrate this as

[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]

or

[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]

This will then give us

[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]

where k is the constant of integration. Combining the terms on the left hand side, we get

[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]

or

[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]

Solving for y, we get

[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]

We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].

Therefore, the final form of the solution to the differential equation above is

[tex]y = \dfrac{1}{1+2e^x}[/tex]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the dimension of the dam is not given.

However, a general way of calculating volume is to calculate the base area and the multiply by height.

Take for instance,the dam has a rectangular base of 20m by 30m.

The base area will be

Area = 20m * 30m = 600m²

If the height of the water in the dam is 40m, then the volume is:

Volume = 600m² * 40m

Volume = 24000m³

Answer:

4 1/8 units

Step-by-step explanation:

I believe this to be so if these points were on a number line. You would add the two points together to get the distance between the two points.

Answer:

(-1.0) (2.0) is the answer

Using the slope concept, it is found that the distances from the shore at each moment are given by:

a) 2664 feet.

b) 976 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

Item a:

The vertical distance is of 280 feet, with an angle of 6º. The distance from the shore is the horizontal distance of x. Hence:

[tex]\tan{6^\circ} = \frac{280}{x}[/tex]

[tex]x = \frac{280}{\tan{6^\circ}}[/tex]

x = 2664.

Item b:

The vertical distance is of 280 feet, with an angle of 16º. The distance from the shore is the horizontal distance of x. Hence:

[tex]\tan{16^\circ} = \frac{280}{x}[/tex]

[tex]x = \frac{280}{\tan{16^\circ}}[/tex]

x = 976.

More can be learned about the slope concept at https://brainly.com/question/18090623

Answer:

The relationship between the above two triangles is SAS and they are congruent

Answer:

19 billion dollars

Step-by-step explanation:

Given the equation :

S - 1.3x = 6

Where, S = amount of sale of statin in billions of dollars ; x = number of years after 1998

Amount spend in 2008

x = 2008 - 1998 = 10

Put x = 10 in the equation ;

S - 1.3x = 6

S - 1.3(10) = 6

S - 13 = 6

S = 6 + 13

S = 19

People will spend about 19 billion dollars on statin in 2008

Answer:

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 160, standard deviation of 13.

Middle 68% of the scores of all the games that Riley bowls.

Within 1 standard deviation of the mean, so:

160 - 13 = 147.

160 + 13 = 173.

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).

Answer:  

7.79771≤x≤8.20229  

Step-by-step explanation:  

Given the following  

sample size n = 8  

standard deviation s = 0.238  

Sample mean = 2.275  

z-score at 980% = 1.282

Confidence Interval = x ± z×s/√n  

Confidence Interval = 8 ± 1.282×0.238/1.5083)  

Confidence Interval = 8 ± (1.282×0.15779)

Confidence Interval = 8 ±0.20229    

CI = {8-0.20229, 8+0.20229}  

CI = {7.79771, 8.20229}

Hence the required confidence interval is 7.79771≤x≤8.20229

Answer:

The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.

Step-by-step explanation:

If [tex]\vec {c} = m\,\hat{i} + n\,\hat{j} + \hat{k}[/tex] is perpendicular to [tex]\vec {a} = 5\,\hat{i} + \hat{j} -2\,\hat{k}[/tex] and [tex]\vec {b} = 3\,\hat{i} - 3\,\hat{j} + 6\,\hat{k}[/tex], then the following relationships must be observed:

[tex]\vec {c}\,\bullet\,\vec {a} = 0[/tex] (1)

[tex]\vec{c}\,\bullet \,\vec{a} = 0[/tex] (2)

Then, we expand the previous expressions:

[tex](m, n, 1)\,\bullet\,(5, 1, -2) = 0[/tex]

[tex]5\cdot m + n = 2[/tex] (1b)

[tex](m, n, 1)\,\bullet\,(3, -3, 6) = 0[/tex]

[tex]3\cdot m - 3\cdot n = -6[/tex] (2b)

Then, we solve for [tex]m[/tex] and [tex]n[/tex]:

[tex]m = 0, n = 2[/tex]

The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.

Answer:

answer is B 38-18

Step-by-step explanation:

38 + (-18)

38-18

Answer:

[tex]\text{C. }1[/tex]

Step-by-step explanation:

In the question, we're given that the notation [tex]\#\#(a,b,c)[/tex] produces a number [tex]a[/tex] less than the product of [tex]b[/tex] and [tex]c[/tex] raised to the [tex]a[/tex] power. Let the number produced be [tex]n[/tex]. As a mathematical equation, we can write this production as [tex]n=(bc)^a-a[/tex]

For [tex]\#\#(2, 5, x)[/tex], we can assign:

Substituting these values into [tex]n=(bc)^a-a[/tex], we get:

[tex]23=(5x)^2-2[/tex]

Add 2 to both sides:

[tex]25=(5x)^2[/tex]

Take the square root of both sides:

[tex]5=|5x|[/tex]

For [tex]y=|z|[/tex], there are two cases:

[tex]\begin{cases}y=z,\\y=-z\end{cases}[/tex]

Therefore, we have:

[tex]\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}[/tex]

The only answer choice applicable is [tex]\boxed{\text{C. }1}[/tex].

Answer:

7.5 is the difference

Step-by-step explanation:

basketball mean

(13+22+23+24+36+37+42+43+58+69) ÷10 = 36.7

tennis mean

(14+23+24+38+47+48+57+58+66+67) ÷10 = 44.2

tennis mean - basketball mean

44.2 - 36.7= 7.5

Answer:

221

Step-by-step explanation:

5(3)2-4

Answer:

221

Step-by-step explanation:

Answer:

x = 40

Step-by-step explanation:

Two triangles are similar so we can use similarity ratio to find x

x/16 = 35/14 cross multiply expressions

14x = 560 divide both sides by 14

x = 40

Answer:

10x ÷ 5x=2x

10x ÷ 5x = 2x

10x÷ 5x = 2x

Answer:

[tex]e^{2x}=5[/tex]

Step-by-step explanation:

Recall that [tex]\log_b a=c\implies b^c=a[/tex].

In this case, we need to find the base of the logarithm. The logarithm [tex]\ln[/tex] denotes natural [tex]\log[/tex] with a base of [tex]e[/tex], a mathematical constant.

Therefore, we can re-write the equation as:

[tex]\log_e5=2x[/tex]

To write the equation as an exponential equation, recall the definition of log (first sentence of explanation):

[tex]\boxed{e^{2x}=5}[/tex]

Answer:

10 feet

Step-by-step explanation:

The half of 20 is 10. So, hence it is 10 feet.

The radius of a circular swimming pool with a diameter of 20 feet will be 10 feet.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Assume 'r' is the radius of the circle and 'd' is the diameter of the circle.

The radius of the circle is half of the diameter of the circle. Then the equation is given as,

r = d / 2

The diameter of the swimming pool is 20 feet. Then the radius of the swimming pool is given as,

r = 20 / 2

r = 10 feet

The radius of a roundabout pool with a measurement of 20 feet will be 10 feet.

More about the circle link is given below.

https://brainly.com/question/11833983

#SPJ2

Answer:

The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion

Step-by-step explanation:

Confidence interval:

Sample proportion plus/minus margin of error.

In this question:

Sample proportion of 0.45, margin of error of 0.04. So

0.45 - 0.04 = 0.41

0.45 + 0.04 = 0.49

The confidence interval is of (0.41,0.49). The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion

Answer: Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational.

Step-by-step explanation:

Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth

Answer:

[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]

Step-by-step explanation:

Let the one of the side lengths of the rectangle be [tex]x[/tex] and the other be [tex]y[/tex].

We can write the following equations, where [tex]x[/tex] will be the side opposite to the wall:

[tex]x+2y=100,\\xy=\text{Area}[/tex]

From the first equation, we can isolate [tex]x=100-2y[/tex] and substitute into the second equation:

[tex](100-2y)y=\text{Area},\\-2y^2+100=\text{Area}[/tex]

Therefore, the parabola [tex]-2y^2+100y[/tex] denotes the area of this rectangular enclosure. The maximum area possible will occur at the vertex of this parabola.

The x-coordinate of the vertex of a parabola in standard form [tex]ax^2+bx+c[/tex] is given by [tex]\frac{-b}{2a}[/tex].

Therefore, the vertex is:

[tex]\frac{-100}{2(-2)}=\frac{100}{4}=25[/tex]

Plug in [tex]x=25[/tex] to the equation to get the y-coordinate:

[tex]-2(25^2)+100(25)=\boxed{1,250}[/tex]

Thus the vertex of the parabola is at [tex](25, 1250)[/tex]. This tells us the following:

And therefore, the desired answers are:

[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]

Answer:

0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.

0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

CNNBC recently reported that the mean annual cost of auto insurance is 1049 dollars. Assume the standard deviation is 275 dollars.

This means that [tex]\mu = 1049, \sigma = 275[/tex]

Find the probability that a single randomly selected value is less than 962 dollars.

This is the p-value of Z when X = 962. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{962 - 1049}{275}[/tex]

[tex]Z = -0.32[/tex]

[tex]Z = -0.32[/tex] has a p-value of 0.3745

0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.

Sample of 72

This means that [tex]n = 72, s = \frac{275}{\sqrt{72}}[/tex]

Probability that the sample mean is les than 962.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{962 - 1049}{\frac{275}{\sqrt{72}}}[/tex]

[tex]Z = -2.68[/tex]

[tex]Z = -2.68[/tex] has a p-value of 0.0037

0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.

Answer:

x = 17

Step-by-step explanation:

in such a constellation (two beams from the same point of origin cut through the same circle) the relative relation between the segments of these beams to the overall length of the beam have to be the same :

7 × (7+x) = 8 × (8+13)

49 + 7x = 8 × 21 = 168

7x = 119

x = 17

Answer:

[tex]d=20[/tex]

Step-by-step explanation:

[tex]d+67=87[/tex]

Subtract 67 from both sides

[tex]d=20[/tex]

Hope this is helpful

Answer:

d = 20

Step-by-step explanation:

Answer:

Answer: -2 (b)

Step-by-step explanation:

So the slope of the line is the amount that the line changes as it goes along the x or y axis. Think of it like a ramp- goes up or down, steep or flat.

Take a pair of points like (-4, 11) and (2, -1)

{But you can use other points in the chart too. }

-4 to 2 is a distance of 6 --> that is the x

11 to -1 is a distance of -12 --> that is the y

We want the change in y over (or divided by) change in x.

-12 / 6 = -2

Answer:

B

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 11) and (x₂, y₂ ) = (2, - 1) ← 2 ordered pairs from the table

m = [tex]\frac{-1-11}{2-(-4)}[/tex] = [tex]\frac{-12}{2+4}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2 → B

Answer:

A

Step-by-step explanation:

f(x)=-5x³+3x²+x-9

leading coefficient is negative and it is of odd degree.

so it starts from above onthe left  and ends at the bottom ont he right.

Answer:

(6,6)

You can use the midpoint formula.

Answer:

217

Step-by-step explanation: