The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5), as instructed, to ?nd a second solution y2(x)
y"+2y'+y=0; y1=xe^-x.

Answer:

3 x^2 y^2

Step-by-step explanation:

Simplify the following:

3 x y x y

3 x y x y = 3 x^2 y^2:

Answer: 3 x^2 y^2

Answer:

Step-by-step explanation:

To check which option is correct we will first make transition matrix.

Let the state 1 and state 2 represent the automobile and light rail

So, the transition is given by

[tex]P=\left[\begin{array}{ccc}0.80+0.05&0.15\\0.5+0.15&0.80\end{array}\right][/tex]

[tex]P=\left[\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right][/tex]

Since P as no any entry zero so, P as not absorbing stochastic matrix

Also,

[tex]|P| = \left|\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right| \\\\=0.85\times0.8-0.15\times0.2\\\\=0.65\neq0[/tex]

since |P| ≠ 0

Answer:

t = 6.3

Step-by-step explanation:

N=Noe^(-kt)

No = 14 grams

k = .1092

We want to find t when N = 7 or 1/2 of 14

N=Noe^(-kt)

7 = 14 e ^ (-.1092t)

Divide each side by 14

1/2 = e ^ (-.1092t)

take the natural log of each side

ln (1/2) = ln e ^ (-.1092t)

ln (1/2) = -.1092t

Divide each side by -.1092

ln (1/2)/ -.1092 = t

t≈6.3475

Rounding to the nearest tenth

t = 6.3

Answer: 6.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

There was a special program funded, designed to reduce crime in 8 areas of Miami.

The number of crimes per area was recorded before and after the program was established in each area. This is an example of a paired data situation. For each are in Miami you have recorded a pair of values:

X₁: Number of crimes recorded in one of the eight areas of Miami before applying the special program.

X₂: Number of crimes recorded in one of the eight areas of Miami after applying the special program.

Area: (Before; After)

A: (14; 2)

B: (7; 7)

C; (4; 3)

D: (5; 6)

E: (17; 8)

F: (12; 13)

G: (8; 3)

H; (9; 5)

To apply a paired sample test you have to define the variable "difference":

Xd= X₁ - X₂

I'll define it as the difference between the crime rate before the program and after the program.

If the original populations have a normal distribution, we can assume that the  variable defined from them will also have a normal distribution.

Xd~N(μd; σd²)

If the crime rate decreased after the special program started, you'd expect the population mean of the difference between the crime rates before and after the program started to be less than zero, symbolically μd<0

The hypotheses are:

H₀: μd≥0

H₁: μd<0

α: 0.01

[tex]t= \frac{X[bar]_d-Mu_d}{\frac{S_d}{\sqrt{n} } } ~~t_{n-1}[/tex]

To calculate the sample mean and standard deviation of the variable difference, you have to calculate the difference between each value of each pair:

A= 14 - 2= 12

B= 7 - 7= 0

C= 4 - 3= 1

D= 5 - 6= -1

E= 17 - 8= 9

F= 12 - 13= -1

G= 8 - 3= 5

H= 9 - 5= 4

∑Xdi= 12 + 0 + 1 + (-1) + 9 + (-1) + 5 + 4= 29

∑Xdi²= 12²+0²+1²+1²+9²+1²+5²4²= 269

X[bar]d= 29/8= 3.625= 3.63

[tex]S_d=\sqrt{\frac{1}{n-1}[sumX_d^2-\frac{(sumX_d)^2}{n} ] } = \sqrt{\frac{1}{7}[269-\frac{29^2}{8} ] } = 4.84[/tex]

[tex]t_{H_0}= \frac{3.63-0}{\frac{4.86}{\sqrt{8} } } = 2.11[/tex]

This test is one-tailed to the left and so is the p-value, under a t with n-1= 8-1=7 degrees of freedom, the probability of obtaining a value as extreme as the calculated value is:

P(t₇≤-2.11)= 0.0364

The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. Then at a 1% significance level, you can conclude that the special program didn't reduce the crime rate in the 8 designated areas of Miami.

I hope it helps!

Using the t-distribution, it is found that since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.

At the null hypothesis, it is tested if there has been no reduction, that is, the subtraction of the mean after by the mean before is at least 0, hence:

[tex]H_0: \mu_A - \mu_B \geq 0[/tex]

At the alternative hypothesis, it is tested if there has been a reduction, that is, the subtraction of the mean after by the mean before is negative, hence:

[tex]H_1: \mu_A - \mu_B < 0[/tex]

For both before and after, the mean, standard deviation of the sample(this is why the t-distribution is used) and sample sizes are given by:

[tex]\mu_B = 9.5, s_B = 4.504, n_B = 8[/tex]

[tex]\mu_A = 5.875, s_A = 3.5632, n_A = 8[/tex]

The standard errors are given by:

[tex]s_A = \frac{3.5632}{\sqrt{8}} = 1.2596[/tex]

[tex]s_B = \frac{4.504}{\sqrt{8}} = 1.5924[/tex]

For the distribution of differences, the mean and standard error are given by:

[tex]\overline{x} = \mu_A - \mu_B = 5.875 - 9.5 = -3.625[/tex]

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{1.2596^2 + 1.5924^2} = 2.0304[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

Hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{-3.625 - 0}{2.0304}[/tex]

[tex]t = -1.7854[/tex]

The p-value is found using a t-distribution calculator, with t = -1.7854, 8 + 8 - 2 = 14 df and a left-tailed test with a significance level of 0.01, as we are tested if the mean is less than a value.

Since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.

You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630

Answer: student tickets = 208

Adult tickets = 97

Step-by-step explanation:

x + y = 305

x = 305 - y

5x + y = 693

Substituting

5 (305 - y) + y = 693

1525 - 5y + y = 693

-4y = -832

y = 832 / 4 = 208

Answer:

0.1069 = 10.69%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 45, \sigma = 10[/tex]

Between 57 and 69

This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So

X = 69

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

[tex]Z = \frac{69 - 45}{10}[/tex]

[tex]Z = 2.4[/tex]

[tex]Z = 2.4[/tex] has a pvalue of 0.9918

X = 57

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

[tex]Z = \frac{57 - 45}{10}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

0.9918 - 0.8849 = 0.1069 = 10.69%

Answer:

The probability that next year Greenville will receive the following amount of rainfall A) At most 55 inches of rain is 0.7734, B) at least 62 inches of rain is 0.0516, C) Between 46 and 55 inches of rain is 0.0387

D Having rainfall of above 65 inches would be considered as an extremely wet year

Step-by-step explanation:

A. To find the probability that next year Greenville will receive at most 55 inches of rain we would have to make the following calculation:

P(X<55)

=P((X-mean)/s<(55-49)/8)

=P(Z<0.75)

=0.7734

The probability that next year Greenville will receive at most 55 inches of rain is 0.7734

B. To find the probability that next year Greenville will receive at most 62 inches of rain we would have to make the following calculation:

P(X>62)

=P(Z>(62-49)/8)

=P(Z>1.63)

=0.0516

The probability that next year Greenville will receive at most 62 inches of rain is 0.0516

C. To find the probability that next year Greenville will receive at Between 46 and 55 inches of rain we would have to make the following calculation:

P(46<X<54)

=P((46-49)/8 <Z<(54-49)/8)

=P(-0.38 <Z< 0.63)

=0.3837

The probability that next year Greenville will receive Between 46 and 55 inches of rain is 0.3837

D. Here consider a value that is more two standard deviations above the mean as an unusual vale. That is:

X=2σ+μ

=2(8)+49

=65

Therefore, having rainfall of above 65 inches would be considered as an extremely wet year.

5

Step-by-step explanation:

5 goes into 10 but 2 does not go into 5

Answer:

a) 0.505,0.995

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 12, \pi = \frac{9}{12} = 0.75[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.505[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.995[/tex]

So the correct answer is:

a) 0.505,0.995

Answer:

7 3/10

Step-by-step explanation:

7.3=7+0.3= 7+ 3/10= 7 3/10

Answer:

14.50 cm  

Step-by-step explanation:

The Midsegment Theorem states that the midsegment connecting the two sides of a triangle is parallel to the third side, and its length is half that of the third side.  

Thus, ∆XYZ  is similar to ∆QRS with a scale factor of 2.

Also, the perimeter of ∆XYZ  is twice that of ∆QRS.

For ∆QRS, P = 2.93 cm + 2.04 cm + 2.28 cm = 7.25 cm

∴ The perimeter of ∆XYZ = 2 × 7.25 cm =14.50 cm

The Perimeter of triangle WXY is 14.5cm

The formula for calculating the perimeter of the triangle WXY is given as:

Perimeter of triangle WXY = XY + YZ + XY

From the given triangle;

Also,

Perimeter of triangle WXY = 2QR + 2QS + 2RS

Perimeter of triangle WXY = 2(2.93) + 2(2.28) + 2(2.04)

Perimeter of triangle WXY = 5.86 + 4.56 + 4.08

Perimeter of triangle WXY = 14.5cm

Hence the Perimeter of triangle WXY is 14.5cm

Learn more on perimeter of triangles here:  https://brainly.com/question/24382052

Answer:

a) 11.03% probability that exactly two are red.

b) 98.64% probability that at most 2 are red.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the skittles are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

12 + 10 + 8 + 9 + 22 = 61 skittles.

A). exactly 2 are red

Desired outcomes:

2 red, from a set of 8.

3 non-red, from a set of 61 - 8 = 53.

So

[tex]D = C_{8,2}*C_{53,3} = \frac{8!}{2!(8-2)!}*\frac{53!}{3!(53-3)!} = 655928[/tex]

Total outcomes:

Five skittles from a set of 61. So

[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{655928}{5949147} = 0.1103[/tex]

11.03% probability that exactly two are red.

B). At most 2 are red

Desired outcomes:

None red(5 from a set of 53)...

One red(from a set of 8), and four non-read(4 from a set of 53).

Two red(655928), as found in a.

So

[tex]D = C_{53,5} + C_{8,1}*C_{53,4} + 655928 = \frac{53!}{5!48!} + \frac{8!}{1!7!}*\frac{53!}{4!49!} + 655928 = 5868213[/tex]

Total outcomes:

Five skittles from a set of 61. So

[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{5868213}{5949147} = 0.9864[/tex]

98.64% probability that at most 2 are red.

Answer:

43°

Step-by-step explanation:

Answer:

The answer depends on the shape of the trapezoid...

Step-by-step explanation:

A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. (trapezium)

Area = (a+b/2) * h

IF the sides are a = 3 ,b = 3 and height  = 4

THEREFORE:

(3+3/2) * 4

6/2 * 4

3 * 4

12

Hope it helped.... Please mark as brainliest..thanks!!!

Answer:

h=7.65

Step-by-step explanation:

H is directly proportional to the square root of p;

Let k be the constant of proportionality;

Means h=k√p

This means for corresponding points of h and p such that (h1,p1) and (h2,p2) we have;

h1/√p1=h2/√p2

Let h= 5.4 when p = 1.44 and h when p =2.89 be respectively (h1,p1) and (h2,p2)

So that

5.4/√1.44=h/√2.89

5.4/√1.44 ×√2.89 = h

7.65= h

h=7.65

Answer:

[tex]2\dfrac{11}{12}[/tex]

Step-by-step explanation:

The first step is to ensure that all of the fractions have a common denominator.

[tex]3\dfrac{1}{3}+\left( -2\dfrac{1}{4} \right) + 1\dfrac{5}{6}= \\\\3\dfrac{4}{12} - 2\dfrac{3}{12} +1 \dfrac{10}{12}= \\\\1\dfrac{1}{12}+1\dfrac{10}{12}= \\\\\boxed{2\dfrac{11}{12}}[/tex]

Hope this helps!

Answer:

[tex]4a^3(5a^3-11)[/tex]

Step-by-step explanation:

→Take out the GCF (Greatest Common Factor). The GCF is [tex]4a^3[/tex] because both [tex]-44a^3[/tex] and [tex]20a^6[/tex] can be divided by it, like so:

[tex]-44a^3+20a^6[/tex]

[tex]4a^3(5a^3-11)[/tex]

Answer:

47.85

Step-by-step explanation:

33% of 145

of means multiply

Changing to decimal form

.33* 145

47.85

Step-by-step explanation:

cross multiply, set up ur equation like so

33. x

100 = 145

100x=4785

100

x=47.85

Answer:

y=3

Step-by-step explanation:

If we use LCM and take 3 plus y it equals x so if x equals x it is then y

Answer:

D

Step-by-step explanation:

I took the Plato Course

Answer:

24 g

Step-by-step explanation:

We first find the mass of 24 % alcohol in 400 g of hand sanitizer. Let x be the mass of alcohol. So, x/400 × 100 % = 24 %

x/400 = 0.24

x = 0.24 × 400

  = 96 g

The mass of the other chemicals is thus 400 g - 96 g = 304 g

We now find the mass of 30 % alcohol in 400 g of hand sanitizer. Let y be the mass of alcohol. So, y/400 × 100 % = 30 %

y/400 = 0.30

y = 0.30 × 400

  = 120 g

The mass of the other chemicals is thus 400 g - 120 g = 280 g

The mass of other chemicals that needs to be evaporated is thus 304 g - 280 g = 24 g

Answer:

The set of all output values of a function. Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then the range is {1,4,9,...}

Answer:

100

Step-by-step explanation:

40 / 100= .4

.4 x 45 = 18

18/18= 1

1x 100= 100

Answer:

100

Step-by-step explanation:

:D

Answer:

I). X= 1,0. II) 1.72

Step-by-step explanation:

Using quadratic formula

Answer:

46

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

8 + 15 + 17 = 40

**Hope this helped!!**

**If I was right then please mark brainliest!!**

Answer:

  81

Step-by-step explanation:

2-digit squares are 16, 25, 36, 49, 64, 81.

Their sums of digits, are ...

  7, 7, 9, 13, 10, 9

The square 81 has a sum of digits equal to its square root.

Answer:

It would be 131.95 if they want the answer in pi it would be 42 pi

Step-by-step explanation:

Answer:

14.69% of men are SHORTER than 67 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches.

This means that [tex]\mu = 69.8, \sigma = 2.67[/tex]

What percentage of men are SHORTER than 67 inches

This is the pvalue of Z when X = 67. So

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

[tex]Z = \frac{67 - 69.8}{2.67}[/tex]

[tex]Z = -1.05[/tex]

[tex]Z = -1.05[/tex] has a pvalue of 0.1469

14.69% of men are SHORTER than 67 inches

Answer:

Step-by-step explanation:

hello

from 4x-y=8 we can say that y = 4x-8

we substitute in the first equation to get

5x + 4 (4x-8) = 10

then

5x + 16 x -32 = 10

<=> 21x = 32+10=42

<=> x = 42/21 = 2

and then y = 8-8=0

don t hesitate if you need any further explanation

thanks

Answer: x = 2, y = 0 or (2 , 0)

Step-by-step explanation:

Solving using substitution is where you solve for a variable in one of the two equations in the system then plug it into the other.

For an easier plug in we can take the second equation. 4x-y = 8.

From here we need to isolate the y variable which is easier to isolate than x, in my opinion.

Subtract the 4x over.

-y = 8-4x

Now divide by a -1 so y is positive.

y= -8 + 4x

Now plug this in for y in the other equation.

5x + 4(-8 + 4x) = 10

Distribute the 4.

5x - 32 + 16x = 10

Combine like terms

21x - 32 = 10

Add the 32.

21x = 42

Divide by 21.

x = 2

Now that we have solved for one variable we can plug this into either equation and solve for the other.

I will plug it into the second equation.

4(2) - y = 8

Simplify.

8 - y = 8

Subtract 8.

-y = 0

Divide by -1.

y = 0

So the x and y values are.

x = 2

y = 0

Answer:

[tex]-4\pm 3\sqrt{3}[/tex]

Step-by-step explanation:

[tex]3(x+4)^2-81=0 \\\\3(x^2+8x+16)-81=0 \\\\3x^2+24x+48-81=0 \\\\3x^2+24x-33=0 \\\\x=\dfrac{-24\pm\sqrt{24^2+4(3)(33)}}{2(3)}= \\\\\dfrac{-24\pm\sqrt{972}}{6}= \\\\\dfrac{-24\pm 18\sqrt{3}}{6}= \\\\-4\pm 3\sqrt{3}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]

Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

In our case, a = 1, b = -4 and c =2. Then the solutions are

[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]

[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]

We have that x = u-1. So the original solutions are

[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]

[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]

Answer: x+4

Step-by-step explanation: part one- x+4

Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4