Verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power x2n + 1 let k = n + 1.] y = (-1) nx2n, (1 + x2)y' + 2xy = 0

Answer:

b = -4

Step-by-step explanation:

Well we already have m which is slope which is -1.

And if we start at (-2,-2) and go down using the slope we get -4 as the y intercept or b.

Thus,

-4 is the y intercept or b.

Hope this helps :)

Answer:

b = -4.

Step-by-step explanation:

In this case, y = -2, m = -1, and x = -2.

-2 = (-1) * (-2) + b

-2 = 2 + b

b + 2 = -2

b = -4

Hope this helps!

Answer:

nine hundred five thousand two hundred thirty-eight

Answer:

0.6921 (69.21%)

Step-by-step explanation:

The area of the shaded region between the two z-scores refer to the probability between the two z-scores value( The total area under a standard normal distribution curve is 1)

So the area we want to determine in this case is as follows;

P(-1.24<z<0.84) = P(z<0.84) - P(z<-1.24)

What we use to calculate this finally is the standard normal distribution table

We use this to get these values so we can calculate the probability.

Using the standard normal distribution table;

P(-1.24<z<0.84) = 0.69206 which is approximately 0.6921

Answer:

Hey there!

The slope of a vertical line is undefined! The run is zero, and as we know, dividing by zero is undefined!

Hope this helps :)

Answer:

Undefined

Step-by-step explanation:

A vertical line has an undefined slope or there is no slope of the line.

Answer: B) -2/3

Step-by-step explanation:

First turn this equation into slope-intercept form(y = mx + b), where m is the slope.

2x+3y=4

3y=-2x+4

y=-2/3x+4/3

Thus, the slope is -2/3

Hope it helps <3

Answer:

Step-by-step explanation:

[tex]2x + 3y = 4?\\\mathrm{Slope}\:\mathbf{m}\:\mathrm{of\:a\:line\:of\:the\:form}\:\mathbf{Ax+By=C}\:\mathrm{equals}\:\mathbf{-\frac{A}{B}}\\\mathbf{A}=2,\:\mathbf{B}=3\\m=-\frac{2}{3}[/tex]

Answer:

The  number expected to pass that test is  [tex]k = 14 \ employees[/tex]

Step-by-step explanation:

From the question we are told that

      The probability of  success is  p  =  0.91

       The sample size is  n  =  15  

 The number of employee that will pass the test is mathematically represented as

          [tex]k = n * p[/tex]

substituting values

        [tex]k = 15 * 0.91[/tex]

      [tex]k = 14 \ employees[/tex]

Answer:

  0

Step-by-step explanation:

The determinant of this matrix is zero (0).

sum of angles = 10800

measurement of a single angle= 1350

Therefore,

No. of sides = sum of angles / single angle

No of sides = 10800 / 1350

No of sides = 8

Answer:

8 sides.

Step-by-step explanation:

If the sum of the angles is 10,800 degrees, and each angle is 1,350 degrees, the deck will have the number of sides of the sum of the angle measurements divided by each angle's measurements.

10,800 / 1,350 = 1,080 / 135 = 8 sides.

Hope this helps!

Answer:

The answer is 1 - 16b.

Step-by-step explanation:

You have to collect like-terms :

[tex]1 - 5b - b - 8b - 2b[/tex]

[tex] = 1 + b( - 5 - 1 - 8 - 2)[/tex]

[tex] = 1 + b( - 16)[/tex]

[tex] = 1 - 16b[/tex]

Answer:

The answer is

Step-by-step explanation:

1 – 5b + – b + – 8b – 2b can be written as

1 - 5b - b- 8b - 2b

Subtract the like terms

That's

We have the final answer as

1 - 16b

Hope this helps you

Answer:

x=−3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  7*x-8-(8*x-5)=0

Pull out like factors :  -x - 3  =   -1 • (x + 3)

Solve  :    -x-3 = 0  

Add  3  to both sides of the equation :    -x = 3

Multiply both sides of the equation by (-1) :  x = -3

Answer:

56x^2−99x+40

Step-by-step explanation:

 Evaluate (8x−5)(7x−8)

Apply the distributive property by multiplying each term of 8x−5 by each term of 7x−8.

56x^2−64x−35x+40

Combine −64x and −35x to get −99x.

56x^2−99x+40

The answer is C.) I, III, and V

The statement 1, 2, and 5 will be correct hence option (C) will be correct.

A frequency table is a list of objects with the frequency of each item shown in the table.

In other words, a frequency table is a table in which we have some data and their frequency.

The frequency of an occurrence or a value is the number of times it happens.

In option (C)

1st statement;

Math is the most popular subject in the 10th grade.

In 10th grade, maths is 104 rest are less so it is correct.

3rd statement;

Science is more popular than math among 12th-grade students.

The number of science lovers in the 12th is 78

The number of maths lovers in 12th is 52

So it is also correct.

5th statement;

Overall favorite course is history.

A number of overall favorite courses is history = 403 which is higher than others hence it is also correct.

So option (C) is correct rest are incorrect.

To learn more about the frequency table

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Work Shown:

A = mass, in kg, of 1 apple

B = mass, in kg, of 1 empty basket

10A = mass of 10 apples

10A+B = mass of 10 apples and basket = 0.5

35A = mass of 35 apples

35A + B = mass of 35 apples and basket = 1.05

The system of equations we have is

[tex]\begin{cases}10A+B = 0.5\\35A+B = 1.05\end{cases}[/tex]

There are a number of ways to solve. As the top left corner of your paper indicates, we can use a matrix to solve. Either using row reduction or matrix inverse math.

We could also use elimination which I find easiest in this case. I'll use that method. Subtract the equations straight down. Note how the B terms become B-B = 0B = 0 which go away. The A terms become 10A-35A = -25A, and the terms on the right hand side become 0.5-1.05 = -0.55

--------

We're left with the equation

-25A = -0.55

Divide both sides by -25 to isolate A

A = -0.55/(-25)

A = 0.022

The mass of one apple is 0.022 kg

--------

Use this value of A to find B

10A + B = 0.5

10*0.022 + B = 0.5

0.22 + B = 0.5

B = 0.5 - 0.22

B = 0.28

Or we could use the other equation to solve for B

35A + B = 1.05

35(0.022) + B = 1.05

0.77 + B = 1.05

B = 1.05 - 0.77

B = 0.28

Either way, the empty basket's mass is 0.28 kg

Answer:

1. D

2. B

3. A

Step-by-step explanation:

Question 1:

The pair of <JKL and <LKM can be referred to as linear pairs. They are two adjacent angles that are formed from the intersecting of two lines.

Question 2:

Given that <KLM = x°

<KML = 50°

<JKL = (2x - 15)°

According to the exterior angle theorem, exterior ∠ JKL = <KLM + KML.

2x - 15 = x + 50

Solve for x

2x - x = 15 + 50

x = 65

Therefore, <KLM = 65°

QUESTION 3:

<JKL = 2x - 15

Plug in the value of x

<JKL = 2(65) - 15

= 130 - 15

<JKL = 115°

Answer:

Definitely 3 hmmm..

Step-by-step explanation:

6/2=3 so 9/z=3

tfo 9/3=3

The missing variables have values of 12, 5, 9, and 3, respectively, for x, y, w and z.

Given that there are two similar polygons with dimension:

Larger polygon = 9, 6, w, 15, x.

Smaller polygon = z, 2, 3, y, 4.

We need to find the missing value of the side length.

According to the definition of the similar polygons, the corresponding sides shows proportionality.

9/z = 6/2 = w/3 = 15/y = x/4

Solving for each variable =

i) Solve for z:

9/z = 6/2

Cross-multiplying:

6z = 9 × 2

6z = 18

Dividing both sides by 6:

z = 18/6

z = 3

ii) Solve for w:

6/2 = w/3

Cross-multiplying:

2w = 6 × 3

2w = 18

Dividing both sides by 2:

w = 18/2

w = 9

iii) Solve for y:

6/2 = 15/y

Cross-multiplying:

6y = 30

Dividing both sides by 6:

y = 5

iv) Solve for x:

6/2 = x/4

Cross-multiplying:

2x = 24

Dividing both sides by 2:

x = 12

Hence the values of the missing variables are x = 12, y = 5, w = 9 and z = 3.

Learn more about similar polygons, click;

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Answer:

Fibonacci numbers is a series of numbers in which each number is sum of two preceding numbers.

Step-by-step explanation:

It is a sequence in mathematics denoted F. Fibonacci numbers have important contribution to western mathematics. The first two Fibonacci numbers are 0 and 1, all the numbers are then sum of previous two numbers. Fibonacci sequence is widely used in engineering applications for data algorithms. Fibonacci sequence is basis for golden ratio which is used in architecture and design. It can be seen in petals of flower and snail's shell.

Answer:

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

Step-by-step explanation:

For this problem we have the following equation given:

[tex]\frac{x^2}{169} + \frac{y^2}{25}= 1[/tex]

If we compare this with the general expression of an ellipse given by:

[tex] \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1[/tex]

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

Answer:

18. b. 4/14

19. b. 30/40

20. c. 21/48

21. a. 9/20

22. a. 6/24

Step-by-step explanation:

So in these questions all we do is multiply the fractions.

18)

[tex]\frac{4}{7} * \frac{1}{2}[/tex]

4*1 = 4

7*2 = 14

b. 4/14

19)

[tex]\frac{15}{2}*\frac{2}{20}[/tex]

15*2 = 30

2*20 = 40

b. 30/40

20)

[tex]\frac{3}{6}*\frac{7}{8}[/tex]

3*7 = 21

6*8 = 48

c. 21/48

21)

[tex]\frac{9}{10}*\frac{1}{2}[/tex]

9*1 = 9

10*2 = 20

a. 9/20

22)

[tex]\frac{3}{6}*\frac{2}{4}[/tex]

3*2 = 6

6*4=24

a. 6/24

Hope this helps :)

Answer:

5,000

Step-by-step explanation:

If it decreases by 5% a year, it'll decrease by 75% in 15 years

i.e 1 year = 5%

15 years = x

Cross multiply

x = 75%

Therefore, since it decreases by 75%

100 - 75 x 20,000 = 5,000

100

Answer:

x = 60°

Step-by-step explanation:

All the angles in a triangle add up to 180°. So, you have this equation.

87° + 33° + x = 180°

120° + x = 180°

x = 60°

The measure of angle x is 60°.

Hope that helps.

Answer:

a) P(B'|A) = 0.042

b) P(B|A') = 0.625

Step-by-step explanation:

Given that:

80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered

Of the aircraft that are discovered, 63% have an emergency locator,

whereas 89% of the aircraft not discovered do not have such a locator.

From the given information; it is suitable we define the events in order to calculate the probabilities.

So, Let :

A = Locator

B = Discovered

A' = No Locator

B' = No Discovered

So; P(B) = 0.8

P(B') = 1 - P(B)

P(B') = 1- 0.8

P(B') = 0.2

P(A|B) = 0.63

P(A'|B) = 1 - P(A|B)

P(A'|B) = 1- 0.63

P(A'|B) = 0.37

P(A'|B') = 0.89

P(A|B') = 1 - P(A'|B')

P(A|B') = 1 - 0.89

P(A|B') = 0.11

Also;

P(B ∩ A) = P(A|B) P(B)

P(B ∩ A) = 0.63 × 0.8

P(B ∩ A) = 0.504

P(B ∩ A') =  P(A'|B) P(B)

P(B ∩ A') = 0.37 × 0.8

P(B ∩ A') = 0.296

P(B' ∩ A) = P(A|B') P(B')

P(B' ∩ A) = 0.11 × 0.2

P(B' ∩ A) = 0.022

P(B' ∩ A') =  P(A'|B') P(B')

P(B' ∩ A') = 0.89 × 0.2

P(B' ∩ A') = 0.178

Similarly:

P(A) = P(B  ∩  A ) + P(B'  ∩  A)

P(A) = 0.504 + 0.022

P(A) = 0.526

P(A') = 1 - P(A)

P(A') = 1 - 0.526

P(A') =  0.474

The probability that it will not be discovered given that it has an emergency locator is,

P(B'|A) =  P(B' ∩ A)/P(A)

P(B'|A) = 0.022/0.526

P(B'|A) = 0.042

(b) If it does not have an emergency locator, what is the probability that it will be discovered?

The probability that it will be discovered given that it does not have an emergency locator is:

P(B|A') = P(B ∩ A')/P(A')

P(B|A') = 0.296/0.474

P(B|A') = 0.625

Answer:

-7 > x

Step-by-step explanation:

3(x-4)>5x+2

Distribute

3x-12>5x+2

Subtract 3x from each side

3x-12-3x>5x-3x+2

-12 > 2x+2

Subtract 2 from each side

-12-2>2x+2-2

-14 > 2x

Divide by 2

-14/2 > 2x/2

-7 > x

Answer:

[tex]\boxed{x<-7}[/tex]

Step-by-step explanation:

3(x-4)>5x+2

Expand brackets.

3x - 12 > 5x+2

Subtract 3x and 2 on both sides.

-12 - 2 > 5x - 3x

-14 > 2x

Divide both sides by 2.

-7 > x

Switch sides.

x < -7

Answer:

C. (x-3)(x+2)(x+1)

Step-by-step explanation:

We can use the rational roots test to help factor out the original equation.

The leading term is 1 and the constant is 6

p/q= 6/1

Now we find factors (all these are plus and minus)

1,2,3,6

1

We find the common ones (+1 and -1) and use -1 because it ends up being the root of the function

Factor, (x+1)

Now we have (x+1)(x^2-x-6)

Factor this with whatever method you perfer, I use AC method

Find two that are a product of -6 and add to -1 (-3 and 2)

We get (x+1)(x-3)(x+2)

C

Answer:

[tex]\boxed{C}[/tex]

Step-by-step explanation:

Let's solve all of the option and see which equals x³-7x-6

Option A)

[tex](x-4)(x-2)(x+1)[/tex]

=> [tex](x^2-6x+8)(x+1)[/tex]

=> [tex]x^3+x^2-6x^2-6x+8x+1\\x^3-5x^2+2x+1[/tex]

So, A is not correct

Option B)

[tex](x-6)(x-1)(x+1)\\(x+6)(x^2-1)\\x^3-x+6x^2-6\\x^2+6x^2-x-6[/tex]

This is also not correct

Option C)    ← Correct

[tex](x-3)(x+2)(x+1)\\(x^2-x-6)(x+1)\\x^3+x^2-x^2-x-6x-6\\x^3-7x-6[/tex]

This equals to x³-7x-6, So, this is the correct option. No need to do Option D since we have the right option now!

Answer:

93%

Step-by-step explanation:

mean=45,000 standard deviation=2000 value of concern=48,000

We can easily see that since the value of concern (48,000) is GREATER than the mean, we can rule out the last two choices.

There is no possible way a number can be greater than the mean, but less than the 50th percentile.

convert 48,000 into a z-score, which is given as:

(x-mean)/standard deviation

or in this case:

(48000-45000)/2000=1.5

using my z-score table or calculator, I can see that a z-score of 1.5 corresponds to about the 93th percentile

Answer:

[tex]-5<x<26[/tex].

Step-by-step explanation:

We know that if two corresponding sides of two triangles are equal, then third sides of the triangles depend on angle between equal sides.

Angle opposite to larger side is larger.

Since, 14 < 15, therefore

[tex]2x+10<62[/tex]

[tex]2x<62-10[/tex]

[tex]2x<52[/tex]

[tex]x<26[/tex]          ...(1)

We know that, angle can not not negative.

[tex]2x+10>0[/tex]

[tex]2x>-10[/tex]

[tex]x>-5[/tex]        ...(2)

From (1) and (2), we get

[tex]-5<x<26[/tex]

Therefore, the range of values of x is [tex]-5<x<26[/tex].

Answer:

-11/24

Step-by-step explanation:

5/12 - 7/8

We need to get a common denominator of 24

5/12 *2/2  - 7/8 *3/3

10/24 - 21/24

-11/24

Answer:

-11/24

Step-by-step explanation:

Well to solve 5/12 - 7/8 we need to find the LCM.

12 - 12, 24, 36, 48

8 - 8, 16, 24, 32, 40

So the LCM is 24.

Meaning we need to make both denominators 24.

12*2 = 24 5*2 = 10

10/24

8*3 = 24 7*3 = 21

21/24

10/24 - 21/24

= -11/24

Thus,

the answer is -11/24.

Hope this helps :)

Answer:

b

Step-by-step explanation:

A, b, c, and d are all points. the line segements are: ab, bc, cd, da, and ac

Answer:

answer is B

Step-by-step explanation:

Answer:

The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5  or greater or much lesser than the average. It would not give an approximate value of occurrences.

Step-by-step explanation:

Mean is the averaage of all the values.

Median is the value of the data which gives an estimate of the middle value. Middle values can be different than the average values.

The mean is

1) rigorously defined by a mathematical formula.

2) based on all the observations of the data

3) affected by extreme values

The meadian is

1) computed for open end classes like income etc.

2) not rigorously defined

3) is located when the values are not capable of quantitative measurment.

4) is not affected by extreme values.

The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5  or greater or much lesser than the average. It would not give an approximate value of occurrences.

Answer:

a)P [ z > 1,38 ] = 0,08379

b) P [ 1,233 < z < 2,43 ]  = 0,1012

c)  P [ z > -2,43 ]  = 0,99245

Step-by-step explanation:

a) P [ z > 1,38 ] = 1 -  P [ z < 1,38 ]

From z-table  P [ z < 1,38 ] = 0,91621

P [ z > 1,38 ] = 1 - 0,91621

P [ z > 1,38 ] = 0,08379

b)  P [ 1,233 - 2,43 ]  must be  P [ 1,233 < z < 2,43 ]

P [ 1,233 < z < 2,43 ]  = P [ z < 2,43 ] - P [ z > 1,233 ]

P [ z < 2,43 ]  = 0,99245

P [ z > 1,233 ] = 0,89125    ( approximated value  without interpolation)

Then

P [ 1,233 < z < 2,43 ]  = 0,99245 - 0,89125

P [ 1,233 < z < 2,43 ]  = 0,1012

c) P [ z > -2,43 ]

Fom z-table

P [ z > -2,43 ] = 1 - P [ z < -2,43 ]

P [ z > -2,43 ] = 1 - 0,00755

P [ z > -2,43 ]  = 0,99245

If the path is perpendicular to the field it is zero.

If the path is along the field it is positive or negative depending on it's direction.

See the attached picture.