Consider the differential equation (x - 1)y" + y' = 0. By using power series so- lution about the ordinary point 0 we obtain: c_{k+1)=[(k+1)/(k+2)] C_(K); k=1,2,3.... c_(K+2)=[(k+1)/(k+2)] C_(K+1); k=0,1,2,3... None of them c_(k+2)=[(k+1)/(k+2)] C_(k+1); k=1,2,3....​

The measurement of each of the squares will guarantee Mrs. O'Dell has 8 different squares and they are all the same size are 75 centimeters by 100 centimeters.

To begin, let's identify the best way to divide the total area. For this, there are 2 options:

Let's use the first pattern:

Based on this, the dimensions for each section should be 75 centimeters by 100 centimeters.

Note: This question is incomplete; here is the missing section:

Dimensions of the garden: 3 meters x 2 meters

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Answer:

23552

Step-by-step explanation:

23, 92, 368...   is a geometric sequence.

first term = a = 23

common ratio = r = 2 term ÷ first term = 92 ÷ 23 = 4

nth term = \(ar^n^-^1\)

6th term = \(23*(4)^6^-^1\)

\(=23*4^5\)

\(=23*1024\)

\(=23552\)

Hope this helps :)

Pls brainliest...

Step-by-step explanation:

what is your questions

Answer:

The answer would be 13.5 pints

Step-by-step explanation:

when you do 2 gallons - 2 pints you get 1.75 gallons

then when you do 1.75 - 1 cup you get 13.5 pints

Answer:

x^2y^4

Step-by-step explanation:

b because u have to add the exponents of the like variable. x^4 and x^-2 are the like terms in this equations so 4+(-2) so its basically flipping the signs plus and the negative sign so it's just -2

Answer: adults or pre teens

Step-by-step explanation:

The predicted population in the year 2030 is 10 people

From the question, we have the following parameters that can be used in our computation:

Population function, P(t)= 15е⁻⁰.⁰¹²⁺

Also from the question, we have

The variable t represents the number of years since 2020

This means that the value of t in 2030 is

t = 2030 - 2020

t = 10

So, we have

P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰

Evaluate the above products

P(10)= 15е⁻⁰.¹²

Evaluate the exponents

P(10)= 13.30

Approximate the above expression

P(10) = 13

This means that the number of people is 13

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Answer:

Properties:

Find x:

Find y:

Find z:

Answer:

x=10

y = 21°

z=8°

Step-by-step explanation:

we have

AB = AD, CB = CD,

AC perpendicular to DB, AC is angle bisector of DAB and DCB

Perimeter = 140

2(2x + 7 + 4x +3) = 140

6x + 10 = 70

6x = 60

x = 60/6=10

x=10

again

3y - 1 +28° =90

3y - 1 = 90° - 28°

3y - 1 = 62°

3y = 63°

y = 21°

again

4z+58°=90

4z = 90° - 58

4z = 32°

z=32/4

z=8°

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer:

The answer is B

Step-by-step explanation:

Answer:

y = -3x + 2

Step-by-step explanation:

use the slope formula to find the slope

replace x and y into slope intercept form with the slope you just found

Answer:

- 5

Step-by-step explanation:

Probability of a coin toss : (H, T)

With probability of 0.5 each

X : ____100 ____ - 110

P(x) :___ 0.5 ____ 0.5

Expected value ; E(X) = ΣX*p(X)

E(X) = (100 * 0.5) + (-110 * 0.5)

E(X) = 50 - 55

E(X) = - 5

Expected value = - 5

Answer:

4.4 ounces/ 4 ounce (if rounded)

Step-by-step explanation:

There are 16 ounces in a pound, therefore the equation 12/16 will be useful since 16 ounces in a pound can be divided by 12, in conclusion 12/16=0.75 which is how much an ounce costs.

Then you will take $3.30 and divide it by 0.75 to get your answer for how many ounces you can buy for $3.30 which will equal 4.4 ounces but if you were to round it would be 4 ounces

Hope this helps!

Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter. The number of elements in the finite set is known as the cardinality (or the cardinal number) of a set. Let us take an example:

A = {1, 2, 3, 4, 5 }

Since a set is usually represented by the capital letter. Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated. All the set elements are represented in small letter in case of alphabets. Also, we can write it as 1 ∈ A, 2 ∈ A etc. The cardinal number of the set is 5. Some commonly used sets are as follows:

N: Set of all natural numbers

Z: Set of all integers

Q: Set of all rational numbers

R: Set of all real numbers

Z+: Set of all positive integers

A non empty is a set that has one or more elements.A “set” is just a well-defined collection of distinct objects, and their union—the set—is an object itself. A set can contain anywhere from 0 to an infinite number of items.

Finite sets are sets having a finite/countable number of members. Finite sets are also known as countable sets, as they can be counted. The process will run out of elements to list if the elements of this set have a finite number of members

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Answer:

1 hour and 40 minutes

Step-by-step explanation:

im high asfff

The zeros of the function defined by

h(x) = x³ – 4x² – 5x are x = 0, x = 5 and x = -1

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0. It is simply the values of x when f(x) is equal to 0.

For x = 0, we substitute 0 for x in the function h(x);

h(0) = (0)³ - 4(0)² - 5(0)

h(0) = 0

For x = 1, we substitute 1 for x in the function h(x);

h(1) = (1)³ - 4(1)² - 5(1)

h(1) = 1 - 4 - 5

h(1) = -8

For x = -5, we substitute -5 for x in the function h(x);

h(-5) = (-5)³ - 4(-5)² - 5(-5)

h(-5) = -125 - 100 +25

h(-5) = -200

For x = 5, we substitute 5 for x in the function h(x);

h(5) = (5)³ - 4(5)² - 5(5)

h(5) = 125 - 100 - 25

h(5) = 0

For x = -1, we substitute -1 for x in the function h(x);

h(-1) = (-1)³ - 4(-1)² - 5(-1)

h(-1) = -1 - 4 + 5

h(-1) = 0

Therefore, the values of x that makes the function h(x) = x³ – 4x² – 5x equal to zero are; 0, 5, and -1, they are the zeros of the function h(x).

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first you need to find the gradient of the line and to do that you divide the height of a part of the line by its length. so to find the height we do -3-0=-3 and to find the length we do 2-1=1. then divide -3 by 1 and the gradient is -3. so now we know the equation is y=-3x+b. to find b we replace y with the y coordinate of one of the 2 points. lets take the first point. so it will be 0=-3+b. Now we can easily find b by doing 0-(-3) which is 3. so the equation of the line is y=-3x+3. Also please mark this as brainliest answer if you found it helpful thanks.

Answer:

y = - 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ )  = (1, 0 ) and (x₂, y₂ ) = (2, - 3 )

m = \(\frac{-3-0}{2-1}\) = \(\frac{-3}{1}\) = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 3 )

- 3 = - 3(2) + c = - 6 + c ( add 6 to both sides )

3 = c

y = - 3x + 3 ← equation of line

Answer:

The answer is: 0

Hope this helps!

Answer:

The value of this expression is 0.

Step-by-step explanation:

Note:  You want to "evaluate" this expression, not find the "answer."

Any work that happens inside parentheses must be done first.  Therefore,

4[2(6 · 4) - 8 · 6] becomes 4[2(24) - 8 · 6].  Next, according to Order of Operations rules, multiplication and division happen before addition or subtraction.

Thus we have 4[48 - 48]  =  4[0]  =  0

Refer to attatchment.

Answer:

4x2+4x-5

Step-by-step explanation:

Hopes this helps

Plz markas brainliest

Answer:

x = 60

Step-by-step explanation:

(x + 50)° + (x + 10)° = 180° (interior angles on the same side of transversal)

(2x + 60)° = 180°

2x + 60 = 180

2x = 180 - 60

2x = 120

x = 120/2

x = 60

Answer:

9.9%

Step-by-step explanation:

Well, you would just divide the "other" category and the "total" category and then move the decimal over 2 spaces, because you need to multiply by 100 to turn your answer into a percent, so:

Then once you multiply by 100, or move the decimal to the left 2 spaces, it becomes:

9.9%, which could be rounded to 10% or 9%.

Answer:

The unit rate is $20 per hour?

Step-by-step explanation:

For every hour Mike is tutored, he pays $20. 20:1

If Mike payed $20 every two hours, then the unit rate would be $10 per hour.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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Answer:

Step-by-step explanation:

Because this problem is not easily solvable through factoring, we must use long division to find the answer.

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

When performing long division on polynomials, we should try to cancel out the term with the greatest power first. So, we must figure out how many x's go into x3, because x is the first term of the first polynomial and x3 is the first term of the second polynomial. x*x2 = x3, so:

     x2

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

  (-)  x3 + 14x2

         (k-14)x2 - 34x

Then, we see how many x's go into (k-14)x2. x*(k-14)x = (k-14)x2, so:

     x2 + (k-14)x

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

  (-)  x3 + 14x2

         (k-14)x2          - 34x

    (-)  (k-14)x2 - 7kx - 98x

                        -7kx - 132x + 56= (-7k-132)x + 56

x*(-7k-132) = (-7k-132)x, so:

     x2 + (k-14)x + (-7k-132)

      _______________                                                                                  x+7 | x3 + kx2 - 34x + 56

  (-)  x3 + 14x2

         (k-14)x2          - 34x

    (-)  (k-14)x2 - 7kx - 98x

                        (-7k-132)x          + 56

                    (-) (-7k-132)x - 7k - 924

                                          -7k - 868

The answer is x2 + (k-14)x + (-7k-132) - [(7k-868)/(x+7)]

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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