Consider the differential equation4y'' − 4y' + y = 0; ex/2, xex/2.Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]).The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) =

1+19.1+9.97 = 30.07 km....,...

Answer:

the answer to this is

27

Answer:

The cost of that car in 2012 dollars is $20,755

Step-by-step explanation:

We take a look at inflation values of the dollar to solve this question.

100 dollars in 1976 are equivalent to 469.48 dollars in 2021.

100 dollars in 2012 are worth 113 dollars today.

So, to find the 2012 equivalent, we divide 469.48 by 113/100 = 1.13. So

469.48/1.13 = 415.5.

That is, 100 dollars in 1976 are equivalent to 415.5 dollars in 2012, that is, 1 dollar in 1976 was worth 4.155 dollars in 2012.

In 1976, a certain model of car cost $5,000. What would be the cost of that car in 2012 dollars?

Multiplying by 4.155

5000*4.155 = 20,755

The cost of that car in 2012 dollars is $20,755

The variable t becomes the subject of the equation c=t³ - 8v by adding 8v to both sides and taking the cube root, giving t = ∛(c + 8v).

We need to make t the subject of the equation c=t³ - 8v. To do this, we first add 8v to both sides of the equation to isolate t³ on one side, giving us t³ = c + 8v. We then need to take the cube root of both sides to solve for t. Hence, t = ∛(c + 8v). Now, t is the subject of the equation.

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Answer:

The student's average velocity will be "1.69 m/s".

Displacement and Velocity:

The main distinction between velocity as well as speed would be that velocity, like speed, seems to have a direction and therefore it is a vector quantity.

This same distance travelled together along a straight line throughout a particular direction from either the beginning point is defined as displacement. Because displacement has both size as well as the direction, it's a vector quantity.

Given values:

Displacement, d = 304 m

Time, t = 180 s

We know,

The velocity (v):

= displacement/time

By substituting the values, we get

304/180=

1.69m/s

Answer:

The correct answer is that x = 0.

Answer:

x=0

Step-by-step explanation:

6+x=6

x=6-6

x=0

Answer: 5/8 as a fraction 0.625 as a decimal

Step-by-step explanation:

Answer:

2/100

Step-by-step explanation:

to find a percentage you times by a hundred

The Least Common Denominator (LCD) of 9/8 and 11/12 is 24.

The two given fractions are -

9/8 and 11/12

We have to find out the Least Common Denominator (LCD) of 9/8 and 11/12.

Firstly, we have to check if we can simplify the two given fractions. In this case, we have 9/8 and 11/12 which cannot be simplified further.

Now, we have to multiply the denominators with natural numbers until they there is a first common number in the denominators of the two given fractions.

Multiplying 8 with 2 gives 16. However, there 16 is not a multiple of 12,

Multiplying 8 with 3 gives 24. 12 when multiplied with 2 also gives 24.

So, the Least Common Denominator (LCD) of 9/8 and 11/12 is 24.

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Answer:

angle nol equals 67⁰

Step-by-step explanation:

since they make a straight line they both equal 180⁰ when added together

Answer:

67

Step-by-step explanation:

Those angles are supplementary so they add up to 180. so if you do 180-113 you'll end up with 67°.

Answer:

Step-by-step explanation:

fork knife

Answer: it is b

Step-by-step explanation: just count how many lines between x and x' to the right its positive to the left its negative

Answer:

2y + 17

Step-by-step explanation:

x and y will be used to represent the prime numbers

x is the larger,

y is the smaller

x - y = 17

that means that

x = y + 17

so then

x + y

= y + 17 + y

= 2y + 17

more information must be given to solve this problem, but for now, a general equation is

2y + 17

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Step-by-step explanation:

Given,

a student (Charles) bought a car and sold it in 15 % profit for $4669.

we have the formula,

\(cp = \frac{sp \times 100}{100 + p\%} \)

so,

\(cp = \frac{4669 \times 100}{100 + 15} \)

by simplifying it we get,

CP is $4060.

Therefore, the cp was $4060.

Hope it helps...

The probability of choosing a number that is not a multiple of 2 is P = 0.44

We need to count the number of options for each digit.

The total number of combinations is the product between the numbers of options:

C = 8*9*9 = 648

If we want our number to not be a multiple of 2 then it must end in a odd digit, the combinations that meet that condition are:

C = 8*9*4 = 288

Then the probability of selecting a 3 digit number that is not a multiple of 2 is:

P = 288/648 = 0.44

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The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3

The pattern in the question is given as

1.3, 8.3, 27.3, 64.3,…

In the above expressions and pattern, we can see that

From the above, we have the following

Current term = (n)³.3

Note that the decimal does not represent product

And also the pattern is a geometric sequence

Hence, the pattern for the sequence is f(n) = (n)³.3

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162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

Answer:

75,310,000

75,340,000

75,360,000

75,370,000

75,380,000

75,390,000

75,400,000

Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

= 2+9 /6

= 11/6

= 3+4 /12

= 7/12

The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

The number of people that nare expected to vote in the election is 260,000. people.

Simply put, a fraction is a portion of a whole. Mathematically, the number is represented as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers. On the other hand, a complex fraction has a fraction in either the numerator or the denominator.

In this situation, the pre-election survey showed that two out of every three eligible voters would cast ballots in the county election and there are 390,000 eligible voters in the county.

The number of people expected to vote will be:

= Fraction of expected voters × Total number of people

= 2/3 × 390000

= 2 × 130000

= 260000

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Note that where Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value Of $50,000, his annual premium, if his age for insurance purposes is thirty-one is: $7,665.

The insured pays a premium to the insurer on a regular basis to cover his risk. The risk is transferred from the insured to the insurer under an insurance arrangement. The premium is the amount charged by the insurer for accepting this risk.

To compute the Premium Payable, you must apply the stipulated rate against the sum insured.

Since the Sum assured is $50,000; and

The applicable rate for a 31-year-old is 15.33%

Thus the Insurance Premium for an Ordinary Whole Life Insurance Policy is:

(50,000 * 15.33)/100

= 766500/100

=  $7,665.

Thus Lowe to be entitled to an annual Life Insurance cover of $50,000 must pay $ $7,665 every year.

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Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.

Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.

In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.

The number of pages Li Wei can read in a week = 90

The number of pages Collen can read in a week = 126

Li Wei's reading rate per hour = 30 pages

Collen's reading rate per hour = 24 pages

Let the hours that Li Wei and Colleen can be on the same page= x

The total number of pages Li Wei can read = 90 + 30x

The total number of pages Colleen can read = 126 + 24x

For Li Wei and Colleen to be on the same, the two expressions are equated.

90 + 30x = 126 + 24x

6x =  36

x = 6

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Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

Step-by-step explanation:

Total no. of goods, n = 200

no. of defective units in the goods, d = 20

hence the no. of proper units,

g = n-d

g = = 200-20

g = 180

a)

ways in which a vending company buys fifteen of these microwaves and receive no defective units be:

\(^{180}C_{15}=\frac{180!}{15!\times (180-15)!}\)

\(\approx 2.83\times 10^{21}\)

b)

ways in which a vending company buys fifteen of these microwaves and receive exactly two defective units be:

\(^{20}C_2\times ^{180}C_{13}=\frac{20!}{2!\times (20-2)!} \times \frac{180!}{13!\times (180-13)!}\)

\(\approx 190\times (2.146\times 10^{19})\)

\(\approx 4.076\times 10^{21}\)

c)

ways in which a vending company buys fifteen of these microwaves and receive at least one defective units be:

\(^{20}C_{1}\times ^{199}C_{14}=\frac{20!}{1!\times (20-1)!} \times \frac{199!}{13!\times (199-13)!}\)

\(\approx 20\times (8.258\times 10^{19})\)

\(\approx 1.652\times 10^{21}\)