What is the rate of return when 30 shares of Stock
A, purchased for $15/share, are sold for $480? The
commission on the sale is $6.
Rate of Return = [?] %
Give your answer as a percent rounded to the
nearest tenth

The differential equation of y'' + 3y' + 2y = 1/4+ex is

               \(y=c_{1} e^-^2^x+c_{3} e^-^x+4e^-^2^xln(4+e^x)+e^xln(4+e^x)\)

The given differential equation is y'' + 3y' + 2y = 1/4+ex

As we are considering the LHS part looks like a Quadratic equation.

y''+3y'+2y=m²+3m+2

m²+3m+2=0 ---(1)

finding the roots for eq(1)

m²+2m+m+2=0

m(m+2)+1(m+2)

(m+2) (m+1)=0

m=-2,m=-1

Yc=C₁e⁻²ˣ+C₂eˣ   ----(2)

equation (2) is called a complementary function.

A complementary function is only one part of the solution to a linear, and autonomous differential equation.

An ordinary differential equation (ODE) defines the sum of a function and its derivatives. When the explicit functions y = f(x) + cg(x) form the solution, g is called the complementary function; f is the particular integral.

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The geometric sequence that describes Nelson's debt after each month is given as follows:

E. 950,967.1, 984.51, 1002.23, 1020.27.

In a geometric sequence, each term of the sequence is obtained as the multiplication of the previous term of the sequence by the common ratio.

The interest rate in this problem is of:

1.8%.

Then each month, the debt will be the previous month's debt multiplied by 100 + 1.8 = 101.8% = 1.018, hence the common ratio is given as follows:

1.018.

Hence the terms of the sequence are given as follows:

Hence the correct option is given by Option E.

The complete problem is given by the image presented at the end of the answer.

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Answer:

41.48/year

Step-by-step explanation:

4.95 x 12 = 59.40

59.40 × .30 = 17.82

59.40 - 17.82 = 41.48

Answer:

Step-by-step explanation:

vol = 18 x 20 x 10

vol = 3600 mm³

Step-by-step explanation:

18*20*10 = 3,600

After using the elimination method we get the value of y as 2.

Given we have the following set:

2x + 4y = 6

3x + 5y = 7

Solving simaltanious equation by elimination

2x + 4y = 6 -------------(I)

3x + 5y = 7 ---------------(II)

To eliminate x, multiply equation (I) by (-3) and equation (II) by 2. Then add the two equations. Now, 'x' will be eliminated and we can find the value of 'y'.

(I) *(-3)             -6x  - 12y = -18

(II)*2                  6x +  10y  = 14    {Now add}              

                               - 2y  = -4

                                  y = -4/-2

y = 2

Hence after eliminating x we get the value of y as 2.

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investment at 12 %  =  $8485

investment at 10%   = $2042

What does investing mean?

The act of investing entails using money now in the hopes that it will appreciate over time.

           An investment is putting resources—such as time, money, effort, etc.—to work in the expectation of receiving a return that is greater than the initial investment.

Let x = investment at 12%

      y = investment at 10%

    x + y = 10,527

given interest earned from 12% exceed

   10%  by 814

  0.12x  =  0.1y + 814

  y = 10527 - x

 0.12x = 0.1( 10527 - x ) + 814

0.12x = 1052.7x - 0.1x + 814

 0.22x = 1866.7

    x = 1866.7/0.22

     x =  8485

   y = 10527 - 8485  = 2042

investment at 12 %  =  $8485

investment at 10%   = $2042

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The hill makes an angle of approximately 11.98 degrees with the horizontal.

From the information, a force of 5 lb is required to hold a 24-lb crate on a hill and we want to know the angle that the hill make with the horizontal.

F = W * sin(θ)

where sin(θ) is the sine of the angle θ.

Solving for sin(θ), we get:

sin(θ) = F / W

       = 5 lb / 24 lb

       ≈ 0.2083

θ = arcsin(0.2083)

  ≈ 11.98 degrees

Therefore, the hill makes an angle of approximately 11.98 degrees with the horizontal.

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Answer:

Step-by-step explanation:

They are all Parallelogram. Properties of parallelogram: the opposite angles are equal. The consecutive or adjacent angles are supplementary (mean add together equal 180°).

7.     ∠E+110°=180°       ∠E=70°

8.     （3x+21)°=（2x+43)°

               3x+21=2x+43

                 x=22

          given ∠G=(2X+43)°, we got x=22 above

                    ∠G=(2*22+43)°=87°

9.      (2x+25)°+104°=180°

          (2x+25)°=180° - 104 °

                (2x+25)°=76°

                 2x+25=76

                           x=25.5

10.     (2x+20)°+(3x-85)°=180°

         2x+20+3x-85=180

                   5x=245

                      x=49

        given ∠A=(3X-85)°, we got x=49 above

                   ∠A=62°

The percentage of our new facility's seating is full will be 76%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

Our new training room can seat 150 employees.

If 6 tables consisting of 6 chairs are now taken.

Then the number of occupied seats by tables will be

⇒ 6 x 6

⇒ 36

Then the percentage of our new facility's seating is full will be

P = [(150 - 36) / 150]  x 100

P = (114/150) x 100

P = 0.76 x 100

P = 76%

The percentage of our new facility's seating is full will be 76%.

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the ratio of students do not wear glass to total students

\(\frac{12}{25}\)

the ratio of students wear glass to total number of students is

\(\frac{13}{25}\)

Given

In a class of 25 students, 13 students wear glasses and 12 students do not wear glasses

The ratio of glasses to non-glasses wearing students is 13:12.

Explanation :

we need to find the ratio students wear glasses to whole students

There are total of 25 students.

13 students wear glass

So the ratio of students wear glass to total number of students is

\(\frac{13}{25}\)

Similarly , we can find the ratio of students do not wear glass to total students

\(\frac{12}{25}\)

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Answer:

2, 4, 6

Step-by-step explanation:

The experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

The experimental probability of the next train to pull into Lakeside Station being full can be calculated by dividing the number of times a full train occurred by the total number of trains observed.

Given that out of the last 20 trains, 14 were full, we can express the experimental probability as a fraction:

P(full) = Number of full trains / Total number of trains observed

P(full) = 14 / 20

Simplifying the fraction, we get:

P(full) = 7 / 10

Therefore, the experimental probability that the next train to pull into Lakeside Station will be full is 7/10.

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There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

thw answer is c if you count the blocks

While an absolute value may be any number, the output from an absolute value expression is always greater than or equal to zero

The absolute value | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero along real number line.

The absolute value of any number is seen to be always greater than or equal to zero. Both a number and its opposite are the same distance from zero on the number line. Since they have the same distance from zero, they have the same absolute value.

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Answer:

Yes, Melanie's statement that the basketball season starts in 15 weeks is reasonable.

To see why, we can estimate the number of days in 15 weeks. Since 1 week is equal to 7 days, 15 weeks would be approximately equal to:

15 weeks x 7 days/week = 105 days

The amount of strawberries is represented on the y-axis, and the amount of bananas is represented on the x-axis. Then, the point (1, 2.5) means that 1 cup of bananas is related to 2.5 cups of strawberries

The expression given is,

Apply rule:

Add the numbers:

Hence, the answer is 18.

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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Answer:1.53

Step-by-step explanation:

The bathtub take 7.11 minutes to empty.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A bathtub has 32 gallons of water in it and is being drained at a rate of 4.5 gallons per minute.

Now,

Since, A bathtub has 32 gallons of water in it and is being drained at a rate of 4.5 gallons per minute.

Hence, The time for empty the bathtub = 32 / 4.5

                                                             = 7.11 minutes

Thus, The bathtub take 7.11 minutes to empty.

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Answer:

20.

Step-by-step explanation:

60 - 40 = 20

Answer:

There are 5 prime numbers between 40 and 60.

Step-by-step explanation:

A prime number is a number that is ONLY divisible by itself and 1 with no remainder. For example 3 can only be divided by 1 or 3 without a remainder left.

Between 40 and 60 there are 5 prime numbers: 41, 43, 47, 53, and 59.

Answer:

a). 85 people

b). 4362 people

Step-by-step explanation:

The given bar graph shows how many people per 100 spelled each word correctly.

a. From the graph given extreme end of the bar for the word "weird" is between 80 - 90.

Therefore, approximate number of the persons who spelled weird correctly will be 85 (rounded to the nearest 5).

b. The number of people who can correctly spelled word "weird" = 85

The number of people who can correctly spelled word "inoculate" = 35

In 100 people, number of people who can correctly spell "weird" more than "inoculate"

= 85 - 35

= 50

in a group of 8724 randomly selected people, number of people who can spell the word "weird" correctly more than "inoculate"

= \(\frac{50}{100}\times 8724\)

= 4362 people

Random selection means each individual has equal chance of being selected.

Given graph has the following information:

Total number of people under survey=100

a. To estimate the number of people per 100 who spelled weird correctly

From the graph it is around 84 and rounding it to nearest 5 will results in 85.

b. From the graph,

Number of people can correctly spell inoculate= 35

Number of people can correctly spell weird than inoculate=85-35

=50 out of 100

Using unitary method as follows:

100-------->50

1------------>1/2

8724------>1/2x8724

=4362

Thus, out of  8724 randomly selected​ people, 4362 people can correctly spell weird than inoculate.

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The function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The coordinate points from the graph are (10, 550) and (30, 200).

Here, slope = (200-550)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 550) in y=mx+c, we get

550=-17.5(10)+c

c=550+175

c=725

So, the equation is y= -17.5x+725

Thus, f(n)= -17.5n+725

a) The fine at every speed should go up by $10.

So, the coordinates are (10, 560) and (30, 210)

New slope (m)= (210-560)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 560) in y=mx+c, we get

560=-17.5(10)+c

c=550+175

c=735

So, the equation is y= -17.5x+735

Thus, f(n)= -17.5n+735

b) The fine at every speed should be doubled in construction zones.

So, the coordinates are (20, 550) and (60, 200)

New slope (m)= (200-550)(60-20)

= -350/40

= -8.75

Substitute m= -8.75 and (x, y)=(20, 550) in y=mx+c, we get

550=-8.75(10)+c

c=550+87.5

c=637.5

So, the equation is y= -8.75x+637.5

Thus, f(n)= -8.75n+637.5

Therefore, the function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

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Answer:

y=-3/4x+10/4

Step-by-step explanation:

1) Change given equation to slope intercept form:

3x+4y=12

4y=12-3x

y=3-(3/4)x

y=-(3/4)x+3

2) Parallel lines have the same slope, so the first part of the equation is:

y=-(3/4)x+b

3) To find b, we plug in y=2 and x=1 given the prompt:

2=-(3/4)(1)+b

2=-3/4+b

2 3/4=b

10/4=b

4) Therefore, the correct equation is:

y=-3/4x+10/4

Given a line segment with two end points AB

Step 1: Write out the coordinates and define the (x,y) values

Step 2: write out the formula for the distance between two point

Step 3: Substitute the x and y values in the above formula

Hence the length of the side AB is 5 units

Answer:)Angle FIH and GIE after keeping angle EIH at 140° is 40° while ∠FIG will is the opposite angle of ∠EIH so it will remain the same as 140°.

Step-by-step explanation:We need to intersect both lines and make ∠EIH > 135°

So,Let's keep ∠EIH = 140°

Then,∠FIG = 140° (opposite angle)∠FIH = ∠GIE = x (opposite angle)

Now,The Sum of all angles around I will be 360 degrees.

So,140 + x + 140 +  x = 360 ,2x + 280 = 360, 2x = 80 ⇒ x = 40°.