16. show that y =2/3e^x +e^{-2x} is a solution of the differential equation y' + 2y = 2e^x. 17. Find the general solution to the differential equation using separation of variables: dy/dx = 63 +9y + 7x + xy

Answer:

44.1

Step-by-step explanation:

- To find the distance, we have to use the distance formula:

d = √(x2 - x1)² + (y2 - y1)²

d = √(-19 - 5)² + (-12 - 25)²

d = √(-24)² + (-37)²

d = √(576) + (1369)

d = √1945

d = 44.1

The smallest measurement used in the apothecary system for volume is the minim.

The apothecary system is an outdated system of measurements primarily used in pharmacy and medicine. It includes various units for measuring volume, weight, and other quantities.

In the apothecary system, the minim is the smallest unit of measurement for volume. It is equivalent to approximately 0.0616 milliliters.

The minim is a small unit of measurement and is typically used for precise dosing of liquids in the apothecary system. It is commonly used in pharmaceutical compounding and in the preparation of medications.

However, it's important to note that the apothecary system is no longer widely used in modern healthcare practices. The metric system, with units such as milliliters and liters, has become the standard for measuring volume in most countries.

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Answer:

The marginal revenue is \(MT_d = 116.66\)

Step-by-step explanation:

From the question we are told that

    The inverse demand for a downstream firm is  \(P = 150 -Q\)

    The cost of the critical input produced by  upstream division is  \(CU(Q_d) = 5(Q_d)^2\)

     The cost of the critical input produced by downstream firm  is  Cd(Q) = 10Q

Generally

The marginal revenue of the downstream firm - The marginal cost  of the downstream firm =  Net marginal revenue of downstream

i.e

    \(MR_d - MC_d = MT_d\)

Also  

  The marginal revenue of the downstream firm - The marginal cost  of the downstream firm =  Marginal upstream cost  

       i.e

            \(MR_d - MC_d = MC_u\)

So

     \(MR_d - MC_d = MC_u\)

Generally the total revenue of  downstream firm is mathematically represented as

          \(TR = P * Q\)

Here Q stands for quantity produced by the downstream firm  and  TR is the total revenue

         \(TR = [150 - Q] * Q\)

=>      \(TR = 150Q - Q^2\)

Generally the marginal revenue of the downstream firm is mathematically evaluated as  

         \(MR_d =\frac{d (TR)}{d Q} = 150 - 2Q\)

Generally marginal downstream first cost is mathematically evaluated as

         \(MC_d = \frac{d(Cd(Q)) }{dQ} = 10\)

Generally the net marginal revenue of the downstream firm is mathematically represented as

            \(150 - 2Q -10 = MT_d\)

=>        \(MT_d = 140 - 2Q\)

Generally the marginal upstream cost is mathematically represented a

               \(MC _u =\frac{d [CU(Q_d)]}{dQ_d} = 10(Q_d)\)

Generally  \(Q_d = Q\) this because \(Q_d\) represents the quantity produced by the downstream firm and also  Q is associated with the cost of the downstream quantity  

So

            \(MC _u =\frac{d [CU(Q)]}{dQ} = 10Q\)

=>         \(10(Q) = 140 -2Q\)

=>          \(Q = 11.67\)

So the net marginal revenue of the downstream firm is mathematically represented as

=>        \(MT_d = 140 - 2(11.67)\)

=>        \(MT_d = 116.66\)

Answer:

x = -4/3, 2/3

Step-by-step explanation:

Step 1: Factor

(3x + 4)(3x - 2) = 0

Step 2: Find roots

3x + 4 = 0

3x = -4

x = -4/3

3x - 2 = 0

3x = 2

x = 2/3

Answer:

x₁ = -4/3

x₂ = 2/3

Step-by-step explanation:

9x² + 6x - 8 = 0

9x² + 12x - 6x - 8 = 0

3xx(3x + 4) - 6x - 8 = 0

3xx(3x + 4) - 2(3x + 4) = 0

(3x + 4) × (3x - 2) = 0

3x + 4 = 0 → x = -4/3

3x - 2 = 0 → x = 2/3

Hope this helps! :)

Answer:

x=8 y=21

Step-by-step explanation:

7x+12=12x-28

x=8

plug in x

12x8-21=68

68+9y-77=180

y=21

The values of [x] and [y] will be 8 and 21 respectively.

This term indicates that the line 'l' is parallel to the line 'm'.

Given is the image and the measurement of angles.

It can be seen in the figure that, ∠(7x + 12) and ∠(12x - 28) from alternate interior angles as line 'l' and 'm' are parallel. These angles will be equal to each other. Therefore, we can write -

7x + 12 = 12x - 28

12x - 7x = 12 + 28

5x = 40

x = 8

Now, ∠(12x - 28) and ∠(9y - 77) form a straight angle. Therefore, we can write -

(12x - 28) + (9y - 77) = 180

(12 x 8 - 28) + (9y - 77) = 180

68 + 9y - 77 = 180

9y = 180 + 9

9y = 189

y = 21

Therefore, the values of [x] and [y] will be 8 and 21 respectively.

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[Image needed for complete question is attached with the answer]

Answer:

9 + 4(1) \(\neq \\\) 17

Step-by-step explanation:

to satisfy inequality

9 + 4(1) < 17

13 < 17

Answer:

32% of 200 is 64.

Step-by-step explanation:

To find the equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3), follow these steps: 1. Find the derivative of the function: dy/dx r,

Represents the slope of the tangent line at any point (x, y) on the curve.
y = 9x - (6/x)
dy/dx = d(9x)/dx - d(6/x)/dx

Using the power rule for the first term and the quotient rule for the second term:
dy/dx = 9 - (-6/x^2)
dy/dx = 9 + 6/x^2

2. Find the slope of the tangent line at the given point (1, 3) by plugging x = 1 into the derivative:
m = 9 + 6/1^2
m = 9 + 6
m = 15

3. Use the point-slope form of a linear equation to find the equation of the tangent line:
y - y1 = m(x - x1)
where (x1, y1) is the given point (1, 3) and m is the slope:
y - 3 = 15(x - 1)

4. Solve for y to get the equation of the tangent line:
y = 15(x - 1) + 3
y = 15x - 15 + 3
y = 15x - 12

The equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3) is y = 15x - 12.

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An all-night study session can help you catch up on school assignments. The only way to become a straight-A student is efficient study habits.

Most students pseudo-work and end up wasting valuable time.

The correct option is (C)

This is based on an article about pseudo-working which is something that students do where they read for long hours and appear very serious in reading when in fact they do not focus on the reading and therefore end up not grasping much.

The author was trying to express that most students do this and that it is simply a waste of time which could have been spent actually studying.

The correct option is (C).

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The given question is incomplete, complete question is:

What central idea about studying does the author express in Passage 1?

A Straight-A students know how to work harder than other students.

B The only way to become a straight-A student is efficient study habits.

C Most students pseudo-work and end up wasting valuable time.

D An all-night study session can help you catch up on school assignments.

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The constant term (85) in the expression represents the company's net sales in billions at the end of the year 2008.

We have,

The expression is t² + 14t + 85.

The variable in the expression is t.

The constant term is 85.

In the context of the company's net sales from 2008 to 2018, the constant term (85) in the expression t + 14t + 85 represents the initial net sales of the company at the end of the year 2008.

It indicates the net sales value, in billions, that the company had at the starting point of the time period under consideration

(i.e., the end of 2008).

Thus,

The constant term (85) in the expression represents the company's net sales in billions at the end of the year 2008.

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The complete question:

What does the constant term (85) in the expression t² + 14t + 85 represent in the context of the company's net sales from 2008 to 2018?"

Answer:

Im pretty sure it would be C

Step-by-step explanation:

The location of R on the number line will be 15/7 so option (C) will be correct.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

A horizontal number line is the most common representation and can be extended infinitely in any direction.

Distance from S to T = 3 + 9 = 12

So,

SR + RT = 12

And given,

SR/RT = 3/4 ⇒ SR = (3/4)RT

By substitution,

(3/4)RT + RT = 12

RT ( 7/4) = 12

RT = 48/7

Now the location of point R ⇒

OT - RT = 9 - 48/7 = 15/7

Hence "The location of R on the number line will be 15/7".

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Since the sales representative calls on four hospitals in westchester county, the numbers of ways can he organize his calls is option A: 24  possible ways.

Throughout every stage of the sales process, a sales representative deals directly with customers. They must determine a customer's needs, make a compelling case for pertinent items or services, and guarantee a positive overall experience.

Note that:

For the first call he makes, he has 4 choices.

For the first call he makes, he has  3 choices.

For the first call he makes, he has choices.

For the first call he makes, he has choice.

Solution:

4 x 3 x 2 x 1 = 24 possible combinations.

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See options below

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?

24

7

120  

37

Explanation:

Draw a circle and split it into thirds. The sister will take one of the slices, so we have 2 left over. That accounts for the 2/3 left over.

Then split each of those two slices in half to get 2*2 = 4 smaller slices. The mother takes 3 of those smaller slices which represents 1/2.

Or you could say (2/3)*(3/4) = (2*3)/(3*4) = 2/4 = 1/2.

The diagram is shown below. The white portion is the 1/3 the sister gets at first. The pink portion represents the fractional amount the mother drank, which is 3/6 = 1/2.

Skew lines are the lines that are neither parallel nor intersecting.

The above statement is not possible for coplanar lines so it can be concluded that skew lines are non coplanar.

Hence the statement Lines that do not intersect and are not in the same plane which is option D justifies the definition of skew lines.

Hence option D is correct.

Answer:

23.3

Step-by-step explanation:

Answer:

45 degrees

Step-by-step explanation:

angle QRS is same as (2x + 3) because it is an isosceles triangle

so, 90 + (2x+3) + (2x+3) =180 degrees

             2x+3 +2x+3=180-90

2x+2x +3+3=90

4x+6=90

4x=90-6

4x=84

x=84/4

x=21

substitute x=21 in (2x+3)

2*21+3=45

Answer:

63%

Step-by-step explanation:

9.5/15

hope this helps

your  grade is a %63.333333333333

The probability of selecting a boy from the class is 15/25, or 3/5, since there are 15 boys in a class of 25 students.

When selecting two students randomly without replacement, the probability of selecting a boy on the first draw is 15/25, and the probability of selecting another boy on the second draw (assuming the first student selected was a boy) is 14/24, since there will be 14 boys left out of 24 students remaining.

So the probability of selecting two boys in a row is:

(15/25) * (14/24) = 7/20

Therefore, the probability that both students chosen for the presentation are boys is 7/20, or approximately 0.35.

To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

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Statistical analyses are least likely to be found in a (D) qualitative research.

Therefore, statistical analyses are least likely to be found in a (D) qualitative research.

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Answer:

it's A

Step-by-step explanation:

The percentage of people in the U.S. celebrate winter holidays such as hanukkah, christmas, and kwanzaa is above 90%.

This holiday season, it should be noted that that 92% of Americans will celebrate Christmas, 5% will celebrate Hanukkah, and 3% will celebrate Kwanzaa. Five percent will celebrate more than one holiday

America has come to appreciate Hanukkah. Hanukkah is celebrated by the majority of American Jews, at least with a family meal or the lighting of a menorah, and the majority of non-Jews in America are aware of the holiday.

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36% of the variability equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).

Given:

Correlation value: 0.6

The amount of variation in the dependent variable that can be predicted from the independent variable is shown by the coefficient of determination.

The correlation coefficient is equal to;

Since the correlation in this instance is equal to 0.6, our coefficient is 0.36. Therefore, the age of the home can account for 36% of the variation in equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).

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Answer:

Can you include the picture because i don't know which question you are talking about.

Step-by-step explanation:

In a chi-square test of goodness of fit, if the value of the test statistics is 10.42 and there are four populations, then the p-value is 0.0156.

Chi-square test of goodness of fit is a statistical test which is used to determine whether there is any significant difference between the observed data and the expected data. It compares the observed frequencies with the expected frequencies to determine how well the model fits the data.

The formula for the chi-square test of goodness of fit is given below:χ2 = ∑ (O − E)2 / E

where, χ2 is the chi-square test statistic,O is the observed frequency, E is the expected frequency, ∑ is the summation over all the categories or groups.

The degrees of freedom for the chi-square test of goodness of fit is (k - 1), where k is the number of categories or groups. In the given problem, we are given that the value of the test statistics is 10.42 and there are four populations. Let us assume that the level of significance is α = 0.05.

The p-value for the chi-square test of goodness of fit is calculated as follows:

p-value = P(χ₂ ≥ 10.42), where χ₂ is the chi-square test statistic with (4 - 1) = 3 degrees of freedom (df).

The p-value can be calculated using a chi-square distribution table. Using a chi-square distribution table, we can find that:

P(χ₂ ≥ 10.42) = 0.0156

Therefore, the p-value is 0.0156 (rounded to 4 decimal places).

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Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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Answer:

ok

Step-by-step explanation: