How many solutions exist for the given equation? 12x 1 = 3(4x 1) – 2

(d) non-homogeneous and non-separable. The differential equation dx/dt = x + 2xt + cost/(1+t) is a non-homogeneous and non-separable differential equation.

Classification of the given differential equation:

dx/dt = x + 2xt + cost/(1+t)ds.

The given differential equation can be written as:

dx/dt - x = 2xt + cost/(1+t)

The integrating factor for the above differential equation is:eⁿᵗ where n = -1On

multiplying the given differential equation by the integrating factor, we get:

eⁿᵗ(dx/dt) - xeⁿᵗ = 2xteⁿᵗ + cost/(1+t) * eⁿᵗ(dt/dt)

On simplifying, we get:

d/dt (xeⁿᵗ) = 2xteⁿᵗ + cost/(1+t) * eⁿᵗ

Now, integrating both sides with respect to t, we get:

xeⁿᵗ = ∫2xteⁿᵗ dt + ∫cost/(1+t) * eⁿᵗ dt

On solving the above integral using integration by parts, we get:

xeⁿᵗ = (x * eⁿᵗ * t²)/2 + sint/(1+t) + ∫((2t - 1)/(1+t) * sint) dt

The differential equation dx/dt = x + 2xt + cost/(1+t) is a non-homogeneous and non-separable differential equation.

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Answer:

\(\huge\boxed{\sf \frac{y-5}{y-3} }\)

Step-by-step explanation:

Solving it by mid-term break method:

\(\displaystyle =\frac{y^2-3y-40}{y^2-11y+24} \\\\= \frac{y^2 -8y+5y-40}{y^2-3y-8y+24} \\\\= \frac{y(y-8)+5(y-8)}{y(y-3)-8(y-3)} \\\\Take \ (y-8) \ and \ (y-3)\ common\\\\= \frac{(y-8)(y-5)}{(y-8)(y-3)} \\\\= \frac{y-5}{y-3} \\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

\(\frac{y+5}{y-3} \textrm{ where } y \ne 8\)

Step-by-step explanation:

We'll first factorize the quadratic equations by finding their zero-points:

\(y^2 - 3y - 40 = 0\\\Delta = (-3)^2 - 4\cdot 1 \cdot -40 = 9 + 160 = 169\\\sqrt{\Delta} = 13\\y = \frac{3 \pm 13}{2}\\y_1 = 8\\y_2 = -5\\y^2 - 3y - 40 = (y - 8)(y + 5)\\~\\y^2 - 11y + 24 = 0\\\Delta = (-11)^2 - 4\cdot 1\cdot 24 = 121 - 96 = 25\\\sqrt{\Delta}} = 5\\y = \frac{11 \pm 5}{2}\\y_1 = 8\\y_2 = 3\\y^2 - 11y + 24 = (y - 8)(y - 3)\)

Now we can use this to simplify the whole division:

\(\frac{y^2-3y-40}{y^2-11y+24} = \frac{(y-8)(y+5)}{(y-8)(y-3)} = \frac{y+5}{y-3} \textrm{ where } y \ne 8\)

The accrued amount of an investment is equal to the sum of the principal amount and the interest earned:

Write the expression in terms of the interest:

To calculate the interest, the first step is to determine the accrued amount after 5 years.

The savings account compounds annually, to determine the accrued amount you have to apply the following formula:

Where

A is the accrued amount

P is the principal amount

r is the interest rate expressed as a decimal value

t is the time in years

n is the number of compounding periods

The principal amount is P= $800

The interest rate of the account is 14%, to express it as a decimal value, divide it by 100

The time period for the investment is 5 years.

The account compounds annually, which means that there is only one compounding period per year, so, n=1.

Calculate the accrued amount:

After 5 years the accrued amount will be A= $1540.33

Finally, calculate the interest:

After 5 years she will have $740.33 of interest.

Answer:

74 inches

Step-by-step explanation:

1 yard = 36 inches

then 2 yards = 72

and 72 + 2 inches = 74 inches

Answer:

Step-by-step explanation:

If you're asking for the area of the sector, it's the central angle of 360, times the area of the circle, for example, if the central angle is 60, and the two radiuses forming it are 20 inches, you would divide 60 by 360 to get 1/6.

The requried area of a sector bounded by a 180° arc is 8π square inches.

The area of a sector is a portion of the circle enclosed by two radii and an arc and is given by the formula A = (θ/360)πr², where θ is the angle in degrees and r is the radius of the circle.

Here,
The area of a sector bounded by a 180° arc in a circle with a radius of 4 inches can be found using the formula;

A = (θ/360)πr²

Where θ is the angle in degrees and r is the radius.
Since the angle is 180°, we have:

A = (180/360)π(4²) = 8π square inches.

Thus, the area of a sector bounded by a 180° arc is 8π square inches.

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The values οf a sample statistic fοr different randοm samples οf the same size frοm the same pοpulatiοn are nοt guaranteed tο be the same. In fact, it is highly unlikely that the values will be exactly the same. This is because each randοm sample will have its οwn unique set οf values, even if the samples are drawn frοm the same pοpulatiοn.

Fοr example, cοnsider the sample mean, which is a cοmmοn sample statistic. If we take multiple randοm samples οf the same size frοm the same pοpulatiοn, the sample means will generally be different. This is because each sample will have its οwn set οf values, which will lead tο a different mean.

Hοwever, as the sample size gets larger, the sample means will tend tο cοnverge tο the pοpulatiοn mean, and the variatiοn between different samples will decrease. This is knοwn as the law οf large numbers, which states that as the sample size gets larger, the sample mean will becοme mοre accurate and clοser tο the true pοpulatiοn mean. But, even fοr large sample sizes, the sample means will nοt be exactly the same fοr different randοm samples frοm the same pοpulatiοn.

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A Mathematical model for the determination of total area under glucose tolerance and other metabolic curves is called: Tai Mathematical model.

The Team Assisted Individualization method is a learning method developed by Slavin, Leavy, Kraweit and Madden in 1982 to 1985 in the book Cooperatine Learning: Theory, Research and Practice.

The Team Assisted Individualization method is structured to solve problems in teaching programs, for example in terms of individual student learning difficulties. This model pays attention to differences in the initial knowledge of each student to achieve learning achievement.

Students individually study learning material that has been prepared by the teacher. Individual learning outcomes are brought to groups to be discussed and mutually discussed by group members and all group members are responsible for the overall answer as a shared responsibility.

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Answer:

ok so its 170(if there's a decimal 170.6)

Step-by-step explanation:

basically, just divide three and 512. Hope this helps

Answer: $$5$$ movies

Step-by-step explanation: Given: A movie club, one time fee

=

$

25

, movies

=

$

7

2nd club,

$

0

fee, movies

=

$

12

Cost equations for each club:

club 1:

C

1

=

25

+

7

M

club 2:

C

2

=

12

M

For the clubs cost to be equal:

C

1

=

C

2

25

+

7

M

=

12

M

Subtract

7

M

from both sides:

25

=

5

M

Divide by

5

:

M

=

25

5

=

5

5

movies

CHECK:

C

1

=

25

+

7

⋅

5

=

25

+

35

=

$

60

C

2

=

12

⋅

5

=

$

60

Answer:

5 movies

Step-by-step explanation:

Define the variables:

Create two equations from the given information.

Equation 1

Given:

⇒ y = 25 + 7x

Equation 2

Given:

⇒ y = 12x

To find how many movies a member must purchase for the total cost of the two clubs to be equal, substitute Equation 2 into Equation 1 and solve for x:

⇒ 12x = 25 + 7x

⇒ 12x - 7x = 25 + 7x - 7x

⇒ 5x = 25

⇒ 5x ÷ 5 = 25 ÷ 5

⇒ x = 5

Therefore, a member must purchase 5 movies for the total cost of the two clubs to be equal.

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Answer:

it should be G.

Step-by-step explanation:

The probability of rolling a one on the first die and a six on the second die is 1/36.

Probability measures the likelihood or chance of an event happening.

A number between 0 and 1, where 0 represents an impossibility and 1 represents certainty, is used to express it.

By dividing the number of favourable outcomes by the total number of possible outcomes, one can determine the probability of an event.

The probability of rolling a one on the first die is 1/6, and the probability of rolling a six on the second die is also 1/6.

Since the two events are independent, we can use the multiplication rule of probability to find the probability of both events occurring together:

P(rolling a one on the first die and a six on the second die) = P(rolling a one on the first die) × P(rolling a six on the second die)

= (1/6) × (1/6)

= 1/36

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Answer: The compound interest is $409.49, and the total amount after one year is $3,665.49.

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

P = the principal (in this case, $3,256)

r = the annual interest rate (100%, or 1 as a decimal)

n = the number of times the interest is compounded per year (4, since it's compounded quarterly)

t = the number of years (1)

Plugging in the values we know, we get:

A = $3,256(1 + 1/4)^(4*1)

A = $3,256(1.25)^4

A = $3,665.49 (rounded to the nearest cent)

To find the compound interest, we can subtract the principal from the total amount:

Compound interest = $3,665.49 - $3,256 = $409.49

Therefore, the compound interest is $409.49, and the total amount after one year is $3,665.49.

Answer:

P=5 and Q=-3

Step-by-step explanation:

-3+8=p=5

4-7=q=-3

<p, q>= <5,-3>

The composition of the translations; T < − 3 ,  4 >  ⋅  T < 8 , − 7 >   (x, y) as one translation gives;

T < 5 ,  − 3 >   (x, y)

     We want to compose the translations; T < − 3 ,  4 > ⋅  T < 8 , − 7 >   (x, y) as one translation;

Now, translation is usually a map defined as;

T < a ,  b>  < x ,  y> = (x + a, y + b)

Thus, the image of the first translation is given as;

T < 8 , − 7 >   (x, y) = (x + 8, y - 7)

Finally;

T < − 3 ,  4 > ⋅  T < 8 , − 7 >   (x, y) = T < − 3 ,  4 > ⋅ (x + 8, y - 7)

⇒ (x + 8 - 3, y - 7 + 4)

⇒ (x + 5, y - 3)

Since T < a ,  b>  < x ,  y> = (x + a, y + b)

Then; (a, b) = (5, -3)

As one translation gives;

T < 5 ,  − 3 >   (x, y)

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Step-by-step explanation:

6y+12+12+3y

=9y+24

=3(3y+8)

a) The estimated model relating annual salary to firm sales and market value, in equation form, is: Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval), where log denotes the natural logarithm.

b) Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.

a) The estimated model relating annual salary to firm sales and market value, in equation form, is:

Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval)

where log denotes the natural logarithm.

b) To determine if your friend would be asking too much for an annual salary of $500,000, we need to plug the values of firm sales and market value into the model and calculate the expected salary.

Using the given values:

- Firm sales (sales) = $5,000,000

- Market value (mktval) = $20,000,000

We first need to take the logarithm of the sales and market value:

log(sales) = log(5,000,000)

log(mktval) = log(20,000,000)

Then, we can substitute these values into the equation:

Expected Salary = 4.6209 + 0.1621 * log(5,000,000) + 0.1067 * log(20,000,000)

Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.

Note: Make sure to use the natural logarithm (ln) in the calculations.

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Answer:

It's A and C, 6x6x6 and 18

We can say with 99% confidence that the true average number of sick days an employee who is 49 years old will take per year is between 0.85 and 3.30 sick days.

To find the 99% confidence interval for the average number of sick days an employee will take per year, given the employee is 49, we first need to calculate the predicted value of sick days for an employee who is 49 years old using the estimated regression line:

Sick Days = 14.310162 - 0.2369(Age)

Sick Days = 14.310162 - 0.2369(49)

Sick Days = 2.073273

So, we predict that an employee who is 49 years old will take an average of 2.07 sick days per year.

Next, we need to calculate the 99% confidence interval using the formula:

CI = predicted value ± t-value (α/2, n-2) × standard error

where α = 0.01 (since we want a 99% confidence interval), n = 10 (from the sample size), and t-value (α/2, n-2) is the critical value from the t-distribution table with α/2 = 0.005 and n-2 = 8 degrees of freedom.

Looking up the t-value in the table, we find t(0.005,8) = 3.355.

Plugging in the values, we get:

CI = 2.073273 ± 3.355 × 1.682207/√10

CI = 2.073273 ± 2.228079

CI = (0.845194, 3.301352)

Therefore, we can say with 99% confidence that the true average number of sick days an employee who is 49 years old will take per year is between 0.85 and 3.30 sick days

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Full Question:  The personnel director of a large hospital is interested in determining the relationship (if any) between an employee's age and the number of sick days the employee takes per year. The director randomly selects ten employees and records their age and the number of sick days which they took in the previous year. Employee 1 2 5 3 4 5 6 7 8 9 10 Age 30 50 40 55 30 28 60 25 30 45 Sick Days 7. 4 3 2 9 10 0 8 5 2

The estimated regression line and the standard error are given.

Sick Days=14.310162−0.2369(Age).

se=1.682207

Find the 99% confidence interval for the average number of sick days an employee will take per year, given the employee is 49. Round your answer to two decimal places.

If a red ball is drawn from two urns containing colored balls , then the probability that it came from the first urn is  0.625 or 62.5%   .

Let A = the event that the first urn is chosen, and

B is = the event that a red ball is drawn.

We have to find P(A|B), which means , the probability that the first urn was chosen given that a red ball was drawn.

So , By Bayes' theorem:

we have , P(A|B) = P(B|A) × P(A) / P(B)  ;

Since each urn has an equal probability of being chosen, we have P(A) = P(B) = 1/2 ; and

the probability of drawing a red ball is the same regardless of which urn was chosen.

We need to find P(B|A), the probability of drawing a red ball from the first urn is 50/100 = 0.5   ;

To find P(B), the overall probability of drawing a red ball, we can use the law of total probability:

that is ; P(B) = P(B|A) × P(A) + P(B|A') × P(A')  ;

where A' = event that the second urn was chosen.

Now , we find P(B|A'), which is the probability of drawing a red ball from the second urn is = 30/100 = 0.3    ;

We know that P(A') = 1/2 = 0.5 , because there are only 2 urns.

So , we have : P(A|B) = P(B|A)×P(A) / P(B)  ;

= (0.5×0.5) / (0.5×0.5 + 0.3×0.5)

= 5/8

= 0.625

Therefore, the probability that the red ball came from the first urn is 0.625 or 62.5%   .

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From the inequality graph, the solution to the inequalities is: (4, -2/3)

There are different tyes of inequalities such as:

Greater than

Less than

Greater than or equal to

Less than or equal to

Now, the inequalities are given as:

y < (1/3)x - 2

x < 4

Thus, the solution to the given inequalities will be gotten by plotting a graph of both and the point of intersection will be the soilution which in the attached graph we see it as (4, -2/3)

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The correct statement is (a) The graph has an x-intercept at −2.

If a division has a remainder of 0 when divided by x+2, it means that the divisor, x+2, is a factor of the dividend. In other words, when x is equal to -2, the polynomial function evaluates to 0, resulting in an x-intercept at -2.

To see why the other options are not true:

Option (b) states that the graph has an x-intercept at 2, which is not necessarily true based on the given information.

Option (c) states that f(0) = -2, which is not necessarily true based on the given information.

Option (d) states that f(2) = 0, which is also not necessarily true based on the given information.

Therefore, the only statement that can be inferred from the given information is that the graph has an x-intercept at -2.

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Answer:

3x+4

Step-by-step explanation:

f(g(x))=3(x+2)-2

=3x+6-2

=3x+4

Answer:

Step-by-step explanation:

f(x) = 3x - 2   When you see something like f(g(x)) it means that wherever you see an x on the right, you put g(x).

f(g(x)) = 3(g(x)) - 2               Now wherever you see g(x) on the right, you put in x + 2

f(g(x)) = 3(x + 2) - 2            Now remove the brackets

f(g(x)) = 3x + 6 - 2

f(g(x)) = 3x + 4

I'm not sure what the 3 in line 4 means. 3x + 4 seems to be the answer you want however.

================================================

Work Shown:

Plug in t = 2 and we get the following

\(a = 500*\left(\frac{3}{4}\right)^{t}\\\\a = 500*\left(\frac{3}{4}\right)^{2}\\\\a = 500*\left(0.75\right)^{2}\\\\a = 500*0.5625\\\\a = 281.25\\\\\)

The answer is choice D. There are 281.25 mg of aspirin in the bloodstream after 2 hours.

-----------------

Side notes:

Answer:

375

Step-by-step explanation:

because if you look at the question 3\4 is 1 hour with the aspren 500 after 2 hours you 2 the ammount i think

Answer:

-85.9

Step-by-step explanation:

The 2972 square feet of surface area that Shane will paint, if he will paint the 4 rectangular sides, 2 triangular pieces and he will not paint the rectangular sections of roof.      

The given is,

Shane wants to paint,

4 rectangular sides

2 triangular sides

From the given diagram,

Total surface area of paint = (4 Rectangular sides surface area ) +(2 triangular sides surface area)....(1)

Surface area of 4 rectangular sides,

For Left side(rectangle) surface area,

A = lb ...........................................................(2)

From the given diagram.

= (45.5 × 20)

= 910 Square feet

Dimensions of left side and right side are equal, so area of right side equal to the left side.

Area of right side = 910 square feet

Area of left and right sides,

= Left side area+ Right side area

= 910 + 910

= 1820 square feet

For front side area,

A= lb ...........................................................(3)

From the given diagram,

= (24 × 20 )

= 480 square feet

Dimensions of front side and back sides are equal, so area of front side equal to the back side.

Area of front side = 480 square feet

Area of front and back sides,

= front side area+ back side area

= 480 + 480

= 960 square feet

Surface area of rectangular sides,

= Area of left and right sides + Area of front and back sides

=  1820 + 960 = 2780 square feet

Surface area of 2 triangular faces,

For area of triangular sides,

\(A= \frac{hb}{2}\) ...............................................(4)

From the given values,

= \(\frac{8 (24)}{2}\)

= \(\frac{192}{2}\)

= 96 square feet

Dimensions of front side triangle and back side triangles are equal, so area of front side triangle equal to the back side triangle.

Area of front side triangle = 96 square meters

Area of front and back side triangles,

= front side triangle area+ back side triangle area

= 96 + 96

= 192 square feet

From the equation (1),

Total surface area of paint = 2780 + 192

Total surface area of paint = 2972 square feet

The 2972 square feet of surface area that Shane will paint, if he will paint the 4 rectangular sides, 2 triangular pieces and he will not paint the rectangular sections of roof.              

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The derivative of y = (5x6 − 3x4 + 2x2 − 1)(4x9 + 3x7 − 5x2 + 4x) is (30x^5 - 12x^3 + 4x)(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(36x^8 + 21x^6 - 10x + 4).

Using the product rule of differentiation, we have:

y' = (5x^6 - 3x^4 + 2x^2 - 1)'(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(4x^9 + 3x^7 - 5x^2 + 4x)'

Taking the derivative of the first term using the power rule, we get:

(5x^6 - 3x^4 + 2x^2 - 1)' = 30x^5 - 12x^3 + 4x

Taking the derivative of the second term using the product rule, we get:

(4x^9 + 3x^7 - 5x^2 + 4x)' = 36x^8 + 21x^6 - 10x + 4

Therefore, we have:

y' = (30x^5 - 12x^3 + 4x)(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(36x^8 + 21x^6 - 10x + 4)

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Answer: 14 cm

Step-by-step explanation:

Answer:

R=14 cm

total area= πr²

=22/7*196=616 cm²

r2= 3.5 cm

area of the small circles= 2*πr²=2*12.25*22/7=77 cm²

length of rectangle=3

breadth=1

area =lb=3 cm²

area of the small circles+area of rectangle=77+3=80 cm²

remaining area=616-80=536 cm²

the height of the mailbag decreases as time increases, and the mailbag reaches the ground at t = 5.33 seconds.

The height of the mailbag after its release is given by the equation h = 3.05t3. At t = 2.35 seconds, the height of the mailbag is h = 3.05 * 2.35 * 2.35 = 39.58 meters. This means that the mailbag is still 39.58 meters above the ground. The equation for the height of the mailbag tells us that the height of the mailbag is decreasing at a rate of 9.15t2 meters per second. This means that the mailbag will take 39.58 / 9.15 = 4.33 seconds to reach the ground.

Therefore, the mailbag will reach the ground after 1 + 4.33 = 5.33 seconds

Here is a table of the height of the mailbag over time:

Time (seconds) | Height (meters)

------- | --------

2.35 | 39.58

2.36 | 35.43

2.37 | 31.28

... | ...

5.33 | 0

As you can see, the height of the mailbag decreases as time increases, and the mailbag reaches the ground at t = 5.33 seconds.

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