Solve the compound inequality​

\(u_{2} = u_{1} + 8 \\ u_{3} = u_{2} + 4 \\ u_{4} = u_{3} + 2 \\ u_{5} = u_{4} + 1 \\ u_{6} = u_{5} + 0.5 \\ ....\)

\(u_{2} = u_{1} + 2 {}^{3} \\ u_{3} = u_{2} + 2 {}^{2} \\ u_{4} = u_{3} + 2 {}^{1} \\ u_{5} = u_{4} + 2 {}^{0} \\ u_{6} = u_{5} + 2 {}^{ - 1} \\ ....\)

\(u_{n + 1} = u_{n} + 2 {}^{4 - n} \)

9514 1404 393

Answer:

  3x^2 -4x -4 +1/(2x -1)

Step-by-step explanation:

Polynomial long division is performed virtually the same way numerical long division is performed. Each quotient term is simply and completely the ratio of the leading dividend term to the leading divisor term. The product of that quotient term and the divisor is subtracted from the dividend to get the new dividend. When the new dividend has a degree less than that of the divisor, then the exercise is finished, and the remaining dividend is the remainder.

The details are shown in the attachment. The quotient is ...

   3x^2 -4x -4 +1/(2x -1)

Answer:

Quotient = 3x^2 - 4x - 4

Remainder = 1

Step-by-step explanation:

The given differential equation y x²y² = x² is a nonlinear and not separable differential equation, which corresponds to option (D).

A linear differential equation can be written in the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x. In this equation, the term x²y² makes it nonlinear.

A separable differential equation can be written in the form g(y)dy = f(x)dx, where g(y) and f(x) are functions of y and x, respectively. However, in the given equation, we cannot separate the variables y and x to obtain such a form.

To solve this particular differential equation, one approach is to rewrite it in a more manageable form. Let's rearrange the terms:

x² = y/(x²y²)

Now, we can multiply both sides by (x²y²) to eliminate the denominator:

x²(x²y²) = y

This equation is still nonlinear but can be used to find a particular solution for y given a specific initial condition.

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Answer:

No, it is not a right triangle

Step-by-step explanation:

A scalene right triangle comprised of integers must have the same ration as 5:4:3, and 5:6:8 is not it.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.

In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.

Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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Answer:

The graph is not visible

Step-by-step explanation:

Do something about it

Answer:

x = -2

Step-by-step explanation:

\(\:\frac{1}{2}x+4=3\)

\(\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\)

\(\frac{1}{2}x+4-4=3-4\)

\(\mathrm{Simplify}\)

\(\frac{1}{2}x=-1\)

\(\mathrm{Multiply\:both\:sides\:by\:}2\)

\(2\cdot \frac{1}{2}x=2\left(-1\right)\)

\(\mathrm{Simplify}\)

\(x=-2\)

[RevyBreeze]

Answer:

The quotient is (x-2)

Step-by-step explanation:

Using a system of equations, it is found that:

In our system, we have that:

Those 3 compromise 97% of the flavors, hence:

\(x + y + z = 97\)

Vanilla sells 10% more than twice strawberry, hence:

\(x = 10 + 2y\)

Chocolate sells 7% more than vanilla, hence:

\(z = x + 7\)

Since \(x = 10 + 2y\)

\(z = 10 + 2y + 7\)

\(z = 2y + 17\)

Replacing in the first equation, we can solve for y:

\(x + y + z = 97\)

\(10 + 2y + y + 2y + 17 = 97\)

\(5y = 70\)

\(y = \frac{70}{5}\)

\(y = 14\)

With y, we can solve for x and for z.

\(x = 10 + 2y = 10 + 2(14) = 38\)

\(y = 2y + 17 = 2(14) + 17 = 45\)

Hence:

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The correct option related to enrollment of sam in university is C (We cannot be certain whether Sam is or is not a college freshman.)

What is enrollment?

The act of putting yourself or some other person onto the official list of members of a course, faculty or university, or group.

Main body:

as all college freshmen at highlands university take english composition , which means he is enrolled in university.

Sam is enrolled in english composition at highlands university which means he has English as a subject.

But it doses not tell us about his current year , which year he is studying.

therefore ,We cannot be certain whether Sam is or is not a college freshman.

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Answer:

a) 1/8 b) 1/6

Step-by-step explanation:

b) 6/36 = 1/6

a) 1/2 x 1/2 x 1/2 = 1/8

Answer:

2

Step-by-step explanation:

Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8

Answer:

B. Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4.

Step-by-step explanation:

Look for a pattern within the table.

10 : 2.5

16 : 4

? : 7.5

48 : 12

10/2.5 = 4

16/4 = 4

14/12 = 4

this means that if we multiply 7.5 by 4 we will be able to find the missing number!

Therefore, the answer is B.

Hope this helps! :)

Answer:

jhgfghjk

Step-by-step explanation:

tngbunjregtnmf rejdmnf vfrjelkfnm e3jkwnrmfd

The selection of the appropriate immune suppressant is made by healthcare professionals based on the specific needs of each patient.

The most commonly used immune suppressant in medical practice is a medication called "cyclosporine." Cyclosporine belongs to a class of drugs known as calcineurin inhibitors and is primarily used to prevent organ transplant rejection.

The activity of T-cells, which are a type of immune cell involved in the body's immune response.

Cyclosporine is also used in the treatment of various autoimmune diseases, such as rheumatoid arthritis and psoriasis, where the immune system mistakenly attacks the body's own tissues.

T-cell activity, cyclosporine helps to reduce the inflammatory response and prevent further damage to the affected organs or tissues.

It's important to note that there are several other immune suppressants available, and the choice of medication depends on the specific condition being treated, the patient's overall health, and individual factors.

A commonly used immune suppressants include corticosteroid methotrexate, azathioprine, mycophenolate mofetil, and tacrolimus.

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Complete question:

While studying the T- and B-cell immune suppressors, the nursing students learn that the most commonly used immune suppressant is what?

The sum of the infinite geometric series 0.5+0.05+0.005+ . . .  is S = 0.55556

The given geometric series is:

 0.5 + 0.05 + 0.005 + . . .

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 0.5

a(2) = 0.05

a(3) = 0.005

Hence, the common ratio is

   r = a(2) / a(1) = 0.05/0.5 = 0.1

Since 0 < r < 1, the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 0.5 and r = 0.1 into the formula:

S = 0.5 / (1 - 0.1)

   = 0.5 / (0.9)

   = 0.55556

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Answer: Information given below…

Step-by-step explanation:

9. An equilateral triangle has all three sides of the same length.

The perimeter of the triangle is 45 cm.

To find the perimeter of a triangle, we simply add the three lengths together.

a + b + c = 45 cm (Perimeter)

15 + 15 + 15 = 45 cm.

Answer:

See below

Step-by-step explanation:

As we can see by the first graph (on the top), we have two lines that intersect at only one point. As lines go through every point that are solutions to that line, the point that is intersected by both of those lines is a solution to both of the lines.

Since this is the only point that is shared by both of those lines, those lines only have ONE solution, and the reason for this is because the graphs intersect at one point, so that point satisfies both equations.

We can see in the middle graph that there are two lines that do not intersect with each other. Because of this, we can conclude that the lines do not share any solutions with each other, because the lines do not intersect.

Therefore, these lines have no solutions, and the reason for that is because the lines never intersect, so the equations are never satisfied by the same point.

On the bottom graph, we can see there are two lines, one red and one orange that overlap with each other. This means that both of these lines are the same equation, and therefore they share all of their solutions.

This means that these lines have infinitely many solutions. This is because the lines intersect at every point, so the equations are satisfied by all points along the line.

Answer:

2:3

Step-by-step explanation:

r_1^3:r_2^3=8:27

r_1:r_2=2:3

Answer:

2/3

Step-by-step explanation:

solve volume formula for r and then use v1 and v2 from the ratio to find r1 and r2

v = 4/3 Pi r**3

(3/4 v) / Pi = r**3

r = (3v/4Pi)**1/3

Then

r1 = (3*8/4pi)**3

   = (6/Pi)**1/3

   = 1.24

r2 = (3*27/4Pi)**3

   = (81/4Pi)**3

   = (6.45)**3

   = 1.8

Then

r1/r2 = 1.24/1.8 = .6666666 or 2/3

Answer:

C. Triangle RAP = 12cm

Step-by-step explanation:

I want to preface this by saying this is not a good way of solving this question, but it gave me an answer nonetheless.

The perimeter of ROSE is the outside rectangle which is given as 22cm.

So the perimeter of PROA and ASEP are both equal to 11.

PR and OA (as well as AS and PE) are equal to each other.

So we can just as easily guess two equal numbers, plus another number that makes 11.

I chose 4 + 4 and 3 to make 11

We can use this same logic for RAPS

The broken line RAPS is equal to 13.

RA and PS are equal to each other, and plus PA are all equal to 13

So we can just as easily guess two equal numbers, plus another number that makes 13.

I chose 5 + 5 and 3 to make 13.

We can use this same logic for RAPS

If I add PA, RA and RP together

3 + 5 + 4, I will get 12cm

This is not the only combination that works, but every combination will give your triangle RAP to equal 12cm.

I have added an image that shows some of my working out and logic along the way, as well as other guesses that still will give you 12cm once you work them out

Answer:

y= 4545454545454550/909090909090909

Hope this helps!!

The  volume of the largest right circular cone that can be inscribed in a sphere of radius r is  8/27 (volume of sphere)

Let r serve as the foundation. the volume of the area, and radius x is the separation between the base and the sphere's center. Height h of the cone = R + x

∴    V= 1/3πr² h= π/ 3 (R² −x²)(R + x)

       = π/3​ (R² + R² x − Rx² −x² )

∴   dV/ dx​ = π​ /3 [R²−2Rx−3x² ]

  d²V/ dx²​ = π/3​ [−2R−6x]

For max or min V dV/dx​ =0

∴   R² −2Rx−3x² =0

⇒(R + x)(x−3x)=0    

2) x=−R, x​/3 but x = −R

When x= R/3 d² V/dx² <0  V is max only when x= R/3

​∴   Max V= 1/3π(R² − R²/9 )(R+ R/3 )

= 32πR³/81

= 8/27 ( 4/3 πR³)

= 8/27 (volume of sphere)

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Answer:

Step-by-step explanation:

\(f(x)=-2x+13\)

To find f(-4), substitute the value of x that's - 4 into f(x). That is for every x in f(x) replace it with - 4

We have

\(f( - 4) = - 2( - 4) + 13 \\ = 8 + 13 \\ = 21 \: \: \: \: \: \: \: \: \)

We have the final answer as

Hope this helps you

Answer: x=3 and y=4

Step-by-step explanation:

Rewrite equations:

x+3y=15;2x−2y=−2

Step: Solve x+3y=15 for x:

x+3y=15

x+3y+−3y=15+−3y(Add -3y to both sides)

x=−3y+15

Step: Substitute−3y+15 for x in 2x−2y=−2:

2x−2y=−2

2(−3y+15)−2y=−2

−8y+30=−2(Simplify both sides of the equation)

−8y+30+−30=−2+−30(Add -30 to both sides)

−8y=−32

−8y over −8 = −32 over −8

(Divide both sides by -8)

y=4

Step: Substitute 4 for y in x=−3y+15:

x=−3y+15

x=(−3)(4)+15

x=3(Simplify both sides of the equation)

The answer is B!

The whole denominator of h(x) is the function of g(x) since g(x) is the object of h(x)

The quotient obtained when the expression 28a⁴b + 4a²b² - 12ab is divided by 4ab is 7a³ + ab - 3 (2nd option)

Quotient is the result obtained when we carry out division operation.

The quotient for the expression (28a⁴b + 4a²b² - 12ab) / 4ab can be obtain as illustrated below:

(28a⁴b + 4a²b² - 12ab) / 4ab

Factorizing the numerator, we have:

(28a⁴b + 4a²b² - 12ab) / 4ab = 4ab(7a³ + ab - 3) / 4ab

Canceling out 4ab, we have:

(28a⁴b + 4a²b² - 12ab) / 4ab = 7a³ + ab - 3

Thus, from the above calculation, we can conclude that the quotient for the expression (28a⁴b + 4a²b² - 12ab) / 4ab is 7a³ + ab - 3 (2nd option)

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Answer:

5 days

(the exact number of days below)

Step-by-step explanation:

65/7=9.28571429

9.28571429 sec = 1 dollar

464285.715 seconds=50000 dollars

464285.715 seconds=5.373677256944 days