It might be useful to represent numbers in ways that simplify
calculations. Create an algebraic expression including at least one variable
and at least one number that can be simplified using minimum 3 of the
exponent laws:

Pls include steps

Answer:

Yes, it can

Step-by-step explanation:

The solution to the initial value problem using the method of Laplace transforms is y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t

From the question, we have the following parameters that can be used in our computation:

y" - 3y' - lOy = 0, y(0) = 1, y'(0) = 12

Let L{y(t)} = Y(s),

Take the Laplace transform of both sides, we have:

s^2Y(s) - sy(0) - y'(0) - 3sY(s) + 3y(0) + 10Y(s) = 0

Using initial conditions y(0) = 1 and y'(0) = 12, we get:

s^2Y(s) - s - 12 - 3sY(s) + 3 + 10Y(s) = 0

Solving for Y(s), we have:

Y(s) = (s + 12)/(s^2 + 3s + 10)

Taking inverse Laplace transform of Y(s), we have:

y(t) = L^-1{Y(s)}

y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t

Hence, the solution is y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t

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Answer:

Step-by-step explanation:

a.0.002

Answer:

Try continuity formula you get your answer

The expected value of the rate of return is 23.5%

It is a branch of mathematics that deals with the occurrence of a random event.

Given is a table which gives the probability distribution of the annual rate of return on the stock of MNP Company, Inc. We have to find out  the expected value of the rate of return

Let X be the return and p probability

Then

X     15%     20%    30%     35%  Total

p     0.2       0.4     0.3       0.1        1

x(p)  3           8        9          3.5     23.5

Hence Expected rate of return

E(x)= 23.5%

Hence, the expected value of the rate of return is 23.5%

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The events described are known as a compound probability experiment.

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The uncertainty of the total distance is 0.2 cm.

As per the given data, the distance between the diffraction slit and the screen on which the pattern forms,

[tex]x_{1}[/tex] = (15.8 ± 0.2) cm

[tex]x_{2}[/tex] = (6.7 ± 0.1) cm

[tex]x_{3}[/tex] = (11.3 ± 0.1) cm

Let, the uncertainty in the measurements,

[tex]x_{1}[/tex], [tex]x_{2}[/tex] and [tex]x_{3}[/tex]  is [tex]e_{1}[/tex], [tex]e_{2}[/tex] and [tex]e_{3}[/tex] respectively.

So,

[tex]e_{1}[/tex] = 0.2 cm

[tex]e_{2}[/tex] = 0.1 cm

[tex]e_{3}[/tex] = 0.1 cm

Again, let the uncertainty in the total distance

[tex]\mathrm{x} =\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3[/tex] is e(error propagation).

The impact of a variable's uncertainty on the uncertainty of a function depending on it is known as propagation of uncertainty. When the variables are experimental measurement values, measurement limits cause uncertainties that are propagated via the function's combination of variables.

Then the error propagation is given as,

e = [tex]\sqrt{\mathrm{e}_1^2+\mathrm{e}_2^2+\mathrm{e}_3^2} \\[/tex]

So, e = [tex]\sqrt{(0.2)^2+(0.1)^2+(0.1)^2} \\[/tex]

Therefore e = [tex]\sqrt{0.06} \\[/tex]

e = 0.245 cm

e ≅ 0.2 cm

Therefore uncertainty of the total distance 0.2 cm

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The number of rolls of paper used per wall will be 1.5 rolls per wall.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Andy is hanging wallpaper in his kitchen. He is to cover 2 2/5 of the walls in the room using 6 rolls of paper. We know that the room has 4 walls.

Then the number of rolls of paper used per wall is given as,

⇒ 6 / 4

⇒ 1.5 rolls per wall

The number of rolls of paper used per wall will be 1.5 rolls per wall.

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Answer: DF is 24

Step-by-step explanation: DEF is 6x larger than triangle ABC so since AC is 4 DF is 24.

The number of calories that you would consume if you eat 3 mini-muffins is 41.66.

To know the number of calories per muffin, let's divide the total of calories (250) by the number of muffins.

Regular muffins: 250 / 12 = 20.83 calories

Mini-muffins: 250 / 18 = 13.88 calories.

This shows that one mini-muffin contains 13.88 calories, while the original recipe contains 20.83 calories per muffin.

13.88 calories x 3 = 41.66 calories

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a. A function to model taking the 10% discount will be 0.9x.

b. A function to model taking the 25% discount first will be 0.75x.

c. If I was an employee, I'll prefer the 25% discount.

From the information given, the store is offering a 10% discount on all items and in addition, employees get a 25% discount.

Let the price of the goods be given as x.

A function to model taking the 10% discount will be:

= x - (10% × x)

= x - 0.1x

= 0.9x

A function to model taking the 25% discount first will be:

x - (25% × x)

= x - 0.25x

= 0.75x

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The three values are not in the given list of options

From the question, we have the following parameters that can be used in our computation:

8n + 4 ≤ 2

Subtract 4 from both sides of the expression

So, we have

8n  ≤ -2

Divide both sides by 8

This gives

n  ≤ -0.25

This means that the values do not exceed -0.25

None of the valies in the option meet this condition

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The interquartile range of the following data set 4, 6, 10, 13, 18, 28, 34, 46, 50, 58 is 36.

What is interquartile range?

The difference between the third and the first quartile is defined by the interquartile range. The partitioned values known as quartiles divide the entire series into four equally sized segments. There are so three quartiles. The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the upper quartile equals the interquartile range.

The data set given is - 4, 6, 10, 13, 18, 28, 34, 46, 50, 58

Divide the data set into two parts -

D1 = 4, 6, 10, 13, 18

D2 = 28, 34, 46, 50, 58

The two middle value for data set is 18 and 28.

The median of D1 and D2 is -

Median = (18 + 28) / 2

Median = 46 / 2

Median = 23

The middle value for D1 is Q1 = 10 and for D2 is Q3 = 46.

The interquartile range is given as -

Q3 - Q1

46 - 10

36

Therefore, the interquartile range is 36.

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Answer:

winston receives 20carrots

Sam receives 15carrots

Chris receives 25carrots

Step-by-step explanation:

number of carrots are 60

Winston has a family of 4

Sam lives in a family of 3

Chris lives in a family of 5

total =5+3+4=12

thus

Winston - 4/12×60=20 carrots

Sam= 3/12×60=15 carrots

Chris=5/12×60=25 carrots

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The expression is -63 + 37|-1|. The absolute value of -1 is 1, so the expression becomes -63 + 37(1) = -26.

The value of depends on the context in which they are used. In general, words can have a variety of different values, such as conveying information, expressing an opinion, or providing entertainment. Each individual word can have different meanings and associations depending on the situation. writing is important in any context in which words are used, as it ensures that the ideas expressed are original and properly attributed.

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Let the random variables x and y have joint pdf as follows: f(x,y) = 1/5(11x^2 + 4y^2) so Cov(x,y) (round off to third decimal place) is 0.241.

The covariance formula in statistics is used to evaluate the relationship between two variables. In essence, it serves as a gauge for the variation between two variables. Covariance is calculated by multiplying the units of the two variables, and it is expressed in units. Any positive or negative value might be the variance.

E[(X−EX)(Y−EY)]

=E[XY−X(EY)−(EX)Y+(EX)(EY)]

=E[XY]−(EX)(EY)−(EX)(EY)+(EX)(EY)

=E[XY]−(EX)(EY).

E(Y) = ∫ 1/x dx = ∫ 11/5 = ln 11/5 = 0.788

E(XY) = E[X 1/X]= 1

It is feasible to get the correlation coefficient formula from the covariance using the aforementioned formula, and vice versa. Units of covariance are calculated by multiplying the units of the two provided variables.

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Answer:

B

Step-by-step explanation:

sqrt(243x⁷) = sqrt(9×9×3x³x³x) = 9x³×sqrt(3x)

The value of each limit functions are:

Let's try to solve each problem we have:

1. [tex]\lim_{x \to \--3} 2x^2+4x+1[/tex]

= 2(-3)² + 4(-3) +1

= 2(9) + 4(-3) + 1

= 18 - 12 + 1

= 7

2. [tex]\lim_{x \to \-3} \sqrt{x+1}[/tex]

= √(3+1)

=√4 = 2

3. [tex]\lim_{x \to \-3} \frac{\sqrt{x+2} }{x-4}[/tex]

= √(3+2) / (3-4)

= √5 / (-1) = - √5

4. [tex]\lim_{x \to \-2} \frac{x^3-8}{x-2}[/tex]  -->hint: use L'hospital rule

= [tex]\frac{(x^3-8)'}{(x-2)'}[/tex]

= 3x² / 1

= 3(2)²

= 12

5. [tex]\lim_{x \to \--1} \frac{2x^2-x-3}{x+1}[/tex]

= [tex]\lim_{x \to \--1} \frac{(2x-3)(x+1)}{(x+1)}[/tex]

= 2(-1) - 3

= -5

6. [tex]\lim_{x\to \-3} \frac{\sqrt{x+1}-2 }{x-3}[/tex]

= [tex]\frac{(\sqrt{x+1}-2)' }{(x-3)'}[/tex]

= 1/2√(x+1)

= 1/2√(3+1)

= 1/4

7.[tex]\lim_{x \to \-0} \frac{sin x}{5x}[/tex]

= [tex]\lim_{x \to \-0} \frac{sin x}{x} .\frac{1}{5}[/tex]

= 1/5 ([tex]\lim_{x \to \-0} \frac{sin x}{x}[/tex])

= 1/5 (1)

= 1/5

8. [tex]\lim_{x \to \pi/2}\frac{cosx}{cotx}[/tex]

= [tex]\lim_{x \to \pi/2}\frac{cosx}{\frac{cosx}{sinx} }[/tex]

= [tex]\lim_{x \to \pi/2}{cosx}.\frac{sinx}{cosx}[/tex]

= [tex]\lim_{x \to \pi/2}\ sinx[/tex]

= sin (π/2)

= 1

9. [tex]\lim_{h \to \-0} \frac{f(x+h)-f(x)}{h}[/tex] = f'(x)

a. f(x) = 3x - 2

    f'(x) = 3

b. f(x) = √x

   f'(x) = 1/2√x

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Step-by-step explanation:

that's your answer im hoping so

The largest possible area for a rectangle with a base on the x-axis and both upper vertices on the curve y=5−x² , is equals to the 20√15/ 9 .

In optimizing the objective function f(x), solve for the critical points by putting the first derivative f′(x), equals to zero. Then the objective function is evaluated at the critical points to determine the it's minimum or maximum. We have, a rectangle with base as x-aixs and both upper vertices on the curve y = 5 − x², which is a parabola equation. Thus width of the rectangle is based from the equation of the parabola y= 5 - x² --(1)

Area of rectangle is expressed as A = xy , where x -->length of it and y-->width or vertices of curve. The length of the rectangle with base x- axis is equal to 2x. Therefore, the area is A = w× l

= 2x( 5 - x² )

A = 10x - 2x³ --(2)

If area is maximum, then dA/dx = 0

Differentiating the equation (2) with respect to x

dA/dx = 10 - 6x²

so, 10 - 6x² = 0

=> 6x² = 10

=> x² = 10/6

=> x² = 5/3

=> x = ±√5/3

but x represents the length so, it's value always be positive. Thus, x = √5/3. The area is equal to A = 10x - 2x³

= 10(√5/3) - 2(√5/3)³

=> A = 10√5/3 - 10/3(√5/3)

=> A = √5/3( 10 - 10/3) = 20√5/3√3

=> A = 20√15/ 9 ( using rationalzation )

Hence, the required area is 20√15/ 9 .

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The slope of the new regression line with length measured in inches would be 0.068 inches/minute.

The slope of the regression line for predicting icicle length, in centimeters, from time, in minutes, is 0.173 cm/minute.

To convert this to inches, we need to multiply the slope by the conversion factor from centimeters to inches, which is 2.54 cm/inch:

0.173 cm/minute x  (1 inch/2.54 cm) = 0.068 inches/minute

So, the slope of the new regression line with length measured in inches would be 0.068 inches/minute.

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The frequency of the A allele is 82.7%.

The frequency of the B allele is 17.3%.

We know that :

10,000 individuals

6,840 individuals have blood type AA

2,860 individuals have blood type AB

300 individuals have blood type BB

AA genotype frequency: 68.4%

AB genotype frequency: 28.6%

BB genotype frequency: 3%

The A allele occurs 6,840 * 2 + 2,860 * 1 = 16,540 times, which is a frequency of 82.7%, meaning the B allele occurs 3,460 times, which is a frequency of 17.3%. In the next generation, 3%, or 750, individuals would have blood type BB.

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The complete question is:

A hypothetical population of 10,000 humans has 6840 individuals with the blood type AA, 2860 individuals with blood type AB, and 300 individuals with the blood type BB.

What is the frequency of each genotype in this population?

What does the frequency of the A allele?

What is the frequency of the B allele?

The rank of the points having a maximum moment of inertia is c > a > b.

The figure of 25 % snipped off square-shaped uniform metal plate.

We can rank the points according to the moment of inertia using the relation between the moment of inertia and the radius of gyration of the elements.

The formulae are as follows:

I = mh²

Where h = Radius of gyration, m is mass, and I is the moment of inertia.

Here,

I = mh²

So, the final moment of inertia will be maximum for the axis, which consists of elements having more h (which are more distant from the axis).

From this, it can be concluded that the moment of inertia about an axis through point c is maximum, followed by (a) and then (b).

Rank is c > a > b

Therefore, the points can be ranked according to the moment of inertia about the axis passing through it using its relationship with the radius of gyration.

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Answer:

x = 4; 27°

Step-by-step explanation:

JN=NL; JL = KM

therefore you can say 2(4x+6) = 5x+24

Just solve to find x = 4

JN = NL

KN = NM

JK = ML

triangles JKN and MLN are therefore congruent (sss)

Making the angles equal.

Answer:

x = 4; 27°

Step-by-step explanation:

The square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.

Co-interior angles, also known as consecutive interior angles, are those between two lines that are split by a third line (transversal), and are located on the same side of the transversal.

Given that, r^2 + 4r + 4.

Expand the terms as follows:

r^2 + 4r + 4.

r^2 + 2r + 2r + 4 = 0

r(r + 2) + 2(r + 2) = 0

(r + 2) (r + 2)= 0

The sum of co-interior angles is 180 degrees:

x + 40 = 180

x = 140 degrees.

Hence, the square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.

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Answer:

The total length of the commercial breaks is 4.5 minutes x 2 = 9 minutes.

So the length of the program itself is 7:00 P.M. - 6:30 P.M. - 9 minutes = 30 minutes - 9 minutes = 21 minutes.

Answer:

21 minutes

Step-by-step explanation:

30-9-21 minutes of program

Answer:

For k = 43, the possible values of (x,y,z) are (2,2,3), (2,3,2), and (3,2,2). For k = 44, the possible values of (x,y,z) are (8,-7,-5), (8,-5,-7), (-5,-7,8), (-5,8,-7), (-7,-5,8), and (-7,8,-5). For k = 54, the possible values of (x,y,z) are (13,-11,-7). For k = 55, the possible values of (x,y,z) are (1,3,3), (3,1,3), (3,3,1), and (1,3,1). For k = 62, the possible values of (x,y,z) are (3,3,2), (2,3,3), and (3,2,3). For k = 64, the possible values of (x,y,z) are (0,0,4) and (0,4,0).

Step-by-step explanation:

collect like terms

The corresponding sample space is S = {x|150 ≤ x ≤ 150}.

An experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre.

The yield is assumed to be between 150 and 250 bushels.

A sample space is a collection of probable outcomes from a random event. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.

Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

Then the sample space should be

S = {x|150 ≤ x ≤ 150}

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The complete question is:

Consider an experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre. The yield is assumed to be between 150 and 250 bushels.

Determine the corresponding sample space.