Which histogram represents the following data set?
45, 55, 25, 48, 36, 61, 52, 31, 8, 41, 58, 40, 55, 47, 60, 28, 44, 63, 18, 50, 57, 37, 16, 56, 40, 50

After solving, the regular singular points are x=0, 5i, -5i.

We have to determine the singular points of the given differential equation. Classify each singular point as regular or irregular.

(x^3+25x)y"–5xy'+6y = 0

On comparing with the equation P(x)y''+Q(x)y'+R(x)y=0

P(x) = (x^3+25x)

P(x)=0

x^3+25x = 0

x=0, 5i, –5i be the singular point.

Now write equation 1 in the standard form

Divide by x^3+25x on both side, we get;

y"–5x/(x^3+25x) y'+6/(x^3+25x) y = 0

y"–5/(x^2+25) y'+6/x(x^2+25) y = 0

Comparing with the standard form of equation;

y''+P(x)y'+Q(x)y = 0

P(x) = –5/(x^2+25)      Q(x)=6/x(x^2+25)

We know that if [tex]\lim_{x \to x_{o}}(x-x_{o})p(x)\text{ and }\lim_{x \to x_{o}}(x-x_{o})^2q(x)[/tex] exist finite. Then the singular point [tex]x_{o}[/tex] is regular singular point else irregular singular point.

(a) At [tex]x_{o}[/tex]=0

[tex]\lim_{x \to 0}(x-0)p(x)=\lim_{x \to 0}\frac{-5x}{x^2+25}[/tex]

[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)

[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x^2}{x(x^2+25)}[/tex]

[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x}{(x^2+25)}[/tex]

[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)

So x=0 is a regular singular point.

(b) At [tex]x_{o}[/tex]=5i

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5(x-5i)}{(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5}{(x+5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = -1/i (Finite)

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)^2}{x(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)}{x(x+5i)}[/tex]

[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = 0 (Finite)

So x=5i is a regular singular point.

(c) At [tex]x_{o}[/tex]=-5i

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5(x+5i)}{(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5}{(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 1/i (Finite)

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)^2}{x(x+5i)(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)}{x(x-5i)}[/tex]

[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 0 (Finite)

So x=-5i is a regular singular point.

Hence, the regular singular points are x=0, 5i, -5i.

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X (the number that reach a live person) have a binomial distribution.

In this question we have been given when an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random dialing machine make 15 calls, X is the number that reach a live person.

We need to state whether X have a binomial distribution.

20% of the calls reach a live person.

So, the probability that any individual call reaches a live person is 0.2

The sample size (n) = 15 calls

X represent the number of calls that actually reach a live person.

So there are 15 attempts, 15 calls that will attempt to reach a live person.

The probability that any one of those individual calls actually reaches a live person is 0.20 and X will represent the number out of those 15 calls that are placed actual represent the number of those calls that actually reached a live person.

Therefore, the X is a binomial random variable.

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The angle measures in this problem are given as follows:

42. m < KMN = 101º.

43. m < M = 20º.

The angle measures are obtained considering that the sum of the measures of the internal angles of a triangle is of 180º.

Additionally, an angle is also supplementary with it's exterior angle, meaning that the sum of their measures is also of 180º.

Considering the missing angle as y, the equations for item 42 are given as follows:

Hence:

13x + 36 = 4x + 81

9x = 45

x = 5.

Then the measure of angle KMN is of:

m <KMN = 13 x 5 + 36 = 101º.

For problem 43, the triangles are similar, meaning that they have the same angle measures, which are given as follows:

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The cost of the flooring task is $35

Consider the image I attached:

Actual area of floor = Area of  rectangle A + Area of  rectangle B

Actual area of floor = (6×3) + (2×1) = 18 + 2 = 20 ft²

With Estimate of 5% more than the actual area in case of mistakes:

Area = 20 + (5/100 × 20)

Area = 20 + 1 = 21 ft²

Since Cost: $20 for 12 square feet of flooring. Thus:  

Cost of task = 21/12 × 20 = $35

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The inequality of each model cutting, sewing finishing packaging and shipping profit

The maximum value = 5x + 8y

1R + 3/2 C ≤ 900

1/2 R + 1/3 C ≤ 300

1/8 R + 1/4 C ≤ 100

R, C ≥ 0

Consider x be the number of regular model of gloves to be produced

y be the catcher’s model of gloves to be produced

The maximum value = 5x + 8y

Then the inequality will be

The inequality of Cutting and Sewing

1R + 3/2 C ≤ 900

The inequality of Finishing

1/2 R + 1/3 C ≤ 300

The inequality of Packaging and Shipping

1/8 R + 1/4 C ≤ 100

R, C ≥ 0

Therefore, the inequality of each model cutting, sewing finishing packaging and shipping profit has been found

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Therefore, the answer to this question is option (C) ex ante forecasts

To face the challenge of improving operational performance while increasing production efficiency, performance forecasting is a crucial service to help decision-making in the idea, design, and operational phases of an asset.

Here,

As to evaluate forecasting performance of a model or compare relative performance of two models,

can be examined on the basis of ex ante forecasts

The term "ex-ante forecast" refers to a forecast that only takes into account the data (i.e., the value of economic variables) that is available at the time of the actual forecast and not the value of some variables that will be available later on.

Therefore, the answer to this question is option (C) ex ante forecasts

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No, Then the matrix has three columns and the eigenspaces' sum of dimensions is zero. The eigenspace's dimensions and the number of columns must add up to be equal.

A matrix is a rectangular arrangement of a collection of numbers into a fixed number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.

A matrix, also spelled "matrices," is a rectangular table, array, or set of letters, numbers, or phrases that are arranged in rows and columns to represent a mathematical object or a property of such an entity.

There are three eigen-spaces, since A has three eigen values, the dimension of each of the eigen value is at least one as there is at least one non-zero eigen vector in them.

Therefore,

No, Then the matrix has three columns and the eigenspaces' sum of dimensions is zero. The eigenspace's dimensions and the number of columns must add up to be equal.

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The logarithm of base 7 of t, as a logarithm of base 2 is given as follows:

log2(t)/log2(7).

A logarithm is defined as follows:

log_a(b).

In which:

To change the logarithm to a new base c, the logarithm is written by the fraction presented as follows:

log_c(b)/log_c(a).

In this problem, the logarithm is defined as follows:

log_7 t.

The new base is given as follows:

2.

(as stated in the problem, since we want the logarithm as a logarithm of base 2).

Hence, applying the change of base, the logarithm of base 2 will be given as follows:

log2(t)/log2(7).

As the term log2 represents the logarithm of base 2 of the term.

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Answer: they didnt distribute the 7 to the 4.5

Step-by-step explanation:

when distributing something outside of a parenthesis, you have to distribute it to all terms within the parenthesis, not just the variable

Regroup means regrouping refers to rearranging integers into place value-based groupings to facilitate operations.

Given that,

We have to find what does it mean to regroup.

We know that,

When performing operations like subtraction and addition, regrouping is accomplished by creating groups of tens. Regrouping refers to rearranging integers into place value-based groupings to facilitate operations.

Because you must rearrange the numbers into place value to complete the procedure, it is known as regrouping. Regrouping is an excellent approach to simplify complicated mathematics, especially for kids. Regrouping with subtraction is sometimes referred to as "borrowing."

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The value of y can be written as y=(x+5)/4.

Here our task is not to find the value of x or y but to find the relation between x and y by eliminating the t from both the equations.

Given that,

Curve equations are  x= 2t-1 y=1/2t+1

x= 2t-1 and y=1/2t+1

2t = x+1

t = (x+1)/2

substitute t value in y

y = t/2 + 1

y = (x+1/2)/2 + 1

y = x+5/4

you can also write x =4y-5

But generally when we have to draw the graph we will be taking x as input value and y as output value so y can be written as y=(x+5)/4

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Answer:

[tex]\boxed{26.74}.[/tex]

Step-by-step explanation:

John spends $2.75 on donuts for his office employees every weekday, so he spends 5 * $2.75 = $<<5*2.75=13.75>>13.75 on donuts for his office employees throughout the week.

He also spends $12.99 on donuts on Sunday mornings, so in total he spends $13.75 + $12.99 = $<<13.75+12.99=26.74>>26.74 on donuts throughout the week. Answer: \boxed{26.74}.

175/26 large tiles can she stick to the ground.

Two or more expressions with an Equal sign is called as Equation.

Given,

A cement mix calls for 2 cups of water and [tex]1\frac{1}{4}[/tex] pounds of mix to make five large tiles stick to the ground,

2+ [tex]1\frac{1}{4}[/tex]=5

2+5/4

13/4

Which means 13/4 is needed for 5 large tiles.

Yolanda has plenty of water but only [tex]4\frac{3}{8}[/tex] pounds of mix

We need to find how many large tiles can she stick to the ground.

Let x be the number of tiles.

[tex]4\frac{3}{8}[/tex] =35/8

So

(13/4)/5=(35/8)/x

Apply cross multiplication

13/4x=35/8×5

13/4x=175/8

x=175/8×4/13

x=700/104=350/52=175/26

Hence, 175/26 large tiles can she stick to the ground.

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Answer:

The Tree diagram here is given as:  {HRR,HRB,HRW,HRG,HBB,HBW,HBG,HWG,HGG,TRR,TRB,TRW,TRG,TBB,TBW,TBG,TWG ,TGG}

Sample space for the compound experiment is : {HRR,HRB,HRW,HRG,HBB,HBW,HBG,HWG,HGG,TRR,TRB,TRW,TRG,TBB,TBW,TBG,TWG ,TGG}

Probability of 2nd ball drawn is green = 8/18=4/9

Probability of a head is flipped on the penny = 9/18=1/2

Step-by-step explanation:

Part A tree diagram: Document attached below

Part B:

Sample space for the compound experiment is : {HRR,HRB,HRW,HRG,HBB,HBW,HBG,HWG,HGG,TRR,TRB,TRW,TRG,TBB,TBW,TBG,TWG ,TGG}

N(s)=18

Part c:

A=Choosing Head

P(A)=n(a)/n(s)

P(A)= 1/18

B= Choosing tail

P(B)=n(B)/n(s)

P(B)= 1/18

c=Choosing red balls

P(C)=n(C)/n(s)

P(C)= 3/18=1/6

D= Choosing blue balls

P(D)=n(D)/n(s)

P(D)= 4/18=2/9

E=Choosing white balls

P(E)=n(E)/n(s)

P(E)= 1/18

F = Choosing green balls

P(F)=n(F)/n(s)

P(F)= 2/18=1/9

Part D:

Probability of 2nd ball drawn is green = 8/18=4/9

Part E:

Probability of a head is flipped on the penny = 9/18=1/2

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The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.

What is standard form of an equation ?

The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.

If you rewrite this equation in a different way, you'll obtain y by itself on the left side, it then forms y = mx +b.

An assertion of equality between two expressions containing variables and/or numbers is called an equation.

In essence, equations are questions, and attempts to discover systematic answers to those questions have spurred the development of mathematics.

Linear equations can be written in three different ways: point-slope form, standard form, and slope-intercept form.

General Procedure:

Equation in slope intercept form has the basic structure

y = mx + b

y - mx = (mx - mx ) + b

y - mx = b

y - mx - b = b - b

y - mx - b = 0

-mx + y - b = 0−mx+y−b=0

If m is an integer, then B will equal 1.

-A/Bx + y - b = 0−

x+y−b=0

-Ax + By - Bb = 0−Ax+By−Bb=0

-Ax + By - C = 0−Ax+By−C=0

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According to the Mean value theorem conditions. The answer will be (a) that is Mean Value Theorem can be applied.

The Mean Value Theorem says that there exists a point c in the interval    (a, b) such that f'(c) equals the function's average rate of change throughout [a , b] if a function f is continuous on the closed interval [a , b] and differentiable on the open interval (a , b).

The name derives from the fact that an average rate of change during an interval may be considered as an average (or mean) of the instantaneous rates of change along the interval thanks to the fundamental theorem of calculus.

[tex]f(x) = 9\sin x[/tex] is continuous on [0,1] since every value for [tex]9\sin x[/tex] exist in that interval.

[tex]f(x) = 9\sin x[/tex] is differentiable on (0,1) since at every point the derivative exist that is [tex]9 \cos x[/tex] is valid in that interval.

The answer is (a) that is Yes, The Mean Value Theorem can be applied.

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Answer:

58 degrees

Step-by-step explanation:

a - 15 + a + 43 + 36 = 180

2a - 15 + 79 = 180

2a + 64 = 180

2a = 180 - 64

2a = 116

2/2 a = 116/2

a = 58 degrees

The percentage of the hotel rooms in the city which were occupied during the convention is 98%.

What is percentage?

A percentage is a piece of a whole expressed as a number between 0 to 100. Nothing is said to be zero percent; everything is said to be 100 percent; half of something is said to be 50 percent; and nothing is zero percent.

You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

As given in the question,

Number of hotel room occupied = 9,800

Number of hotel room unoccupied = 200

Total number of the rooms in city = 9800 + 200

Total number of the rooms in city = 10,000

To calculate the percentage we proceeds as follow:

(9800/10000)100 = 98%

Therefore, the percentage is 98%.

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Answer: 9.1 lb/in.^2

Step-by-step explanation:

To begin, plug in your X value to get P=14.7e^(-0.21(2.3)).

With this you can solve for P=9.1 lb/in.^2

The fraction of height at which the collision occured is , y/y₀ = 1/2 + v₀²/(2 g y₀) .

For ball A

Given that the ball is dropped and its initial velocity is zero, the equation is

= - 2 g (y₀-y)

For ball B

v {B}^2 = v₀² - 2 g y

We swap out

2v {B}^2 = -2 g (y₀ -y)

g y0 + 2 g y = -v B2

v {B}^2 = v₀² - 2gy

It can be solved because it is a system of two equations with two unknowns. Let's add and multiply by -1.

0 = g y₀ + v₀² -2gy

Bypassing the height

y = (g yo plus v02) / 2g

y = yo / 2 + v₀² / 2g

In this exercise, we'll assume that the building's height and ball B's initial velocity are both known.

The percentage is

y/yo

= 1/2 + v₀²/(2gyo) (2gyo)

Velocity and speed describe how quickly or slowly an object is moving. We frequently encounter circumstances when we must determine which of two or more moving objects is going faster.

If the two are travelling on the same route in the same direction, it is simple to determine which is quicker.

It is challenging to identify who is moving the fastest when their motion is in the other direction.

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The complementary angle is x= 36 degrees.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

The complementary angle is x

Complementary angles total to a straight angle (90 degrees) (90 degrees).

x + (2/3)x = 90

(3/3)x + (2/3)x = 90

(5/3)x = 90

x = 90(3/5)

x = 54 degrees

The angle is 2/3 of this

The angle is (2/3)54 = 36 degrees

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Both the inequalities (- 3 > 1 - 3 = 3)  and  (1 < 3 - 3 < 1) are false.

We have the following integers -

- 3, 1 and 3.

The given inequality are -

- 3 > 1 - 3 = 3

1 < 3 - 3 < 1

- 3 > 1 - 3 = 3

- 3 > - 2 = 3

Which is false.

1 < 3 - 3 < 1

1 < 0 < 1

Which is false.

Therefore, both the inequalities (- 3 > 1 - 3 = 3)  and  (1 < 3 - 3 < 1) are false.

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The volume of cylinder is denoted as πr²h

The density of a cylinder is determined by its volume, which indicates how much material it can hold or how much can be submerged inside it. The volume of a cylinder can be calculated using the formula r2h, where r denotes the radius of the circular base and h denotes the height of the cylinder. Any substance that can be evenly put into the cylinder, including liquid, may be used as the material. Shape volumes can be seen here.

This article contains a basic explanation of cylinder volume as well as examples with solutions for your convenience. The study of shapes and their characteristics is a key component of geometry in mathematics. Any three-dimensional shape must have both volume and surface area.

Hence, the volume of cylinder is denoted as πr²h

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The simplest form of (4y^2)^3(3y^2) is 192 y⁸.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given expression is (4y²)³(3y²).

The law of exponent formula are:

(a^m)^n = a^(mn)

(a^m)(a^n) = a^(m+n).

Now applying the formula (a^m)^n = a^(mn) in (4y²)³

(4y²)³ = 4³× y²ˣ³ = 64y⁶

Putting (4y²)³ = 64y⁶ in (4y²)³(3y²):

(4y²)³(3y²) = 64y⁶ × (3y²)

Now applying the formula (a^m)(a^n) = a^(m+n):

(4y²)³(3y²) = (64× 3) y⁶⁺²

(4y²)³(3y²) = 192 y⁸

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The greatest common factor for the fraction is 26.

What is fraction?

A fraction represents a district of an entire or, additional typically, any range of equal components. once spoken in everyday English, a fraction describes what number components of an exact size there area unit.

Main body:

According to the question,

fraction = 52/78

to find its common factor , we need to write it in form of multiples of its factors,

52 = 2*2*13

78 = 2*3*13

from this it is clear that both 52, 78 has factor as 2*13

Hence the greatest common factor for the fraction is 26

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The inequality we want to write is:

100 + W*50 ≥ 1800

And its graph can be seen in the image at the end.

We know that you start the game with 100 points and you get 50 extra for each word you make.

So, if you make W words, the total number of points that you get is:

100 + W*50

And that must be equal to or larger than 1,800, so we can writ the inequality:

100 + W*50 ≥ 1800

To solve it, we can isolate W.

100 + W*50 ≥ 1800

W*50 ≥ 1800 - 100

W ≥ 1700/50

W ≥ 34

So the number line is a point on W = 34 and a line that extends to the right, like the one below.

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The cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

What is cumulative distribution function?

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x in probability theory and statistics.

We have to find the c.d.f  of ax + b for a > 0 and a < 0.

F(x) = P(X < x)

a>0:

P(aX + b < x) = P(aX < (x - b)) = P(X < (x - b)/a) = F((x - b)/a)

a < 0 :

P(aX + b < x) = P(aX < (x - b)) = P(X > (x - b)/a) = 1 - P(X < (x - b)/a) =

1 -  F((x - b)/a).

Hence, the cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

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Answer:

the slope is 1

Step-by-step explanation:

where: m is the slope and b is the y-intercept. Therefore, for the equation y=x+5 , the slope is 1 , and the y-intercept is 5

Using the regression model you predict the sales to be $ 250.38 on day 60.

A regression model is an equation used to ascertain the relationship between two variables.

Given that an electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day.

The model can be written as follows:

ŷ = 103.38 + 2.45x

where ŷ is in thousands of dollars.

Since we require the sales gtowth after 0 days, substituting x = 60 into the equation for the regression model, we have that

ŷ = 103.38 + 2.45x

ŷ = 103.38 + 2.45(60)

ŷ = 103.38 + 2.45(60)

ŷ = 103.38 + 147

ŷ = 250.38

So, you predict the sales to be $ 250.38 on day 60.

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Answer: C = 25.1 yards

Step-by-step explanation: The circumference formula is as follows C = 2[tex]\pi[/tex]r^2 C being circumference, [tex]\pi[/tex] Being pi or 3.14, and r^2 The radius squared

The radius is given to us in the image being the midsegment from the center of the circle or 4 and we will input all our values into the equation.

C = 2 x 3.14 x 4^2 ≅ 25.13

We round to the nearest tenth to get

C = 25.1 yards