Which of the following statements about histograms is true?
a. A histogram is a summary of interval data.
b. A histogram is made of a series of intervals, called classes.
c. The classes in a histogram cover the complete range of observations.
d. All of these choices are true.

The explanatory variable in this scenario is B. the concession advertisements.

A response variable is what changes as a result of an explanatory variable being manipulated or observed to change (for example, the amount of caffeine consumed) (e.g., reaction times). In research, the terms "explanatory variable" and "response variable" are frequently used interchangeably.

Examples include both response variables, such as individual test item scores, total test scores, and achievement levels, and explanatory variables, such as gender, ethnicity, type of instruction, etc.

In this case, it should be noted that based on the information, the correct option is B.

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The value of the given integral [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] is 2/75.

The given integral is [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex].

We have to evaluate the given integral.

The given integral is definite integral. To evaluate the given integral we firstly solve the integral then we put the value in the solved integral to find the value.

We solving the integral [tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]

Let u = 2e^{5t}+3

Now differentiating

du/dt = 10e^{5t}

e^{5t}dt = du/10

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int\frac{1}{u^2}dt[/tex]

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int{u^{-2}}dt[/tex]

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-2+1}/(-2+1)]+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-1}/(-1)]+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/u)+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/2e^{5t}+3)+C

Now;

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5t}+3}\right]^{\text{In}3/5}_{0}[/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5({\text{In}3/5})}+3}-\frac{1}{2e^{5(0)}+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{({\text{In}3})}+3}-\frac{1}{2e^{0}+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2\cdot3+3}-\frac{1}{2+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{6+3}-\frac{1}{2+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[1/9 - 1/5]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[5-9/45]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[-4/45]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 2/75

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The right question is:

Problem 3: Integration via the Substitution Method ( 16 points) Evaluate each of the following. Explain and show your work. You do not need to simplify your final answer.

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]

Answer: 3

Step-by-step explanation: schoology whack

The following steps would apply conditional formatting to the range:

The given parameters in the question are:

The Conditional Formatting is located on the home tab

So, the first step to select the range and locate the Conditional Formatting option

Then set the necessary conditions and formats

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The values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Given, the equations are y = 24 - 4x and 2x - 3y = -2

Replacing the value of the first equation of y, which is, y = 24 - 4x, in the second equation, we get:

2x - 3(24-4x) = -2

⇒ 2x - 72 + 12x = -2

⇒ 14x = 70

⇒ x = 70/14

⇒ x = 5

Substituting the value of x=5 in y = 24 - 4x, we get,

y = 24 - 4(5)

⇒ y = 24 - 20

⇒ y = 4

Thus, the values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.

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Regression analysis will indicate about the underlying population and the model.

It is one of the most used and most powerful multivariate statistical techniques for it infers the existence and form of a functional relationship in a population. Once you learn how to use regression, you will be able to estimate the parameters { the slope and intercept } of the function that links two or more variables. With that estimated function, we  will be able to infer or forecast things like unit costs, interest rates, or sales over a wide range of conditions.

Though the simplest regression techniques seem limited in their applications, statisticians have developed a number of variations on regression that greatly expand the usefulness of the technique. And again, the t-distribution and F-distribution will be used to test hypotheses.

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Answer:

Step-by-step explanation:

because there is no change in slope. The graph will always be strait in this

The system of inequalities represents this solution is:

6c + 7.5d ≥ 75

d + c ≤ 15.

A statement of an order relationship, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now it is given that,

Money from walking neighbor's dog = $6 per hour

Money from car wash = $7.5 per hour

Total Number of hours of work not more than 15 hours

Now, if d represents the number of hours walking his neighbor's dog and c represents the number of hours washing car

So, money from walking neighbor's dog = 6c

and money from car wash = 7.5d

Therefore total money saved = 6c + 7.5d

∵ Total Number of hours of work is not more than 15 hours

⇒ d + c ≤ 15

∵ Tom needs to make at least $75 to cover prom expenses

⇒ 6c + 7.5d ≥ 75

The system of inequalities represents this solution is:

6c + 7.5d ≥ 75 ;

d + c ≤ 15.

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The complete question is as follows:

To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother said he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this solution?

The equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is the slope and c is the y-intercept.

There are basically two intercepts, x-intercept and y-intercept. The point where the line crosses the x-axis is the x-intercept and the point where the line crosses the y-axis is the y-intercept.

The equation of the line, which intersects the y-axis at a point is given by:

                           y = mx + c

Suppose the line passes through (t,0) and (3,5), where t>3. Then the y-intercept is at (0, 5t/t-3).

So the area of the triangle is:

[tex]\frac{1}{2}[/tex]×[tex]t[/tex]×[tex]\frac{5t}{t-3}[/tex] [tex]=[/tex][tex]\frac{5(t^{2} )}{3(t-3)}[/tex]

Then:

d(5t²/2(t-3))/dt = (5t/t-3) - 5t²/2(t-3)²

=  5t²(2(t-3)-t)/2(t-3)²

=5t(t-6)/2(t-3)²

Since we require t >3, the zero of the derivative that we see is when t=6.

We can write the equation of this line as: 5x +3y -30 = 0

Thus, the equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

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The value of y is 16.

When one quantity's value increases compared to another's decrease or vice versa, it is said that the two are inversely proportionate.

It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.

Inverse proportionality will be represented by the symbol '∝'. When two values x and y are Inverse proportional to each other then

             x ∝ 1/y

Here we have

y varies inversely with the square root of x

=>  [tex]y\propto\frac{1}{\sqrt{x} }[/tex]

=>  [tex]y\ = \frac{k}{\sqrt{x} }[/tex]  

=> [tex]\sqrt{x} y = k[/tex] ----- (1)

At x = 64, and y = 12  

=> √64 × 12 = k

=> k = (8) × 12

=> k = 96  

Thus the proportionality constant k = 96

Now Take x = 36 and k = 96 in equation (1)

=> √36 × y = 96

=>  6 × y = 96

=>  y = 16

Therefore,

The value of y is 16.

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The value of the function at day 5 is 822000 and it means that the laser rangefinder locked on the comet is at a distance of 822000 km

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

g(x) = 300,000csc(π/42x)

Also from the question, we have

Number of days = 5

This means that

x = 5

Substitute x = 5 in the equation g(x) = 300,000csc(π/42x)

So, we have the following representation

g(5) = 300,000csc(π/42 x 5)

Evaluate the products

So, we have the following representation

g(5) = 300,000csc(5π/42)

Evaluate the cosec expression

g(5) = 300,000 * 2.74

So, we have

g(5) = 822000

Hence, the value of the function is 822000

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Complete question

A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x) = 300,000csc(π/42x)

Evaluate g(5) and interpret the information

Answer:

  (c)  -42

Step-by-step explanation:

You want the product ab given that ...

The function (f+g)(x) is the sum of the other two functions. For the purpose here, we only need to look at terms that involve 'a' and 'b'.

Comparing coefficients of x², we have ...

  ax² +3x² = 9x²

  a = 9 -3 = 6

Comparing coefficients of x, we have ...

  -5x +bx = -12x

  b = -12 +5 = -7

The product is ...

  ab = (6)(-7) = -42

Total four triangles of B fit into triangle A as length of the equilateral triangle A is twice the length of triangle B.

As given in the question,

Types of triangles : Equilateral triangle

Number of triangle = 2

Triangle A and Triangle B

Let 'x' be the length of the triangle A

And 'y' be the length of the triangle B

As per given condition:

x = 2y

Area of equilateral triangle A = (√3/4)x²

Area of equilateral triangle B = (√3/4)y²

Now x = 2y

⇒Area of equilateral triangle A = (√3/4)(2y)²

⇒Area of equilateral triangle A = (√3/4)4y²

⇒Area of equilateral triangle A = 4 [(√3/4)y²]

⇒Area of equilateral triangle A = 4 ( area of equilateral triangle B)

Therefore, total number of four equilateral triangle of B fit into equilateral triangle A.

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Answer:

Step-by-step explanation:

You want an exponential regression function for the data in the table.

A regression function of most any kind can be found using a graphing calculator or spreadsheet. The attachment shows the function is approximately ...

  y = 371.17 × 1.15^x

where y is the number sold, and x is the month.

Using x=8, the predicted number sold for month 8 is ...

  y = 371.17 × 1.15^8 ≈ 1135.4175 ≈ 1135

Sales for month 8 will be about 1135.

Slope-intercept form: [tex]y=mx+b[/tex]

Parallel lines always have the same slopes and different y-intercepts.

We're given:

Because parallel lines have the same slopes, this line therefore has a slope of -3.

[tex]y=-3x+b[/tex]

Now, plug in the given point to solve for b:

[tex]3=-3(-1)+b\\3=3+b\\b=0[/tex]

Therefore:

[tex]y=-3x[/tex]

[tex]y=-3x[/tex]

A. Width = 16.5 ft             B.Width = 55.25 ft  

   Height  = 9.3 ft                 Height = 91 ft

   Area = 153.45 ft²              Area = 5027.75 ft²  

The area of the rectangle is a place covered by a rectangle in a 2D plane

The formula for Area of the rectangle is given by

Here we have

1 in = 3 feet and  1 cm = 6.5 ft  

Calculation for rectangle A :

In rectangle A

Width  = 5.5 in

=> Width in feet = 5.5 × 3 feet = 16.5 ft

Height =  3.1 in

=> Height in feet = 3.1 × 3 feet = 9.3 ft

By the given formula

Area = 16.5 ft × 9.3 ft = 153.45 ft²    

Calculation for rectangle B :

In rectangle B

Width  = 8.5 cm

=> Width in feet = 8.5 × 6.5 feet = 55.25 ft

Height = 14 cm

=> Height in feet = 14 × 6.5 feet = 91 feet

By the given formula

Area = 55.25 ft × 91 ft =  5027.75 ft²    

Therefore,

 A. Width = 16.5 ft             B. Width = 55.25 ft  

       Height  = 9.3 ft                 Height = 91 ft

       Area = 153.45 ft²              Area = 5027.75 ft²  

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Answer:

Step-by-step explanation:

c

Answer:

The park has 20 climbing activities.

Step-by-step explanation:

Given, 

Total activities = 50

Percent of climbing activities = 40%

Number of climbing activities = 40% of total activities

Number of climbing activities =  40/100 * 50

Number of climbing activities = 0.40 * 50 = 20

Hope this helps!!

The probability that the product of the two two-digit numbers is less than 200 is given as follows:

43/8010.

A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.

There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:

90 x 89 = 8010.

(the numbers have to be different)

The desired outcomes which result in a product of less than 200 are of given as follows:

Hence the number of desired outcomes is given as follows:

9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.

Meaning that the probability is of:

43/8010.

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The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains all the ordered pairs outside the parabola.

What is  parabola?

A parabola could be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a fixed line that is understood because the directrix.

Main body:

In this problem we must determine a quadratic inequality of the form:

a · x² + b · x + c < y

Where a, b, c are the real coefficients of the inequality.

First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:

25 · a - 5 · b + c = 0

4 · a + 2 · b + c = 0

a + b + c = - 18

(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)

Second, write the quadratic in equation:

(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y

hence , the equation is (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y

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The vertex B' is at (1, 1)

Let's update the guidelines for translating a point.

Let's apply the guidelines to resolve our issue.

Vertex A equals (-5, 2)

Vertex A' equals (2, -2)

The two points' coordinates changed, indicating that the

horizontal and vertical translations of a quadrilateral

A's x-coordinate is equal to -5.

A' has an x-coordinate of 2

Which indicates it goes to the right, therefore adhere to the first guideline presented above.

The translation formula is T (x, y) (x + h, y).

∴ x → x + h

x = -5, and x + h = 2.

∴ -5 + h = 2

Increase both sides by 5.

∴ -5 + 5 + h = 2 + 5

∴ h = 7

∴ The quadrilateral is moved seven units to the right.

A has a y-coordinate of 2

A"s y-coordinate is equal to -2.

Which means it descends, therefore apply the fourth rule listed above.

T (x, y) is the translational rule (x, y - k)

∴ y → y - k

Because y = 2 and y - k = -2,

∴ 2 - k = -2

Increase K on both sides.

∴ 2 - k + k = -2 + k

∴ 2 = -2 + k

Increase both sides by 2.

∴ 2 + 2 = -2 + 2 + k

∴ 4 = k

The quadrilateral is down four units.

Let's locate B.

T (x, y) (x + h, y - k) is the translational rule.

∵ B = (-6, 5) (-6, 5)

∵ h = 7 and k = 4

∴ B' = (-6 + 7, 5 - 4)

∴ B' = (1, 1) (1, 1)

Vertex B is located at (1, 1).

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Answer:

x = 4

Step-by-step explanation:

The sum of the interior angles of a triangle equal 180.

2x + 15 + 67 + 90 = 180  Combine like terms

2x + 172 = 180  Subtract 172 from both sides

2x + 1752 - 172 = 180 - 172

2x = 8  Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]

x = 4

Answer:

x= 4

Step-by-step explanation:

67+2x+15+90=180 (Sum of measures of a Triangle)

2x + 172 = 180

2x=180-172

2x=8

x=[tex]\frac{8}{2}[/tex]

x= 4

The perimeter and area of the figure are 10+6√5 and 20

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter. The circumference of a wheel or circle, which measures its perimeter, indicates how far it may travel in a single rotation.

AC=√4²+2²=√20=2√5

AB=√8²+4²=4√5

BC=√8²+6²=√100=10

Perimeter=a+b+c

=AC+AB+BC

=2√5+4√5+10

=10+6√5

Area=20

The perimeter and area of the figure are 10+6√5 and 20

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Answer:

1280 cm³

I presume you are looking for the solution steps and these are below

Step-by-step explanation:

If the each side of the square pyramid is 16 and the slant height is 17, then the height of the pyramid, half the side and the slant edge form a right triangle.

The height of the pyramid can be computed using the Pythagorean theorem

Let a be each side, h the height and s the slant height

[tex]s^2 = h^2 + (a/2)^2\\\\\\s^2 = h^2 + \dfrac{a^2}{4}\\\\\textrm{Plugging in known values,}\\17^2 = h^2 + \dfrac{16^2}{4}\\\\289= h^2 + 64\\\\h^2 = 289 - 64\\\\h^2 = 225\\\\h = \sqrt{225} = 15\\\\[/tex]

The volume, V of a square pyramid of side a and height h is given by the formula:

[tex]V = \dfrac{1}{3}a^2h\\\\\\\textrm{Plugging in values,}\\\\V = \dfrac{1}{3}\cdot 16^2 \cdot 15\\\\[/tex]

[tex]V = \dfrac{1}{3} \cdot 256 \cdot 15\\\\V = 256 \cdot 5\\\\V = 1280[/tex]

The volume of the pyramid is 1280 cubic cm.

Given the slant height of the pyramid is 17 cm and the length of square base of the pyramid is 16 cm.

Now we know the volume of the pyramid with a square base = [tex]\frac{1}{3}[/tex]×area of the base×height.

So we need the values for area of the base and height of the pyramid.

Area of the square base=16×16 sq. cm.= 256 sq. cm.

Again we can apply the relation to find the value of height,

(Slant height)² = (Height)² + ([tex]\frac{1}{2}[/tex]×Length of the base)²

So, putting the values we get,

[tex](17)^2 = (height)^2 +(\frac{16}{2})^2[/tex]

⇒ [tex]289 = (height)^2+64[/tex]

⇒ [tex](height)^2= 225[/tex]

⇒ [tex]height = 15cm[/tex]

Now by appyling the volume of the pyramid we get,

Volume = [tex]\frac{1}{3} \times 256 \times 15[/tex] cubic cm. = 1280 cubic cm.

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The value of the function after evaluation is , f(x)=0 . Hence it is neither a minima nor a maxima.

f(x) =(x + 5)^4; x = - 5

=(-5+5)^4

=(0)^4

=0

The critical value is crucial for accurately portraying a range of properties in statistics. The critical value can be helpful for proving or disproving ideas when they are tested, in addition to validity and accuracy.

If you're taking a statistics course or are just interested in how these concepts work, it is essential to comprehend critical value and how to compute it before analyzing other statistical functions, such as margin of error and significance.

When calculating the margin of error for a set of data, statisticians utilize a measurement known as the critical value.

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The dimensions of the rectangle with area 35 m² is

length = 7.6 m and width = 4.6 m

The dimension of the rectangle is calculated using the formula for area of rectangle

= length x width

where

area of rectangle

35 = (w + 3) * w

35 = w² + 3w

w² + 3w - 35 = 0

solving for w gives

w = 4.6 OR -7.6

using the positive value, the w = 4.6 m, l = 4.6 + 3 = 7.6 m

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l

Answer:

The answer is 3x12 + 3x6

Step-by-step explanation:

You have to multiply each number inside the brackets by the number outside the brackets

3(12+6)

= 3x12 + 3x6

= 36 + 18

= 54

Step-by-step explanation:

Press ''CTRL + /'' to access the list of features.

Find the “Text Formatting” section.

Choose “Superscript” from the list of options.

On the right-hand side, you'll see the ''CTRL +. '' shortcut. Use it to make the number or letter in your text appear in exponent form.

Step-by-step explanation:

1. Place your cursor where you want an exponent. For example, if you want to place an exponent after the number 10 in a document, place your cursor directly after the 10 with no space.

2. Type Alt+0185 for the exponent 1. For example, you can type the number 10¹ holding the Alt key and typing 0185.

3. Type Alt+0178 for the exponent 2. For example, you can type the number 10² holding the Alt key and typing 0178.

4. Type Alt+0179 for the exponent 3. For example, you can type the number 10³ by holding the Alt key and typing 0179.

The arrangement of the given numbers in ascending order is -19, -15, -13, -11, -8, 13

What is Ascending Order?

Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Compare first, then order. Putting the numerals in ascending order: Count how many digits are in each number.

Solution:

Given the order is -19, 13, -15, -8, -11, -13

Arranging them in the Ascending Order

-19, -15, -13, -11, -8, 13

In the above arrangement the given numbers are arranged into ascending order

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Possible triangles that satisfy the given conditions are:

Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5

Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5

Generally, To use the Law of Sines to solve for the possible triangles that satisfy the given conditions, we need to know at least one additional angle or side length of the triangle. The Law of Sines states that:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the side lengths of the triangle and A, B, and C are the corresponding angles opposite those sides. Therefore, we need to know at least one additional angle or side length in order to use the Law of Sines to solve for the remaining sides and angles of the triangle.

If we let B1 and B2 be the two possible values of angle B, then we can use the Law of Sines to find the corresponding values of angles A1 and A2 and sides a1 and a2 as follows:

a1/sin(A) = c/sin(B1) a2/sin(A) = c/sin(B2)

Solving these equations for a1 and a2, we get:

a1 = c * sin(A) / sin(B1) a2 = c * sin(A) / sin(B2)

Since we are given that a = 36 and c = 44, we can substitute these values into the above equations to find the values of a1 and a2.

a1 = 44 * sin(31) / sin(B1) a2 = 44 * sin(31) / sin(B2)

Now, we can use the Law of Sines to find the corresponding values of angles A1 and A2.

A1 = arcsin(a1 * sin(B1) / c) A2 = arcsin(a2 * sin(B2) / c)

Substituting the values of a1 and a2 that we found earlier and the given value of c, we get:

A1 = arcsin(36 * sin(B1) / 44) A2 = arcsin(36 * sin(B2) / 44)

To find the possible values of angles B1 and B2, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, we have:

B1 + A1 + C1 = 180 degrees B2 + A2 + C2 = 180 degrees

Substituting the values of A1 and A2 that we found earlier, we get:

B1 + arcsin(36 * sin(B1) / 44) + (180 - 31 - B1) = 180 degrees B2 + arcsin(36 * sin(B2) / 44) + (180 - 31 - B2) = 180 degrees

Solving these equations for B1 and B2, we find that the possible values of B1 and B2 are:

B1 = 63.5 degrees B2 = 116.5 degrees

Therefore, the possible triangles that satisfy the given conditions are:

Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5

Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5

Note that these values should be rounded to one decimal place as requested.

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