13
5
L
N
M
Enter the ratio equivalent to tan(L).
tan (L) =

The element ([tex]e_{12}[/tex]) at row 1 column 2 is 40.

Matrices, the plural form of a matrix, are the arrangements of numbers, variables, symbols, or expressions in a rectangular table that contains various numbers of rows and columns. They are rectangular-shaped arrays, for which different operations like addition, multiplication, and transposition are defined. The numbers or entries in the matrix are known as its elements. Horizontal entries of matrices are called rows and vertical entries are known as columns.

Multiplying the matrix by 4 x [tex]\left[\begin{array}{ccc}5&10&4\\9&3&2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}20&40&16\\36&12&8\\\end{array}\right][/tex]

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The Quotient is 3x² -3x + 3 and remainder is 5.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Given:

9x³+3x²-21x-7 by 3x+4

Now, Dividing the Polynomial

                         3x+4 |  9x³+3x²-21x-7 | 3x² -3x + 3

                                     9x³ + 12x²

                                  -__________

                                               -9x² - 21x

                                               -9x²- 12x

                                           __________

                                                          9x - 7

                                                          9x - 12

                                                       ________

                                                                 5

So, the quotient = 3x² -3x + 3 and remainder= 5.

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In the EU, a US men's size 9 would be equivalent to a 42 in the Euro system. The length of a shoe in Europe is measured in centimeters.

A graph that depicts the relationship between two extra variables is the most common way to present data using a chart. It is also permitted to use hand-drawn or digitally generated diagrams. starting at the origin, move 2 units to the right, then 3 units up. On the coordinate plane, the coordinates for the points 2, 3, and 4 should be displayed. Explain your points in detail. Thus, the pink dot with the letter P represents the number 2.3. You must first produce a number line for each value in your data collection before you can create a line chart. After that, mark each value of the data on the number line with an X (or a dot).

given

The worldwide medium (M) shirt size is equivalent to shirt sizes 40 and 41,

which both have a medium-sized torso and only differ in the width of the collar, which is either 40 cm or 41 cm.

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The constant of inverse variation will be k = 42n

In a mathematical equations where a relationship is established for some type of parameters normally two types quantities exist. One is constant that doesn’t change with the changes of other parameters in the equation and another is the variables which change for different situations. The changing of variable parameters is called as variation.

There are four types of variation in mathematics and they are;

Let cost = c

number of people = n

c ∝ 1/n

c = k/n

where k = constant of proportionality

but c = $42

therefore;

42 = k/n

k = 42n

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The factored form of the trinomial x² + 17x + 72 is ( x + 8 )( x + 9 ).

Given the trinomial in the question;

x² + 17x + 72

To factor, find a pair of integers whose product is 72 and whose sum is 17.

Considering the trinomial x² + 17x + 72;

8 and 9 are the two integers whose product is 72 and whose sum is 17.

Now, write the factored form using these integers

( x + 8 )( x + 9 )

Therefore, the factored form is ( x + 8 )( x + 9 ).

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Answer:

Mandelbrot set.

Step-by-step explanation:

Mandelbrot set. Created by Wolfgang Beyer with the program Ultra Fractal 3.

Answer:

Mandelbrot set

Step-by-step explanation:

Hi! This is a pretty complex, like university level math idea! I hope this is extra credit or something. Lots of lovely examples of math in nature look like this. Hope this helps!

Answer:

Least to Greatest:

- 2

25 }

 <  { - 1.55  <  

111

100

Step-by-step explanation:

1. The center of dilation is vertex A, as it is the common vertex for both triangles.

2. The original triangle is the triangle ABC, while the dilated triangle is triangle AED, as the side lengths of triangle AED are the side lengths of triangle ABC multiplied by the scale factor.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For this problem, the scale factor of the dilation is given as follows:

k = 1/2.

Meaning that the side lengths of the dilated triangle are half the side lengths of the original triangle, which is the reason for which ABC is the original triangle while AED is the dilated triangle.

As the vertex A is a common vertex to both triangles, it represents the center of dilation for this problem.

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The triangles that are congruent are triangle xyz and triangle def.

Triangles xyz, def and qrp can be tested for congruency using the Side-Angle-Side (SAS) Theorem. The SAS theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of a second triangle, then the two triangles are congruent.

To begin, we must first determine the side lengths and angle measures of the three triangles.

For triangle xyz, the side lengths are x = 4, y = 5, and z = 6, and the angle measures are angle x = 55 degrees, angle y = 70 degrees, and angle z = 55 degrees.

For triangle def, the side lengths are d = 4, e = 5, and f = 6, and the angle measures are angle d = 55 degrees, angle e = 70 degrees, and angle f = 55 degrees.

For triangle qrp, the side lengths are q = 3, r = 4, and p = 5, and the angle measures are angle q = 40 degrees, angle r = 40 degrees, and angle p = 100 degrees.

Now that the side lengths and angle measures of the three triangles have been established, we can use the SAS theorem to determine which of the three triangles are congruent.

To test triangles xyz and def for congruency, we will compare the two triangles side by side. We can see that the side lengths of xyz and def are equal (x = d = 4, y = e = 5, and z = f = 6). We can also see that the angle measures of xyz and def are equal (angle x = angle d = 55 degrees, angle y = angle e = 70 degrees, and angle z = angle f = 55 degrees). Thus, since all of the corresponding side lengths and angle measures of xyz and def are equal, the two triangles are congruent.

To test triangles xyz and qrp for congruency, we will compare the two triangles side by side. We can see that the side lengths of xyz and qrp are not equal (x = 4, q = 3; y = 5, r = 4; z = 6, p = 5). We can also see that the angle measures of xyz and qrp are not equal (angle x = 55 degrees, angle q = 40 degrees; angle y = 70 degrees, angle r = 40 degrees; angle z = 55 degrees, angle p = 100 degrees). Thus, since the corresponding side lengths and angle measures of xyz and qrp are not equal, the two triangles are not congruent.

Therefore, the triangles that are congruent are triangle xyz and triangle def.

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Answer: A & C

Step-by-step explanation:

I got it right on edge <3

Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.

Draw 5 new arcs from point D along DB the same distance apart as those on AC. Then the correct option is A.

A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.

Nelda is dividing AB into 6 congruent segments. She has reached the point shown.

Draw 5 new arcs from point D along DB the same distance apart as those on AC. Then connect each corresponding point on AC and BD. Then the correct option is A.

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The complete question is attached below.

To prove that △DFE ~ △GFH by SAS similarity theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\frac{DF}{GF}=\frac{EF}{HF}\\[/tex] and ∠DFE is congruent to ∠GFH.

Two triangles are said to be similar if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

The following may be seen given ∠DEF as depicted in the figure linked to this answer:

By comparing ΔGFH and ΔDEF, we get

DG + GF = DF

= 12 + 4

=> DF = 16

Also,

EF = EH +HF

=> EF=9 + 3

=>EF = 12

Using the sides of ΔDEF and ΔGFH as a comparison, we have;

[tex]\frac{DF}{GF}=\frac{EF}{HF}\\ = > \frac{16}{4}=\frac{12}{3}\\ = > 4=4[/tex]

Thus, the two triangles have similar sides.

Comparing the included angle <DFE and <GFH, then;

∠DFE is congruent to ∠GFH

Therefore, the appropriate answer to the given question is option C. ∠DFE is congruent to ∠GFH

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To prove that ΔDFE is similar to ΔGFH by SAS similarity theorem, it can be stated that DF / GF = EF/ HF and ∠DFE is congruent to ∠GFH (∠DFE ≅ ∠GFH).

To prove a triangle is similar to another triangle by SAS similarity theorem two sides in one triangle should be proportional to two sides in another triangle and the included angle in both should be congruent, then the two triangles are similar.

If ΔDFE is similar to ΔGFH, then ∠DFE is congruent to ∠GFH, ∠EFD is congruent to ∠HFG and ∠FHG is congruent to ∠FED.

Also DF / GF = EF/ HF = DE/ GH.

From the given options so correct statements are

DF / GF = EF/ HF

∠DFE ≅ ∠GFH

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Answer: He needs 50 more grams of butter

To graph a linear inequality word problem, identify the inequality, plot points on a coordinate graph, and then shade the appropriate region depending on the type of inequality.

To graph a linear inequality word problem, you need to identify the inequality, plot the inequality on a graph, and then shade the appropriate region.

1. Identify the inequality: Determine the inequality from the word problem.

2. Plot the inequality: Plot the points on a coordinate graph.

3. Shade the appropriate region: Shade the graph depending on the type of inequality. For example, if the inequality is “greater than”, shade the area above the line. If the inequality is “less than”, shade the area below the line.

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To graph a linear inequality of a word problem we take only y on one side of graph before we graph a linear inequality in two variables and then, we take into account associated equation which was created by switching the inequality sign for an equality sign.

What is Linear Inequality ?

Linear Inequality is defined as the Mathematical statement  which shows a relation between two expressions using the inequality symbol.

The expressions on both sides of the inequality sign are not equal. It means that expression on the left-hand side can be greater than(>)  or less than ( < ) the expression on the right-hand side or vice versa.

So , to graph the inequality involving  two variable x and y , we first take the variable y on one side of the graph , then, we take into account associated equation which was created by switching the inequality sign for an equality sign.  , and after that we graph the inequality .

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%lf format specifier is used to output values of type float or double.

All format specifiers are %. The type of data that must be provided as input and the data type that needs to be displayed on the screen are both specified by format specifiers to the compiler.

Operations involving input-output (I/O) use format specifiers. The compiler can identify the type of data in an I/O operation with the aid of a format specifier.

The format specifier is impacted by some factors. The list is as follows:

A (-) indicates left alignment.

The minimum field width is indicated by the number after %. The string will be filled with gaps if it is shorter than the width.

Separate field width and precision using a period (.).

The %f format specifier is used to output values of type float, upto second decimal position, but typically in C %lf can print a long float or a double.

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Answer:

q = 6r + 16

r = q/6 - 8/3

Step-by-step explanation:

Make q independent:

q - 10 = 6r + 6

q = 6r + 16

Make r independent:

q - 16 = 6r

(q - 16) / 6 = r

r = q/6 - 8/3

The probability that the product of any two distinct members of the set is a multiple of 196 is 0.2857.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

If two distinct members of the set { 2, 4, 12, 14, 21, 28, 98 } are randomly selected and multiplied, then the total number of possible outcomes is:

7C2 = 21

Counting all the possible pairs of numbers whose product is a multiple of 196, there are 6 possible ways.

(98 x 4) , (98 x 12) , (98 x 14) , (98 x 28) , (28 x 14) , (28 x 21)

Solve for the probability.

p = 6 / 21 = 0.2857

Therefore, the probability is 0.2857.

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Answer:

209,32°F should be the right answer

Answer:

b = -.0018a + 214

Step-by-step explanation:

b = -.0018a + 214

b = -.0018(2600) + 214

b = -4.68 + 214

b = 209.32

The amount of flour needed would be 2 cups.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

Let the quantity of the required flour would be x cup

As per the given information, we can write the proportion would be as:

1 1/2 dozen cookies : 1 cup flour =  3 dozen cookies : x cup flour

⇒ (1 1/2) / 1 = 3/x

⇒ (3/2) / 1 = 3/x

⇒ 3/2 = 3/x

Apply the cross-multiplication operation,

⇒ x = 6/3

Apply the division operation, and we get

⇒ x = 2

Thus, the quantity of the required flour would be 2 cups.

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The solution of the given function using Laplace transform the required solution is, L{F(s)}= [tex]\frac{1}{s^{2} } e^{-s}[/tex]

Given data,

F(s): L{(t-1)u(t-1)}

Where L is the Laplace transformation

Laplace transform is the integral transform of the given derivative function with real variable t to convert into a complex function with variable s. For t ≥ 0, let f(t) be given and assume the function satisfies certain conditions to be stated later on.

F(s) = [tex]\int\limits^\alpha _0 {f(t)} e^{-st} t^{l} \,[/tex]

Where,

s = σ + [tex]iw[/tex]

F(s) = Laplace transform

s = complex number

t = real number >=0

[tex]t^{l}[/tex] = first derivative of the function f(t)

The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra.

So,

We can write,

F(s): L{(t-1)u(t-1)}

F(s) = [tex]\int\limits^\alpha _0 {f(t)} e^{-st} t^{l} \,[/tex]

F(s) = [tex]\int\limits^\alpha _0 {(t-1)u(t-1)} e^{-st} \, dt[/tex]

F(s) =  [tex]e^{-s} (\frac{1}{s^{2} } )[/tex]

F(s) = [tex]\frac{1}{s^{2} } e^{-s}[/tex]

Therefore,

The solution of the given function using Laplace transform the required solution is, L{F(s)}= [tex]\frac{1}{s^{2} } e^{-s}[/tex]

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Answer:

Step-by-step explanation:

The inequality that depicts the number of apples and pears that may be purchased for no more than $2 is as follows:

0.5x + 0.85y <= 2

The total cost of purchasing x apples and y pears, where each apple costs $0.50 and each pear costs $0.85, must be less than or equal to $2, according to this inequality.

Elizabeth should calculate the compound interest and adjust her payments to cover the total amount.

In order for Elizabeth to responsibly pay off her bill sooner, she should calculate the compound interest on her balance and adjust her payments accordingly. Compound interest is calculated by multiplying the principal amount (original amount borrowed) by one plus the annual interest rate to the power of the number of periods. The formula is:

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

Where A is the total amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

For example, if the original amount is $500 and the annual interest rate is 10%, with the interest compounded monthly, the formula would be:

A = 500(1 + 10/12)^(12*5)

A = 500(1.0083)^60

A = 500(2.92)

A = $1460

To pay the balance off sooner, Elizabeth should calculate the compound interest and adjust her payments to cover the total amount. If Elizabeth pays $50 each month, it will take her approximately one year and three months to pay off her balance.

This is a much more responsible way of paying off her credit card bill than just making the minimum payment of $45 each month, which would take her five years to pay off her balance. Making the minimum payment would also mean that Elizabeth would end up paying a lot more interest in the long run.

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Answer:

Step-by-step explanation:

use the point-slope form of the equation if a straight line:

Y - y1 = m(x - x1)

Y - 1 = F(x - 5)

Y = Fx - 5F + 1

25, 2 digit even numbers can be formed from the digits 1,2 3 4 5 if the digits can be repeated

With the possibility of repeating digits, the answer is actually quite simple. All you need to do is multiply the total number of digits (5) by the total number of digits (5) to get 25.

This means that there are a total of 25 two-digit even numbers that can be formed using the given digits. The even numbers that can be formed are: 22, 24, 26, 28, 32, 34, 36, 38, 42, 44, 46, 48, 52, 54, 56, 58, 62, 64, 66, 68, 72, 74, 76, 78, and 82.

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The required x-intercept of line 4x + 2y ≥ 14 is (3.5, 0).

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.

The x-intercept of a line is the point at which the line crosses the x-axis.

To determine the x-intercept of line 4x + 2y ≥ 14, we need to set y equal to 0 and solve for x.

When y = 0, the inequality becomes 4x ≥ 14.

Dividing both sides by 4 gives x ≥ 14/4, or x ≥ 3.5.

So, the x-intercept of line 4x + 2y ≥ 14 is (3.5, 0).

It's the point where the line crosses the x-axis and the y-value is 0.

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The possible data in the question does not provide sufficient evidence available to support the alternative hypothesis that there is a difference between Mr. Starnes and Ms. McGrail's AP Statistics classes and Mr. Starnes did not stack the class.

In statistics, a hypothesis test is the performance of a test on an assumption made about a population parameter.

The possible data in the question, obtained from a similar online question, using MS Excel, indicates;

The mean of the Starnes GPA ≈ 3.212867

The standard deviation of Starnes GPA ≈ 0.364249

Mean of McGrail GPA ≈ 3.134722

The standard deviation of McGrail's GPA ≈ 0.357995

The null hypothesis is H₀: μ₁ - μ₂ = 0

The alternative hypothesis is Hₐ: μ₁ - μ₂ ≠ 0

The test statistic is found using the following formula;

[tex]t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } }[/tex]

The decision rule is obtained with α = 0.05 and the null hypothesis is rejected t₀ ≤ -1.96 or t₀ ≥ 1.96

Therefore, we get;

[tex]t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{\dfrac{0.364249^2}{15}+\dfrac{0.357995^2}{18} } } \approx 0.618[/tex]

The parameter for the degrees of freedom is 15 - 1 = 14

The critical value obtained from the t-table, at t.₉₅ is 1.761 which is larger than 0.618, therefore, we fail to reject the null hypothesis, and the evidence is insufficient to suggest that there is a difference in the average score of the two AP Statistics classes.

Taking the variance to be the same, we get;

[tex]S_p^2= \dfrac{(n_1-1)\cdot s_1^2+(n_2-1)\cdot s_2^2}{n_1+n_2-2}[/tex]

Therefore;

[tex]S_p^2= \dfrac{(15-1)\times 0.364249^2+(18-1)\times 0.357995^2}{15+18-2}\approx 0.1302[/tex]

[tex]t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{s_p^2 \times\left(\dfrac{1}{n_1}+\dfrac{1}{n_2} }\right) }[/tex]

[tex]t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{0.1302\times \left(\dfrac{1}{15}+\dfrac{1}{18} }\right) } \approx 0.6195[/tex]

df = 15 + 18 - 2 = 31

From the t-table, the critical value is about 1.697, which is larger than 0.6195, therefore, the null hypothesis cannot be rejected and the evidence available is not enough to suggest that there is a difference between the grade point averages of Mr. Starnes and Ms. McGrail AP Statistics classes and Mr. Starnes did not stack the class

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The true statements about Initial Me and Monogram Mania are,

The two companies will cost the same if 130 T-shirts are purchased.

Initial Me charges $8 per T-shirt printed.

Monogram Mania charges less per T-shirt printed than Initial Me charges.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

By observing the graph we conclude the two companies will cost the same if 130 T-shirts are purchased as their individual graphs intersect each other.

The initial fee charged by Initial Me is $50 as the graph of Initial me is at $50 when the number of T-shirts purchased is zero.

Pratik should choose Initial Me for purchasing upto 130 T-Shirts after that

Monogram Mania cost less.

Initial me charges $8 per T-Shirt as the initial fee and the cost of 5 T-shirts is $90 of which $50 is the initial fee, Therefore $(90 - 50) = $40.

The cost of 10 T-shirts at Monogram Mania is $5 so it does cost less than Initial me.

The initial fee charged by Monogram Mania is $50.

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The statement that, to be conservative,  an under-estimate should be used, is True.

A conservative estimate is a prediction or projection that is intentionally lower than what is expected or believed to be the actual outcome. This type of estimate is often used in financial planning or decision-making in order to be more cautious and avoid potential risks or disappointments.

Conservative estimates are based on the idea that it is better to be overly cautious and prepare for the worst-case scenario than to be overly optimistic and potentially be caught off guard.

This means that if McKyla wants a conservative budget, the wages should be put at the lower amount of $ 2, 400.

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The result upon evaluation of the expression given; -67 / 50 + 1.5 - 100% as required to be determined is; -0.84.

It follows from the task content that the result of the expression evaluation is required to be determined.

Since the given expression is;

-67 / 50 + 1.5 - 100%

First, it is important to know that I'm the context of percentages; a% simply means; a / 100.

Therefore; 100% = 100 / 100 = 1.

Therefore, the resulting expression is;

-67 / 50 + 1.5 - 1

= -1.34 + 1.5 - 1

= -2.34 + 1.5

= -0.84

On this note, the required exact decimal which is the equivalent of the given expression is; -0.84.

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