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The dimensions of the rectangular page (in inches)  to be use the least amount of paper will be 8.37 inch and 4.18 inch.

A Rectangular shape is a four sided-polygon, having all the internal angles equal to 90 degrees or one right angle. The two sides at each corner meet at right angles. The opposite sides of the rectangle are equal in length.

Let, x width of the rectangular area that is to be printed

y height of the area that is to be printed.

Given that A rectangular page contains 35 square inches of print.

so  xy= 35 a constant-------------(1)[ by the formula of rectangular area]

we want to minimize.

f(x, y) = (x+4)(y+2)

        = xy+4y+2x+8

        = 35+8+4y+2x [putting the value from equation (1)]

       = 43+4y+2x

We have to minimize the function

   g(x, y)= 4y+2x

            = 4(35/x)+ 2x

            = 140/x+2x

Let us take h(x)= 140/x+2x

                  h'(x)= d/dx( 140/x+2x)

                          = -140/x² + 2

For minimum value we will take h'(x)=0

                           -140/x² + 2=0

                           ⇒2x² =140

                            ⇒x² =70

                            ⇒x= √70=8.37

y =35/√70= 4.18

Hence, the dimensions of the page (in inches) to be use the least amount of paper will be 8.37 inch and 4.18 inch.

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The rate of change (slope) is -2.

To determine if the table of values describes a linear function, we need to check if there is a constant rate of change between any two points.

Using the first two points, we can find the rate of change (slope) as:

slope = (y2 - y1) / (x2 - x1)

         = (8 - 10) / (6 - 5)

         = -2

Using the second two points, we can also find the rate of change as:

slope = (y2 - y1) / (x2 - x1)

       = (6 - 8) / (7 - 6)

       = -2

Since both rates of change are the same, the table of values describes a linear function. The rate of change (slope) is -2.

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This expression can be simplified by using some trigonometric identities12. First, we can use the identity sin(2x) = 2sin(x)cos(x) to rewrite the first term. Then, we can use the identity cos(2x) = cos^2(x) - sin^2(x) to rewrite the fourth term. We get:

sin(x) + 2cos(x) - cos(2x) + cos(x) = 2sin(x)cos(x) + 2cos(x) - (cos^2(x) - sin^2(x)) + cos(x) = 2sin(x)cos(x) + 3cos(x) - cos^2(x) + sin^2(x)

Next, we can use the identity sin^2(x) + cos^2(x) = 1 to simplify the last two terms. We get:

= 2sin(x)cos(x) + 3cos(x) - cos^2(x) + sin^2(x) = 2sin(x)cos(x) + 3cos(x) - cos^2(x) + (1 - cos^2(x)) = 2sin(x)cos(x) + 3cos(x) + 1

This is the simplest form of the expression.

Answer:

[tex] \frac{1}{3} [/tex]

The answer is B

Step-by-step explanation:

There are six outcomes in total (numbers: 1; 2; 3; 4; 5 and 6)

The number she had spinned must be greater than 4 (that means there are two favorable outcomes: 5 and 6)

n = 6

m = 2

[tex]p = \frac{m}{n} = \frac{2}{6} = \frac{1}{3} [/tex]

Answer: the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7)

Step-by-step explanation:

Given a1=38,a17=-74. a17=a1+(n-1)d. =38+(17-1)d. -74=38+16d. -74-38=16d. -112=16d. d= -7. the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7).

Answer: 7

Step-by-step explanation: number adds up by 7

||u|| = 16.492; θ = 165.964°  are the vector magnitude and direction of u.

What is a straightforward definition of a vector?

A quantity or phenomena with both size and direction being independent of one another is called a vector. Also, the phrase specifies how such a quantity is represented mathematically or geometrically. Examples of vectors in nature include weight, force, electromagnetic fields, momentum, and velocity.

Let's find the magnitude of each component:

Let

(x₁,y₁ ) = (4,4)

(x₂ , y₂ ) = (-12 , 8 )

  u = ax + by

 ll u ll = √a² + b²

     So, let's find a and b:

    a = l x₂ - x₁ l =l -12 - 4 l = l -16 l  = 16

    b = l y₂ - y₁ l = l 8 - 4 l = l4l = 4

so,

        ll u ll = √16² + 4²

                = √272

                ≈ 16.492

And the direction is:

     θ = 180 - tan⁻¹ (b/a )

         = 180 - tan⁻¹(4/16)

    θ ≈ 180 - tan⁻¹ (4/16)

       ≈ 165.953.

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To find out how many craft items Chelsea can make, we need to divide the total amount of material she has by the amount of material needed to make one craft item.

First, we need to convert 3 1/3 yards to an improper fraction:

3 1/3 = (3 x 3) + 1 = 10/3 yards

Now we can set up the division:

10/3 yards ÷ 2/3 yards per craft item

To divide fractions, we can multiply by the reciprocal of the second fraction:

10/3 yards x 3/2 yards per craft item = 15/2 or 7.5 craft items

Therefore, Chelsea can make 7.5 craft items with 3 1/3 yards of material. Since she can't make a fraction of a craft item, she could make 7 craft items with some material left over.

First, we multiply the first equation by 5 and the second equation by 7, then subtract the first equation from the second equation to eliminate y. Next, we substitute x = 11/2 into one of the original equations to solve for y. The solution is (x, y) = (11/2, 2). To find the value of y2, we square the value of y.

A mathematical statement known as an equation utilizes the equal symbol (=) to demonstrate the equality of two expressions. A mathematical equation normally consists of constants, variables, and operations such addition, subtraction, multiplication, and division.

To solve this system of equations, we can use the method of elimination.

First, we will multiply the first equation by 5 and the second equation by 7 to get:

10x - 35y = -15

28x - 35y = 84

Now, we can subtract the first equation from the second equation to eliminate y:

28x - 10x - 35y + 35y = 84 - (-15)

18x = 99

x = 99/18 = 11/2

Next, we can substitute x = 11/2 into one of the original equations to solve for y. We'll use the first equation:

2x - 7y = -3

2(11/2) - 7y = -3

11 - 7y = -3

-7y = -14

y = 2

Therefore, the solution to the system of equations is (x, y) = (11/2, 2).

To find the value of y², we simply square the value of y:

y² = 2² = 4

So the value of y² is 4.

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Answer: The GCF of 7, 15, & 21 is 1

Step-by-step explanation: the greatest number that divides all three numbers is 1

The given statement "as the size of a sample increases, the standard deviation of the distribution of sample means increases always." is false. As the sample size increases, the standard deviation of the distribution of sample means decreases, not increases.

This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, as the sample size gets larger, the distribution becomes more concentrated around the population mean, which results in a smaller standard deviation. This is why larger sample sizes are generally preferred in statistical analysis, as they provide more accurate estimates of the population parameters.

So, the given statement is false.

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Answer:

i cant solve what i cant see

Step-by-step explanation:

there is no problem

a) The sample space of randomly selecting 2 lollipops with replacement is {GG, GC, GL, CG, CC, CL, LG, LC, LL}

b) The sample space of randomly selecting 2 lollipops without replacement is {GC, GL, CG, CL, LG, LC}.

c) The experiment in Part B shows dependent events. The experiment in Part A shows independent events.

It is denoted by the symbol "S" and is a fundamental concept in probability theory because it provides a way to describe all the possible outcomes of an experiment or event.

Part A: The sample space of randomly selecting 2 lollipops with replacement is:

{GG, GC, GL, CG, CC, CL, LG, LC, LL}

Part B: The sample space of randomly selecting 2 lollipops without replacement is:

{GC, GL, CG, CL, LG, LC}

Part C: The experiment in Part B shows dependent events because the outcome of the first draw affects the outcome of the second draw. For example, if the first lollipop drawn is grape, then there is only one grape lollipop remaining, which affects the probability of drawing another grape lollipop on the second draw. The experiment in Part A shows independent events because each draw is done with replacement, so the outcome of the first draw does not affect the probability of the second draw. For example, the probability of drawing a grape lollipop on the second draw is the same whether or not a grape lollipop was drawn on the first draw.

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Answer:

Blue

Step-by-step explanation:

i did this before

The probability that the response time exceeds 5 seconds is about 0.2231. The probability that the response time exceeds 10 seconds is about 0.0498. These probabilities are calculated using the CDF of the exponential distribution with mean 3 seconds.

The probability that the response time exceeds 5 seconds can be calculated using the cumulative distribution function (CDF) of the exponential distribution:

P(X > 5) = 1 - P(X ≤ 5) = 1 - F(5)

where F(x) is the CDF of the exponential distribution with mean 3 seconds. The CDF is given by:

F(x) = 1 - e^(-x/3)

Substituting x=5, we get:

P(X > 5) = 1 - F(5) = 1 - (1 - e^(-5/3)) = e^(-5/3) ≈ 0.2231

Therefore, the probability that the response time exceeds 5 seconds is approximately 0.2231.

Using the same method as above, we can calculate the probability that the response time exceeds 10 seconds:

P(X > 10) = 1 - P(X ≤ 10) = 1 - F(10) = 1 - (1 - e^(-10/3)) = e^(-10/3) ≈ 0.0498

Therefore, the probability that the response time exceeds 10 seconds is approximately 0.0498.

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The required probability of rolling a 2 exactly 4 times in 7 rolls of a six-sided die is [tex]\frac{161}{5000}[/tex] in fraction form or approximately 0.03226 as a decimal.

A number that indicates how likely an event is to occur is called its probability. It is expressed as a number between 0 and 1 or as a percentage using percentage notation between 0% and 100%. The higher the probability, the more likely the event is to occur.

[tex]$\begin{aligned} P(X = 4) &= \binom{7}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^3 \\&= \frac{7!}{4!3!} \cdot \frac{1}{6^4} \cdot \frac{5^3}{6^3} \\&= \frac{35 \cdot 125}{6^7} \\&= \frac{4375}{135216} \\&\approx 0.03226\end{aligned}[/tex]

Therefore, the probability of rolling a 2 exactly 4 times in 7 rolls of a six-sided die is [tex]\frac{161}{5000}[/tex] in fraction form or approximately 0.03226 as a decimal.

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Answer please mark as brainliest:

Allstars typically have the tallest players.

Step-by-step explanation:

To determine which team typically has the tallest players, we can compare the measures of center for each team. The measures of center we can use are the mean and median.

Using a calculator or a spreadsheet, we can calculate the mean and median for each team:

Allstars mean: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 67.1 inches

Allstars median: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.

Champs mean: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 66.4 inches

Champs median: arrange the heights in order from smallest to largest: 58, 60, 60, 62, 65, 67, 67, 68, 69, 69, 70, 70, 70, 75. The median is the middle value, which is 67 inches.

Based on the measures of center, we can see that the Allstars have a higher mean and median height than the Champs. Therefore, we can conclude that the Allstars typically have the tallest players.

Therefore , the solution of the given problem of coordinates comes out to be B''' = (-4, -1) and C''' = (-6, 4)

Using a variety of elements or coordinates, a reference frame can precisely determine position when used in conjunction with other mathematical elements on this location, such as Euclidean space. One can find a thing or a location in mirrored flight by using the coordinates of the which appear like collections of numbers. A pair surface is able to be used to locate an item using the y and x coordinates.

Here,

We flip a point across the x-axis while maintaining the y-coordinate to mirror it over the x-axis.

We flip a point across the y-axis while maintaining the x-coordinate to mirror it over the y-axis.

Overlooking the x-axis:

A' = (2, 0) -> A'' = (2, -0) = (2, 0)

B' = (4, 1) -> B'' = (4, -1)

C' = (6, -4) -> C'' = (6, 4)

Considering the y-axis:

A'' = (2, 0) -> A''' = (-2, 0)

B'' = (4, -1) -> B''' = (-4, -1)

C'' = (6, 4) -> C''' = (-6, 4)

As a result, after reflecting A, B, and C over the x-axis and then the y-axis, the finished image is as follows: A''' = (-2, 0)

B''' = (-4, -1)

C''' = (-6, 4)

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a) The probability that in the next eight tries, the number of free throws he will make exactly 8 is equals to the 0.27249.

b) The probability that in the next eight tries, the number of free throws he will make exactly 5 is equals to the 0.08386.

We have a professional basketball player makes 80% of the free throws he tries.

let X be the number of free throws he will make in the next 8 tries. He makes 80% of the free thwors he tries. So, for binomial distribution, X~Bin(8,0.80)

so the probability mass function of X is P[X =x] = ⁸Cₓ 0.85ˣ (1-0.85)⁽⁸⁻ˣ⁾, x = 0,1, 2,..8

P[ X = x] = 0 otherwise.

a) So, the probability that he makes exactly 8 throws isP,(X=8)

= ⁸C₈(0.85)⁸ (1- 0.85)⁰

=0.27249

b) the probability that he makes exactly 5 throws is, P[X=5]

=⁸C₅0.855(1-0.85)⁽⁸⁻³⁾=56×0.855×0.153

=0.08386

Hence required probability is 0.083.

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The appropriate test statistic for the hypothesis being tested and to compare the test statistic to a critical value from a distribution table.

An index that is calculated from sample data and whose value determines whether to accept or reject a null hypothesis is a test statistic.

A test statistic is used to determine the probability of obtaining the observed data under the null hypothesis.

If the test statistic falls within a specified range, the null hypothesis is accepted.

If the test statistic falls outside of the specified range, the null hypothesis is rejected.

The test statistic is calculated from the sample data and is based on the distribution of the sample data.

There are many different types of test statistics, each of which is used to test a different hypothesis.

Some common test statistics include the t-statistic, the F-statistic, and the chi-square statistic.
The t-statistic is used to test the difference between the means of two populations.

The F-statistic is used to test the equality of variances between two populations.

The chi-square statistic is used to test the independence of two categorical variables.
In order to calculate a test statistic, one must first formulate a null hypothesis and an alternative hypothesis.

The null hypothesis is the hypothesis that is assumed to be true, and the alternative hypothesis is the hypothesis that is being tested. The test statistic is then calculated from the sample data, and its value is compared to a critical value from a distribution table.

If the test statistic is greater than or equal to the critical value, the null hypothesis is rejected. If the test statistic is less than the critical value, the null hypothesis is accepted.
In conclusion, a test statistic is an index that is calculated from sample data and is used to determine whether to accept or reject a null hypothesis.

It is important to use the appropriate test statistic for the hypothesis being tested and to compare the test statistic to a critical value from a distribution table.

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5x² - 25x - 30 has a common factor with 4x² - 25x + 6, which is (x - 6).

option C.

To find the common factor of two polynomials, we can use the method of polynomial factorization.

First, let's factor the polynomial 4x² - 25x + 6:

4x² - 25x + 6 = (4x - 1)(x - 6)

Now, let's factor each of the answer choices:

We can see that only choice C has a common factor with 4x² - 25x + 6, which is (x - 6). Therefore, the answer is C.

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The most appropriate representation to show the relationship between the number of chapters and the total pages of a book would be a scatter plot titled "School Library".

with the x-axis labeled "Number of Chapters" ranging from 0 to 20 and the y-axis labeled "Total Pages" ranging from 0 to 275 with points at (3, 18), (4, 38), (5, 45), (8, 85), (10, 76), (12, 145), (13, 138), (14, 160), (16, 180), and (20, 220).

A scatter plot is a graph used to display the relationship between two variables. In this case, the two variables are the number of chapters and the total number of pages in a book. The plot consists of dots, each representing a single data point. The x-axis represents the independent variable, which in this case is the number of chapters. The y-axis represents the dependent variable, which is the total number of pages. By plotting each data point on the graph, it is easier to visualize the relationship between the two variables.

A line graph is not appropriate for this situation because it suggests a continuous relationship between the two variables, which is not the case here. The number of chapters and total pages are discrete variables, and there is no natural order to the data points that would justify connecting them with a line.

The first scatter plot option is not appropriate because it shows the y-axis ranging up to 450, which is much higher than the maximum value of 275 for the total pages in this data set. This exaggerates the differences between the data points and can be misleading.

The chosen scatter plot is appropriate because it clearly shows the relationship between the number of chapters and the total pages of a book. It is easy to see that as the number of chapters increases, the total pages also tend to increase. The scatter plot also helps to identify any outliers or patterns in the data that may not be apparent from just looking at the numbers. It is a visual tool that helps to quickly understand the data and draw conclusions from it.

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This is the original expression x(x + 1) =  [tex]x^{2}[/tex]  + x  that we started with, so we can be confident that our factorization is correct.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

To factorize an expression means to write it as a product of factors. In this case, we want to write [tex]x^{2}[/tex] + x as a product of factors. One way to do this is to look for common factors that we can take out of both terms in the expression.

In this case, the only common factor in both   [tex]x^{2}[/tex]  and x is x itself. Therefore, we can take out an x from both terms to get:

x(x + 1)

This is the fully factorized form of the expression  [tex]x^{2}[/tex]  + x. It shows that  [tex]x^{2}[/tex]  + x can be written as a product of two factors: x and (x + 1).

We can verify that this is correct by multiplying out the two factors:

x(x + 1) =  [tex]x^{2}[/tex]  + x

Therefore, This is the original expression x(x + 1) =  [tex]x^{2}[/tex]  + x  that we started with, so we can be confident that our factorization is correct.

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By answering the presented question, we may conclude that So, the equation python is 176 inches longer than the garter snake.

In mathematics, an equation is a claim that two expressions are equivalent. Two sides that are separated by the algebraic symbol (=) make form an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is the goal of equation solving. Equations can include one or more parts and be straightforward or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. In many different branches of mathematics, including algebra, calculus, and geometry, lines are used.

Let's use "P" to represent the length of the python in inches.

P = 9(22):

P = 198

Therefore, the python is 198 inches long.

198 - 22 = 176

So, the python is 176 inches longer than the garter snake.

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Answer:

Step-by-step explanation:

-9x^2-36x-45

Answer:

----------------------------

The vertex form of a parabola is:

Given equation is:

Hence h = - 2, k = - 4, therefore its vertex is (- 2, - 4).

Given function:

It has a = 1, hence the graph opens up, therefore the function has a minimum.

Answer:

-86

Step-by-step explanation:

Calculate the expression in the brackets:

7 + ( 5 - 92 + 3 x 2 )

Simplify:

7 + ( 5 - 92 + 6 )

7 + ( 5 - 98 )

7 + ( -93 )

7 - 93

-86

Answer: supplementary same side exterior angles

Step-by-step explanation:

The number 357 in binary is 101100101 and x^2 - 3x - 10 when factored is (x - 5)(x + 2). Other solutions are below

The triangle and the loci are attached

(a) To convert 357 to a binary number, we can use the division-by-2 method:

357/2 gives 178 R 1

178/2 gives 89 R 0

89/2 gives 44 R 1

44/2 gives 22 R 0

22/2 gives 11 R 0

11/2 gives 5 R 1

5/2 gives 2R1

2/2 gives 1R0

1/2 gives 0 R 1

Therefore, 357 in binary is 101100101

(b) To factorise x^2 - 3x - 10, we have

x^2 - 3x - 10 = (x - 5)(x + 2)

(c) To solve 5x^2 - 7x + 1 = 0 using completing the square, we have:

x^2 - (7/5)x + 1/5 = 0 -- make the coefficient of x^2 equals 1

So, we have

x^2 - (7/5)x = -1/5

Next, we have

x^2 - (7/5)x + (7/10)^2 = -1/5 + (7/10)^2

Factorize

(x - 7/100)^2 = -1/5 + (7/10)^2

Simplifying the right-hand side, we get:

(x - 7/10)^2 = 29/100

Taking the square root of both sides, we get:

x - 7/10 = ±√29/10

Adding 7/10 to both sides, we get:

x = 7/10 ±√29/10

So, we have

x = 7/10 + √29/10 or x = 7/10 - √29/10

Evaluate

x = 1.24 or x = 0.16

Therefore, the solutions are x = 0.160 and x = 1.24, rounded to 2 decimal places.

(a) To evaluate 102 (mod 4), we divide 102 by 4 and find the remainder:

102 divided by 4 gives a quotient of 25 with a remainder of 2.

Therefore, 102 (mod 4) is 2.

(b) First, we need to find the volume of the bucket. We can do this by treating it as a frustum of a cone:

The radius of the top of the frustum is 10m, the radius of the bottom is 6m, and the height is 16 m.

The volume of a frustum of a cone is given by:

V = (1/3)πh(R^2 + r^2 + Rr),

Plugging in the values, we get:

V = (1/3) * 3.14 * 16 * (10^2 + 6^2 + 10*6)

V = 3282.35 m^3

Finally, we can find the depth of water in the rectangular tin by using the formula for volume:

V = Bh

where B is the area of the base of the tin and h is the height of the water in the tin.

Plugging in the values, we get:

3282.35 m^3 = 48 cm^2 h

So, we have

3282.35 m^3 = 0.0048 m^2 h

Solving for h, we get:

h = 683822.916667 m

Approximate

h = 683822.92 m

Therefore, the depth of water in the tin is 683822.92 m

The area of a sector of a circle is given by:

A = (θ/360)πr^2,

So, we have

300 = (θ/360)

300 = (θ/360) * (22) * 112

Solving for θ, we get:

θ = 300 * 360 * 1/(22 * 112)

θ ≈ 43.83 degrees

The perimeter of the sector is the sum of the arc length and the lengths of the two radii that form the sector.

The arc length is given by:

s = (θ/360)2πr

Plugging in the values, we get:

s = (43.83/360)(2)(22/7)(28)

s ≈ 21.43 cm

The length of each radius is 28 cm. Therefore, the perimeter of the sector is:

P = 2(28) + 21.43

P ≈ 77.43 cm

Therefore, the perimeter of the sector is 77.43 cm, rounded to 2 decimal places.

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Ans:-

[tex] \: [/tex]

Solution:-

[tex]↣ \: \textsf{-5 ( -2 )³ + 8 ( -2 )²}[/tex]

[tex] \: [/tex]

[tex] ↣ \: \textsf{-5 ( -8 ) + 8 ( -4 )}[/tex]

[tex] \: [/tex]

[tex] ↣ \: \textsf{40 + ( -32 ) }[/tex]

[tex] \: [/tex]

[tex] \textsf{[ + , - = - ]}[/tex]

[tex] \: [/tex]

[tex]↣ \: \textsf{40 - 32 }[/tex]

[tex] \: [/tex]

[tex] \underline{ \underline{↣ \textsf \orange{ \: \: 8 \: \: \: }}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps!:)