(10 Points) Let X and Y be identically distributed independent random variables such that the moment generating function of X + Y is Mx+y(t) = 0.09e^-2t + 0.24e^t + 0.34 + 0.24e^t + 0.09e^2t, -oo < t < oo.
Compute the probability P(X ≤ 0)

Yes, the Mean Value Theorem can be applied to f on the closed interval [1,9]. To determine if the Mean Value Theorem can be applied to the function f(x) = (x - 10)/x on the closed interval [a, b] = [1, 9], we need to check if the function is continuous on the interval and differentiable on the open interval (a, b) = (1, 9).

1. Continuity: The function f(x) = (x - 10)/x is continuous for all x ≠ 0. Since the interval [1, 9] does not include x = 0, the function is continuous on this interval.

2. Differentiability: To check differentiability, we need to find the derivative of f(x). The derivative of f(x) = (x - 10)/x can be found using the Quotient Rule:

f'(x) = [(1)(x) - (x - 10)(1)]/(x^2) = [x - (x - 10)]/(x^2) = 10/x^2

Since the derivative exists for all x ≠ 0 and the interval (1, 9) does not include x = 0, the function is differentiable on this open interval.

Therefore, the Mean Value Theorem can be applied to the function f(x) = (x - 10)/x on the closed interval [1, 9].

Your answer: Yes, the Mean Value Theorem can be applied.

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The list of the temperature from coldest to warmest temperature includes:

The temperatures (Fahrenheit) of the 4 cities from coldest to warmest includes -9 degrees, -7 degrees, -6 degrees, 5 degrees and 12 degrees.

The coldest temperature is -9 degrees, followed by -7 degrees, then -6 degrees. The positive temperature is  5 degrees and 12 degrees.

We must note these temperatures are in Fahrenheit which is not the standard unit of measurement used in all countries, so, we must specify the unit when reporting temperatures.

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Simulation is a method that uses repeated random sampling of values in order to represent uncertainty in a model that represents a real system and computes the values of model outputs. The given statement is True.

Simulation is a powerful method that is widely used to model real-world systems, particularly those that are complex, uncertain, or have many variables. The main idea behind simulation is to create a computer model that represents the real system, and then use random sampling to generate values for the input variables of the model. These values are used to compute the values of the model outputs, which represent the behavior or performance of the system under different scenarios or conditions.

The key advantage of simulation is that it allows researchers to explore the behavior of a system under different conditions, without actually having to run experiments or collect data from the real system. This can save time, money, and resources, while also providing valuable insights into the behavior of the system. Simulation is used in many different fields, including engineering, finance, healthcare, and environmental science, among others.

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The number 36 should be placed in the blank space. So, Multiplying by 1. 36 is the same as increasing by 36 percent from a decimal number.

The decimal system has a base of ten . These numbers are generally represented by the dot "." between the digits called "decimal point". We can express an integer as a decimal by putting a decimal point after the digit in one's place and writing 0 onwards. The term "percent" is a number or ratio that represents a fraction of 100. Steps to convert decimal to Percent :

We have to fill up a blank space with a number. We have a decimal number 1.36. From above discussion, we need to convert this decimal value into a percent : 0.36 × 100 = 36% So, multiplying by 1.36 is the same as increasing by 36%. Hence, required value is 36.

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Number of the Great Danes that weigh less than 126.6 lbs is: 428 people

The formula for z-score here is:

z = (x' - μ)/σ

Where:

x' is sample mean

μ is population mean

σ is standard deviation

We are given:

x' = 126.6 lbs

μ = 133 lbs

σ = 6.4 lb.

Thus:

z = (126.6 - 133)/6.4

z = -1

We are looking for P(X > 126.6)

Thus, from z-score table, we have:

p-value = 0.1587

Thus:

Number of the Great Danes that weigh less than 126.6 lbs is:

0.1587 * 2700 = 428 people

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Answer: 384

Step-by-step explanation:

you would find the volume and then divide by 2

If point A is located at (-5, 8) and point C is located at (8, -2), the x-coordinate of point B is 29.375.

First, we need to find the coordinates of point B. We can use the ratio of AB to BC to find the distance from A to B and from B to C:

Let the distance from A to B be 3x, and the distance from B to C be 2x.

Then we can use the distance formula to find the coordinates of point B:

x-coordinate of B = x-coordinate of A + (distance from A to B)

x-coordinate of B = -5 + 3x

To find x, we need to solve for x given that B lies on the line segment AC.

The slope of the line segment AC is:

m = (y2 - y1) / (x2 - x1) = (-2 - 8) / (8 - (-5)) = -10 / 13

The equation of the line segment AC is:

y - y1 = m(x - x1)

Substituting in the values we know:

y - 8 = (-10 / 13)(x + 5)

Simplifying:

y = (-10 / 13)x - 250 / 13 + 104 / 13

y = (-10 / 13)x - 146 / 13

Since point B lies on the line segment AC, we can substitute the x-coordinate of B and solve for y:

y = (-10 / 13)(-5 + 3x) - 146 / 13

Now we have a system of equations:

y = (-10 / 13)(-5 + 3x) - 146 / 13

y = (2 / 3)x + 38 / 3

We can solve for x by setting the two expressions for y equal to each other:

(-10 / 13)(-5 + 3x) - 146 / 13 = (2 / 3)x + 38 / 3

Multiplying both sides by 39 to get rid of the fractions:

-30(5 - 3x) - 146 = 26x + 494

Expanding and simplifying:

-150 + 90x - 146 = 26x + 494

Subtracting 26x and adding 296 to both sides:

64x = 840

Dividing by 64:

x = 13.125

Therefore, the x-coordinate of point B is:

x-coordinate of B = -5 + 3x

x-coordinate of B = -5 + 3(13.125)

x-coordinate of B = 29.375 (rounded to the nearest tenth)

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The median of the data is 6.

Looking at the box plot you provided, we can see that it's divided into four sections, or quartiles. The median, or the middle value of the data, is represented by the line that divides the box in half.

To find the median number of books read by the students, we need to look at the box plot and identify the median line. Then we can follow that line until it intersects with the y-axis, which represents the number of books read. The value at that point is the median number of books read by the students.

By looking through the box plot we have identified that te median is 6.

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The approximate value of yz is 13.85641.

We can simplify the expression for yz by using the fact that the square root of a product is equal to the product of the square roots:

yz = √24 × √80

yz = √(24×80) (using the property of square root of product)

yz = √(1920)

we can simplify √(1920) by factoring out perfect squares.

First, we note that 1920 is divisible by 16,

so we can write:

√(1920) = √(16×120)

Next, we note that 1920 is divisible by 16,

so we can write:

√(16120) = √(164×30)

               = √(16×4)×√30

               = 8√30

Therefore, yz is approximately 8√30.

To get a numerical approximation, we can use a calculator or a tool such as Wolfram Alpha to get:

yz = 13.85641 (rounded to 5 decimal places).

Therefore, the approximate value of yz is 13.85641.

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Based on the table, it is clear that the larger the size of the

section, the more plants grew. This is supported by the fact

that section2, which had the largest size of 125 square feet,

had the highest number of plants with 38. Section 1 had the

smallest size with only 25 square feet and the lowest number

of plants with only 13. However, itis important to note that the

number of plants can also be affected by other factors such

as the quality of soil, amount of water and sunlight given

to each section, and the type of seeds planted. It would be

beneficial for the scientist to consider these factors in future

experiments to obtain more accurate and reliable results.

If the French club is sponsoring a bake sale to raise at least $395. The number of  pastries they must they sell at $2.35 each in order to reach their goal  is: D. at least 168.

Set up an equation:

Total amount raised =Number of pastries x Price per pastry

Let x represent the number of pastries:

x × $2.35 = $395

To solve for x we need to isolate it on one side of the equation

x = $395 / $2.35

x = 168

Based on the above calculation the French club must sell at least 168 pastries to raise at least $395.

Therefore the correct option is D.

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Thus, [tex]$1,5$[/tex] are linearly independent over [tex]$\mathbb{Q}$[/tex], which implies that [tex]$\mathbb{Q}(5) = \mathbb{Q}[5]$[/tex].

(a) Since [tex]$5 = e^{2i/3}$[/tex], we have [tex]$5^3 = e^{2i} = 1$[/tex]. Thus, [tex]$5$[/tex] is a root of the polynomial [tex]$p(x) = x^3 - 1$[/tex]. Moreover, [tex]$p(5) = 5^3 - 1 = 124 \neq 0$[/tex], which implies that $p(x)$ is the minimal polynomial of [tex]$5$[/tex] over [tex]$\mathbb{Q}$[/tex]. Therefore, [tex]${1, 5, 5^2}$[/tex] is a basis for [tex]$\mathbb{Q}[5]$[/tex] as a vector space over [tex]$\mathbb{Q}$[/tex]. Any element of [tex]$\mathbb{Q}[5]$[/tex] can be written in the form [tex]$a+ b5 + c5^2$[/tex] for some [tex]$a,b,c \in \mathbb{Q}$[/tex]. Thus, [tex]$Q[S] = {a+b5|a,b \in Q}$[/tex].

(b) Let [tex]$a+b5, c+d5 \in \mathbb{Q}(5)$[/tex]. Then, [tex]$(a+b5)+(c+d5) = (a+c) + (b+d)5 \in \mathbb{Q}(5)$[/tex] and [tex]$(a+b5)(c+d5) = ac + (ad+bc)5 + bd5^2 = (ac-bd) + (ad+bc)5 \in \mathbb{Q}(5)$[/tex]. Therefore, [tex]$\mathbb{Q}(5)$[/tex] is a subfield of [tex]$\mathbb{C}$[/tex] containing [tex]$\mathbb{Q}$[/tex]. To show that [tex]$\mathbb{Q}(5) = \mathbb{Q}[5]$[/tex], it suffices to show that [tex]$1,5$[/tex] are linearly independent over [tex]$\mathbb{Q}$[/tex].

Suppose [tex]$a+ b5 = 0$[/tex] for some[tex]$a,b \in \mathbb{Q}$[/tex], not both zero. Then, [tex]$b \neq 0$[/tex] and we have [tex]$5 = -a/b \in \mathbb{Q}$[/tex], a contradiction. Thus, [tex]$1,5$[/tex] are linearly independent over [tex]$\mathbb{Q}$[/tex], which implies that [tex]$\mathbb{Q}(5) = \mathbb{Q}[5]$[/tex].

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The vertices that could represent the other three vertices of the rectangle are (6, 4), (0, 2), and (6, 2)

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

Vertex = (0, 4)

The rectangle has at least one side with a length of 6 units

So, we have

Possible vertices = (6, 4), (0, 2), and (6, 2)

In the above vertices, we have

Lengths = 6 units and 2 units

Hence, the vertices that could represent the other three vertices of the rectangle are (6, 4), (0, 2), and (6, 2)

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More than 30 cans of food will be needed for 4 adults for 7 days. To find the number of cans needed for 4 adults for 7 days, given that 15 cans of food are needed for 7 adults for 2 days, we can follow these steps:

1. Determine the number of cans needed for 1 adult for 2 days: Divide the total number of cans (15) by the number of adults (7).
  15 cans / 7 adults = 2.14 cans per adult for 2 days (approximately)

2. Determine the number of cans needed for 1 adult for 7 days: Multiply the cans needed for 1 adult for 2 days by 3.5 (since 7 days is 3.5 times longer than 2 days).
  2.14 cans * 3.5 = 7.49 cans per adult for 7 days (approximately)

3. Determine the number of cans needed for 4 adults for 7 days: Multiply the cans needed for 1 adult for 7 days by the number of adults (4).
  7.49 cans * 4 adults = 29.96 cans

Since you cannot have a fraction of a can, round up to the nearest whole number. Thus, you would need 30 cans of food for 4 adults for 7 days.

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The quadratic function is f(x)= x²+1-6

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

If f(x) = y, a quadratic equation is written as;

y = ax²+bx+c

if alpha and beta are the roots of a quadratic equation when y = 0, the the equation of the quadratic is formed by the formula;

x²-(alpha+beta) x + alpha × beta

alpha = -3

beta = 2

alpha × beta = -3×2 = -6

alpha +beta = -3+2 = -1

Therefore the quadratic function = x²-(-1) +(-6)

f(x)= x²+1-6

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The difference in minutes between 55 minutes and 1 3/4 hours is 50 minutes.

We have,

To convert 1 3/4 hours to minutes, we can multiply it by 60 (since there are 60 minutes in an hour):

So,

1 3/4 hours

= (1 x 60) + (3/4 x 60)

= 60 + 45

= 105 minutes

Now we can find the difference between 105 minutes and 55 minutes:

= 105 minutes - 55 minutes

= 50 minutes

Therefore,

The difference in minutes between 55 minutes and 1 3/4 hours is 50 minutes.

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Answer:

At Marco Market, a chewy toy costs $2 and a cat collar costs $6. Meanwhile, at Sonia Superstore, a chewy toy for dogs costs $4 and a cat collar costs $4. To represent the quantities of each item that can be purchased at each store, an equation can be used.

Step-by-step explanation:

At Marco Market, a chewy toy costs $2 and a cat collar costs $6. Meanwhile, at Sonia Superstore, a chewy toy for dogs costs $4 and a cat collar costs $4. To represent the quantities of each item that can be purchased at each store, an equation can be used.

The probability of spinning a 3 and flipping heads is 1/8.

Given that, sample space of spinner is {1, 2, 3, 4}

Sample space of flipping the coin {Heads, Tails}

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Probability of spinning a 3 = 1/4

Probability of flipping heads = 1/2

Probability of an event = 1/4 × 1/2

= 1/8

Therefore, the probability of spinning a 3 and flipping heads is 1/8.

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There are several factors that can decrease the supply of U.S. dollars in the foreign exchange market. One of the most significant factor is a decrease in U.S. exports.

When a country's exports decrease, it means that there is less demand for its currency, which can lead to a decrease in the supply of that currency in the foreign exchange market.

Another factor that can decrease the supply of U.S. dollars is a decrease in foreign investment in the U.S. When foreign investors exchange their U.S. dollars for their own currency, it can reduce the supply of U.S. dollars in the market.

Furthermore, a decrease in the U.S. trade deficit can also decrease the supply of U.S. dollars in the foreign exchange market. When the U.S. imports less than it exports, there is less demand for U.S. dollars to purchase foreign goods and services, which can lead to a decrease in the supply of U.S. dollars.

In conclusion, factors such as a decrease in exports, foreign investment, and trade deficits can all lead to a decrease in the supply of U.S. dollars in the foreign exchange market.

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The probability that the first card will be a club, the second card will be a black card, and the third card will be an ace is 1/104.

There are 13 clubs, 26 black cards (13 clubs and 13 spades), and 4 aces in a standard deck of cards. Since the cards are drawn with replacement, the probability of drawing a club on the first draw is 13/52 = 1/4. The probability of drawing a black card on the second draw is 26/52 = 1/2, and the probability of drawing an ace on the third draw is 4/52 = 1/13.

By the multiplication rule of probability, the probability of all three events occurring together is the product of their individual probabilities:

P(club, black, ace) = P(club) × P(black) × P(ace)

= (1/4) × (1/2) × (1/13)

= 1/104

Therefore, the probability that the first card will be a club, the second card will be a black card, and the third card will be an ace is 1/104.

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Answer:

es el grande 63poe que tienes mas

The probability of making a Type II error (i.e., failing to reject the null hypothesis when the true proportion is actually 0.25) is 0.0104.

What is error?

An error is the difference between a true value and an estimated or approximate representation of that value in applied mathematics. A truncation error occurs when an infinite series is ignored for all but a small number of terms. power 1 P (type II error)

In this case, if the market share in Ontario is actually 0.22, the probability that 90 or fewer Hewlett-Packard computers will be observed out of 427 randomly selected purchases is quite small. The probability of 90 or fewer successes for a binomial distribution with n = 427 and p = 0.22 is approximately 0.219, or 21.9%.

Therefore, the probability of making a Type II error (ie, failing to reject the null hypothesis incorrectly) is approximately 78.1%. This means that if Hewlett-Packard's market share in Ontario is actually 0.22, it is still relatively high. the possibility that the market researcher's test fails to detect this difference and incorrectly concludes that their market share does not exceed 0.198.

Therefore, the probability of a Type II error (ie, failing to reject the null hypothesis when the true proportion is actually 0.25) is 0.0104.

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The study you mentioned investigated the effect of dim light at night on weight gain in mice. The results showed that mice exposed to dim light during nighttime had increased body weight compared to those in complete darkness. The 95% confidence interval helps us understand the reliability of these results.

A 95% confidence interval means that if the study were to be repeated 100 times, 95 of those repetitions would yield results within the interval range. This interval provides a range of plausible values for the true difference in weight gain between mice exposed to dim light and those in complete darkness. A smaller interval suggests more precise results, while a larger interval indicates more variability in the data.

To interpret the study, follow these steps:

1. Identify the confidence interval values: Find the range of values provided by the 95% confidence interval.
2. Evaluate the interval: Determine if the interval is relatively small, indicating precise results, or large, suggesting more variability.
3. Check for significance: If the interval does not include zero, the difference in weight gain between the two groups is statistically significant.
4. Draw conclusions: Based on the confidence interval, conclude whether the study provides strong evidence that dim light at night leads to increased weight gain in mice.

In conclusion, the study found that mice exposed to dim light at night experienced more significant weight gain than those in complete darkness, with a 95% confidence interval supporting the reliability of the results. This finding suggests that exposure to dim light at night may have an impact on body weight, at least in the studied population of mice.

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The reference angle for -400 is 5.729 degrees.

We have,

To find the reference angle for -400, we need to find the acute angle formed by the terminal side of the angle and the x-axis.

We start by drawing the angle in the standard position, which means placing the initial side of the angle along the positive x-axis and rotating the terminal side in the clockwise direction.

Since -400 is in the fourth quadrant, the terminal side of the angle would lie 400 units clockwise from the negative x-axis.

To find the reference angle, we need to find the acute angle formed by the terminal side and the x-axis.

This is simply the angle formed by the terminal side and a perpendicular line dropped from the endpoint of the terminal side to the x-axis.

In this case, the perpendicular line would drop 40 units to the x-axis, forming a right triangle with legs of 40 and 400 units.

Using the Pythagorean theorem, we can find the hypotenuse of this right triangle, which is the distance from the origin to the endpoint of the terminal side:

h = √(40² + 400²) = 404

The sine of the reference angle is the ratio of the opposite leg to the hypotenuse:

sin Ф = opposite/hypotenuse = 40/404 = 0.099

Taking the inverse sine of this value, we can find the reference angle:

Ф = [tex]Sin^{-1}[/tex](0.099) = 5.729 degrees

Therefore,

The reference angle for -400 is 5.729 degrees.

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Answer:

The probability of selecting a pen from the first box is 3/4, and the probability of selecting a crayon from the second box is 5/10 or 1/2.

To find the probability of both events occurring together, we multiply the probabilities:

(3/4) × (1/2) = 3/8

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 3/8.

Step-by-step explanation:

Answer:

There are 4 items in the first box and 10 items in the second box, so there are 4 x 10 = 40 possible combinations of one item from each box.

The probability of selecting a pen from the first box is 3/4, since 3 of the 4 items in the first box are pens. The probability of selecting a crayon from the second box is 5/10 or 1/2, since there are 5 crayons in the second box out of 10 total items.

To find the probability of selecting a pen from the first box and a crayon from the second box, we need to multiply the probabilities of the two events:

P(pen from first box and crayon from second box) = P(pen from first box) * P(crayon from second box)

P(pen from first box and crayon from second box) = (3/4) * (1/2)

P(pen from first box and crayon from second box) = 3/8

Therefore, the probability that a pen from the first box and a crayon from the second box are selected is 3/8.

C. Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the median. Add "whiskers" extending to the low and high values.

Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the median. Add "whiskers" extending to the low and high values. Quartiles are three values ​​that divide the statistical data into four parts, each containing the same observation. A quarter is a type of quantity. First quartile: Also called Q1 or lower quartile. Second quartile: Also called Q2 or median. Third quarter: Also called Q3 or upper quarter.

Quartiles are values ​​that divide a list of numeric data into quarters. The three-quarter median measures the center of the distribution and shows the data near the center. The lower half of the quartile represents only half of the dataset below the median, and the upper half represents the remaining half above the median. In summary, quartiles describe the distribution or distribution of a data set.

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The given statement, "You can infer statistical significance from a 95% CI. "A 95% CI gives you information about the precision of the association." and "A study with a small sample will have a wider 95% CI." are true and "A 95% CI gives you information about the precision of the association, but not the strength of the association." is false.

The statement You can infer statistical significance from a 95% CI is true, as it is a measure of the precision of the association between two variables.

A 95% CI will be wider for a study with a smaller sample size, but this does not necessarily indicate a weaker association. In other words, the width of a 95% CI does not indicate the strength of the association, and so the statement that A 95% CI gives you information about the precision of the association, but not the strength of the association is false.

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Full Question ;

Identify the true and false statements about 95% confidence intervals.

- You can infer statistical significance from a 95% CI.

- A 95% CI gives you information about the precision of the association.

- A study with a small sample will have a wider 95% CI.

-A 95% CI gives you information about the strength of the association.

Answer:

Step-by-step explanation:

300

in sequare

Answer: 3060 in³

Step-by-step explanation:

Volume is how much a shape can hold.  It's a 3 dimensional measurement so you need to multiply 3 dimensions

V= length x width x height

Sometimes students get confused with which is which side but it really doesn't matter because multiplication is commutative meaning you can switch it and it doesn't matter.  Like  5x2 is the same thing as 2x5  both will still be 10

length=15

width=12

height= 17

If Volume = length x width x height

=15 x 12 x 17 =  =3060

Because it's 3 dimensional, units are are cubed as well. but questions says no units

Answer:

[tex]\large \boxed{\boxed{\textsf{$(x+2)(x-4)$}}}[/tex]

[tex]\boxed{\boxed{\large \textsf{$x=-2, x=4$}}}[/tex]

This is a quadratic expression, in the form:

[tex]\boxed{\large \textsf{$ ax^2+bx+c$, where$\ a \neq 0$}}[/tex]

To factorise this expression, we will need to have 4 terms. Currently there are only 3. To do this, we need to find 2 integers, that add together to form the middle term, -2, and multiply together to form the constant term, -8.

[tex]\large \textsf{the 2 integers $\Rightarrow$ 2 and -4}\\ \textsf{$-4+2 = -2$\ (coefficient of middle term)}\\ \textsf{$-4 \times 2=-8$\ (constant term)}[/tex]

Now we can split the middle term into 2 terms, using the integers we just found:

[tex]\large \textsf{$x^2+2x-4x-8$}[/tex]

Now we can factorise this.

[tex]\large \textsf{Group each pair of terms together, and take out a common factor.}\\ \\ \large \textsf{$x(x+2)-4(x+2)$}\\ \\ \large \textsf{Now take out the common factor from the expression: (x+2)} \\ \\ \large \textsf{$(x+2)(x-4)$}[/tex]

This leaves us with our fully factorised expression:

[tex]\large \boxed{\boxed{\textsf{$(x+2)(x-4)$}}}[/tex]

To solve the quadratic expression, we can make it equal to zero:

[tex]\large \textsf{$x^2-2x-8=0$}[/tex]

Primarily, to solve this, we can used the factorised form from above, and apply the zero-product property.

The zero-product property states that:[tex]\large \textsf{If $a\times b=0$, then $a=0$ or $b=0$ (or both $a=0$ AND b=0)}[/tex]

[tex]\large \textsf{$\therefore$ if $(x+2)(x-4)=0$, then $(x+2)=0$, and/or $(x-4)=0$ }[/tex]

[tex]\large \textsf{$\implies \boxed{\boxed{x=-2, x=4}}$ }[/tex]

Similarly, we can also use the quadratic formula to solve this equation:

[tex]\boxed{\Large \textsf{$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$} \large \textsf{, for $ax^2+bx+c=0$}}[/tex]

[tex]\large \textsf{$\Rightarrow a=1, b=-2, c=-8$}\\ \\ \Large \textsf{$x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-8)}}{2(1)}$}\\ \\ \boxed{\boxed{\large \textsf{$\therefore x=4, x=-2$}}}[/tex]

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