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True
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Answer:

[tex](x+2)^2-16[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]x^2+4x-12[/tex]

To complete the square, add and subtract the square of half the coefficient of the term in x after the term in x:

[tex]\implies x^2+4x+\left(\dfrac{4}{2}\right)^2-\left(\dfrac{4}{2}\right)^2-12[/tex]

Simplify:

[tex]\implies x^2+4x+\left(2\right)^2-\left(2\right)^2-12[/tex]

[tex]\implies x^2+4x+4-4-12[/tex]

The first three terms form a perfect square trinomial which can be factored:

[tex]\implies \boxed{x^2+4x+4}-4-12[/tex]

[tex]\implies \boxed{(x+2)^2}-4-12[/tex]

Finally, subtract the numbers:

[tex]\implies (x+2)^2-16[/tex]

Answer:

the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units

Answer: It's  much easier to form a rectangle and multiply the width and the length and then divide it by 2  

The probability that the total sum of all rolls does not exceed 375 is approximately 0.7165

Assuming the die is a fair six-sided die, the possible outcomes for each roll are numbers 1 through 6, each with a probability of 1/6.

Let X be the total sum of all rolls. Then X follows a discrete uniform distribution with parameters n = 104 (number of rolls) and a = 1 (minimum value of each roll). The expected value of X is:

E(X) = n × (a + b) / 2 = 104 × (1 + 6) / 2 = 365

The variance of X is

Var(X) = n × (b - a + 1)^2 / 12 = 104 × 6^2 / 12 = 312

The standard deviation of X is

SD(X) = sqrt(Var(X)) = sqrt(312) = 17.67

To calculate the probability that the total sum of all rolls does not exceed 375, we need to calculate the cumulative distribution function (CDF) of X and evaluate it at 375

P(X <= 375) = F(375)

where F(x) = P(X <= x) is the CDF of X.

Using the normal approximation to the binomial distribution, we can approximate X as a normal distribution with mean E(X) = 365 and standard deviation SD(X) = 17.67

Z = (X - E(X)) / SD(X)

Z follows a standard normal distribution with mean 0 and standard deviation 1.

P(X <= 375) = P(Z <= (375 - E(X)) / SD(X))

= P(Z <= (375 - 365) / 17.67)

= P(Z <= 0.566)

Using a standard normal distribution table or a calculator, we can find that P(Z <= 0.566) is approximately 0.7165.

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The given question is incomplete, the complete question is :

A die is continuously rolled 104 times. what is the probability that the total sum of all rolls does not exceed 375 ?

If one flag pole is y feet tall and casts a shadow x feet long, and another nearby flag pole casts a shadow p feet long at the same time of day, we can use similar triangles to determine the shadow of the second flag pole.

In this scenario, the two flag poles and the ground form two similar right triangles. The height of the first flag pole (y) corresponds to one leg of the first triangle, and the length of its shadow (x) corresponds to the other leg.

Similarly, the height of the second flag pole (h) corresponds to one leg of the second triangle, and the length of its shadow (p) corresponds to the other leg.

Therefore, the height of the second flag pole is equal to the product of the height of the first flag pole and the length of the shadow of the second flag pole, divided by the length of the shadow of the first flag pole.

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The answer this riddle is time as it is always in a hurry, constantly moves forward and waits for no one. And time is often represented as being in a high position, such as on a clock or a calendar.

A riddle is a type of puzzle or question that is designed to challenge and engage the mind. It usually presents a seemingly paradoxical or enigmatic situation or description, and the goal is to figure out the hidden meaning or answer through careful thought and analysis.

Riddles can take many different forms, but they often involve wordplay, metaphor, or clever misdirection to lead the solver towards the solution. Riddles have been used for entertainment, education, and even as a means of passing on cultural knowledge and wisdom from one generation to the next.

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Answer: 1,023 combinations & 4/5 chance

Step-by-step explanation: A bunch of weird math with the first answer, but the 2nd answer is just every clothing article that isn't red over the total amount of articles simplified (8/10 = 4/5).

Hope this helped!

The total number of combinations of sandwiches possible is 360.

A local sub shop offers five different breads, four different meats, three different cheeses, and six different vegetables. You can choose one bread and any number of the other items.

To find the total number of combinations of sandwiches possible, we can use the multiplication rule.The multiplication rule states that if there are m ways to do one task and n ways to do another task, then there are m × n ways to do both tasks.

Similarly, if there are m ways to do one task, n ways to do another task, and p ways to do a third task, then there are m × n × p ways to do all three tasks.

To apply the multiplication rule to this problem, we can multiply the number of options for each component:Breads: 5 optionsMeats: 4 optionsCheeses: 3 optionsVegetables: 6 options

To find the total number of combinations, we can multiply the number of options for each component:5 × 4 × 3 × 6 = 360Therefore, there are 360 possible combinations of sandwiches.

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Answer:yes it is a triangle

Step-by-step explanation:

let's assume this triangle's sides are a,b and c.

we know this equation: [tex]a+b > c > |a-b|\\c+b > a > |c-b|\\a+c > b > |a-c|\\a=6\\b=7\\c=9\\13 > 9 > 1--- > which is true\\16 > 6 > 2----- > which is true as well\\15 > 7 > 3------ > it is true,too\\all of this equations are true so, this is a triangle[/tex]

The factors that affect the width of a confidence interval are a. population variation, c. sample size, and d. confidence level

Confidence interval refers to a statistical measure that attempts to estimate the range of values that could plausibly contain the true value of a population parameter. A confidence interval, in other words, is a statistical range that tells us how sure we are that a statistical estimate we're interested in lies between two values.

There are several factors that can affect the width of a confidence interval. Here are some of them:

The Question was Incomplete, Find the full content below :

what factors of the following affect the width of a confidence interval?

a. population variation

b. none of them

c. sample size

d. confidence level

e. sample mean

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Answer:

x > 8

Step-by-step explanation:

-6x + 18 < 2 - 4x

-2x + 18 < 2

-2x < -16

x > 8

Mean = 77

Standard Deviation = 1

Let's dive deeper into the details below.

The population has a mean µ=77 and a standard deviation δ=9.

To find the mean and standard deviation of a sampling distribution of sample means with a sample size n = 81.

μx = 77 (the mean of the population)

σx = δ/√nσx = 9/√81σx = 1

The mean of the sampling distribution is 77, and the standard deviation is 1.

Therefore, the value of μx is 77.

The formula to find the standard deviation of the sampling distribution is given by;

σx = δ/√nσx = 9/√81σx = 1

The value of the standard deviation of the sampling distribution is 1.

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Answer:

$329.99

Step-by-step explanation:

Proofs attached to answer

Answer:

13xy^2 - 7x^2y

Step-by-step explanation:

1) Collect like terms.

13xy^2+(-12x^2y+5x^2y)

2) Simplify.

13xy^2 - 7x^2y

In the given pairs of intersecting parallel lines, the measure of ∠MPQ=125°.

Parallel lines are coplanar infinite straight lines in geometry that never cross. In the same three-dimensional geometry, parallel planes are any planes that never cross. Curves with a fixed minimal distance between them and no contact or intersection are said to be parallel.

The angles created when a diagonal intersects two parallel lines are known as corresponding angles. According to the definition of corresponding angles, when two parallel lines cross a third one, the angles that are in the same relative location at each intersection are referred to as being corresponding angles to one another.

In this figure, ∠LMN=∠MPQ since they are corresponding angles

5x=3x+50

on solving, we get

x=25

Therefore, ∠MPQ= 125°

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Answer:B

Step-by-step explanation:

Adjacent side to the given angle = 7.072

Hypotenuse = opposite side to given angle ^2 + adjacent side to given angle ^2

Hypotenuse = 8.27666502886

The total amount Mary still owes is $1,184.46.

The total cost of the washer and dryer is $1,234.46, and Mary made a down payment of $100. This means she still owes:

$1,234.46 - $100 = $1,134.46

In addition, Mary decides to purchase a rack for the dryer for $50.00. Therefore, the total amount Mary still owes is:

$1,134.46 + $50.00 = $1,184.46

Mary purchased a washer and dryer for $1,234.46 on a tax-free sale day using a three-month no-interest credit plan. She made a down payment of $100 and later decided to buy a rack for the dryer for $50.00.  So Mary still owes $1,184.46.

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The functions g(x) and f(x) that correspond to h(x) = [tex]\rm (sin\ x)^{3}[/tex] are g(x) = cos x and f(x) = [tex]\rm (sin\ x)^{1/3[/tex].

Trigonometric functions are mathematical functions that are related to the angles of a right triangle to the lengths of its sides. They are widely used in mathematics, physics, engineering, and other fields to describe and analyze periodic phenomena and wave motion.

To find g(x) and f(x) from h(x) = [tex]\rm (sin\ x)^{3}[/tex], we need to use inverse operations to isolate sin x.

First, we can take the cube root of both sides of the equation to undo the cube power:

[tex]\rm h(x)^{1/3}[/tex] = (sin x)

Now we can substitute this expression for sin x in the standard functions g(x) and f(x):

g(x) = cos x

f(x) = [tex]\rm h(x)^{1/3}[/tex] =  [tex]\rm (sin\ x)^{3}[/tex]

Therefore, the functions g(x) and f(x) that correspond to h(x) =  [tex]\rm (sin\ x)^{3}[/tex] are g(x) = cos x and f(x) = [tex]\rm (sin\ x)^{3}[/tex].

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The answer of the given question based on the trigonometry is , to calculate YZ, we should use the cosine function with the angle 35.5°.

The sine function is a mathematical function that relates the ratios of the lengths of two sides of a right triangle with the measure of one of its non-right angles. Specifically, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

To use trigonometry to calculate YZ, we need to find a trigonometric ratio that involves the given side XZ and the angle opposite the requested side, which is angle YXZ. We don't have the measure of this angle, but we know that it is supplementary to the given angle 35.5°, so it must measure:

180° - 35.5° = 144.5°

We can use this angle and the given side XZ to find the length of YZ using the sine or cosine function.

In this case, the length of the opposite side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 144.5°. So we can write:

sin(144.5°) = YZ / XZ

Solving for YZ, we get:

YZ = XZ * sin(144.5°)

On the other hand, the cosine function , this case, the length of the adjacent side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 35.5°. So we can write:

cos(35.5°) = YZ / XZ

Solving for YZ, we get:

YZ = XZ * cos(35.5°)

Therefore, to calculate YZ, we should use the cosine function with the angle 35.5°.

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The answer of the given question based on the pentagon is , the apothem of the pentagon is approximately 13.76 meters, and the area of the pentagon is approximately 688 meter².

An apothem is line segment that is drawn from center of regular polygon to midpoint of one of its sides. The apothem is always perpendicular to the side it intersects and is typically used to calculate the area of the polygon. In a regular polygon, all sides are congruent and all interior angles are also congruent. The apothem, therefore, is the radius of the inscribed circle of the polygon.

Apothem can be found using the formula:

a = (s/2) * (1/tan(π/n))

where s is the length of one side of the pentagon, and n is the number of sides (in this case, n=5 for a pentagon).

Plugging in s=20 and n=5, we get:

a = (20/2) * (1/tan(π/5))

a ≈ 13.76m

So the apothem of the pentagon is approximately 13.76 meters.

To find the area of the pentagon, we can divide it into five congruent triangles, each with base equal to the length of one side (20m) and height equal to the apothem (13.76m). The area of each triangle is:

(1/2) * base * height = (1/2) * 20m * 13.76m ≈ 137.6m²

So the area of the pentagon is the sum of the areas of the five triangles:

A = 5 * (1/2) * base * height = 5 * 137.6m² ≈ 688m²

Therefore, the apothem of the pentagon is approximately 13.76 meters, and the area of the pentagon is approximately 688 meter².

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The given statement "Adding together all the residuals from a regression plot will always sum to 0" is False. A residual is defined as the difference between the observed value and the predicted value for each data point in a regression plot. The sum of residuals is not always equal to 0.

In a linear regression plot, the predicted values for each data point are calculated using the line of best fit. The residual for each data point is calculated as the difference between the observed value and the predicted value. The residuals are a measure of how well the line of best fit predicts the observed data. Ideally, the residuals should be randomly distributed around 0.

The sum of the residuals will be 0 only if the line of best fit perfectly predicts the observed data. However, this is not always the case. In fact, a good regression plot will have some residuals that are positive and some that are negative, resulting in a sum that is not equal to 0. This is because the line of best fit is only an estimate of the relationship between the variables being studied and will never perfectly predict the observed data.

Therefore, the statement "Adding together all the residuals from a regression plot will always sum to 0" is False. The sum of residuals may be close to 0 in some cases, but it will not always be exactly equal to 0.

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Answer:

Solve 6^2 + 5^2= c^2 for c

6^2 + 5^2= c^2

36 + 25= c^2

61= c^2

√61= c

value of c is √61

Step-by-step explanation:

edmentum answer

The difference in the volume of a small cube with a side length 6y is placed inside a larger cube with a side length is 5616y³

To find: the difference in the volume of the cubes.
Let the length of the larger cube be x.
So, the volume of the smaller cube is (6y)³ and the volume of the larger cube is x³.

As the smaller cube is placed inside the larger cube, it means that its side length is equal to the side length of the smaller cube plus twice the side length of the smaller cube.
So, x = 6y + 2(6y) = 18y.

The volume of the smaller cube = (6y)³ = 216y³
The volume of the larger cube = x³ = (18y)³ = 5832y³.

So, the difference in volume

= Volume of the larger cube - Volume of the smaller cube
= 5832y³ - 216y³
= 5616y³.

Therefore, the difference in the volume of the cubes is 5616y³.

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The volume for each cylinder, given the dimensions, is as follows:

1. r = 4 units, h = 6 units, V = 96π units².

2. r = 8 units , h = 3 units , V = 192π units².

3. r = 1 unit(half of the diameter), h = 5 units, V = 5 units².

4. r = 5 units, h = 7 units, V = 175π units².

The volume of a cylinder of radius r and height h is given by the equation presented as follows, in which the square of the radius is multiplied by π and the height, hence:

V = πr²h.

Then the equation is applied to each option in this problem with the given dimensions to obtain the volumes.

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The triangle shown in the image above that has sides 8, 24, and 25 is a right triangle because it satisfies the Pythagorean theorem.

A triangle with sides 8, 24, 25 is a right triangle.

This is because the sides satisfy the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse).

In this case, we have:

8² + 24² = 64 + 576 = 640

25² = 625

Since 8² + 24² = 25², the triangle satisfies the Pythagorean theorem, and is therefore a right triangle.

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Using the volume formula it is obtained that the least number of bags Martin should buy is Option C: 13.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

First, we need to convert the height of the cylinder from inches to feet -

6 inches = 6/12 feet = 0.5 feet

The volume of the cylinder can be calculated as -

V = πr²h

where r is the radius and h is the height.

Substituting the given values, we get -

V = 3.14 x 2² x 0.5

V = 6.28 cubic feet

Since each bag contains 0.5 cubic feet of sand, we can find the number of bags needed by dividing the total volume by the volume of each bag -

n = V / 0.5

n = 6.28 / 0.5

n = 12.56

Since we can't buy a fractional number of bags, we must round up to the nearest whole number.

Therefore, Martin needs to buy at least 13 bags of sand.

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Answer:

Step-by-step explanation:

Supplementary Angles and Adjacent Angles

Answer: It would be both supplementary and adjacent angles

Step-by-step explanation: both of the angles add up to 180 degrees

Answer: 150 degrees

Step-by-step explanation:

It just is

Answer:

Step-by-step explanation:

The measure of an angle in a regular dodecagon can be found using the formula:

angle = (n-2) x 180° / n

where n is the number of sides of the polygon. For a regular dodecagon, n = 12, so the formula becomes:

angle = (12-2) x 180° / 12 = 150°

Therefore, the measure of an angle in a regular dodecagon is 150 degrees. Answer: 150.

the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%

Probability refers to the measure of the likelihood or chance of a particular event occurring. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.

The formula for the binomial distribution can be used to resolve this issue:

P(X=k) = (n choose k) × pᵇ×(1-p)ⁿ⁻ˣ

where:

The number of trials, n, is five in this instance.

bis the number of successes we want (in this case, b = 2)

p is the probability of success on each trial (in this case, p = 0.20)

So, plugging in the values:

P(X=2) = (5 choose 2) ×0.20² × (1-0.20)⁵⁻²

= 10 × 0.04×0.512

= 0.2048

Therefore, the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%.

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The most reasonable domain of the function C = 4ⁿ is all positive integers, which is answer choice (c) i.e. all whole numbers .

A function is a mathematical object that takes one or more inputs, performs a specified operation on them, and produces an output.

The inputs to a function are called the domain, and the outputs are called the range.

An equation, a graph, or a table can all be used to depict a function.

The function that represents the number of new coins the jester receives on the n-th day after January 1 is given by C = 4ⁿ.

Since n represents the number of days after January 1, it is most reasonable to assume that n is a positive integer, because it doesn't make sense to talk about a negative or fractional number of days in this context.

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The complete question is given below.