3-2 Roof area can be broken down into three basic shapes: rectangle, triangle, and trapezoid. (True or False)

When expressed as percentage, 660 parts per million will equal to 0.0066%.

Part per million (ppm) should be multiplied by 0.001 of it could be divided by 10000 to convert it into percentage. In order to convert 660 ppm to a percentage, divide it by 10,000, which yields 0.066.

This needs to be multiplied by 100 to achieve the final result of 0.066%, which is how we may describe it as a percentage. Because the answer is less than 1%, you'll see that we added a leading zero.

As a result, the answer is 0.066%.

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The costs of each treat are

To solve this, we use the followign representations

x = cookies

y = ice cream 1

z = ice cream 2

Treat 1

Using the columns to generate the system of equations, we have

x + y + z = 25.71

z + 2x = 23.21

3y = 26.94

So, we have

y = 8.98

The other equations become:

x + 8.98 + z = 25.71

z + 2x = 23.21

When solved, we have

x = 6.48

z = 10.25

Treat 2

Using the rows to generate the system of equations, we have

x + 2y = 7.17

y + 2x = 5.37

3z = 14.97

So, we have

z = 4.99

The other equations when solved, we have

x = 1.19

y = 2.99

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The regular triangle, regular hexagon, and regular dodecagon have special triangles formed by their radius and apothem, which are congruent right triangles with legs equal to half the length of one side and hypotenuse equal to the radius or apothem, and are 30-60-90 triangles.

Regular polygons with three special triangles formed by their radius and apothem are,

Regular triangle

The radius and apothem of an equilateral triangle are equal. Therefore, the special triangles formed by the radius and apothem are congruent right triangles with legs equal to half the length of one side of the equilateral triangle and hypotenuse equal to the radius or apothem. In other words, the special triangles are 30-60-90 triangles.

Regular hexagon

The radius of a regular hexagon is equal to the length of one side, and the apothem is equal to the height of an equilateral triangle with side length equal to the length of one side of the hexagon.

Regular dodecagon

The radius of a regular dodecagon is equal to the length of one side multiplied by the square root of 2 plus the square root of 2 times the square root of 3. The apothem is equal to the height of an isosceles triangle with base equal to one side of the dodecagon and legs equal to the radius of the dodecagon.

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For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.

The three regular polygons that have special triangles formed by their radius and apothem are the triangle, square, and hexagon.

For the triangle, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the shorter leg.

For the square, the special triangle formed by its radius and apothem is a 45-45-90 right triangle, where the radius is the hypotenuse and the apothem is one of the legs.

For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.

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Answer:

Factoring the polynomials and then simplifying:

[tex] \frac{ {x}^{2} - 20x + 91}{ {x}^{2} - 35x + 196} \times \frac{ {x}^{2} - 74x + 1288}{ {x}^{2} - 92x + 2116 } [/tex]

[tex] \frac{(x - 7)(x - 13)}{(x - 7)(x - 28)} \times \frac{(x - 28)(x - 46)}{(x - 46)(x - 46)} [/tex]

[tex] \frac{x - 13}{x - 46} [/tex]

Answer:

x−46

x−13

Step-by-step explanation:

Explanation in picture :)

Answer: B

Step-by-step explanation:

Answer:

The answer is B) -35.16 grams per half-life cycle

The 99.9% confidence interval for the mean weight is (14.042, 14.202).

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To construct a 99.9% confidence interval for the mean weight, we can use the formula:

CI = X ± Zα/2 * (σ/√n)

where X is the sample mean, Zα/2 is the critical value from the standard normal distribution corresponding to a 99.9% confidence level (which is 3.291), σ is the population standard deviation (which we don't know, so we will use the sample standard deviation as an estimate), and n is the sample size.

First, we need to calculate the sample mean and sample standard deviation:

X = (14.07 + 13.99 + 14.16 + 14.17 + 14.15 + 14.11 + 14.24 + 13.99 + 14.14 + 14.13 + 14.20 + 14.21 + 14.06 + 14.05) / 14 = 14.122

s = sqrt((1/(n-1)) * ∑(xᵢ - X)²) = 0.072

where n is the sample size and ∑(xᵢ - X)² is the sum of squared deviations from the sample mean.

Plugging in the values, we get:

CI = 14.122 ± 3.291 * (0.072/√14) = (14.042, 14.202)

Therefore, the 99.9% confidence interval for the mean weight is (14.042, 14.202).

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The test score that is 0.6 standard deviations above the mean is 111.

We can use the formula for z-score to find the test score that is 0.6 standard deviations above the mean:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.

In this case, we want to find x when z = 0.6, μ = 105, and σ = 10:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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The test score that is 0.6 standard deviations above the mean is 111.

To find the test score that is 0.6 standard deviations above the mean, we can use the formula

z = (x - μ) / σ

where z is the number of standard deviations from the mean,

x is the test score we want to find,

μ is the mean of the distribution (105), and

σ is the standard deviation of the distribution (10).

We know that the desired test score is 0.6 standard deviations above the mean,

so we can set z = 0.6 and solve for x:

0.6 = (x - 105) / 10

Multiplying both sides by 10, we get:

6 = x - 105

Adding 105 to both sides, we get:

x = 111

Therefore, the test score that is 0.6 standard deviations above the mean is 111.

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Answer: no 3 is grade then -6 as 3 is positive number and 6 is negative number so positive is greater then negative number.

Step-by-step explanation:

In order to indicate if a number is greater than or less than another, we use the symbols > and <. For example, 10 is greater than 3, so we write it 10 > 3.

The maximum number of mail swaps that Bagelbot can perform between officials from A and officials from B can be 150 .

It can be determined by calculating the maximum number of edges possible for a bipartite graph between A and B. A bipartite graph is a graph in which the vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set.

In this case, the officials from A and officials from B represent the two disjoint sets.

The maximum number of edges in a bipartite graph between A and B can be calculated as the product of the number of officials in A and the number of officials in B. Therefore, if there are n officials in A and m officials in B, the maximum number of mail swaps that Bagelbot can perform is n x m.

For example, if there are 10 officials in A and 15 officials in B, the maximum number of mail swaps that Bagelbot can perform is 10 x 15 = 150.

This means that Bagelbot can potentially redirect up to 150 pieces of mail between officials from A and officials from B.

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The slope from of (−4, 6) to (2, 2/3) can be written as  -17/18

The slope of line can be represented as =slope whereby (x1, y1) = serves as the coordinates of first point in the line (x2, y2)serve as as the  coordinates of second point in the line

From the question, x1 = -4, y1 = 6 , x2 = 2, y2 =2/3 then we can set up into the formula as  

(y2 - y1) / (x2 - x1)

(y2 - y1) =(2/3 - 6) =-17/3

(x2 - x1) = (2 - (-4))= 6

Hence slope = -17/18

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The square of binomial have in common is x² - 14x + 49

The first two products you have given, (x + 9)(x + 9) and (x - 7)(x - 7), are examples of the square of a binomial. To find the product of two binomials, we use what's called the FOIL method. FOIL stands for First, Outer, Inner, Last, and it's a way to remember the steps involved in multiplying two binomials.

When we multiply (x + 9)(x + 9), we first multiply the first terms in each binomial: x * x = x². Then we multiply the outer terms: x * 9 = 9x. Next, we multiply the inner terms: 9 * x = 9x. Finally, we multiply the last terms in each binomial: 9 * 9 = 81. So, putting it all together, we get:

(x + 9)(x + 9) = x² + 9x + 9x + 81

= x² + 18x + 81

Similarly, when we multiply (x - 7)(x - 7), we get:

(x - 7)(x - 7) = x² - 7x - 7x + 49

= x² - 14x + 49

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Complete Question:

Find each product. (x + 9) (x + 9) , (x - 7)(x - 7) (2x - 1 )²

a. What do all products of the square of a binomial have in common?

To fill the entire pool we will 2,255 need gallons of water.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 8 feet.

From the general formula of the volume of a cylinder,

Volume = pi × radius² × height

In our case,

radius = 8/2 = 4

Height = 6

Thus, Volume = 3.14 × 4 × 4 × 6

The volume of the Pool = 301.44 Cubic foot

Since there are 7.48 gallons of water in a cubic foot

Thus,

The volume of the pool in gallons = 301.44 × 7.48

The volume of the pool in gallons = 2,254.77

Therefore, to fill the entire pool we will 2,255 need gallons of water.

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Answer:

To fill the entire pool we will 2,255 need gallons of water.

Step-by-step explanation:

If he uses the beach as one side. the minimum length, to 2 decimal places, of rope needed is: 70 meters of rope.

Let's assume that the length of the swimming area is L and the width is W. The perimeter of the swimming area will be the length of the rope that Kyle needs to rope off the area.

From the problem, we know that one side of the swimming area is the beach, so we have:

L + W + L = 70

Simplifying this equation, we get:

2L + W = 70

To find the minimum length of rope needed, we need to minimize the perimeter of the swimming area. We can use the above equation to express W in terms of L:

W = 70 - 2L

Substituting this expression for W into the formula for the perimeter, we get:

P = L + W + L

= 2L + (70 - 2L)

= 70

So the perimeter of the swimming area is fixed at 70 m, regardless of the values of L and W. Therefore, the minimum length of rope needed to rope off the area is simply the perimeter of the swimming area, which is 70 meters.

Therefore, Kyle needs a minimum of 70 meters of rope.

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Answer:

999,000,000 bytes

Step-by-step explanation:

if you subtract the total of the gigabytes from the total of the megabytes you get this answer.

Answer: 26 degrees

Step-by-step explanation:

12/24 = 1/2

Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.

Simple interest (SI) is calculated as a percentage added to the principle amount deposited or borrowed for a given period of time. SI is typically expressed as years.

Given data:

Simple interest formula:

SI = PRT / 100

SI = 3500*7.5*5 / 100

SI = 1312.5

Now,

Amount = principal + simple interest

Amount = 3500 + 1312.5

Amount = $4812.50

Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.

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Answer:

10%

Step-by-step explanation:

The measure of angle FCD is 130 degrees.

What is an angle?

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The Latin word "angulus" (which means "corner") is where the word "angle" first arose.

The pair of alternative internal angles that are congruent must first be found. The angles formed on the opposing sides of the transversal EF are known as alternate internal angles since AB and CD are parallel lines. We possess

Angle AGE and angle FCD are alternate interior angles.

Angle AGE measures 130 degrees.

Therefore, we can conclude that angle FCD also measures 130 degrees. So, the measure of angle FCD is 130 degrees.

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Answer:

Step-by-step explanation:

The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.

In linear equation, The required days for which Bryan's workout would be the same in either pool is 2 days.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Here.

Let the number of days of B'ryan workout be x, the total yard he swims be y,

According to the question,

he swims at the rec center pool, will complete a 100-yard warm-up, and then swim laps in a lane that is 39 yards long.

y = 100 + 39x

Jason swims at the indoor pool at his gym, he will complete a 104-yard warmup, plus the main set that consists of 37 yards per lap.

y = 104 + 37x

Equating both the equation,

100 + 39x =  104 + 37x

39x - 37x =  104 - 100

2x = 4

x = 2  days

Thus, the requried days for which Bryan's workout would be the same in either pool is 2 days.

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The result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].

Rotation is a transformation in geometry that involves turning or spinning an object around a fixed point called the center of rotation. The center of rotation remains stationary while all the points of the object move along circular paths, at the same angle and distance from the center.

To rotate a point [x/y] counterclockwise by 90 degrees, we can use a 2x2 matrix of the form:

[ 0 -1 ]

[ 1 0 ]

To multiply this matrix by a point [x/y], we can use the following matrix multiplication:

[ 0 -1 ] [ x ] [ -y ]

[ 1 0 ] [ y ] = [ x ]

So, if we have a point [x/y] and we want to rotate it 90 degrees counterclockwise, we can multiply it by the matrix [ 0 -1 ; 1 0 ] to get the new point [-y/x].

To rotate a point 90 degrees counterclockwise using a matrix, we need to represent the point as a column matrix and then multiply it by the 2x2 rotation matrix.

Assuming that the point is [x, y] = [-5, 2], we can represent it as a column matrix:

| -5 |

| 2 |

To rotate the point counterclockwise by 90 degrees, we can use the following 2x2 rotation matrix:

| 0 -1 |

| 1 0 |

Multiplying the rotation matrix by the column matrix representing the point gives:

| 0 -1 | | -5 | | 2 |

| 1 0 | ×| 2 | = | -5 |

So the result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].

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Step-by-step explanation:

to vary inversely means that

y = k/x

the opposite would be to vary directly :

y = kx

so, in our case

5 = k/1

k = 5

y = 5/x

therefore, for x = -3

y = 5/-3 = -5/3 = -1.666666666...

The option (3) is correct the quotient is −5x³ + x + 3.

To solve quadratic equations by factoring, we first express the quadratic polynomial into a product of factors by using middle term splitting or different identities and then set each factor equal to 0. The equation a x 2 + b x + c = 0 ( a ≠ 0 ) can be written as.

According to given question

To divide[tex]15x^5[/tex] − 3x³ − 9x² by −3x² using the factorization method, we can factor out −3x² from the expression and simplify to get:

[tex]15x^5[/tex]− 3x³ − 9x²= −3x²(−5x³ + x + 3)

Therefore, the quotient is −5x³ + x + 3.

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Given statement: On a 1500 square foot gable roof, there will be approximately 11% waste.

The given statement is False.

The statement provides information on the amount of waste but does not provide sufficient information to determine the total area of roofing material required for the gable roof.

Therefore, it is impossible to determine whether the waste percentage is accurate or not.

The statement "On a 1500 square foot gable roof, there will be approximately 11% waste" can be either True or False depending on the specific roofing materials and project details.
However, it's not uncommon for roofing projects to have waste percentages in that range (around 10-15%), especially for complex designs or when using materials like shingles.

Keep in mind that waste factors may vary depending on the type of roof, materials used, and installation methods. Always consult with a professional to get accurate waste estimates for your specific project.

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The probability that a sample mean of 40 unemployed individuals will be within 1 week of the population mean of 18.5 weeks with a population standard deviation of 4 weeks is 0.6827, rounded to four decimal places.

Given that the population mean length of unemployment is 18.5 weeks and the population standard deviation is 4 weeks, we want to find the probability that a simple random sample of 40 unemployed individuals will provide a sample mean within 1 week of the population mean.

The standard error of the sample mean is given by the formula

standard error = population standard deviation / sqrt(sample size) = 4 / sqrt(40) = 0.6325

Using the central limit theorem, we can assume that the sample mean follows a normal distribution with a mean of 18.5 weeks and a standard deviation of 0.6325 weeks.

To find the probability that the sample mean will be within 1 week of the population mean, we need to calculate the z-score for the lower and upper limits of the sample mean

z1 = (18.5 - 1 - 18.5) / 0.6325 = -1

z2 = (18.5 + 1 - 18.5) / 0.6325 = 1

Using calculator, we can find that the area between z = -1 and z = 1 is 0.6827.

Therefore, the probability that a simple random sample of 40 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.6827 or 68.27% (rounded to four decimal places).

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Answer: |x + 9| > 0 or |x + 5| < 4

Step-by-step explanation: To begin with, ready to utilize the frame |x - b| > c to speak to the arrangement x < -9:

|x - (-9)| >

Rearranging this gives:

|x + 9| >

Another, we are able utilize the frame |x - b| < c to speak to the arrangement x ≥ -5. Ready to select a esteem of c that's more noteworthy than the remove from -5 to the closest endpoint of the arrangement set (which is -9):

|x - (-5)| < 4

Rearranging this gives:

|x + 5| < 4

Joining these two supreme esteem disparities with an "or" explanation gives:

|x + 9| > or |x + 5| < 4

Rearranging this gives:

x < -9 or -9 < x < -1

We will see that the primary portion of the arrangement set (x < -9) is as of now spoken to within the to begin with supreme esteem imbalance, and the moment portion (x ≥ -5) is spoken to by the moment supreme esteem imbalance.

If we throw, a coin in twice, then pay off for throw exactly two heads is $120. The expected win value in the game in 742 trials is equals to the $1669.5.

We have to two tosses a coin and we gift with payouts according to results of tossing. When we throw exactly two heads in two tosses of a coin, then pay out is $120. If not throw two heads then payout is $37… Now, number of times we play the game that is trials = 742

We have to determine value of expected value to win or loss for 742 trials. First we determine the excepted value of proposition. Total possible outcomes on two tosses of a coin = 4 = {HH,TT, HT, TH}

Probability of throwing two heads = 1/4

= 0.25

Probability of not throwing two heads

= 1 - 1/4 = 3/4 = 0.75

That is when x (pay off) = $120, P( x)

= 0.25 ; x (payout) = -$37, P( X) = 0.75. Now, the excepted value formula is written as, [tex]E( x) = \sum x× P(x) [/tex]

= $120 × 0.25 - $37 ×0.75

= $2.25

So, the expected value of win with 575 trials of gane = 2.25 × 742

= 1669.5

Hence, required excepted win value is $1669.5.

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The length of the hip on a hip roof rises 1.5 feet vertically.

The hip roof has a slope of 6 inches per foot ( hip slope factor = 1.5) and a hip run of 14 feet

Length of hip = (square root of (hip run squared + (hip slope factor x roof span squared)))
Plugging in the given values, we get:
Length of hip = (square root of (14 squared + (1.5 x 14 squared)))
Length of hip = (square root of (196 + 294))
Length of hip = (square root of 490)
Length of hip = 22 feet (rounded to the nearest whole number)
Therefore, the correct answer is C. 22.
It's important to note that the hip slope factor is a value used to calculate the actual slope of the hip, which is typically steeper than the pitch of the roof. In this case, the hip slope factor of 1.5 means that for every foot of horizontal run, the hip rises 1.5 feet vertically.

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According to the Equation, the provided question's conclusion is that the object strikes the top of the tree in roughly 4 seconds.

An equation is a mathematical statement that demonstrates the equality of two expressions and is typically denoted by the equals symbol (=). Equations can be used to solve issues and make predictions as well as to express a wide variety of mathematical relationships.

The formula for the distance travelled by an object under constant acceleration can be used to solve this issue:

d = 1/2 * g * t²

where:

The distance travelled is d.

Gravitational acceleration (g) is around 32.2 feet per second squared.

T is the passing of time

Since the object is being dropped in this scenario, we know that its initial height is 0 feet and its ending height is 44 feet. For the duration of the trip, we may construct the following equation:

The required time is t seconds.

h(t) = 44

Simplifying:

-16t² + 300 = 44

16t² = 300 - 44

t² = 256/16

t² = 16

When both sides are squared:

t = 4 seconds

The time it takes for the object to strike the tree's top is therefore 4 seconds.

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The complete question is,

Let's say the object lands 44 feet above the ground, at the top of a tree. You may calculate the number of seconds after being dropped by writing and solving an equation.