How do you write 4/15 as a decimal?

The expression x^4 + 5x^2 - 8 in quadratic form is: (x^2 + 8)(x^2 - 1)

It should be noted that to express the given expression x^4+5x^2 - 8 in quadratic form, we need to identify a suitable substitution that will allow us to rewrite the expression as a quadratic in a new variable.

One possible substitution is to let u = x^2, so that we can write:

x^4 + 5x^2 - 8 = u^2 + 5u - 8

We can then factor this quadratic expression as:

u^2 + 5u - 8 = (u + 8)(u - 1)

Substituting back u = x^2, we get:

x^4 + 5x^2 - 8 = (x^2 + 8)(x^2 - 1)

Therefore, the expression x^4 + 5x^2 - 8 in quadratic form is:

(x^2 + 8)(x^2 - 1)

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Answer:

To evaluate the composite functions (f◦g), (g◦f), (f◦f), and (g◦g), we need to substitute one function into the other and simplify the resulting expression.

(a) (f◦g)(4):

To find (f◦g)(4), we need to first find g(4) and then substitute it into f(x):

g(4) = 7 - 1/2(4)^2

= 7 - 8

= -1

Now we substitute g(4) = -1 into f(x):

(f◦g)(4) = f(g(4))

= f(-1)

= 3(-1)^2 - 2

= 1

Therefore, (f◦g)(4) = 1.

(b) (g◦f)(2):

To find (g◦f)(2), we need to first find f(2) and then substitute it into g(x):

f(2) = 3(2)^2 - 2

= 10

Now we substitute f(2) = 10 into g(x):

(g◦f)(2) = g(f(2))

= g(10)

= 7 - 1/2(10)^2

= -43

Therefore, (g◦f)(2) = -43.

(c) (f◦f)(1):

To find (f◦f)(1), we need to find f(f(1)):

f(1) = 3(1)^2 - 2

= 1

Now we substitute f(1) = 1 into f(x):

(f◦f)(1) = f(f(1))

= f(1)

= 1

Therefore, (f◦f)(1) = 1.

(d) (g◦g)(0):

To find (g◦g)(0), we need to find g(g(0)):

g(0) = 7 - 1/2(0)^2

= 7

Now we substitute g(0) = 7 into g(x):

(g◦g)(0) = g(g(0))

= g(7)

= 7 - 1/2(7)^2

= -17/2

Therefore, (g◦g)(0) = -17/2.

The answer are in angle m∠5+m∠6=180°,m∠2+m∠3=m∠6,m∠2+m∠3+m∠5=180°.

Angle is a geometric concept that is used to describe the relationship between two lines or planes. It is measured in degrees, with a full circle being 360 degrees. Angles are used in mathematics to measure the size of a shape and the amount of turn between two lines. In physics, angles are used to describe the force of friction, the direction of a force, and the direction of light. Angles can also be used to describe the orientation of objects in space.

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary by angles

m∠4=180°-m∠3 ----> equation B

substitute the equation- B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary to angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of any of tAnswer:

Step-by-step explanation:

he interior angles that of a triangle must be equal to 180 degrees

therefore

This option is true for sure

case E) we have

m∠2+m∠3+m∠5=180°.

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The scalar projection and projection vector of vector (5,3) onto vector (7,-2) can be calculated by using the appropriate formulas and then interpreted graphically.

The scalar projection of (5,3) onto (7,-2) was found to be 29/53, and the projection vector was found to be (203/53, -58/53). This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).

Graph is a data structure that consists of nodes and edges, which are used to represent relationships between different objects. A graph is often used to represent the real-world relationships between objects such as cities, towns, and roads. Graphs can also represent abstract relationships such as between two people or mathematical formulas. Graphs are widely used in computer science, networking, and mathematics.

(a) Scalar Projection:
The scalar projection of vector A onto vector B can be calculated by using the following formula:

Projection = (A⋅B)/|B|

In this case, the scalar projection of (5,3) onto (7,-2) is:

Projection = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2))
           = (35 - 6)/53
           = 29/53

Projection Vector:
The projection vector of vector A onto vector B can be calculated by using the following formula:

Projection Vector = (A⋅B/|B|²)B

In this case, the projection vector of (5,3) onto (7,-2) is:

Projection Vector = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2)) ⋅ (7,-2)
                 = (35 - 6)/53 ⋅ (7,-2)
                 = (29/53)⋅(7,-2)
                 = (203/53, -58/53)

(b) Interpretation Graphically:
The projection of vector (5,3) onto vector (7,-2) can be interpreted graphically as follows:

First, draw the two vectors (5,3) and (7,-2) on a graph. Then draw a line from the origin to the tip of vector (7,-2). This line will represent vector (7,-2). Next, draw a line from the origin to the tip of vector (5,3). This line will represent vector (5,3).

Finally, draw a line from the tip of vector (7,-2) to the tip of vector (5,3). This line will represent the projection vector of (5,3) onto (7,-2). The length of this line will be the scalar projection of (5,3) onto (7,-2).

This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).

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The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.

The set 2Z is defined as follows:

2Z = {2n | n ∈ Z, a * b = a + b}

Associative element:

There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.

Let a, b, and c be arbitrary elements of 2Z:

a = 2n₁

b = 2n₂

c = 2n₃

Then we have:

a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)

(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)

Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.

Identity element:

There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.

Let e be an arbitrary element of 2Z:

e = 2n

Then we have:

ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z

ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z

Therefore, e = 2n is an identity element in 2Z.

Inverse element:

There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.

Let a be an arbitrary element of 2Z:

a = 2n

Then we need to find an element b in 2Z such that ab = ba = e = 2.

We have:

ab = ba = 2n*b = 2

Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.

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Answer:

K = √-6k

i did the math and got this answer and it was right

Answer:

k = 10

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ MYZ is an exterior angle of the triangle , then

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

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

Exterior angle of a triangle is equal to the sum of remote interior angles.

In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.

Set up equation and solve for k:

Therefore the value of k is 10.

Answer:

[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]

A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.

Answer:

21.6n-1.2

Step-by-step explanation:

=2.8n-24n-1.2-0.4n

=21.6n-1.2

a) The system of equations can be written in the matrix form AV-B as: | -3 3 | | V2 | | -10 |

b) V1 = 369/22 volts and V2 = -51/22 volts.

A matrix is a rectangular array of numbers or symbols, arranged in rows and columns. Matrices are often used in mathematics, science, engineering, and other fields to represent and manipulate data, perform operations, and solve equations. The size of a matrix is determined by the number of rows and columns it contains, and is usually written in the form "m x n", where "m" is the number of rows and "n" is the number of columns. Matrices can be added, subtracted, multiplied, transposed, and inverted, and can be used to represent a wide range of mathematical objects, including systems of linear equations, transformations, and graphs.

a) The system of equations can be written in the matrix form AV-B as:

| 15 -7 | | V1 | | 60 |

| | x | | = | |

| -3 3 | | V2 | | -10 |

b) To solve for V1 and V2 using matrix algebra, we can use the inverse of matrix A as follows:

AV = B

V = A⁻¹B

First, let's find the inverse of matrix A:

A = | 15 -7 |

| -3 3 |

To find the inverse of A, we need to calculate the determinant of A:

det(A) = (15)(3) - (-7)(-3) = 66

Then, we can find the inverse of A as follows:

A⁻¹ = (1/det(A)) x | 3 7 |

| 3 15 |

Now, we can solve for V by multiplying A⁻¹ and B:

| V1 | | 3 7 | | 60 | | 369/22 |

| | = | | x | | = | |

| V2 | | 3 15 | |-10 | | -51/22 |

Therefore, V1 = 369/22 volts and V2 = -51/22 volts.

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer:

B

Step-by-step explanation:

The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).

In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.

For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.

In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.

The formula for calculating the volume of air passing through a filter is:

Volume = Filter Area x Airflow Velocity

Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:

Filter Area = Length x Width

Filter Area = 4 ft x 2 ft

Filter Area = 8 square feet

Now we can substitute the values into the formula:

Volume = Filter Area x Airflow Velocity

Volume = 8 sq ft x 100 ft/min

Volume = 800 cubic feet per minute (CFM)

Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

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Answer:

s/3

Step-by-step explanation:

since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.

Answer:

1/4 of the pot is left.

Step-by-step explanation:

Let x be the total amount of pasta in the pot.

Then the amount of pasta her mother got= 1x/12

The amount of pasta her brother got=  1x/6

The total amount of pasta he serve= 1x/12 + 1x/6

First, convert them into like fractions, then

The total amount of pasta he serve= 1x/12 + 2x/12 = (x+2x)/12 = 3x/12 = 1x/4

Hence, 1/4 of the pot is left over.

Step-by-step explanation:

Mom: 1/12

Brother: 1/6

1/6 × 2/2 = 2/12

2/12 + 1/12 = 3/12

12/12 (= 1 whole) - 3/12 = 9/12 of pasta is left

Answer: there all divided by 2

so it's 2

91.3 pounds of fruit are left

Jason bought = 91.5 pounds

class ate = 0.2 pounds

You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.

91.5 - 0.2 = 91.3 pounds

The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.

Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.

To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).

cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.

Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.

Substituting this value into the expression, we get:

sin⁻¹(0) = 0

Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.

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Answer:

The answer is Zack garden

The missing piece of information z-score is -1.

Explain information

Information refers to data or knowledge that has been transmitted or received. It can be expressed in different forms, including numerical data, text, images, or sound. The information serves as a basis for understanding, analysis, and decision-making. It can be processed and analyzed using mathematical methods and tools such as statistics, probability, and data analysis. The effective management and utilization of information are essential for progress and innovation in many fields, including science, technology, and business.

According to the given information

Using the formula z = (x - μ) / σ, we can plug in the given values and calculate:

z = (75 - 80) / 5

z = -1

Therefore, the z-score is -1.

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Answer:

yes it is pretty hard but I believe I. you

Answer:

124

Step-by-step explanation:

You'll need a calculator for this one

It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to√(0.861(1.0.861)/410) = 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

What is a proportion?

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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The correct option is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

An interval refers to a range of values between two points on a numerical scale. It can be represented by two numbers, called endpoints, and includes all the values that lie between these endpoints.

The two common types of intervals are closed intervals and open intervals.

According to the given information:

In a confidence interval, the range of values within which the true population parameter (in this case, the mean amount of money each customer spends per visit) is likely to fall is estimated. A 95% confidence interval means that there is a 95% probability that the true population parameter falls within the interval.

In this case, the confidence interval is ($10.53, $31.89), which means that we are 95% confident that the true mean amount customers spend per visit falls between $10.53 and $31.89. Since the interval does not contain $35, it is not reasonable to believe that the manager will receive a bonus, as the estimated mean amount spent per visit is below $35 according to the confidence interval.

The correct answer is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

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Answer:

Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

On Thursday, she practiced for 5 minutes according to the table.

On Friday, she practiced for 9 minutes according to the table.

Adding these two times together, we get:

5 minutes + 9 minutes = 14 minutes

Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.

The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

The equation of a circle with center (a,b) and radius r is given by the equation:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:

(x - 1/2)^2 + (y - 0)^2 = 2^2

Expanding and simplifying, we get:

(x - 1/2)^2 + y^2 = 4 - 1/4

Therefore, the equation of the circle is:

(x - 1/2)^2 + y^2 = 15/4

So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

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Answer:

3n+15

Step-by-step explanation:

18, 21, 24

+3. +3

3n

18-3=15

3n+15