Determine the domain and range of the graph of this function.

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:

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.

Is the graph increasing, decreasing, or constant: C. Constant.

In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.

In conclusion, the above is constant, rather than increasing or decreasing.

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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: 104%

Step-by-step explanation: 26% times 4 years

Answer:

yes it is pretty hard but I believe I. you

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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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.

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 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 total number of employees is 112.

Explain numbers

Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.

According to the given information

Let's use x to represent the total number of employees.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.

So, we can set up the following proportion:

4/9 = x/(x - 140)

To solve for x, we can cross-multiply and simplify:

4(x - 140) = 9x

4x - 560 = 9x

560 = 5x

x = 112

Therefore, the total number of employees is 112.

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The correct answer is: Decrease total assets and net income.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.

When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.

Therefore, the correct answer is: Decrease total assets and net income.

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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:

124

Step-by-step explanation:

You'll need a calculator for this one

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:

The answer is Zack garden

Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

slope of line AB is m = 2

line AB crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line AB

We can say that f(x) has a local maximum at A and a local minimum at B.

A function is a mathematical rule that assigns a unique output value to each input value. It describes the relationship between the input and output variables.

Critical numbers of a function are the values of the independent variable where the derivative is zero or undefined, indicating possible extrema or inflection points.

According to the given information:

To find the critical numbers of the function f(x), we need to find the values of x where f'(x) = 0 or f'(x) is undefined.

f(x) = cos(x) + √2/2

f'(x) = -sin(x)

Setting f'(x) = -sin(x) = 0, we get sin(x) = 0, which is true for x = nπ, where n is an integer. However, we only need to consider the values of x in the interval [0,2].

For n = 0, x = 0 is a critical number.

For n = 1, x = π is a critical number.

For n = 2, x = 2π is not in the interval [0,2], so we don't need to consider it.

Therefore, the critical numbers of f(x) in the interval [0,2] are A = 0 and B = π.

To find the nature of the critical points, we need to find the second derivative of f(x).

f''(x) = -cos(x)

Evaluating f''(x) at A and B, we get:

f''(A) = -cos(0) = -1, which means that f(x) has a local maximum at A.

f''(B) = -cos(π) = 1, which means that f(x) has a local minimum at B.

Therefore, we can say that f(x) has a local maximum at A and a local minimum at B.

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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.

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:

Step-by-step explanation:

There are two ways to write 4/15 as a decimal.

**Method 1: Using long division**

1. Divide 4 by 15.

2. The quotient is 0.26.

3. The remainder is 6.

4. Since the remainder is not zero, we need to bring down a zero and continue dividing.

5. We get 0.266666...

**Method 2: Using a calculator**

1. Enter 4/15 into the calculator.

2. Press the "equals" button.

3. The answer is 0.266666...

The decimal representation of 4/15 is 0.266666..., which is a repeating decimal. This means that the 6 repeats indefinitely.

Answer:

The answer is 0.2666

Step-by-step explanation:

4/15

=0.2666

Answer:

3n+15

Step-by-step explanation:

18, 21, 24

+3. +3

3n

18-3=15

3n+15

Solving the system of equations using matrices is : = -66, y = 163, and z = 11.

To solve this system of equations using matrices, we can write it in the form AX = B, where:

A = coefficient matrix

X = variable matrix (containing x, y, and z)

B = constant matrix (containing the constants on the right-hand side of each equation)

So, we have:

| 2  -1  3 |   | x |   | 180 |

| -4  2  3 | x | y | = | 225 |

| 3  -4  0 |   | z |   | 270 |

We can solve for X by multiplying both sides of the equation by the inverse of A:

X = A^-1 * B

First, we need to find the inverse of A. We can do this by using the formula:

A^-1 = (1 / det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

The cofactor matrix is:

| 2  9  6 |

| 12  0  -2 |

| 13  -9  8 |

Taking the transpose of the cofactor matrix gives us the adjugate of A:

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

So, we have:

A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

Multiplying A^-1 by B gives us:

| x |   | -66 |

| y | = | 163 |

| z |   | 11  |

Therefore, x = -66, y = 163, and z = 11.

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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

Step-by-step explanation:

the answer is 115 remainder 1

Angle A equals 41.81°

c: