a compound inequality is an inequality that combines two inequalities. write an compound inequality for the situation

The function of the linear equation shows that the slope(m) = -7, the x-intercepts is (-1/7,0), and the y-intercepts is (0,-1)

The function of a linear equation takes the form y = ax + b. In this situation, the values of y can be determined when x = 0, and the values of x can be determined when y = 0

From the given information:

y = f(x) = -7x - 1

We can determine the:

y = -7x - 1

Slope (m) = -7

Set the values of y = 0 to determine the x-intercepts.

0 = -7x - 1

7x = - 1

x = -1/7

x-intercepts = (-1/7, 0)

Set the values of x = 0 to find the y-intercepts.

y = -7(0) - 1

y = - 1

y-intercepts = (-1, 0)

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Answer:

B=47

Step-by-step explanation:

The angle of a straight line is 180 so:

3b-6+(b-2) =180

3b-6+b-2=180

4b-8=180

4b=180+8

4b=188

B=47

The cost of the water bottle per ounce is $0.077.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a 36-oz bottle of water costs $2.88. The cost of 1 ounce of the bottle is calculated as,

1 OZ = 1.04 ounces

36 OZ = 36 x 1.04 ounces

36 OZ = 37.44 ounces

37.44 ounces = $2.44

1 ounce = $2.44 / 37.44

1 ounces = $0.077

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The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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hope it helps

Answer:

4a + b)( 1 + 4a - b )

Step-by-step explanation:

4a + b + 16a² - b²

Step 1 :- Use a² - b² = ( a - b ) ( a + b ) to factor the expression.

4a + b + ( 4a - b ) ( 4a + b ).

Step 2 :- Factor out 4a + b from the expression.

(4a + b)( 1 + 4a - b )

2)

When we say that w = 4, it means that we can rewrite the expression and instead of "w", we will put "4", so

Now we have a numerical expression to solve, we can easily solve it!

Therefore, the final answer is

5)

Here we will do the same thing, the "hard" part is solving the numeric expression, it will be a little bit harder than the 2).

Again, repeat the same process, rewrite the expression, and instead of "m" you put "5"

Again, another expression to simplify, remember that we always solve what is inside ( ) first, and we have a multiplication inside ( ) so we must solve it first

Now we solve the multiplication inside ( ) we can do the subctration

The last step is just to solve another multiplication

Now we simplified everything we can have the final answer:

6)

Here we have a division, but it's similar with 5) and 2), we have

No secrets, repeat the process, but here, "a" will turn into "15", then

We can do the multiplication at the numerator of the fraction

Now we can simplify the fraction, 30 divided by 3 is 10, then

Now just do the sum and it's done!

Hence the final answer is

ANSWERS:

1) 43

2) 13

3) 67

4) 12

5) 39

6) 23

Answer:

10 dollars left, four hours of tubing

Step-by-step explanation:

To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

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Answer:

Step-by-step explanation:

\(\text{Since the enrollment decreases every year this is exponential decay of the form}\\ \\ F=Ir^t\\ \\ F=12000(1-.05)^t\\ \\ S(n)=12000(0.95)^n\)

To find the width of the box, we need to solve an equation. Let's denote the width as "w". The equation representing the volume of the box is w^3 = 96. The width of the box is 4 cm.

Let's denote the width of the box as "w". The volume of a rectangular box is given by the formula V = lwh, where l represents the length, w represents the width, and h represents the height. In this case, since we are only interested in finding the width, we can assume that the length and height are equal.

Given that the volume is 96 cubic centimeters, we have the equation w^3 = 96. To solve for w, we need to find the cube root of both sides of the equation. Taking the cube root of 96, we find that w = 4.

Therefore, the width of the box is 4 centimeters.

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Answer:

11) -11

12) -12

13) 7

14) -60

15) -56

16) -378

17) -126

18) -4

19) -3

20) -12

Answer:

see below

Step-by-step explanation:

1.  75

2.  -14

3.  91

4.  67

5.  24

6.  112

7.  91

8.  44

9.  15

10.  -11

11.  -11

12.  -12

13.  7

14.  -60

15.  -56

16.  -378

17.  -126

18.  -4

19.  -3

20.  -12

Answer:

129024

Step-by-step explanation:

hope this help:)

Answer:

1440

Step-by-step explanation:

You add 8 + 112 then divide that by inches

Answer:

700

Step-by-step explanation:

The '7' in the number 1273  ..it is in the second place which represents 'tens' so it is equal to    '70'   ten times this amount would be  700.    If you have a list of numbers to choose from.....choose one with the '7' in the THIRD position.

The angle measures of each vertex of the garden are 53.13 degrees.

In Parallelogram ABCD, diagonals AC and BD intersect at point A = √7.

Angle is a geometric figure that can be described as the amount of rotation between two straight line or planes and angle is measured in degree with a full circle being 360°.

1. To determine the angle measures of each vertex of the garden, we must first calculate the angles formed by each side. For example, the angle formed by sides AB and BC can be found by using the inverse tangent function. The equation would be

arctan(BC/AB) = arctan (4/3) = 53.13 degrees.

The angles for the other sides can be calculated in the same way. We can then use the sum of angles theorem to calculate the angles at each vertex. Since the garden is an irregular shape, the angles at each vertex will be different.

2. In Parallelogram ABCD, diagonals AC and BD intersect at point A. To calculate , we can use the distance formula.

The equation would be = √((x2 – x1)2 + (y2 – y1)2).

For the coordinates given, we would have

= √((2 – 5)2 + (5 – 1)2)

= √(-9 + 16)

= √7.

Answer 3: To determine whether quadrilateral ABCD is a rectangle, rhombus, or square, we must first calculate the slope.

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Mr. Brown’s gross wage for the week is; $41800

We are given;

Total normal work hours for the week = 40 hours

Total amount paid for the total normal work hours = $32000

Number of hours worked overtime on Saturday = 5 hours

Number of hours worked overtime on Sunday = 3 hours

From the total number of hours per week and amount, we can say that;

Amount paid per hour normally = 32000/40 = $800 per hour

We are told that Saturday is paid at 1¹/₄ of the normal rate.

Thus; Amount earned on Saturday = 1¹/₄ * 800 * 5 = $5000

Amount earned on Sunday = 2 * 800 * 3 = $4800

Thus;

Gross wage for the week = $32000 + $5000 + 4800 = $41800

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The disadvantage of simulation mentioned in the question is that it is a trial-and-error approach that may produce different solutions in different runs.

This variability introduces uncertainty and may make it hard to achieve constant and reliable consequences. Moreover, the execution of simulation programs can interfere with manufacturing structures, inflicting disruptions or delays in real-international operations.

Additionally, simulations regularly have obstacles within the styles of chance distributions they can efficaciously version, potentially proscribing their accuracy and applicability in certain situations. Furthermore, even as simulations are valuable for information and reading structures, they may war to deal with pretty complex problem answers that contain complicated interactions and dependencies.

Lastly, simulations can lack flexibility as they're usually designed for unique purposes and may not easily adapt to converting situations or accommodate unexpected elements.

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the answer is 524.47500

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In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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The method for finding and classifying critical points of a function involves finding the first derivative of the function and setting it equal to zero to find the critical points. Then, the second derivative test is used to classify the critical points as local maxima, local minima, or saddle points.

The given function is not provided in the question. Therefore, we cannot find and classify the critical points of the function. However, I can provide the general method for finding and classifying critical points of a function.

Finding the critical points: To find the critical points of a function, we need to find the values of x where the first derivative of the function is equal to zero or does not exist. These points are called critical points. Mathematically, we can express this as follows:

f′(x) = 0 or f′(x) does not exist

Classifying the critical points: Once we have found the critical points of the function, we can classify them using the second derivative test. This test involves finding the second derivative of the function at the critical points and determining its sign.

If the second derivative is positive, then the critical point is a local minimum. If the second derivative is negative, then the critical point is a local maximum. If the second derivative is zero or undefined, then the critical point is a saddle point.

Mathematically, we can express this as follows:

f′′(x) > 0, then (x, f(x)) is a local minimum.
f′′(x) < 0, then (x, f(x)) is a local maximum.
f′′(x) = 0 or does not exist, then (x, f(x)) is a saddle point.

Once we have found and classified the critical points of the function, we can then enter the list of ordered pairs (x, y) where the max/min/saddle occurs for each classification. If there are no points for a classification, we enter "dne" (does not exist).

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The component of a linear programming model that is NOT listed is "Decision variables."

A linear programming model consists of several components that work together to optimize a given objective while considering various constraints. The components of a linear programming model include:

Constraints: These are the limitations or restrictions that define the feasible set of solutions. Constraints restrict the values that decision variables can take.

Objective Function: This function represents the goal or objective of the linear programming problem. It is either minimized or maximized based on specific criteria.

Feasible Region: Also known as the feasible set or feasible solution space, this refers to the collection of all points that satisfy each constraint in the linear programming problem. It represents the set of possible solutions that meet all the given constraints.

However, "Decision variables" is not a component of a linear programming model but rather the unknowns or variables that we want to determine in order to optimize the objective function.

Decision variables are not a component of a linear programming model. The components of a linear programming model include constraints, objective function, and feasible region. The feasible region refers to the collection of all points that satisfy each constraint in the linear programming problem.

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Answer:

:) The Inverse of the Function f(x) = 2x + 1 is f-1(x) = x/2 - 1/2.

Step-by-step explanation:

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The number of quasi-prime numbers that are less than 500 = 92

Quasi-prime numbers are those numbers that are also known as semi prime numbers which can not be divided by 2,7 or 11.

They are often derived from prime numbers which are 95 in number from 2 - 499. ( less than 500).

The 95 prime numbers - 3 numbers( such as 2,7 or 11) = 92

Therefore, the number of quasi-prime numbers that are less than 500 = 92

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Answer:

m=21g g being gallons

21 times 7 = 147

Step-by-step explanation:

The common difference in the arithmetic sequence is d = 6 (each term increases by 6 compared to the previous term). The first term is a_1 = 7.

To write the sum of the first 51 terms using sigma notation with the lower limit n=2, we need to find the upper limit of the summation. We can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

Setting a_n equal to the last term we want to include in the sum (which is the 51st term), we get:

a_51 = 7 + (51-1)6 = 307

So the upper limit of the summation is n = 51.

Now we can use sigma notation to write the sum of the first 51 terms:

∑(n=2 to 51) (7 + (n-1)6)

This notation means that we start the summation from n = 2 and add up the terms in the sequence for n = 2, 3, 4, ..., 51. The term inside the parentheses represents each term in the sequence, which is 7 plus the common difference multiplied by (n-1).

To evaluate this summation, we can simplify the expression inside the parentheses:

7 + (n-1)6 = 6n + 1

Now we can substitute this expression back into the sigma notation:

∑(n=2 to 51) (6n + 1)

Expanding the summation, we get:

(6(2) + 1) + (6(3) + 1) + (6(4) + 1) + ... + (6(51) + 1)

Simplifying, we get:

13 + 19 + 25 + ... + 307

To find the sum of this arithmetic series, we can use the formula:

S_n = (n/2)(a_1 + a_n)

where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Plugging in the values, we get:

S_51 = (51/2)(7 + 307) = 7863

Therefore, the sum of the first 51 terms of the arithmetic sequence is 7863.

The sample standard deviation of errors (residuals) around the regression line is 1.693.

The sample standard deviation of errors is a measure of the dispersion of the residuals around the regression line. In this case, the sample standard deviation of errors is 1.693, indicating that the residuals have a relatively high amount of variation. This could suggest that the regression line may not be a good fit for the data and that additional analysis is needed to determine the relationship between the independent and dependent variables.

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Answer: 4k^7

Step-by-step explanation: