For the sample of weight of corn chips dispensed in dispensing machine, probability that the sample mean weight of these 100 bags falls between 10.50 and 10.80 ounces is equals to 0.4332.
We have a sample of weight of corn chips dispensed by the dispensing machine.
Dispensed weight of bag by the dispensing machine = 10 ounces
The sample of weight of bags follows the normal distribution with, sample mean, [tex] \bar x[/tex] = 10.5 ounces
standard deviations = 2 ounces
Randomly selected from this dispensing machine. Sample size, n = 100
We have to determine probability that the sample mean weight of these 100 bags falls between 10.50 and 10.80 ounces,
[tex]P( 10.50 < \bar x < 10.80),[/tex]
Using Z-score formula for sample mean in normal distribution, [tex]Z = \frac{ \bar x - \mu}{ \frac{\sigma}{\sqrt{n}} }[/tex]
where μ--> population mean
σ -->standard deviations
n --> Sample size
Now, the required probability is [tex]P( 10.50 < \bar x < 10.80)[/tex]
= [tex]P(\frac{ 10.50 - \mu }{\frac{\sigma}{\sqrt{n}}} < \frac{ \bar x - \mu}{ \frac{\sigma}{\sqrt{n}} } < \frac{ 10.80 - \mu }{\frac{\sigma}{\sqrt{n}}} )[/tex]
= [tex]P(\frac{ 10.50 - 10 }{\frac{2}{\sqrt{100}}} < z< \frac{ 10.80 - 10 }{\frac{2}{\sqrt{100}}} )[/tex]
= [tex]P(\frac{ 0.50 }{\frac{2}{10} }< z< \frac{ 0.80 }{\frac{2}{10}})[/tex]
= [tex]P(2.5 < z< 4)[/tex]
= 0.4332
Hence, required value is 0.4332.
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What is i^33 simplified?
i³³ simplified is i.
What is the Complex Number?
A complex number is a number in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
When raising a complex number to a power, we can use the property [tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]
It is also possible to simplify the powers of complex numbers using De Moivre's Theorem:
[tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]
Where [tex](a + bi)^n = r^n * (cos(n\theta) + i*sin(n\theta))[/tex]
Where r is the magnitude, θ is the argument, and n is an integer.
For example, if we raise i to the power of 3, we can use De Moivre's Theorem:
i³ = (cos(90) + isin(90))³ = cos(270) + isin(270) = -i
So, i³ = -i
When raising complex numbers to powers, the magnitude will be raised to the power of n while the argument will be multiplied by n.
i² = -1, so i³³ can be written as (i²)¹⁶ * i = (-1)¹⁶ * i = i
Therefore, i³³ simplified is i.
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A car moving at a contant peed paed a timing device at t0. After econd, the car ha traveled ft. Write a linear function rule to model the ditance in feet d the car ha traveled any number of econd t after paing the timing device
The required equation is:
1. d = 81t
2. f(t) = 81t
Now, According to the question:
Given that a car moving at a constant speed passed a timing device at t=0.
In other words, at t = 0 second, d = 0 ft.
We know that
distance = rate × t
After 7 seconds, the car has traveled 567 ft.
In other words, at t = 7 seconds, d = 567 ft
Thus, there are two points
(0, 0)
(7, 567)
Finding the slope between (0, 0) and (7, 567)
Using the formula
Slope = Rate of change = [y₂-y₁] / [x₂-x₁]
= [567 - 0] / [7-0]
= 567 / 7
= 81 ft./second
Given that the car is moving at constant speed. So, we don't have any other factor or term to consider
Thus, the required equation is:
distance = rate × t
d = 81 × t
d = 81t
or
f(t) = 81t
VERIFICATION
Given the equation
d = 81 × t
Put t = 0 to find the distance in 1 sec
d = 81 × (0) = 0 ft.
Put t = 7 to find the distance in 7 seconds
d = 81 × (7) = 567 ft.
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The complete question is this:
A car moving at a constant speed passed a timing device at t=0. After 7 seconds, the car has traveled 567 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
Which set of ordered pairs does not represent a function?
○ {(−1, -3), (3, 7), (−4, 7), (−2, —2)}
O {(2, 4), (7, 9), (-6, 8), (-5,4)}
O {(9,-2), (9,5), (-9, 1), (3,0)}
O {(-4,-8), (-2, 7), (-5, -6), (3, 7)}
Submit Answer
There is no function in the first set of ordered pairs. It is not a function because the X value of 7 repeats.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
Only the first set of ordered pairs is a function; the second, third, and fourth do not represent functions.
This is due to the need that each x value have a unique y value. So you note that, with the exception of the first set of ordered pairs, all sets of ordered pairs have two distinct x-values that share a same y-value, which is not possible.
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Let's suppose that the strength in newton of usual men can be
found by f = 500 ln(w + 1), where w is the man's weight in
pounds. Find the strength of a man who is 200 pounds. Round
your answer to the nearest tenth.
newton
So the strength of a man who is 200 pounds is approximately 2649.2 newton, rounded to the nearest tenth.
What is weight?Weight is a measure of the force exerted on an object due to gravity. It is measured in units of force such as pounds, kilograms, or newtons. The weight of an object is equal to the force of gravity acting on it and is equal to the mass of the object multiplied by the acceleration due to gravity.
What is newton?Newton (N) is the unit of force in the International System of Units (SI). It is named after Sir Isaac Newton, the famous English physicist, mathematician, and astronomer. It is defined as the force that is required to accelerate an object with a mass of one kilogram at a rate of one meter per second squared.
f = 500 ln(200 + 1)
f = 500 ln(201)
then we can calculate the value of ln(201) using a calculator, and the result is 5.298317366548036
then we can substitute the result into the original equation and get
f = 500 * 5.298317366548036 = 2649.15868
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helppppppppppp me nooow !!!!!!!!!!!!!!!!!! as fast please
Answer:
100
Step-by-step explanation:
week 7 = 110
week 8 = 100
week 9 = 90
week 10 = 110
........
One Canadian dollar i valued at 0. 96 of a US Dollar. One Canadian dollar i valued at what fraction of a US Dollar
Can Someone Help plssss
Answer:
<B = 83* and x = 5
Step-by-step explanation:
<D = 83*
<CAD = 50* = <BCA
<ACD = 180 - (50+83) = 47* = <CAB
<B = 180 (sum of interior angles of triangle ABC) - <BCA - <CAB
<B = 180 - 50 - 47 = 83*
AD = BC
5x = 25
x = 5
Hope this helps!
for a given recipe, 16 cups of flour are mixed with 8 cups of sugar. How many cups of flour should be used if 12 cups of sugar are used?
Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x.
Answer:
24 cups
Step-by-step explanation:
16/8 = 2
[tex]\frac{2}{1}[/tex] = [tex]\frac{x}{12}[/tex]
Since 1 x 12 = 12, then 2 x 12 = 24
Use the graph below to fill in the blank with the correct number: (1 point)
f(−2) = _______
The solution would be 2.The point's y value at x = -2 provides a clue as to how f(-2) would behave.
What do you mean By graph Intercept function?
The set of ordered pairs where f(x)=y is displayed as the graph of a function in mathematics. These pairs are the Cartesian coordinates of points in two-dimensional space and, in the typical case where x and f(x) are real numbers, they form a subset of this plane.See if any vertical lines that were drawn intersect the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does represent a function if no vertical line can cross the curve more than once.To know more about relations of a function here
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Do sides 5 cm 12cm and 13cm form a right-angled triangle give reason?
Answer:
No they do not
Step-by-step explanation:
Sides 5 cm and 12cm can form a right angled triangle because 5 + 12 = 17 which is a greater number than 13 meaning it cannot
Based on the above graph, which of the four occupations listed is expected to add the greatest number of jobs from 2006 to 2016?
a.
Registered nurses
b.
Postsecondary teachers
c.
Waiters and waitresses
d.
Computer systems analysts
Registered nurses is expected to add the greatest number of jobs from 2006 to 2016.
Hence, Option A is correct
What do you mean by graph Growth Rate?
A graph displaying the evolution of a nation's population may serve as an illustration of a growth curve. In statistics, growth curves are frequently used to identify trends in the growth over time of a quantity, whether it be linear, exponential, or cubic.If k0 and a>0, the decay is represented by the function y=f(x)=aekx. The function is a decreasing function, meaning that as x rises, y falls. Range: The range of the graph is always positive real numbers if a>0, and the graph is always above the x axis.By subtracting the current number from the prior value, you may get the growth rate. To obtain a percentage representation of the growth rate, divide this difference by the prior amount and multiply the result by 100.To know more about growth rate of a graph here
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Answer:
a
Step-by-step explanation:
Please help me I have until tomorrow.
Answer:
number 6, y=-6 number 7 x=2 and
Step-by-step explanation:
and number 10, 4 - 6 / -3 + 5, 4 - 6/2, - 2 / 2, Solution: -1
Given mn, find the value of x.
Answer:
(x-17)
(5X-1)
The angles are a pair of linear angles. They complement one another and are close by. They intersect at a right angle. x = 33,
Describe angle.When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
Additional angles add up to 180.
(x-17)+(5x-1) = 180
x-17+5x-1 = 180
(x+5x)+(-17-1) = 180
6x-18 = 180
6x = 180+18
6x = 198
x = 198/6
x = 33
Additional information
x = 33, therefore if
x-17 = 33-17 = 16
5x-1 = 5*33-1 = 165-1 = 164
Angles added together result in 16+164 = 180
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Complete question -
What is the exponential form of root 2?
The Exponential Form of the number root 2 , is represented as [tex](2)^{\frac{1}{2} }[/tex] , because the term "root" means the exponent is [tex]\frac{1}{2}[/tex] .
The Root of a number x ; is defined as another number, which when multiplied by itself by given number of times is equal to x .
The Square Root of a "number x" is ; denoted by symbol "[tex]\sqrt{x}[/tex]" .
we have to express the number root 2 in exponential form ;
So, we write root 2 as ⇒ [tex]\sqrt{2}[/tex] ;
we know that the square root of any number x , in exponential form is written as [tex]x^{\frac{1}{2} }[/tex] ;
So , the exponential form of root 2 is [tex](2)^{\frac{1}{2} }[/tex] .
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I don’t understand this.
Answer: x = 25
Step-by-step explanation:
2x-10 = x+15
x = 15+10
x=25
The required value of x in the given triangle is 25, evaluated by following the definition of angle bisectors.
Given that, MNO is a triangle, where OP is the angle bisector, in the given scenario we have to determine the value of the x.
Following the definition of an angle bisector, the angle bisector for any angle bisects the angle into two equal halves, So,
Angle PNO = Angle PMO
2x-10=x+15
Simplify the above expression to evaluate x.
2x-10=x+15
2x-x=15+10
x=25
Thus, the required value of x in the given triangle is 25, by following the definition of angle bisectors.
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What is the greatest common factor of the polynomial below?
20x^3-14x
—————————————-
A. 2x^2
B. 6x^2
C. 6x
D. 2x
The greatest common factor of the polynomial 20x^3-14x is D. 2x.
What is greatest common factor?The concept that will be sued here is common factor. A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. The largest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.
For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.
The common factor that ca be gotten from 20x² : are: 1, 2, 4, 5, 10, 20, x
The common factor that ca be gotten from 14x are : 1, 2, 7, 14, x
Then greatest common factor of the polynomial is 2x.
Hence, 2x(10x² - 7)
Therefore, option D is correct.
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Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).
x3 + 3x2 + 16x − 20
x3 + 5x2 + 14x − 20
x3 + 8x2 + 11x − 20
x3 + 9x2 + 19x − 20
The value of function f(x) ⋅ g(x) is,
⇒ x³ + 3x² + 16x - 20
What is Function?A relation between a set of inputs having one output each is called a function.
We have to given that;
The functions are,
⇒ f (x) = x² + 3x − 4 and g(x) = x + 5.
Hence, The value of function f(x) ⋅ g(x) is,
⇒ f(x) ⋅ g(x) = (x² + 3x − 4) × (x + 5)
= x³ + 5x + 3x² + 15x - 4x - 20
= x³ + 3x² + 16x - 20
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what is the answer of 12 - y = 5
Answer:
y = 7
Step-by-step explanation:
12-5=7
7+5=12
Answer:
y = 7
Step-by-step explanation:
12 - y = 5
Subtract 12 from both sides.
-y = -7
Multiply both sides by -1.
y = 7
what is the last answer and how do I graph player two? i don’t remember how to write an equation in vertex form
The graph of the player two's function g(t)=16(t-5)²+290 is given in the attachment. The baseball's maximum height is 290 ft. At 5 seconds the baseball was at its maximum height. After 9.25 second the baseball hit the ground.
What is function?A function is a mathematical device that converts one value to another in a predictable manner. We can think of it as a machine. You give the machine an input, it performs some calculations on it, and then returns another value - the result of the calculations.
The function's name is f. We can call it anything we want, but single letters are common. The input* value is referred to as x. Again, we could use anything, but x is common. What the function does with the input is shown to the right of the equals sign.
In this case, the function takes the input x, multiplies it by three, and returns the result.
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Griffith purchased a used car for $9.400. He paid 6%% sales tax. How much tax did he pay in sales tax?
From the provided value of the paid price of the car and sales tax percentages, The answer is $564.
What do you mean by percentages?Percentages are a way to express a number as a part of 100. The symbol for percentage is %. For example, 25% means 25 out of 100, or one quarter. To convert a percentage to a decimal, divide it by 100. For example, 25% = 25/100 = 0.25. To convert a decimal to a percentage, multiply it by 100. For example, 0.25 = 0.25 * 100 = 25%. You can also calculate percentage by multiplying the number with the percentage rate. For example, if you want to find out what 25% of 50 is, you can calculate it by multiplying 50 by 0.25 (since 25% is the same as 0.25 as a decimal).
What do you mean by tax?Tax is a financial charge imposed by a government on individuals, businesses, and other entities. The revenue generated by taxes is used to fund government programs and services such as infrastructure, education, healthcare, and defense. There are many types of taxes, including income tax, sales tax, property tax, and capital gains tax. The specific tax that a person or entity is required to pay depends on the jurisdiction and the type of activity or transaction involved. Tax laws and rates can vary widely between countries and even within a country.
Griffith paid 6% of $9400 in sales tax. To find out how much that is, you can multiply $9400 by 0.06 (since 6% is the same as 0.06 as a decimal).
$9400 * 0.06 = $564
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Would the following compound inequality be classified as an “and” inequality or an “or” inequality? Inequality: 6 > x + 1 > 3
The given inequality 6 > x + 1 > 3 is an "and" inequality.
What is Compound Inequality?
Compound inequalities are kind of inequality expressions which consists of two or more simple inequalities.
"And" inequality represents that both the inequalities are true.
"Or" inequality represents that either of the statement is true.
Given inequality is,
6 > x + 1 > 3
Subtracting 1 from throughout the inequality,
6 - 1 > x > 3 - 1
5 > x > 2
This implies that x is less than and x is greater than 2, for which the value of x are 3 and 4.
Hence the given inequality is an "and" inequality.
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The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball. 2 4. 7
Baseball 1. 6. 5
Soccer 7. 4. 4
Football. 8. 15. 10
Explain what the ratio 5:73 represents.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 5:73 represents the ratio of 7th grade football players to total athletes.
The ratio 5:73 represents the ratio of total athletes to 7th grade football players.
The ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 5, 2,4/5,... Find the 10th term.
The 10th term round to the nearest thousandth of the geometric progression is found as 0.001.
Explain the term geometric progression?A sort of sequence known as geometric progression (GP) is one in which each following phrase is created by multiplying every preceding word by a fixed number, or "common ratio." This progression is sometimes considered to as a pattern-following geometric sequence of numbers.For the stated sequence:
5, 2,4/5,...
Check for AP:
a₂ - a₁ = 5 - 2 = 3
a₃ - a₂ = 4/5 - 2 = -6/10 = -3/10
As the common difference is not same, it is not an AP.
Check for GP:
a₁ = 5
a₂ = a₁ q²⁻¹
a₂ = 5q = 2
a₃ = a₁q³⁻¹
= a₁q²
a₃ = 5q² = 4/5
As,
a₂/ a₁ = 2/5
a₃/a₂ = 2/5, it is an GP
Thus,
a₁₀ = a₁qⁿ⁻¹
= 5*(2/5)⁹
= 0.001
Thus, the 10th term round to the nearest thousandth of the geometric progression is found as 0.001.
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Dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a function in terms of a for the balance of her savings account if she doesn't notice the monthly fee.
Complete the following. Use standard slope-intercept form.
The function in terms of balance of the savings account is B(a) = 200 - 5a.
What are equations?A formula known as an equation uses the equals sign to express how two expressions are equal. The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfil the equality are known as the equation's solutions.
Let the number of months be represented as a.
The fee that would be deducted ever month can thus be represented as 5a.
The initial deposit in the bank is $200, and if we include the deduction the equation is as follows:
B(a) = 200 - 5a
Hence the function in terms of balance of the savings account is B(a) = 200 - 5a.
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What are the 7 triangles?
The seven types of triangles based on side length are equilateral triangle, isosceles triangle, scalene triangle and based on angles are acute triangle, right triangle, obtuse triangle and oblique triangles.
Equilateral triangle: A triangle with all three sides of equal length and all angles of 60 degrees.
Isosceles triangle: A triangle with two sides of equal length and two angles of equal measure.
Scalene triangle: A triangle with all three sides of different lengths and all angles of different measures.
Right triangle: A triangle with one angle measuring exactly 90 degrees.
Acute triangle: A triangle with all angles measuring less than 90 degrees.
Obtuse triangle: A triangle with one angle measuring greater than 90 degrees.
Oblique triangle: A triangle that is not a right triangle, which means all angles are not 90 degrees.
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What are prime factors
Answer:
1.) A prime factor is any prime number that can be multiplied to give the original number.
For example, the prime factor of 24 is:
1, 2, 3, 4, 6, 8, 12, and 24.
2.) A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.
Step-by-step explanation:
You're welcome.
How do you dilate a triangle with center points?
To dilate a triangle with center points we multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.
What is a scale factor?
A scale factor is a numerical value that is used to represent an object's larger or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its initial size. It aids in altering the figure's size but not its shape.
Here,
we have to determine how we dilate a triangle with center points.
We concluded that
The origin is often used as the center of dilation. If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.
Hence, to dilate a triangle with center points we multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.
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What set of transformations are applied to parallelogram ABCD to create A'B'C'D'?
Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at negative 2, 1. Second parallelogram transformed formed by ordered pairs A prime at 1, negative 4, B prime at 2, negative 3, C prime at 2, negative 1, D prime 1, negative 2.
We have to reflect over x- axis to transform parallelogram ABCD to create A'B'C'D'.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
The Coordinates of ABCD are:
A( -4, 1), B(-3, 2), C(-1, 2) and D(-2, 1)
and, Coordinates of A'B'C'D' are:
A'( 4, -1), B'(3, -2), C'(1, -2) and D'(2, -1)
Now, Reflection over the x-axis.
A"(-4, 1)- 2(0, 1) ---> A"( -4, -1)
B"(-3, 2) - 2(0, 2)----> B"(-3, -4)
C"(-1, 2)-2(0, 2)--->C"(-1, -2)
D"(-2, 1)- 2(0,1)--->D"(-2, -1)
and, Reflection over the y-axis.
A"(-4, 1)- 2(-4, 0) ---> A"( 4, 1)
B"(-3, -4) - 2(-3, 0)----> B"(-3, -4)
C"(-1, -2)-2(-1, 0)--->C"(1, -2)
D"(-2, 1)- 2(-2, 0)--->D"(2, -1)
So, we must reflect over the x-axis and then reflect over the y-axis to map parallelogram ABCD onto parallelogram A'B'C'D'.
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The opposite of z is greater than 5. a. What are two possible values of z? What are two values that z cannot be? What must be true about all possible values of z? Show your work³
All values of z are negative numbers less than -5, which are -6, -7 and -8 so on.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, the opposite of z is greater than 5.
So, we have the following absolute value inequality.
|z|>5
This can be written as z>5 or z<-5
5 is a positive number.
So, we make use of the inequality z<-5.
From the above inequality, the possible values of z are -6 and -7
Note that there are other values of z
The values that z cannot be
We have: z>5 or z<-5
The values that z cannot be, are represented with the inequality z>5.
From the above inequality, z cannot be 6 and 7
The true statement about the values of z are, they are all negative numbers less than -5.
Therefore, all values of z are negative numbers less than -5, which are -6, -7 and -8 so on.
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How to find endpoint with midpoint and one endpoint formula?
To find the endpoint with the midpoint and one endpoint formula, use the following steps:
Step 1: Identify the midpoint of the line segment. The midpoint is the point that is exactly halfway between the two endpoints.
Step 2: Identify one endpoint of the line segment. This is the point that you already know.
Step 3: Use the midpoint and one endpoint to find the other endpoint. To do this, add or subtract the difference between the x-coordinates of the midpoint and one endpoint from the x-coordinate of the midpoint to find the x-coordinate of the other endpoint. Then, add or subtract the difference between the y-coordinates of the midpoint and one endpoint from the y-coordinate of the midpoint to find the y-coordinate of the other endpoint.
Step 4: Write the coordinates of the other endpoint. The point (x,y) represents the other endpoint of the line segment.
Note: The x-coordinate of the other endpoint is the x-coordinate of the midpoint + or - the difference of x-coordinate of the midpoint and one endpoint, and the y-coordinate of the other endpoint is the y-coordinate of the midpoint + or - the difference of y-coordinate of the midpoint and one endpoint.
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