If the angle is the opposite of the shorter of the two sides, there are two potential triangles. The perpendicular angle to the shortest side is the smallest angle.
What are angles?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.
When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °.
Acute, right, obtuse, and reflex angles are the other three significant types of angles.
360 degrees make up a circle.
A 720° angle indicates that the object has completed two full rotations.
There are two possible triangles if the angle is the opposite of the shorter of the two sides. The smallest angle is that which is perpendicular to the shortest side.
Therefore, if the angle is the opposite of the shorter of the two sides, there are two potential triangles. The perpendicular angle to the shortest side is the smallest angle.
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What is the mean of 9 and 25?
Answer:
17
Step-by-step explanation:
(9+25)/2 = 34/2 = 17
when finding a mean, you have to add all the numbers and divide the sum by the number of values given.
How will you describe the relationship between the volume of a sphere and the volume of a cylinder?
The relationship between the volume of a sphere and the volume of a cylinder is said to be that the volume of any sphere is 2/3rd of the volume of any with equal radius and height which is equal to the diameter.
Assuming a cylinder with radius r, height h.
We are aware that the cylinder-volume formula is,
V₁ = π * r² * h
Consider a sphere with radius r₁.
We know that the formula for the volume of sphere is,
V₂ = 4/3 * π * r₁³
If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r₁ = r and h = 2r
V₂ = 4/3 * π * r³
And V₁ = π * r² * (2r)
V₁ = 2 * π * r³
V₁ = 2 * 3/4 * V₂
V₁ = 3/2 * V₂
Volume of cylinder = (3 / 2) * Volume of sphere
Therefore, the Volume of a sphere = 2/3 * Volume of a cylinder
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What is whole numbers class 8?
Whole Numbers are the numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}.
Whole Numbers
Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered as whole numbers.
Addition , Subtraction , Division and multiplication are also possible with the whole numbers as they are also numbers . Addition and Multiplication are closed which means the sum and multiplication of two numbers is also a whole number whereas Subtraction and Division are unclosed.
We know that natural numbers refer to a set of counting numbers starting from 1, 2, 3, 4 and so on. In simple words, whole numbers are a set of numbers without fractions, decimals, or even negative integers.
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In which triangle all the sides are equal and all the angles are also equal *?
Equiangular triangle or Equilateral triangle have all the sides equal and all the angles are also equal.
A triangle that has equal-length sides is known as an equilateral triangle in geometry. The three angles that lie across the three equal sides are also equal in size since the three sides are also equal.
With each angle measuring 60 degrees, it is also known as an equiangular triangle.
An equilateral triangle has three interior angles that are all equivalent to one another and each measure 60 degrees in the basic Euclidean geometry. The term "regular triangle" is also used to describe this polygon because it is a regular polygon. The exceptional case of an isosceles triangle with three equal sides and angles is an equilateral triangle.
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what is simplify 4^-4
Answer:
1/256
Step-by-step explanation:
-4 times -4 times -4 times -4 = 256
A negative exponent means it's a fraction!
So, the answer is 1/256
answer :
1/256
steps:
negative exponent means it's a fraction
4^-4 =
1/4^4 :
4^4 =
4 * 4 * 4 * 4 =
256
again negative exponent means it's a fraction so
1/256
How would you describe the end behavior of the graph of a polynomial function based on its equation?
The end behavior of a polynomial function can be determined by examining the leading coefficient and degree of the polynomial. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. If the leading coefficient is negative, the graph will decrease without bound as the x-values increase.
The end behavior of a polynomial function depends on the equation of the function. The degree of a polynomial is the highest power of the variable, and the leading coefficient is the coefficient of the term with the highest degree. If the leading coefficient is positive, the graph will increase without bound as the x-values increase. This is because the terms in the equation with positive coefficients will become increasingly larger than the terms with negative coefficients as the x-values increase. On the other hand, if the leading coefficient is negative, the graph will decrease without bound as the x-values increase. This is because the terms in the equation with negative coefficients will become increasingly larger than the terms with positive coefficients as the x-values increase. In addition, the degree of the polynomial can also affect the end behavior of the graph. If the degree is even, the graph will not have an extreme point. However, if the degree is odd, the graph will have an extreme point. The extreme point will be a maximum or a minimum depending on the sign of the leading coefficient.
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exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa. (a) calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (round your answer to two decimal places.)
95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
What is proportional limit?
The maximum stress at which stress and strain are directly proportional and the stress-strain graph is a straight line with a gradient equal to the elastic modulus of the material is known as the proportional limit.
To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the following formula:
lower confidence bound = sample mean - (t-value * standard error)
The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:
[tex]standard\ error = sample\ standard\ deviation / \sqrt{(sample \ size)}\\\\= 0.78 / \sqrt{(20)}\\\\= 0.19[/tex]
To find the t-value, we can consult a t-distribution table or use a t-distribution calculator. At a 95% confidence level with a sample size of 20, the t-value is approximately 1.725.
Substituting these values into the formula for the lower confidence bound, we get:
lower confidence bound = 8.52 - (1.725 * 0.19)
= 8.52 - 0.327
= 8.19
So the 95% lower confidence bound for the true average proportional limit stress of all such joints is approximately 8.19 mpa.
Hence, 95% confident that the true average proportional limit stress of all such joints is at least 8.19 mpa.
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What is the range of this absolute value function? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line rises through (negative 10, negative 3), (negative 7, 0) to (0, 7), and then it falls through (7, 0), and (10, negative 3). A. -∞ < y ≤ 0 B. 0 ≤ y < ∞ C. -∞ < y ≤ 7 D. -∞ < y < ∞
The range is an absolute value functions is
B. 0 ≤ y < ∞What are absolute value functions?A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function.
Remember that a number's distance from 0 on the number line represents its absolute value.
A number can never have a negative absolute value. hence the negative values will never be in the range
This makes the range to start possibly from zero, from the graph explained 0 is among the values that are in the range
Considering that absolute values are non zero and option B is the only option that does not have a negative value. This is the best option
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Answer:
The range is an absolute value functions is
B. 0 ≤ y < ∞
Step-by-step explanation:
How to solve x3 7x 6?
(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial. A degree three polynomial might be referred to as a cubic polynomial.
what is cubic polynomial ?A degree three polynomial might be referred to as a cubic polynomial. In other words, the number three will be the largest exponent of the variable in a cubic polynomial. A cubic polynomial would therefore have the generic form ax3+bx2+cx+d, where a ≠0.
here
Let p(x)=[tex]x^{3}[/tex]−7x+6
From figure, we have p(1)=0
Thus, (x−1) is a factor of p(x)
The other factor is [tex]x^{2}[/tex]+x−6
=(x+3)(x−2)
Therefore, [tex]x^{3}[/tex]−7x+6 =(x−1)(x+3)(x−2)
(x-1), (x-2) and (x+3) are the three factors of the above cubic polynomial.
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Solve angle ABC by using the measurements angle ABC = 90°, angle BAC = 35°, and a = 10. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
The measure of the sides 'b' and 'c' will be 5.7 units and 8.2 and angle C will be 55°.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = CA / sin B
The measure of the third angle is given as,
∠A + ∠B + ∠C = 180°
35° + 90° + ∠C = 180°
∠C = 55°
Then the measure of the side c (AB) is calculated as,
AB / sin C = BC / sin A
c / sin 55° = 10 / sin 90°
c = 8.2
Then the measure of the side b (AB) is calculated as,
AC / sin B = BC / sin A
b / sin 35° = 10 / sin 90°
b = 5.7
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How do you write more than 50?
More than 50 in mathematical expression is written as >50.
Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.
The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 3x - 2 > 50].
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Is i squared negative 1 or 1?
The value of "i" squared results in:
(-1) = i²
What are numeric sets?Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.
Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
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Why is 2 root 2 equal to root 2?
Therefore , the given expression of this problem of square root
2√2 not equal to √2.
What is square root?The value that results from multiplying the square root of an integer by itself is the number.
Example: Since 5* 5 = 25, 5 is the square root of 25. Observe that (5) (5) also equals 25, proving that (5) is a square root of 25.
Here,
In this case, the mathematical symbol for Root 2 is 2.
Root 2 then multiplied by Root 2.
√2 + √2 = 2√2
If we take the estimated value of 2 = 1.4142
Then
=> 2√2 = 1.4142 x 2
=> 2.8284 (approximately)
Please take note that 2 is an irrational number.
Alternatively, root2* root 2
√2 * √2 = 2
Because 2 is just the square root of 2,
Therefore,
what happens when root 2 + root 2 and root2 root 2 are different
2√2 - 2 = 2.8284 - 2 = 0.8284 (approx)
Therefore , the given expression of this problem of square root
2√2 not equal to √2.'
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in the equation -2 - 6b = 32, the negative coefficient is ____??
Answer:
May be minus
Step-by-step explanation:
minus 2 and minus 6 means minus 8b than we have to find out the value of b so 8into 4 is equal to 32
Hiro painted his room. After 3 33 hours of painting at a rate of 8 88 square meters per hour, he had 28 2828 square meters left to paint. Let y yy represent the area (in square meters) left to paint after x xx hours.
The function representing the area to paint as a function of time is A(t) = 52 - 8t, where A(t) represents the area left to paint after t hours.
The area to paint, A(t), can be represented as a linear function based on the given information. Initially, Hiro had the entire room to paint, which can be represented as A(0) = A₀, where A₀ is the total area of the room.
Given that Hiro painted at a rate of 8 square meters per hour, after t hours, he would have painted 8t square meters.
Therefore, the remaining area to paint after t hours can be expressed as A(t) = A₀ - 8t.
We are told that after 3 hours, Hiro had 28 square meters left to paint. Substituting t = 3 and A(t) = 28 into the equation, we can solve for A₀:
28 = A₀ - 8 x 3
28 = A₀ - 24
A₀ = 52
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The complete question:
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?
What is the median of the following data sample 3 7 4 8 9 6 10 12 13 15?
The Median of the following sample 3 4 6 7 8 9 10 12 13 15 is 8.5.
One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.
When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:
sort the data in ascending or descending order.
If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.
The average of the top two observations is the same as the median of the data given (as determined in step 2).
Median = [tex]\frac{1}{2} [(\frac{n}{2} ) + (\frac{n}{2}+1 )][/tex].
Here n = 10, So [(10/2) + (10/2 + 1)]/2.
=> Median = 8.5.
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Mary want to buy a bookcae to hold all of her 138 book. Bookcae A ha 4 helve and can hold 35 book on each helf. Bookcae B ha 5 helve and can hold 26 book on each helf. Which bookcae hould he buy?Bookcae A or bookcae B?
Answer:
Bookcase A
Step-by-step explanation:
Bookcase A
1 half = 35 book
4 half = 140 books
So, bookcase A can hold 140 books
Bookcase B
1 half = 26 books
5 half = 130 books
So, bookcase B can hold 130 books
So, Mary should buy bookcase A
Answer:
Bookcase A is the answer
Step-by-step explanation:
Mary has 138 books
Bookcase A = 4 shelves holds 35 books per shelf
= 4 * 35=140
Bookcase B = 5 shelves holds 26 books per shelf
= 5 * 26=130
He should buy Bookcase A, it has enough space for his books
suppose x is 5 and y is 7. choose the value of the following expression: (x != 7) && (x <= y)
The value of the following expression is true.
Expressions include operators and can consist of any set of variables and constants that can be evaluated to produce a result. Relational expressions are used in decision-making to compare operands and evaluate to 1 (true) or 0. (false).
If a logical expression is true when it is evaluated by C++, it returns an integer value of 1; if it is false, it returns an integer value of 0. Any value other than zero is treated as true in C++, while a value of zero is considered false.
Correct Question :
Suppose x is 5 and y is 7. Choose the value of the following expression: (x ! = 7) & & (x <= y)
a. false
b. true
c. 0
d. null
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A right triangle has side lengths of 15 in, 12 in, and 9 in. it is dilated by a scale factor and has new side lengths on 5 in, 4in, and 3 in. what was the scale factor?
Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.
For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
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The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
Help me rationalize the denominator
Answer:
[tex]\frac{2}{15} (3+\sqrt[3]{3})[/tex]
or
[tex]\frac{6+2\sqrt[3]{3} }{15}[/tex]
You can rationalize the denominator to simplify the answer so many different ways.
Step-by-step explanation:
Simplify the radicals.
The length of a
rectangle is 5 ft more than twice its width. The
area of the rectangle
is 33 ft^2. Find the dimensions of the rectangle.
The dimensions of the rectangle is length = 5ft and width = 3ft
Define System of equation
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Let,
x = length of rectangle
y = width of rectangle
Next, set up system of equation
We have given, the length of a rectangle is 5 ft more than twice its width.
x = 2y + 5 --------(a)
Next, The area of the rectangle is 33 ft²
xy = 33 ----------(b)
x = 33/y
substitute the value of x in eq(a)
x = 2y + 5
33/y = 2y + 5
33 = 2y² + 5y
2y² + 5y - 33 = 0
Factor it,
2y² + 11y - 6y - 33 = 0
y( 2y + 11) - 3( 2y + 11) = 0
(y - 3) (2y + 11) = 0
Split the values,
y - 3 = 0 and 2y + 11 = 0
y = 3 and y = -11/2 (ignore this as width cannot be -ve)
Substitute y = 3 in eq(b)
x * 3 = 33
x = 11
So, we get
length = 11 ft and width = 3 ft
Hence, the dimensions of the rectangle is length = 5ft and width = 3ft
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How many buses do you need for 500 people if each bus holds 40 people?
Answer:
13
Step-by-step explanation:
Divide 500 by 40 to find the amount of buses you need
500 ÷ 40 = 12.5
BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people
you'll need 13 buses
Answer:
13 buses
Step-by-step explanation:
12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.
We can reduce the margin of error in an interval estimate of p by doing any of the following except ____. increasing the sample size. increasing the planning value p* to .5. increasing a reducing the confidence coefficient.
We can reduce the margin of error in an interval estimate of p by doing any of the following except using a planning value p* closer to 0.5.
The breadth of the confidence interval is affected by the following features:
Increase the sample size - Increasing the sample size is the most feasible strategy to reduce the margin of error.Reduce variability - You can estimate a population parameter more precisely the less variable your data are.Use a one-sided confidence interval - The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval.Lower the confidence level - A narrower, more exact confidence interval is the benefit of a lower confidence level.Correct Question:
We can reduce the margin of error in an interval estimate of p by doing any of the following except ____.
increasing the sample size
using a planning value p* closer to 0.5
increasing the level of significance
reducing the confidence coefficient
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How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation?
The equation of line in slope intercept form passing through (-5,-2) and parallel to y = -2x+1 is y = -2x -12 .
The Slope intercept form of the line is written as " y = mx + c " , where c is the y intercept and m is the slope of line .
the required line is parallel to the line with equation ⇒ y = -2x+1 ,
on comparing it with slope intercept form of line ,
we get the slope(m) as "-2" .
the required line is passing through (-5,-2).
substituting the values , we get ;
-2 = (-2)(-5) + c ,
-2 = 10 + c ,
c = -10 -2
c = -12 .
So , the equation is ⇒ y = -2x -12 .
Therefore , the slope intercept form of the required line is y = -2x -12 .
The given question is incomplete , the complete question is
How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation ? the point is (-5,-2); and is parallel to y = -2x + 1 .
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Which formula can be used to find the missing number in an array of 1 100?
The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.
How to find missing number in an array 1 100?The size of the array is N – 1. So the sum of n elements, that is the sum of numbers from 1 to N can be calculated by using the formula N * (N + 1) / 2. Now find the summation of all elements in the array and subtract it from the summation of first N natural numbers, the value obtained will be the value of the missing element.
The formula can be used to find the missing number in an array of 1 100 is N * (N + 1) / 2.
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What is the coefficient of y² in the expression 3y²+ 4x?
The coefficient of y² in the expression 3y²+ 4x is 3.
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.
Firstly,
The given equation is 3y²+ 4x
To find : The coefficient of y²
The coefficient is nothing but the number beside the variable.
In the equation 3y²+ 4x, the number beside the variable y² is 3 and it is termed as coefficient of y² which is 3.
As we can see that the term that is in multiplication with y² is 3. Similarly, the term that is coefficient of x is 4.
Hence, the coefficient of y² in the equation is 3.
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stephanie knows that a correlation between the number of bars and the number of churches in her city does not, in itself, mean that more bars will lead to a higher number of churches. which of the following would not be a lurking variable in the above scenario? a.) the city's budget b.) stephanie's proximity to the center of the city c.) the day of the week that stephanie attends service d.) population density
The option that would not be a lurking variable in the above scenario is c.) the day of the week that stephanie attends service
What is a lurking variable?a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable. Although it is not taken into account in the study, it might affect how the variables are related.
When researching the relationship between two or more variables, we occasionally neglect the influences on the relationship that exist outside of these two variables. These are also known as lurking variables or extraneous variables. These significantly impact the relationship. Lurking variables are those that were not taken into consideration for the study but have an impact on the two studied variables.
The day of the week will not be a lurking variable since we are talking about the number of churches and bars. Hence, Option c is correct.
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Answer:
Step-by-step explanation:
a.) Correct.
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely street name length is related to the number of bars in a given area.
What is the difference between ≥ and ≤?
The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).
What is Inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way. By comparing the sizes of two numbers on the number line, it is most frequently utilized. Different types of inequalities are represented by a variety of different notations, including:
The symbol a b indicates that an is less than b.
A bigger value for a than a lesser value for b is indicated by the notation a > b.
A is not equal to b in either situation. These relationships are referred to as stringent inequalities, which means that an is strictly less than or strictly bigger than b. Equivalence is not included.
There are two kinds of inequality relations that are not strict, in contrast to strict inequalities:
When something is written with an an or b, it signifies that.
A is smaller than or equal to b when a notation like a ≤ b is used (or, equivalently, at most b, or not greater than b).
A greater or equal value for a indicates that b is greater than it (or, equivalently, at least b, or not less than b).
The symbol for "greater than" that is divided in half by a slash, "not," can also be used to express the connection not greater than. The same applies to and not less than and a b.
Hence, The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).
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It signifies that the supplied variable or number must have a value that is larger than or equal to the specified limit. It is the opposite of less than or equal to.
What is Greater and Lower than equal to function ?The phrase "more than or equal to" denotes that the variable is either greater than or equal to a specific value. When a quantity is bigger than another, the phrase "more than" is used to indicate this. Two quantities are said to be equal when the phrase "is equal to" is used. It is possible for the quantity or amount value limit to be equal to or larger than the stated limit when these phrases are combined to form the new term Greater Than Or Equal To.
The phrase "less than or equal to" denotes that a variable is either less than or equal to another quantity, number, or variable. Other ways to say "less than or equal to" include at most, no more than, a maximum of, and not surpassing.
Inequalities like less than or equal to and greater than or equal to are represented in a different way on a number line. To denote these, we use the closed circle to mark the limit value and point the arrow towards the given condition of inequality.
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can you guys help me with this plsss
Answer:
30 inches
Step-by-step explanation:
The longest piece (15 in) is represented as 5 in the ratio, so we can find what one unit is. We can do 15÷5=3, so one unit is 3 inches. We could multiply each of them by 3 and add them up, but there's a simpler way. We can find the total of the ratio, 2+3+5=10. So, we can do 3x10=30 inches. Therefore, the length of the stick is 30 inches.
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Answer:
Step-by-step explanation: