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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There is another particular medicine that is modeled by the following:
f(t) = -15t² + 120t
1. Where f(t) is the amount of medication (in mg) in the bloodstream at time t (in hours).
2. Determine the maximum amount of medication in the bloodstream.
3.Using a function, determine the concentration of medication in the
bloodstream after 2 hours.
Answer:
Step-by-step explanation:
1. The function f(t) represents the concentration of medication in the bloodstream over time. The function has a parabolic shape, with the maximum value at t = 8 hours.
To find the maximum concentration of the medication, we can set the derivative of the function equal to 0 and solve for t. The derivative of f(t) is:
f'(t) = -30t + 120
Setting this equal to 0 and solving for t, we get:
-30t + 120 = 0
-30t = -120
t = 4
Therefore, the maximum concentration of the medication occurs at t = 4 hours. At this time, the concentration of the medication is:
f(4) = -15(4)^2 + 120(4) = 120 mg
It's important to note that this function represents the concentration of the medication in the bloodstream, not the total amount of medication that has been taken. The total amount of medication taken over a given time period can be found by integrating the function over that time period.
2. To determine the maximum amount of medication in the bloodstream, we need to find the maximum concentration of the medication and then multiply that concentration by the volume of the bloodstream.
We have already determined that the maximum concentration of the medication is 120 mg/L. The volume of the bloodstream in an adult is approximately 5 liters. Therefore, the maximum amount of medication in the bloodstream is:
120 mg/L * 5 L = 600 mg
This is the maximum amount of medication that can be present in the bloodstream at any given time. It's important to note that this amount may be affected by various factors, including the rate at which the medication is metabolized and eliminated from the body.
3. To determine the concentration of medication in the bloodstream after 2 hours, we can substitute 2 for t in the function f(t) and solve for the concentration. The function for the concentration of medication in the bloodstream is:
f(t) = -15t^2 + 120t
Substituting 2 for t, we get:
f(2) = -15(2)^2 + 120(2) = 60 mg/L
Therefore, the concentration of the medication in the bloodstream after 2 hours is 60 mg/L. It's important to note that this represents the concentration of the medication at a specific point in time, not the total amount of medication that has been taken. The total amount of medication taken over a given time period can be found by integrating the function over that time period.
PLEASE HELP IM STUCK
Answer:
option b is the answer of the above
Please give a step by step explanation
The evaluation of the composite figure comprising of a square and an equilateral triangle is as follows;
9 (a) ∠ABD = 90°
(b) ∠BCD = 60°
(c) ∠ADC = 105°
What is a composite figure?A composite figure is a figure comprising of two or more regular geometric figures.
9. The shape of the quadrilateral ABDE = A square
The kind of triangle specified for the triangle ΔBCD = Equilateral triangle
The sides of the square ABDE are congruent by the definition of a square
Therefore; AB = BD = DE = AE by the definition of congruency
(a) Angle ∠ABD is a corner of the square ABDE, therefore;
The size of angle ∠ABD = 90° (properties of the interior angle of a square)
∠ABD = 90°(b) The size of angle ∠BCD = 60° (Interior angle of an equilateral triangle)
∠BCD = 60°(c) The size of angle ∠ADC is found as follows;
Triangles ΔAED and triangle ΔABD formed by the diagonal AD are congruent by Side-Side-Side, SSS congruency postulate
∠DAB ≅ ∠ADB (base angles of isosceles triangle ΔABD)
∠DAB = ∠ADB (Definition of isosceles triangles)
∠ABD + ∠DAB + ∠ADB = 180° (Angle sum properties of a triangle)
90° + 2 × ∠ADB = 180° (substitution property)
∠ADB = (180° - 90°) ÷ 2 = 45°
∠BDC = 60° (Interior angle of an equilateral triangle)
∠ADC = ∠ADB + ∠BDC (Angle addition postulate)
Therefore, ∠ADC = 45° + 60° = 105°
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If f(x) = x² + 1, then f(f(3)) = ?
Answer:
f(f(3))=101
Step-by-step explanation:
To solve this problem, first solve for f(3):
[tex]f(3)=(3)^2+1\\f(3)=9+1\\f(3)=10[/tex]
Then, insert f(3) into f(2) by substituting f(3) in place of x:
[tex]f(f(3))=f(10)\\f(10)=(10)^2+1\\f(10)=101[/tex]
In Angle abc and angle pqr ab:pq=4:5 and a(angle pqr)=125cm² then find a(angle abc)
In Angle abc and angle pqr ab:pq=4:5 and a(angle pqr)=125cm² then the measure of angle ABC is 100 cm².
What is the angle?Generally, To find the measure of angle ABC in the triangle ABC, we can use the fact that the ratios of the measures of the angles in a triangle sum to 180 degrees.
We are given that the ratio of the measures of angles ABC to PQR is 4:5. This means that if we let x represent the measure of angle ABC, then the measure of angle PQR is 5x/4.
The measure of angle PQR is also given to be 125 cm². We can use this to set up the equation:
5x/4 = 125
Solving for x, we find that the measure of angle ABC is:
x = 100
Therefore, the measure of angle ABC is 100 cm².
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What is the width of the rectangular area?
The width of a rectangle is the smaller side length that situated vertically. Width of rectangular area = Area of rectangle/ length of rectangle
or width of rectangular area = (perimeter of rectangle /2) - length of rectangle
what is the perimeter of a shape?The perimeter is the line that goes continuously along the boundary of a geometrical shape.
How can we find the width of rectangle?the width of rectangle can be found from the area of rectangle formula or area of perimeter formula when the value of length, area and perimeter is known to us.
area = length × width
perimeter = 2(length × width)
hence, the width of a rectangle is the smaller side length along the vertical axis.
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How many terms does 3xy have?
3xy has two terms, 3 and xy. The term 3 is a constant and the term xy is a product of two variables.
3xy is a multiplication of three individual components. It consists of three distinct parts, namely 3, x, and y. Each of these components is considered a distinct term, so 3xy has three terms in total. The 3 represents a numerical value, while the x and y are variables that can be assigned any numerical value. When multiplied together, the three terms form a single expression, 3xy, which can then be evaluated for a resulting value.
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What is the smallest number divisible by 3?
The smallest number that is divisible by 3 is 3 itself. Every integer that is divisible by 3 is called a multiple of 3.
For example, some of the multiples of 3 are 6, 9, 12, 15, 18, 21, etc. All of these numbers can be obtained by multiplying 3 by an integer.
What does "divisible" mean in math?If a number evenly divides (leaves no residue) into another number, it can be divided. For instance, 34 may be divided by 2 equally, making it a divisible number. However, because doing so would result in a leftover, 34 cannot be divided by 3.
How are three divided?According to the law of three's divisibility, a number is completely divisible by three if the sum of its digits is also divisible by three. Take 308 as an example. To determine whether or not 308 is divisible by 3, add the digits together and find the sum (3+0+8=11).
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The volume of a rectangular prism is 6x3 + 19x2 + 2x - 3
and the height is x + 3. What is the area of the base of the prism?
To find the area of the base of the rectangular prism, we need to find the expression for the area of a rectangle with dimensions equal to the dimensions of the base of the prism.
The volume of a rectangular prism is given by the formula:
Volume = length * width * height
Substituting the given expressions for the volume and the height into this formula, we get:
6x3 + 19x2 + 2x - 3 = (length * width) * (x + 3)
Expanding the right-hand side of the equation, we get:
6x3 + 19x2 + 2x - 3 = length * width * x + length * width * 3
Matching the terms on the left-hand side of the equation with the corresponding terms on the right-hand side, we can see that the expression for the area of the base of the rectangular prism is:
length * width = 6x3 + 19x2 + 2x - 3 - length * width * 3
Simplifying this expression, we get:
length * width = -3x3 - 17x2 - 2x + 3
Therefore, the area of the base of the rectangular prism is given by the expression -3x3 - 17x2 - 2x + 3.
The probability of an unfavorable outcome plus the probability of a favorable outcome equals 1.
O True
O False
Your answer is False
What is 4 1/2÷(−2 2/3)?
Write the answer as a mixed number in simplest form.
help plssss
Answer:
Step-by-step explanation:
you cant divide fractions so you multiply the reciprocal so your answer would be
1 11/16
A one-pound pack of wall putty costs $3. A 10-pound pack costs $24. What is the percent savings If you buy the 10-pound pack? 2096 24% 25% 60%
Answer:
20%
Step-by-step explanation:
let x = percent savings
$3/lb (cost per lb of a 1 lb pack)
$24/10lb = $2.40/lb (cost per lb for a 10 lb pack)
$3 - $3x = $2.40
-3x = -0.60
x = -0.60/3 = 0.20
0.20 x 100 = 20%
Find the first 5 terms of the sequence.
The first five terms of the expression are -7,-3,1,5, and 9.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
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 , F(1) = -3 and F(n) = F(n-1) + 4. Calculate the first term of the sequence,
F(1) = F(1-1) + 4
-3 = F(0) + 4
F(0) = -7
The common difference is calculated as,
d = -3 - 7
d = 4
The third term will be, -3 + 4 = 1
The fourth term will be, 1 + 4 = 5
The fifth term will be, 5 + 4 = 9
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6 ÷ (–3) + [(4 – (–5)) × (–7)]
answer please
Marcia and Becky shared some money
in the ratio 1:4
Marcia gets £18 less than Becky. How
much does Marcia receive?
The money received by Marcia = £ 6
According to the given information
The money is shared between Marcia and Becky in the ratio = 1 : 4
Let the money got by Becky = £ x
Marcia got £ 18 less than Beck = x - 18
So
Taking the ratio
[tex]\frac{1}{4}=\frac{x-18}{x}[/tex]
Cross multiply both the fractions
x = 4(x - 18)
x = 4x - 72
-3x = -72
x = 24
Money got by Beck = £ 24
Money received by Marcia = 24 - 18
= £ 6
Hence
The money received by Marcia = £ 6
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Yoezer bought 25 shares that had a face value of Nu 100 but were selling at a discount of 5%. A 15% dividend rate was paid at the end of one year. He then sold the stock at a 5% premium.
i. Find the amount of his investment.
ii.Calculate his total profit.
2375 is the amount of his investment and 625 is his total profit
The discount on the shares is 5%, so the price of each share is 100 - (5/100)100 = 95.
The total price Yoezer paid for the shares is 2595 = 2375.
To calculate Yoezer's total profit, we need to find the total dividend he received and the price he sold the shares for.
The dividend rate is 15%, so Yoezer received a dividend of (15/100)100 = 15 on each share.
The total dividend he received is 1525 = 375.
The price Yoezer sold the shares for was increased by a premium of 5%, so the selling price was 100 + (5/100)100 = 105.
The total selling price for the shares is 10525 = 2625.
Yoezer's total profit is the selling price minus the price he paid for the shares plus the dividends he received. This is 2625 - 2375 + 375 = 625.
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How many solutions can 2 linear equations have?
The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.
In the question ,
it is given that ,
the system of 2 linear equations in 2 variables .
we know that the linear equations represent a line .
(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .
(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .
(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .
Therefore , the number of solutions of linear equation is explained above .
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Is Cos 2x continuous?
A circle has center (0,4) and radius 5. Which of the following is an equation of the circle
Answer:
Given that a circle has a center (0,4) and the radius 5. 5. So the standard equation of the given circle is x2+(y−4)2=25.
Step-by-step explanation:
A(n) ____ is a numerical summary of a sample.
A statistic is a numerical summary of a sample.
A sample statistic is explained as any number computed from a sample of data.
Examples include the sample average, median, sample standard deviation, and percentiles. A statistic is a random variable because it is based on data obtained by sampling technique in which each sample has an equal probability of being chosen.
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HELP PLEASE PLEASE A recipe uses 5 cups of milk to make 25 servings. If the same amount of milk is used for each serving, how many servings can be made from one gallon?
The solution is 80 servings
The number of servings that can be made from 1 gallon is 80 servings
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of servings from 1 gallon be = A
Now , the equation will be
The number of cups of milk = 5 cups
The number of servings from 5 cups of milk = 25 servings
So ,
The number of servings from 1 cup of milk = number of servings from 5 cups of milk / 5 cups
Substituting the values in the equation , we get
The number of servings from 1 cup of milk = 25 / 5
The number of servings from 1 cup of milk = 5 servings
Now , 1 gallon = 4 quarts
1 quarts = 2 pints
1 pint = 2 cups
So , 1 gallon = 16 cups
And , number of servings from 1 gallon = number of servings from 16 cups
So ,
The number of servings from 16 cups = number of servings from 1 cup of milk x 16
Substituting the values in the equation , we get
Number of servings from 1 gallon = 5 x 16
Number of servings from 1 gallon = 80 servings
Therefore , the value of A is 80 servings
Hence ,
The number of servings is 80 servings
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How do I follow up on SSS sickness benefit application?
The follow up on SSS loan sickness benefit application are as follows :
Sickness Benefit Application (SBA) FormAny legitimate primary ID card or document, such as an SS ID or UMID, as follows:- Driver’s License
- Passport
- Voter’s ID Card
- National Bureau of Investigation (NBI) Clearance
- Postal Identity Card
- Any other government-issued (secondary) ID cards/documents
supporting medical records, if any, for extended illness or incarceration :- Laboratory, X-ray, ECG, and other diagnostic results
- Operating room/clinical record that will support the diagnosis
For illnesses or injuries that occurred abroad, the issuing nation's official documentation must include an English translation and be properly authenticated by the Philippine Embassy or Consulate Office or properly certified by a notary public of the receiving nation.
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How do you identify congruent in SAS?
find a vector that points in the same direction as the vector (i^+j^) and whose magnitude is 9.
A vector that points in the same direction as the vector (i^+j^) and whose magnitude is 9 is (9i^/ √2 + 9j^/ √2).
Therefore the answer is 9i^/ √2 + 9j^/ √2.
The vector direction is same as i^ + j^. We can obtain a unit vector in that direction by dividing the vector with magnitude of i^ + j^, which is √(1² + 1²) = √2.
Unit vector is (i^ + j^)/ √2.
Given that the required vector is of magnitude 9. We can determine the required vector thus by multiplying the magnitude with the unit vector in the direction, that is
9×(i^ + j^)/ √2
= 9i^/ √2 + 9j^/ √2
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Todd drives 2,365 miles in a month. His average mpg is 20. How much will he pay in gas if gas is $3. 12 per gallon?.
Answer:
He pays:
$368.94
Step-by-step explanation:
20 miles ⇒ 1 gallon
2365 miles ⇒ A gallons
A = 2365 miles * 1 gallon / 20 miles
A = 118,25 gallons
Then:
$3.12 ⇒ 1 gallon
$B ⇒ 118.25 gallons
B = 118.25 gallons * $3.12 / 1 gallon
B = $368,94
7. Explain in your own words why √-4 is not possible.
Answer:
There is no real square root of -4 because it is impossible to square any real number and get a negative answer.
You might think -2 could work. However, a negative times a negative is positive → -2(-2) = +4, so the problem would have to be written as [tex]\sqrt4[/tex] instead of [tex]\sqrt{-4}[/tex]. Hence, there is no real square root of -4.
Note the word real, as it is possible to find a non-real answer to [tex]\sqrt{-4}[/tex] using the imaginary number [tex]i[/tex], which represents [tex]\sqrt{-1}[/tex].
The equation s=100−5m represents the relationship between the total score on Mr. Totten's algebra quiz, s, and the number of questions a student missed, m. Which statement describes the slope in this equation?
The statement that describes the slope in this equation is that the score of each question is 5
How to determine the statement that describes the slope in this equation?From the question, we have the following parameters that can be used in our computation:
Equation: s = 100 - 5m
Also from the question, we have:
s = The total score
m = the number of questions a student missed
Recall that
s = 100 - 5m
A linear equation is represented as
y = mx + c
Where m = slope
By comparing the equations, we have
m = -5
This means that the slope is -5
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How do you find the mean of a set?
Mean mode formula - Mean = {Sum of Observation} ÷ {Total numbers of Observations}
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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Gordon types 2,240 words in 8 minutes.Find the unit rate .
Pls someone help and explain
Answer:
Gordon types 280 words per minute
Step-by-step explanation:
2240word/8min
280/min is the same as 4.6/second (280/60)
The perez family and the smyth family are each taking road trips. The perez family travels at an average rate of 65 miles per hour and the smyth family travels at an average rate of 50 miles per hour. How far does each family travel after 6 hours?.
Answer:
90 miles.
Step-by-step explanation:
65 - 50 = 15
In each hour they have a difference of 15 miles.
In six hours:
6 * 15 = 90 miles