As per the concept of numbers, the way of explaining the greater than, less than, and equal to are defined below.
The term number in math is referred to an arithmetic value used for representing the quantity and used in making calculations.
Here we have to know that the greater than sign (>) denotes that the number after the more than sign is smaller than the number before the symbol whereas less than sign (<) denotes that the number after the sign is bigger than the number before the sign.
Similarly, to this definition, the term equal defines the number as being equal to each other or it can be used to assign the value to the variable that has been placed on the left-hand side.
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please help me with this.
Answer:
55°75°55°15°Step-by-step explanation:
You want the measures of the numbered angles in the figure comprised of overlapping right triangles.
Complementary anglesThe acute angles in a right triangle are complementary, as are the two angles into which a right angle is divided.
∠1 +35° = 90° ⇒ ∠1 = 55°
∠3 +35° = 90° ⇒ ∠3 = 55°
Exterior angleThe angle marked 70° is exterior to the bottom right triangle, so is equal to the sum of angles 3 and 4.
∠3 +∠4 = 70°
55° +∠4 = 70° ⇒ ∠4 = 15°
Angle 2 is the other acute angle in the bottom right triangle, so ...
∠2 = 90° -∠4 = 90° -15°
∠2 = 75°
7.2.C1 Which Of The Following Are Statistics? O2/N
The symbol that represents an expression in statistics are That is option A , B and C.
What is statistics?Statistics is defined as the area of study that is concerned with the collection, organization, analysis, interpretation, and presentation of data.
The importance of statistics is that it helps in conducting research, evaluating results, developing critical thinking and making informed decisions.
The various symbols use in statistics include the following:
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What are the 3 types of rational functions?
Rational functions can have 3 types of asymptotes:
1. Horizontal Asymptotes
2. Vertical Asymptotes
3. Oblique Asymptotes
The ratio of two polynomial functions with a non-zero denominator is known as a rational function.
1. Horizontal Asymptotes:
A graph's horizontal asymptote is a horizontal line with the equation y = b, and when the inputs get closer to 0 or 1, the graph moves toward the line. A graph's slant asymptote is a sloped line, denoted by the equation y = mx + b, where the graph slopes toward the line when the inputs approach 0 or -1.
2. Vertical Asymptotes:
Vertical asymptotes are vertical lines that represent the zeros in a rational function's numerator. Asymptotes can also occur in other situations, such as logarithms, although you'll almost probably run into them when discussing rationals for the first time.
3. Oblique Asymptotes:
These slanted asymptotes, known as oblique asymptotes, demonstrate how a function rises or falls without bound. Slant asymptotes are another name for oblique asymptotes. The slant asymptote won't be a line because the degree of the numerator is 3 and the degree of the denominator is 1, respectively.
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What are the factors of 2x² 7x 15 *?
The factors of 2x² - 7x - 15 are (2x + 3) and (x - 5).
What are the factors of 2x² - 7x - 15?By splitting the middle term and factoring the polynomial,
2x² - 7x - 15
= 2x² - 10x + 3x - 15
= 2x(x - 5) + 3(x - 5)
= (2x + 3)(x - 5)
The factors of 2x² - 7x - 15 are (2x + 3) and (x - 5).
What is factoring?By searching for factors, factoring is the process of attempting to make a mathematical expression resemble a multiplication problem.In essence, factoring is the multiplication process in reverse. It is possible to factor both numerical and algebraic expressions using a specific technique.Finding two integers to multiply to obtain another number can be as simple as factoring. You might also seek out a number's prime factorization when factoring.Of course, numerical expressions are the easiest to factor.A number or other mathematical object is factored when it is written as the product of numerous factors, typically smaller or simpler counterparts of the same kind.To learn more about polynomial, refer:
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Three sisters each purchase a dress of equal value. One of the sisters purchased a purse for $26.00. If the grand total was $249.50, how much did each dress cost?
Answer:
you would take 249.50 and subtract 26.00 from it. then you would divide it by 3 for the initial cost of each dress
Step-by-step explanation:
249.50-26.00=223.05 then divide
223.05÷3= 74.05
hope that helped !
If x has a percentage of 10 and that is equal to y at 100 percent. Then if x is at 100 percent, what is the percentage of y?
If x has a percentage of 10% and that is equal to y at 100%, then x is equal to 10% of y. If x is at 100%, then the percentage of y would be 1000%.
Here's how to arrive at this answer:
First, let's set up the equation to represent the given information:
x = 10% * y
If we solve for y in this equation, we get:
y = x / (10%)
Now, if we set x equal to 100%, we get:
y = (100%) / (10%)
Simplifying this fraction gives us:
y = 10
Since y is equal to 10, the percentage of y is 1000%.
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How do you find a unit rate? For example, $1.40 for 4 apples. Please help.
Answer:5.6
Step-by-step explanation:
Answer: $1.40/4 = $0.35/apple
How do you prove two overlapping triangles are congruent?
If the two triangle are overlapping , then they are congruent.
The term congruent refers the triangles that have three sets of corresponding congruent sides and three sets of corresponding congruent angles.
Here we have to prove that the two overlapping triangles are congruent.
Here we know that the two triangle are overlappling.
Now we have to do the following process to prove that the overlapping triangles are also congruent.
As per the reflexive property of congruence, here when overlapping triangles share a common side or angle because the reflexive property of congruence states that a segment or angle is congruent to itself. Therefore, according to the geometry when two triangles share a side or angle this can be used to prove one set of congruent sides/angles.
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Simplify the polynomial and evaluate for the following values.
x²yxy-xy²xy +xy if x = −3 and y=2
Answer:
1/ simplify polynomial is x^3 y^2 - x^2 y^3 + xy
2/ Answer is -86
Step-by-step explanation:
x²yxy-xy²xy +xy
Simplify each term, and I get
x^3 y^2 - x^2 y^3 + xy
I may be wrong!
Now let's put -3 in for x and 2 in y and evaluate
(-3)^3 (2)^2 - (-3)^2 (2)^3 + (-3 times 2)
(27) (4) - (9) (8) - 6
-86
I may be wrong, but I tried my best to help you since this question has been on for a long time, but no one answered. If I am wrong, I am sorry!
Hannah adjusts photos in her digital
scrapbook. She translates the photo to the
left. Then she dilates the image using a scale
factor of 2 and a center of dilation at the
origin. Hannah thinks the original photo is
congruent and similar to the final image.
Is she correct? Explain your reasoning.
Hannah's thought that the original photo is congruent and similar to the final image is false
How to determine if the statement is correctFrom the question, we have the following parameters that can be used in our computation:
She translates the photo to the left. She dilates the image using a scale factor of 2Translation creates congruent and similar shapes
However, dilation only create similar shapes, but not congruent shapes
This means that the shapes are similar, but not congruent
Hence. Hannah is incorrect
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what is the conjugate of [tex]x+\sqrt{y}[/tex]
By using the concept of conjugate, it can be calculated that
Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]
What is conjugate?
Conjugating is the process of changing a verb in a sentence to match the person, number, gender, tense, mood, and voice of the subject. For example, the verb "to walk" changes to "walked" when conjugated in the past tense. Conjugation is important in many languages, including English, as it helps to make communication more precise. Conjugation involves making changes to the base form of the verb, such as adding suffixes or prefixes, or changing the spelling of the word. Different languages have different rules for conjugating verbs, so it is important to understand the language’s system of conjugation before attempting to use it.
Here the expression is [tex]x + \sqrt{y}[/tex]
Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]
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What's the mode of data?
A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.
In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.
For example, the mode of the set {3, 7, 8, 8, 9}, is 8. Therefore, for a finite number of observations, we can easily find the mode. A set of values may have one mode or more than one mode or no mode at all.
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How many solutions does y 0 and y =- 6 has?
The system of equations has no solution because they are parallel lines.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
In general, any equation of the form y = k, where k is a constant, represents a horizontal line that extends indefinitely in both directions.
The system of equations y=0 and y=-6 describes two lines in the coordinate plane.
The first equation, y=0, is the x-axis.
The second equation, y=-6, is a horizontal line 6 units below the x-axis.
As we know, y = 0 and y = -6 are two parallel lines.
Therefore, no solution exists.
Hence, the system of equations has no solution.
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What is the 3 step process in math?
Identifying the issue, considering potential solutions, and selecting the best course of action are the three primary components of problem-solving.
How the 3 step process work on mathematics?Mathematical issues can be solved in a variety of methods; however, a three-step technique is a streamlined approach that can assist anybody in solving even the most challenging problem.
Three steps is here:
1. Create a mental image of the issue
Daydreaming and the mental imagery that takes place when reading a book are two frequent instances of mental pictures. The images that athletes conjure up during practice or before a competition, describing each step they will take to achieve their objective, are another example.
2. The strategy should be used to solve the issue
A strategy is a way to manipulate numbers, use connections and interactions between numbers to solve an issue. For each procedure, there are a few key tactics. The first thing you do with the statistics is frequently used to label a technique.
3. Conclude by fixing the issue
A conclusion is a claim made after a set of premises and a set of logical principles known as syllogisms have been considered. Deduction is the process of inferring conclusions from premises and syllogisms.
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P(A) = 0.50, P(B) = 0.40, and P(A and B) = 0.15.
What is P(A or B)?
From the concept of algebra of venn diagram we obtain that
P(A or B) = 0.75.
A set is a collection of well-defined objects.
A subset contains all the elements or few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
From set theory, we know that N(A∪B) = N(A) + N(B) - N(A∩B).
It states that N(A) or N(B) is the sum of N(A) and N(B) minus the common intersecting region N(A∩B) as we have already considered the region in the sum of N(A) and N(B) twice.
Similarly, P(A or B) = P(A) + P(B) - P(A∩B)>
Therefore, P(A or B) = 0.50 + 0.40 - 0.15.
P(A or B) = 0.90 - 0.15.
P(A or B) = 0.75.
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Demand for a product and the forecasting department's forecast (naïve model) for a product are shown below. Compute the mean squared error.
Period Actual Demand Forecasted Demand
1 12 - -
2 15 12
3 14 15
4 18 16
a. 4.67 b. 5.33 c. 6.67 d. 3.33
The mean squared error is 4.67. So the option a is correct.
In the given question, demand for a product and the forecasting department's forecast for a product are given.
We have to compute the mean squared error.
Period Actual Forecasted Error Absolute Squared
Demand(E) Demand (F) (E-F) Error |E-F| Error |(E-F)|^2
1 12
2 15 12 3 3 9
3 14 15 -1 1 1
4 18 16 2 2 4
Total=6 Total=14
Now we finding the mean squared error (MAE)
Mean squared error = ∑|(E−F)|^2/n
Mean squared error = 14/3
Mean squared error = 4.67
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The point (2, -3) is the midpoint of segment JK .
Point K is located at (-6, -3).
What is the length of segment JK ?
The required length of line segment JK would be 16 units.
The midpoint of a line segment is the point that divides the line segment into two equal parts. So, to find the length of the line segment JK, we can first find the coordinates of point J, which is the other endpoint of the line segment.
Let the coordinate of the point J would be (x, y)
Since the midpoint of the line segment is (2, -3), and point K is located at (-6, -3), we can use the midpoint formula to find the coordinates of point J:
2 = (x+(-6))/2 ; -3 = (y+(-3))/2
4 = x - 6 ; -6 = y -3
x = 10 ; y = -3
So the coordinate of the point J :(10, -3)
Now that we have the coordinates of both endpoints of the line segment, we can use the distance formula to find the length of the line segment:
length = √((10 - (-6))² + (-3 - (-3))²)
= √((10 + 6)² + (-3 + 3)²)
= √(16² + 0)
= √(256)
= 16
Therefore, the length of line segment JK is 16 units.
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You and your family are visiting some attractions while on vacation. You and your mom visit the shopping mall while your dad and your sister visit the aquarium . You decide to meet at the intersection of lines and p Each unit in the coordinate plane corresponds to 50 yards .
The lines p and q are perpendicular in the coordinate plane.
What is meant by coordinate plane?The name of the other number line, which is a vertical one, is called the y-axis. To graph points, lines, and other objects, one can utilize the coordinate plane. A pair of numerical coordinates that uniquely identify each point in a Cartesian coordinate system in a plane are called the coordinates. These numerical coordinates are signed length measurements that represent the separations between two fixed perpendicular oriented lines and the point.
Let the equation of the line is:
y-y'=m₁(x-x')
m₁=2/6
m₁=1/3
Therefore, the equation of a line with the point (3, 4) and slope m₁=1/3
y-4=(1/3)(x-3)
y=(1/3)x-1+4
y=(1/3)x+3
And m₂= -3
The line equation that is passing through (2,7) and m₂= -3
y-7=(-3)(x-2)
y-7= -3x+6
y= -3x+13
m₁×m₂= -1
(1/3)(-3)= -1
So, the lines that are given in the coordinate plane p and q are perpendicular.
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**What is the value of x in the function
p(x) = 9x - 2 such that p(x) = -3?
Answer:
(D) 1/9
Step-by-step explanation:
9x-2=-3
9x=1
x=1/9
Which shows one way to determine the factors of x³ 4x² 5x 20 by grouping?
The one way of determining the factors of x³ + 4x² + 5x + 20 by grouping is (b) x²(x + 4) + 5(x + 4) .
The Grouping in a polynomial is done by the taking the GCF( greatest common factors) from the different terms .
the expression is given as : x³ + 4x² + 5x + 20 ;
in order to determine the factors by grouping ,
we first take x² common from the first two terms and 5 common from the last two terms .
we get ;
⇒ x²(x + 4) + 5(x + 4)
Therefore , the one way of determining the factors is x²(x + 4) + 5(x + 4) .
The given question is incomplete , the complete question is
Which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping ?
(a) x(x² + 4) + 5(x² + 4)
(b) x²(x + 4) + 5(x + 4)
(c) x²(x + 5) + 4(x + 5)
(d) x(x² + 5) + 4x(x² + 5)
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Lydia owns. Good truck that sells tacos and burritos. She only has enough supplies to make 115 tacos or burritos. She sells each taco for $4 and each burrito for $6.75. Lydia must sell at least $680 worth of tacos and burritos each day. If tacos were sold, determine the minimum number of burritos that Lydia must sell in order to meet the requirements.
Answer and Step-by-step explanation:
Lydia must sell at least $680 worth of tacos and burritos each day, and she only has enough supplies to make 115 tacos or burritos. If she sells each taco for $4, then she can make a maximum of 115 tacos * $4/taco = $<<115*4=460>>460 by selling tacos.
Therefore, in order to make at least $680, Lydia must sell burritos in addition to the tacos. The minimum number of burritos she must sell in order to make at least $680 is $680 - $460 = $<<680-460=220>>220.
Since Lydia sells each burrito for $6.75, she must sell at least $220 / $6.75/burrito = <<220/6.75=32.5>>32.5 burritos to make at least $680. Since she only has enough supplies to make 115 tacos or burritos, and she has already accounted for 115 tacos, she must sell a minimum of 32.5 burritos to meet the requirements.
How do you write greater than 20?
We will write greater than 20 using Inequality sign as ( > 20).
The first number in every inequality sign tells us how the first and second numbers relate to one another, so > 20 means "A number is greater than 20."
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than symbol (>) is used when the first number exceeds the second number. The less than symbol (<) is used when the first number is less than the second number.
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Mrs. Bergstedt teaches four classes. Each class has 15 students. Her first class has 9 juniors, her second class has 12 juniors, her third class has 6 juniors, and her fourth class has 3 juniors. If Mrs. Bergstedt chooses four students at random, what is the probability that exactly two of the students are juniors (rounded to the nearest thousandth)?
The probability that exactly two of the students are juniors is given as follows:
0.270 = 27%.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of these parameters for this problem are given as follows:
[tex]N = 60, n = 4, k = 18[/tex]
Hence the probability that exactly two of the students are juniors is calculated as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,60,4,18) = \frac{C_{18,2}C_{42,2}}{C_{60,4}} = 0.270[/tex]
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For each of the following, define variables, write a system, and solve the system
algebraically:
a) An organization is holding a banquet in honor of its member of the year. Tables and
chairs must be rented in order to seat all the guests. A large table seats 12 and costs
$50. A small table seats 8 and costs $25. How many of each type of table must be
rented to seat 100 guests for $350?
b) The jazz band and choir are attending a concert. The jazz band bought 16 student tickets and 3
adult tickets for $110.50. The choir bought 12 student tickets and 4 adult tickets for $96. Find the
cost of each type of ticket
(i) Large Table Required are 3 and Small Table required are 8
(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5
What is Linear Equation in Two Variable?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
(i)
Seats in Large Table = 12
Cost of Large Table = $50
Seats in Small Table = 8
Cost of Small Table = $25
Let, Number of Large Tables = x
Number of Small Tables = y
According to the Question:
12x + 8y = 100
50x + 25y = 350
x = 3, y = 8 (refer graph 1)
(ii)
Cost of Student Ticket = x
Cost of Adult Ticket = y
According to the Question:
16x + 3y = 110.5
12x + 4y = 96
x = $5.5, y = $7.5 (refer graph 2)
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Removing which ordered pair from the table would make the relation a function of x? x y 1 7 4 7 2 2 4 1 3 9.
You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).
What are the 4 types of function?
There are 4 types of functions:
Functions with arguments and return values. This function has arguments and returns a value: ...
Functions with arguments and without return values. ...
Functions without arguments and with return values. ...
Functions without arguments and without return values.
A function is a relation that for each input value x takes the unique value of output y.
Consider the table
x y
1 7
4 7
2 2
4 1
3 9
You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).
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The following figure shows the entire graph
of a relationship.
Does the graph represent a function?
as a third-grade teacher, you receive the standardized test scores for mary and learn that she has gotten a stanine of 1 on the spelling subtest and a stanine of 3 on the math subtest. you should conclude that mary:
Performed at about average on spelling, but about one standard deviation below average on math.
Any test that (1) requires all test takers to answer the same questions, or a set of questions from a common bank of questions, in the same way and (2) is scored in a "standard" or consistent manner, allowing for comparison of the relative performance of individual test takers, is considered to be standardized.
Students are frequently chosen for certain programs using standardized assessments. For instance, norm-referenced examinations like the SAT (Scholastic Assessment Test) and ACT (American College Test) are used to decide whether high school students get admitted to elite institutions.
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HEL HELP HELP ITS DUE TODAY 700 students attend Ridgewood Junior High School. 10% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
Answer:
If 10% of the students at Ridgewood Junior High School bring their lunch to school every day, and there are 700 students at the school, then 10% of 700 students is equal to 0.1 * 700 = <<10*.01*700=70>>70 students.
Therefore, on Thursday, 70 students brought their lunch to school.
How do you write 8 or more?
We can write '8 or more' as [tex]\geq 8[/tex], using the greater-than equal to sign.
The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number.
Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.
Here, we can use an alternate to the 'greater-than' symbol: a 'greater-than equal to' symbol, denoted as ≥.
Using this, we can write:
[tex]\geq[/tex] 8, denotes a number greater-than or equal to 8.
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S Ivy deposited $530 into a savings account
9 years ago. The account earns 33%
interest, compounded annually. How much
interest has she earned? Answer in dollars
and round to the nearest cent.
Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)
What is earned?To receive as return for effort and especially for work done or services rendered. : to bring in by way of return.
What is compound interest?When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. A = P is the compound interest formula.
A = P[tex](1 + r/n)^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
$530 for 9 years at 33% interest each year using the compound interest formula, where t = number of time periods elapsed
A = P[tex](1 + r/n)^{nt}[/tex]
A= 530 (1 + 0.33/1)^9
A = $6,901.45
So to find interest I = A-P
I = $6901.45 -$530
I = $6,371.45
Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)
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