Answer:
When solving a compound inequality, you can express the solution in two different ways: using a union or intersection.
Using a union:
A union represents the solutions that belong to either one inequality or the other, or both. You can express a union using the symbol "or," or by writing the solutions for each inequality separately and combining them using a "union" symbol (∪). For example, if you have the compound inequality "x > 2 or x < -3," you can express the solution as "x ∈ (-3, 2) ∪ (-∞, -3) ∪ (2, ∞)."
Using an intersection:
An intersection represents the solutions that belong to both inequalities. You can express an intersection using the symbol "and," or by writing the solutions for each inequality separately and combining them using an "intersection" symbol (∩). For example, if you have the compound inequality "x > 2 and x < -3," you can express the solution as "x ∈ (-3, 2) ∩ (-∞, -3) ∩ (2, ∞)."
Which method you use to express the solution will depend on the specific inequalities and the type of solutions you are looking for. It is important to carefully consider the inequality symbols (>, <, ≥, ≤) and the use of "and" or "or" in order to determine the correct solution.
When solving a compound inequality, the solution can be expressed in one of two ways: as an interval or as a union of intervals.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
An interval is a set of all real numbers between two given numbers, and is written in the form (a, b) or [a, b], where a and b are real numbers, and a < b. If a and b are included in the interval, then the interval is written as [a, b]; if a and b are not included in the interval, then the interval is written as (a, b).
A union of intervals is a combination of two or more intervals, and is written in the form (a, b) ∪ (c, d) or [a, b] ∪ [c, d], where a, b, c, and d are real numbers, and a < b and c < d.
When solving a compound inequality, it is important to first simplify the inequality by combining like terms, isolating the variable on one side of the inequality, and combining any separate inequalities into a single inequality. Then, the solution can be found by graphing the inequality on a number line, and shading the portion of the number line that represents the solution.
Once the solution is found the solution can be expressed either as an interval or as a union of intervals depending on the inequality. For example, if the inequality is x>1 and x<3, then the solution would be expressed as (1,3) and this is an example of an interval. If it's x>1 and x≥3 then the solution would be expressed as (1,3] U [3,∞) and this is an example of union of intervals.
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Select all of the true statements below.
1.) 8u+3v+5 is written as a sum of three terms.
2.)8u is a coefficient.
3.)8u and 5 are like terms.
4.)5 is a constant.
5.) 8u is a factor.
6.)None of these are true.
the true statements for 8u + 5 + 3v are:
1.) 8u+3v+5 is written as a sum of three terms.
4.)5 is a constant.
What is constant?The word "constant" in mathematics has several different connotations. When used as a noun, it can have either of the following two meanings: Non-variance (i.e., not changing in relation to some other value) or Variance.
an unchanging number or other non-changing mathematical object that is fixed and well-defined. Sometimes, to distinguish between these two meanings, the terms mathematical constant or physical constant are used.
a function with a constant value (i.e., a constant function).
These constants are frequently represented by a variable that is independent of the main variable or variables in question.
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A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/10 for pink, 1/15 for white, 1/20 for blue, and 1/5 for black. What is the probability of pulling a black or pink card, written as a reduced fraction?
Answer:
wouldn't it be 1/25 black??
A ball is launched from a 25.48-meter tall platform. The equation
for the ball's height h at time t seconds after launch is h (t) =
-4.9t² + 2.94t + 25.48, where his in meters. When does the object
strike the ground?
Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.
Define equation.Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.
Here,
Given : -4.9t² + 2.94t + 25.48
Then,
To find the When does the object strike the ground :
We get :
=> -4.9t² + 2.94t + 25.48 = 0
Using discriminant formula
We find the value of t:
=> t = -19.6 ±[tex]\sqrt{19.6^{2} - 4 (-4.9)(25.48)}[/tex] / 2(-4.9)
=> t =-2 or 6
So we neglect -2
So solution for t = 6 seconds
Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.
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HELP with this equation
Answer:
83°
Step-by-step explanation:
-4m+51-4m+42= 158°
-8m+94= 158
-8m= 64
m= -8
JMK= -4m+51
= -4(-8)+51
= 32=51
= 83°
Which is the graph of the equation y-1=(x-3)?
O
(-31).
10
CO
8
fi
Q
4.
y
Answer:
The graph of the equation "y - 1 = (x - 3)" is a straight line.
To graph this equation, we can start by rearranging the equation to get "y = x - 3 + 1". This simplifies to "y = x - 2".
This equation is in slope-intercept form, which means that the slope of the line is given by the coefficient of the x term, and the y-intercept (the point where the line crosses the y-axis) is given by the constant term. In this case, the slope is 1 and the y-intercept is (-2, 0).
To graph the line, we can start by plotting the y-intercept at the point (0, -2). Then, we can use the slope of 1 to find a second point on the line and draw a straight line through these two points. The graph of the equation "y = x - 2" is shown below:
[asy]
unitsize(1.5cm);
draw((-1.5,0)--(1.5,0));
draw((0,-2.5)--(0,2.5));
draw((-1.5,-2)--(1.5,2),dashed);
label("$x$", (1.5,0), E);
label("$y$", (0,2.5), N);
[/asy]
The graph of the equation "y - 1 = (x - 3)" is the same as the graph of the equation "y = x - 2", except that all the y-values on the graph are increased by 1. This means that the graph of the equation "y - 1 = (x - 3)" is obtained by shifting the graph of "y = x - 2" upward by 1 unit. The graph of the equation "y - 1 = (x - 3)" is shown below:
[asy]
unitsize(1.5cm);
draw((-1.5,0)--(1.5,0));
draw((0,-2.5)--(0,2.5));
draw((-1.5,-1)--(1.5,3),dashed);
label("$x$", (1.5,0), E);
label("$y$", (0,2.5), N);
[/asy]
The answer choices given in the question do not match the description of the graph of the equation "y - 1 = (x - 3)". "O" does not match the description of the graph, as it is not a graph of a straight line. "(-31)" and "10" do not match the description of the graph, as they are not graphs at all. "CO" does not match the description of the graph, as it is the graph of a circle, not a straight line. "8" does not match the description of the graph, as it is the graph of an exponential function, not a straight line. "fi" does not match the description of the graph, as it is not a graph of a function. "Q" does not match the description of the graph, as it is not a graph at all. "4." does not match the description of the graph, as it is not a graph of a function. "y" does not match the description of the graph, as it is not a graph at all.
Select all the correct answers. A farmer wants to build two fenced-off sections within his field, one in the shape of a rectangle and the other in the shape of a square. The side of the square must be equal to the width of the rectangle, x feet. The length of the rectangle must be 50 feet longer than its width. The field the farmer wants to build the two fenced sections in has an area of y square feet. The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet. In addition, the sum of the fenced areas must be less than the area of the field. This is the system of inequalities that represents this situation. Which points represent viable solutions?
(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that the side of the square must be equal to the width of the rectangle, x feet.
The length of the rectangle must be 50 feet longer than its width
The field the farmer wants to build the two fenced sections in has an area of y square feet.
The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet
the sum of the fenced areas must be less than the area of the field.
y≥x²+1000
y>2x²+50x
(20, 2,200) and (5, 3,000) are the viable solutions
Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
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Pls help me I beg u I need help with the red ones
Answer:
see below
Step-by-step explanation:
You want the ingredient quantities for several different multiples of the basic recipe.
Table ValuesTo fill the table, consider what the column heading is as a multiple of the recipe for 12 people. Use that multiplier for the rest of the numbers in the column.
[tex]\begin{array}{ccccc}\text{12 people}&\times2&\times3&\times\dfrac{1}{3}&\times\dfrac{1}{2\vphantom{g_g}}\\\cline{1-5}1\text{ cup}&2&3&\dfrac{1\vphantom{b^b}}{3\vphantom{g_g}}&\dfrac{1}{2}\\3\text{ cups}&6&9&1&1\dfrac{1}{2}\\2\text{ cups}&4&6&\dfrac{2}{3\vphantom{_g}}&1\\\dfrac{1}{2}\text{ cup}&1&1\dfrac{1}{2}&\dfrac{1}{6}&\dfrac{1\vphantom{^b}}{4\vphantom{_g}}\\1\dfrac{\vphantom{^b}1}{3}&2\dfrac{2}{3}&4&\dfrac{4}{9}&\dfrac{2}{3}\end{array}[/tex]
Use the defined variables for the verbal model to write an equation in slope-intercept form that relates the variables.
$2/pound × Pounds of peaches + $1.50/pound × pounds of apples = $15
Let x represent the number of pound of peaches.
Let y represent the number of pounds of apples.
An equation is y = ___
Graph the equation.
An equation is y = -4x/3 + 10.
A graph of the equation is shown in the image attached below.
How to write an equation to model this situation?In order to write and graphically solve an equation that model this situation, we would assign variables to the number of pound of peaches and number of pounds of apples respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pound of peaches.Let the variable y represent the number of pounds of apples.Next, we would translate the word problem into an algebraic equation as follows;
$2/pound × Pounds of peaches = 2x.
$1.50/pound × pounds of apples = 1.50y
Combining the two expressions above, we have the following:
2x + 1.50y = 15
Making y the subject of formula, we have:
1.50y = 15 - 2x
y = (15 - 2x)/1.50
y = -4x/3 + 10
Therefore, an equation in slope-intercept form that relates the variables is y = -4x/3 + 10.
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Use Vocabulary to Describe a Graph
What is the domain of the relation?
✓ -4
5x56
COMPLETE
What is the range of the relation?
-4 ≤ys
DONE ✔
-4
+y
4
2
-2
-4
X
For the given graph, the domain and range of the relation equals [-4, 6].
What in mathematics is a relation?A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. One kind of relation is a function.
In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets. As an illustration, consider the set notation symbols (-2, 1), (4, 3), and (7, -3) with curly brackets.
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Models come in different scales. A model of a G-scale railroad car has a scale ratio of 1:22.5, and the model is 3 in tall, how tall is the actual car?
Please help me answer this, this is due on Monday for me!!!
Which equation has 1 solution? A. (W)=-2. B. (W)=1. C. (W)=-1. D. (W)=0
An equation which has one (1) solution include the following: D. |W| = 0.
What is an absolute value function?In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).
Mathematically, an absolute value function can be represented by this mathematical expression:
|x| = x, x ≥ 0.
|x| = x, x < 0.
Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:
|W| = 0
W = ±0
W = 0
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Someone pls help!!
Construct a circle through points
X, Y, and Z.
Answer:
Here is an example. Check out the uploaded image.
Step-by-step explanation:
Draw Points XY using a Straight Line
Draw a bisector in the middle of the line
Repeat Procedure for lines XZ and YZ
Where the two lines meet is the Center
Extend the compass from the center to any point and complete the circle.
The product of -12 and a number is the same as the sum of the number and 26
-2
Step-by-step explanation:
12x＝x+26
-13x＝26
x＝-2
If given the following scenario: The half-life of Sodium-24 is 15
hours. If you start with 352 grams of Sodium-24 how much would
be left after 8 days?
0.049 grams
Approximately 0 grams
1.375 grams
95.965 grams
Sodium has two radioactive cosmogenic isotopes (22Na, half-life = 2.605 years; 24Na, half-life = ~ 15 hours) that have been used as tracers in hydrologic studies.
Sodium-24 how much would be left after 8 days?Sodium-24, a radioactive isotope having a half life of 15 hours is used medically in blood studies and it decays by beta decay.
Na has received considerable attention in hydrologic research because it is a mobile element that participates in precipitation and dissolution reactions in ground water (clay formation, albitization of plagioclase). Their short half-lives (i.e. high decay rate) make their measurement relatively easy by common radioanalytical techniques.
Substantial concentrations of 22Na and 24Na have been measured in precipitation (Roedel, 1970; Perkins et al., 1970). However, no studies have as yet been published documenting the cosmogenic sodium systematics in ground or surface waters.
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What does 69 divided by 310.5 equal in decimal form?
Write an equation in standard form passing through the given point and parallel to the given line: (-1,-1) y = - x - 5
A: x - y = -2
B: x + y = 0
C: x - y = 0
D: x + y = -2
Option D, x + y = -2 is the equation in standard form passing through the (-1,-1) and parallel to y = -x - 5.
What is standard form?The process of expressing a specific element in mathematics in the most typical way is known as standard form. Every element of mathematics, including big and small numbers, equations and lines, is designated in a standard form.
A standard form is a way of expressing a certain mathematical idea, such as an equation, number, or expression, in a way that adheres to a set of rules. The standard form is used to clearly represent extremely large or extremely small numbers.
To write an equation in standard form passing through the (-1,-1) and parallel to y = - x - 5, we need to find y-intercept form first
We know that parallel lines have same slope, so
y - y1 = m(x - x1)
y -(-1) = -1(x -(-1)
y + 1 = -x - 1
y = -x - 2
y + x = -2
Thus, Option D, x + y = -2 is the equation in standard form passing through the (-1,-1) and parallel to y = -x - 5.
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please help me thank you so much
Question 5, Please Answer and Explain
The trigonometric ratios for the angle x in the triangle are given as follows:
tan(x) = f/e.cos(x) = e/d.sin(x) = f/d.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.In the right triangle in this problem, we have that d represents the hypotenuse, while the sides relative to angle x are given as follows:
Adjacent side: length of e.Opposite side: length of f.These sides are used along with the definitions of each ratio to give the three trigonometric ratios of angle x.
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Kiara invested some money into a savings account that earns 2.7% annual simple interest. At the end of 5 years, she earned $6.62 in interest. How much money did she put into the account initially? Round to the nearest dollar.
The initial amount that was invested in the account was $49.
What is the principal?We know that we can be able to obtain the principal by the use of the formula for the simple interest and by that formula we would now have that;
I = PRT/100
I = interest
P = principal
R = rate
T = time
Then we are going to have that;
R = 2.7
P = ?
I = 6.62
T = 5
Then;
6.62 = P * 2.7 * 5/100
6.62 * 100 = P * 2.7 * 5
P = 6.62 * 100/2.7 * 5
P = 662/13.5
P = 49
Thus we have but in at the beginning about $49
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Rick claims that the equation
×2 + 5x + 9 = 0 has no solution. Jenny claims that there are two solutions. Explain how Rick could be correct, and explain how Jenny could be correct.
Answer: Both Rick and Jenny could be correct because we do not know what "x" is.
Step-by-step explanation:
The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.
I hope this helps :)
Ms. Sharon bought 84 litre of cooking oil. She used 1/3 of it on Monday and another 20 litre
of it on Tuesday.
a) How much oil she used on Monday?
b) How much cooking oil did she use altogether?
c) How much cooking oil was left with her?
d) Write the fraction of cooking oil left with her
Which of the following points is shown in the graph below? Question 5 options:
The point shown on the graph is
(4, -5, 6)
How to find the points shown on the graphAn ordered triplet of lines (the axes) that are pair-wise perpendicular and pass through the same point (the origin) make up a Cartesian coordinate system for a three-dimensional space.
Each axis also has an orientation, and the length of all three axes is equal.
In ordered triplet, the order of the axis is (x, y, z)
z is vertical up positive and down negative
y is horizontal right is positive and left is negative
x is the axis pointing to us which is positive pointing away is negative
Using this information, to trace the point shows that the point marked by a dot is (4, -5, 6).
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Triangle JKL has vertices J(6, -1), K(10,-2), and L(5, -3). Determine the
coordinates of the vertices of the image after a translation along (0,4)
and a reflection in the y-axis.
J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.
What is meant by coordinates of the vertices?[tex](x_1,y_1), (x_2,y_2),[/tex] and [tex](x_3,y_3)[/tex] are the coordinates of a triangle's vertices [tex](x_3,y_3)[/tex]. The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.
When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.
First do the first transformation, the translation.
J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).
After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).
We Utilize those new coordinates to do the reflection in the y axis.
J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).
After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).
Those exists the vertices after the transformations.
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J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.
What is meant by coordinates of the vertices?[tex](x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3})[/tex] are the coordinates of a triangle's vertices . The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.
When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.
First do the first transformation, the translation.
J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).
After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).
We Utilize those new coordinates to do the reflection in the y axis.
J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).
After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).
Those exists the vertices after the transformations.
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please help me with this
Answer: 630
Step-by-step explanation:
Evaluate 9du when d=10 and u=7
⇒9du
input the values of d and u
⇒9 (10)(7)
⇒9 × 10 × 7
⇒630 answer.
hope that helps...
Answer:
630
Step-by-step explanation:
as the problem shows that the variable for d = 10, and u = 7.
it asked to solve 9du (or 9 × d × u )
we can plug in the numbers into the variables:
9 × 10 × 7
9 × 10 = 90 × 7 = 630
Which expression could be used to determine the product of –4 and 3 and one-fourth?
(negative 4) (3) times (negative 4) (one-fourth)
(negative 4) (3) + (negative 4) (one-fourth)
(3) (negative 4) times (3) (one-fourth)
The expression which could be used to determine the product of -4 and 3 and one-fourth as required is; negative 4) (3) + (negative 4) (one-fourth).
Which expression can be used to determine the product of the given word phrase?As evident in the task content; the expression which could be used to determine the product of; -4 and 3 and one-fourth is required to be determined.
Since the given expression is; -4 and 3 and one-fourth; we have that;
-4 × 3 ¼
However, since 3 ¼ can be written as; ( 3 + ¼ ), it follows that we have;
-4 × ( 3 + ¼ )
Ultimately, the resulting expression using the distributive property is;
( -4 ) ( 3 ) + ( -4 ) ( ¼ )
Therefore, the correct answer is; (negative 4) (3) + (negative 4) (one-fourth).
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If a new video game costs the store $25 and they sell it for 37.50, what was the percent markup?
The percent markup of the supplied statement is equal to 50% after the problem is solved.
How much of a markup should I use?There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.
Exactly how is markup determined?The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.
According to the given information:Cost price of game=$25
Selling price of game=$37.50
Profit = selling price - cost price
Profit = 37.50 - 25
Profit / markup percentage = (profit /cost price ) * 100
= (12.50/25) * 100
= 50%
The percent markup of the supplied statement is equal to 50% after the problem is solved.
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Customary American Units of Capacity
1 cup = 8 ounces
1 pint = 2 cups or 16 ounces
1 quart = 2 pints, 4 cups, or 32 ounces
1 gallon = 4 quarts, 8 pints, 16 cups, or 128 ounces
9 cups = ___ pints ____ cups
20.945649350649 c = 9 dry pt, Four pints equal nine cups. The metric system uses the litre and millilitre as the units of capacity. By dividing by 11000, we may convert millilitres into litres.
What is the US customary unit for capacity?In the United States, ounces, cups, pints, quarts, and gallons are the commonly used measurement units for capacity or volume. Cups, pints, quarts, and gallons are some of the volume or capacity measuring units used in the United States. 8 fluid ounces are the equivalent of 1 cup. There are 2 cups in a pint. 1 quart equals 2 pints.
The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. Every liquid has this property. The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. For all liquids, this is true. 4 pints are equal to 9 cups.
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-our classmates were asked to decorate /5 or the bulletn boara In a classroom They divided the section to be decorated equally among the 4 classmates. Whe fraction of the entire bulletin board did each classmate decorate? (5.NF.7)
The fraction of the entire bulletin board decorated by each classmate is N/20.
Fraction of a number.Fraction is a mathematical expression which is made up of denominator and a numerator. So that fractions may generally be categorized into 3 types. These are: proper fraction, improper fraction, and mixed fraction.
Considering the given question, let the size of the bulletin board be represented by N.
The section of the bulletin board to be decorated = 1/5 * N
= N/ 5
There are 4 classmates that has been selected to divide the section to be decorated equally among themselves. So.
Fraction of the board to be decorated by each student = (N/ 5)/ 4
= 1/20 N
The fraction of the board to be decorated by each student is N/20.
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Find the missing angle. Find x.
Please help will mark Brainly
"Mark as brainiest". Click on the option to mark it the best answer.
how to help mark Brainly?The site has a Brainly Basic free option, plus a Brainly Plus paid upgrade where users can ask priority questions and receive verified answers, but there's no option to filter out the unverified answers for browsing or searching.
You can filter your search by subject, grade level, or status by clicking on the list of Subjects on the left, or by school level or status from the grey drop-down list in the middle of the page.
Brainly, at its most simple, is a peer-to-peer network of questions and answers. The idea is to help students with homework questions by using others who may have already answered that question.
To be clear, this isn't a set of answers laid out or a group of professionals giving answers. Rather, this is an open forum-style space in which students can post a question and, hopefully, get an answer from the community of others in education.
To learn more about mark Brainly refer to:
https://brainly.com/question/30119734
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