The 4 steps in solving simple problems in mathematics is explained below.
According to the author called Polya created his famous four-step process for problem solving that one is used all over to aid people in problem solving
The first and foremost Step is to understand the problem which includes identification of the unknowns and figure out what the problem tells you is important and then we have to identify any information that is irrelevant to the problem.
Then the nest step is to Devise a plan which means that Look for a pattern and then by using it we have to make a table, diagram or chart and then write an equation.
Then we have to move onto the next steps that is to carry out the plan which means the process of solving the question.
Then the final step is to Look back problem that is none other than check and interpret its reliability of the solution
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Three vertices of parallelogram ABCD are A(-3,1), B(5, 7) and C(6, 2). Find the coordinates of vertex D
The coordinates of vertex D in the parallelogram ABCD are (7,-3).
What is the relation of vertex in a parallelogram?In a parallelogram, opposite sides are parallel and congruent. Therefore, the vector that goes from vertex A to vertex B is the same as the vector that goes from vertex C to vertex D, and the vector that goes from vertex B to vertex C is the same as the vector that goes from vertex D to vertex A.
The vector from vertex A to vertex B is [tex]< 5-(-3), 7-1 > = < 8,6 >[/tex]
So, the vector from vertex C to vertex D is also [tex]< 8,6 >[/tex]
The vector from vertex B to vertex C is [tex]< 6-5, 2-7 > = < 1,-5 >[/tex]
So, the vector from vertex D to vertex A is also [tex]< 1,-5 >[/tex]
To find the coordinates of vertex D, we can add the vector from vertex C to vertex D to the coordinates of vertex C.
The coordinates of vertex C are (6, 2)
So, the coordinates of vertex D are [tex](6+1, 2-5) = (7, -3)[/tex]
Therefore, the coordinates of vertex D in the parallelogram ABCD are (7,-3).
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What relationship exists between Nand K?
Given:
KLMN is a parallelogram.
Helppppp meee
The relationship exists between N and K are the endpoints of the side KN.
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions.
It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.
we know that for a parallelogram KLMN is a quadrilateral whose two sides are parallel to each other and has two non-parallel sides.
for N and K we could say that the two are endpoints of the line segment KN; which is one of a side of a parallelogram KLMN.
Therefore, The relationship exists between N and K are the endpoints of the side KN.
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Katie plans to paint four toy chests that have the given net. She will buy 10-oz cans of paint that cover 933 square inches each
Two cans of paint are needed to cover the toy chest of 1866 in²
Area:
The area is the amount of space occupied by a two-dimensional object or figure. Area (A) of the rectangle is:
A = length * breadth.
Area of A = 13 * 16 = 208 in²
Area of B = 13 * 25 = 325 in²
Area of C = 25 * 16 = 400 in²
Area of D = 13 * 25 = 325 in²
Area of E = 13 * 16 = 208 in²
Area of F = 25 * 16 = 400 in²
1) Combined Area = 208 + 208 = 416 in²
2) Combined Area = 325 + 325 = 650 in²
3) Combined Area = 400 + 400 = 800 in²
4) Combined Area = 416 + 650 + 800 = 1866 in²
5) Amount of paint = 1866 in² / 933 in² = 2
Therefore, Two cans of paint are needed to cover the toy chest of 1866 in²
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The ranges of values = 40 and the number of sets = 10 , then the length of set is
For example, if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 6}, then x=6>5=y, but if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 7}, then x=6=y. not sufficient.
What is values?Values are ideals or beliefs that a group or an individual hold and are essential for determining what is desirable or undesirable to them. Values can also be seen as overall conceptions people hold toward the world and aligns their behavior, motivation, perceptions, and personality. Values establish a framework through which people can compare what is most important and, in most cases, forms the basis for making choices. People interact with the world based on their values, which vary from person to person.An individual can value integrity, while another will value loyalty, and these values are shaped by a person's past experiences or cultural background. Notably, an individual can have several sets of values, but the degree to which the person can value these things can vary. A good example is someone who values family and wealth. There could be situations whereby such an individual can be faced with choosing between family and wealth, and it is very normal to sacrifice one over the other.To learn more about values refer to:
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Complete question is: If the ranges of values = 40 and the number of sets = 10 , then what will be the length of set ?
help me pleaseeeeeeeee!!
Answer:
2nd
Step-by-step explanation:
Answer: They are not proportional.
Step-by-step explanation: The numerator is multiplied my 0.5 but the denominator is not.
What is an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35?
Answer:
4x - 5y = 10
Step-by-step explanation:
We can use the point-slope form to find the line equation:
[tex] \displaystyle{y - y_1 = m(x - x_1)}[/tex]
Where (x1,y1) is the point that the line intersects and m is slope. We know the line passes through (-5,-6) and the slope is parallel to the line 4x - 5y = 35. Meaning the slope of that line is equal to slope of 4x - 5y = 35.
In this equation form Ax + By = C, we can find slope by m = - A/B. Therefore, m = -4/-5 which equals to 4/5. Hence, the slope is 4/5
[tex] \displaystyle{y - y_1 = \dfrac{4}{5}(x - x_1)}[/tex]
And also it intersects the point (-5,-6). Therefore:
[tex] \displaystyle{y - ( - 6) = \dfrac{4}{5}(x - ( - 5))} \\ \\ \displaystyle{y + 6 = \dfrac{4}{5}(x + 5)}[/tex]
Then convert to Ax + By = C to match with the given equation in problem:
[tex] \displaystyle{5(y + 6 )= 5 \left(\dfrac{4}{5}(x + 5) \right)} \\ \\ \displaystyle{5y + 30 = 4(x + 5)} \\ \\ \displaystyle{5y + 30 = 4x + 20} \\ \\ \displaystyle{ \therefore 4x - 5y = 10}[/tex]
Suppose the average yearly salary of an individual whose final degree is a master's is $ 41 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $ 109 thousand. Find the average yearly salary of an individual with each of these final degrees.
Suppose the average yearly salary of an individual whose final degree is a master's is $ 41 thousand less than twice that of an individual. the average yearly salary of an individual with each of these final degrees is: $50,000 (Bachelor's degree) and $59,000 (Master's degree )
How to find the average yearly salary?Let x represent the average yearly salary of an individual with the bachelor's degree
Let (2x-41000) represent the average yearly salary of an individual with the master's degree
Let the sum of these salaries = 109000
So, x + (2x-41000) = 109000
Simplify and solve:
3x = 109000 + 41,000
3x = 150,000
Divide both side by 3x
x= 150,000/3
x = 50,000 (Bachelor's degree)
So,
(2x-41000)
= 2(50,000) - 41,000
=100,000 - 41,000
= $59,000 (Master's degree )
Therefore the average yearly salary is $50,000 (Bachelor's degree) and $59,000 (Master's degree )
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latifa writes down a number. she says
if i find a cube root of that number and then quadruple the answer, i get 16
what number did latifa write down?
Answer:
8
Step-by-step explanation:
the cubed root of 8 equals 2
if you quadruple 2 (multiply it by 4), you will get 8
When merida divides her age by 3 and adds 5, the result is 9 which equation represents this situation where m is meridas age?
a/ 9= (m ~ 3) x 5
b/ m= (9 - 3 ) + 5
c/ m = (9~3) +5
d/ 9= (m~ 3) +5
When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5.
What is an equation?The link between two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
The definition an equation in algebra is a mathematical expression that indicates the equivalence of two mathematical terms. In equation 6x + 11 = 14, for instance, the two expressions 6x + 11 and 14 are separated by the symbol "equal."
When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5, this represents the situation where m is Merida's age.
correct option: D
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The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45
Customers older than 45 years are 11 in number. This can be solved using stem-and-leaf plot.
What is stem-and-leaf plot?A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.
The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
The stem and leaf plot represents the age of store patrons. The leaf represents the unit digit, while the stem stands for the tens digit. 45 is not taken into account because the question asks us to determine the percentage of consumers who are over 45.
Customers older than 45 years old include: 48, 50, 50, 51, 55, 56, 62, 64, 65, 65, 73.
So, there are a total of 11 clients.
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The complete question is as follows:
The stem-and-leaf plot shows the ages of customers who were interviewed in a survey by a store. How many customers were older than 45
How do you calculate seed number?
To calculate seed number, divide the total number of inches available for crop by the in-row crop spacing. For example, 120 inches divided by one inch per pea seed equals 120 pea seeds.
What is seed?In botany, a seed is an undeveloped plant embryo and food reserve encased in a protective outer covering. In a broader sense, "seed" refers to anything that can be sown, such as seed and husk or tuber.
Seeds are formed when a ripened ovule is fertilised by pollen-derived sperm, resulting in a zygote. The embryo develops from the zygote within a seed, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of seeds is a stage in the reproduction of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, lack seeds and must reproduce exclusively through water.
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What is a 123 triangle?
This is a triangle whose three angles are in the ratio 1:2:3 and respectively measure 30° ( π/6), 60° ( π/3), and 90° ( π/2) and the sides are in the ratio 1:√3: 2.
These triangles are also known as special right triangles, such as 30-60-90 triangles, and 45°-45°-90° triangles. Among all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, √2/2 and the greatest ratio of the altitude from the hypotenuse to the sum of the legs, √2/4.
The 30°-60°-90° triangle is the right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows the fact that if α, α + δ, α + 2δ are the angles in the progression then the sum of the angles 3α + 3δ = 180°. By dividing by 3, the angle α + δ must be 60°. The right angle is 90°, and the remaining angle is 30°.
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It is known that the percent of red M&Ms is 35% in each package. Don went to the vending machine and bought a package of M&Ms. In his package he counted 52 MaMs and 18 were red. If 35% is the true parameter then what is the probability that a package of getting no more than 18 out of 52 M&Ms red?
35% in each package is red.
that means nothing else than for every M&M you pick, the probability is 35% (or 0.35) that is is red.
it also means the probability to get anything but red is 1 - 0.35 = 0.65 (65%).
if I understand you correctly, the question is for the probability that there are no more than 18 red M&Ms in a package of 52.
in other words, the probabilty that there are exactly 18, or exactly 17, or exactly 16 ... or exactly 1, or no red M&Ms.
the probability to get exactly 18 red out of 52 is
0.35¹⁸ × 0.65³⁴
for one of the combinations.
and we have C(52, 18) possible combinations :
52! / (18! × (52-18)!) = 52! / (18! × 34!)
18 red = 0.35¹⁸ × 0.65³⁴ × C(52, 18) = 0.115457378...
17 red = 0.35¹⁷ × 0.65³⁵ × C(52, 17) = 0.110273578...
16 red = 0.35¹⁶ × 0.65³⁶ × C(52, 16) = 0.096708177...
15 red = 0.35¹⁵ × 0.65³⁷ × C(52, 15) = 0.077665254...
14 red = 0.35¹⁴ × 0.65³⁸ × C(52, 14) = 0.056935055...
13 red = 0.35¹³ × 0.65³⁹ × C(52, 13) = 0.037956703...
12 red = 0.35¹² × 0.65⁴⁰ × C(52, 12) = 0.022909582...
11 red = 0.35¹¹ × 0.65⁴¹ × C(52, 11) = 0.012452595...
10 red = 0.35¹⁰ × 0.65⁴² × C(52, 10) = 0.006056874...
9 red = 0.35⁹ × 0.65⁴³ × C(52, 9) = 0.002615926...
8 red = 0.35⁸ × 0.65⁴⁴ × C(52, 8) = 0.000993712...
7 red = 0.35⁷ × 0.65⁴⁵ × C(52, 7) = 0.000328083..
6 red = 0.35⁶ × 0.65⁴⁶ × C(52, 6) = 9.271902896e-005
5 red = 0.35⁵ × 0.65⁴⁷ × C(52, 5) = 2.198201902e-005
4 red = 0.35⁴ × 0.65⁴⁸ × C(52, 4) = 4.252473918e-006
3 red = 0.35³ × 0.65⁴⁹ × C(52, 3) = 6.446899235e-007
2 red = 0.35² × 0.65⁵⁰ × C(52, 2) = 7.183687719e-008
1 red = 0.35 × 0.65⁵¹ × C (52, 1) = 5.231817386e-009
0 red = 0.35⁰ × 0.65⁵² × C(52, 0) =
= 0.65⁵² = 1.868506209e-010
the probability to have no more than 18 reds is the sum of all that :
0.540472593...
Find the value of each expression.
a. 1/4 • (-12)
b. -1/3 • 39
c. (-4/5) • (-75)
d. -2/5 • (-3/4)
e. 8/3• -42
By using simple arithmetic and using calculator we get:
a. 1/4 • (-12) = (-3)
b. -1/3 • 39 = -13
c. (-4/5) • (-75) = 60
d. -2/5 • (-3/4) = 3/10 = 0.3
e. 8/3• -42 = -56
What is arithmetic?Arithmetic is a branch of mathematics that deals with the manipulation of numbers and their properties. It is the study of numbers and the operations that can be performed on them, such as addition, subtraction, multiplication, and division. Arithmetic also includes concepts such as fractions, decimals, and percentages. The study of arithmetic is fundamental to many other branches of mathematics, including algebra, geometry, and calculus, as well as many practical fields like finance, engineering, and computer science.
What is calculator?A calculator is a device that performs mathematical calculations. It can be a handheld device or a software program on a computer or mobile device. Calculators typically have buttons or keys for performing basic arithmetic operations, such as addition, subtraction, multiplication, and division, as well as more advanced functions like trigonometry and logarithms. Some calculators also have the ability to store and recall numbers, perform conversions between units of measurement, and perform other specialized functions.
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Darnel uses 8 fluid ounces of lemon juice in one batch of lemonade. How many batches can he make with 1 pint of lemon juice?
Answer:
16 ounces = 1 pint, 8 times 2 = 16
Step-by-step explanation:
Answer in explanation:
1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.
(8 x 2 = 16
your answer is 2
Hope this helps!
10. Ashton walked into the restaurant and 4 employees were working registers. Use the trend line equation to predict how long he will wait to place his order.
On solving the provided question, we can have that by unitary method the answer will be total salary = 4 * 2340 = $ 9360
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
in a restaurant = 4 employees
salary of 1 = $ 2340
total salary = 4 * 2340 = $ 9360
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GEOMETRY:
I might just be slow but I don't understand what this question is asking at all. Can someone help?
Answer:
[tex]b = 90[/tex]
[tex]d = 100[/tex]
[tex]c = 80[/tex]
Step-by-step explanation:
The problem is asking for the values of the variables [tex]b[/tex], [tex]c[/tex], and [tex]d[/tex] in the given parallelogram with angles [tex]d\textdegree[/tex], [tex]c\textdegree[/tex], [tex](b-10)\textdegree[/tex], and [tex](b+10)\textdegree[/tex].
To solve for these variables, we can construct three equations using the knowledge that any two adjacent angles of a parallelogram are supplementary (their measures add to 180º).
The first equation shows that the top two angles are supplementary:
[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]
The second equation shows that the bottom two angles are supplementary:
[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]
The third equations shows that the left two angles are supplementary:
[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]
First, we can solve for [tex]b[/tex] in the second equation using simple algebraic manipulation.
[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]
[tex](b+b)\textdegree + (10-10)\textdegree = 180\textdegree[/tex]
[tex]2b\textdegree = 180\textdegree[/tex]
[tex]b\textdegree = 90\textdegree[/tex]
[tex]b = 90[/tex]
Using this [tex]b[/tex]-value, we can solve for [tex]d[/tex] by rewriting the third equation, plugging [tex]90[/tex] in for [tex]b[/tex]:
[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]
[tex]d\textdegree + (90-10)\textdegree = 180\textdegree[/tex]
[tex]d\textdegree + 80\textdegree = 180\textdegree[/tex]
[tex]d\textdegree = 100\textdegree[/tex]
[tex]d = 100[/tex]
Finally, we can solve for [tex]c[/tex] in the first equation by plugging [tex]100[/tex] in for [tex]d[/tex]:
[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]
[tex]100\textdegree + c\textdegree = 180\textdegree[/tex]
[tex]c\textdegree = 80\textdegree[/tex]
[tex]c = 80[/tex]
Alyssa's den is 8 feet longer than it is wide. If the den's area is 425 square feet, what are the dimensions of the room?
The dimensions of the room when Alyssa's den is 8 feet longer than it is wide are 15cm as 23cm.
How to illustrate the equation?An equation simply means the statement that shows the relationship between the variables given. It has an equal sign to denote this.
Let the width of the den be x.
The length of the den is x+8.
We can set up the equation x*(x+8)=425 to represent the area of the den.
We can solve this equation by factoring it as x² + 8x =425.
x² + 23x - 15x - 425
x(x + 23) - 15(x + 23)
(x - 15)(x + 23)
Either way, we find that the width of the den is 15 feet and the length is 23 feet.
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If $n$ is a positive integer such that $2n$ has 28 positive divisors and $3n$ has 30 positive divisors, then how many positive divisors does $6n$ have
As per the given equation the total number of positive divisors that $6$ has is 38.
What is the positive divisor?The divisors (or factors) of a positive integer are the integers that evenly divide it.
The formula for calculating the total number of divisor of a number ′n′ where n can be represent as powers of prime numbers is shown as.
If N= paqbrc
Then total number of divisors = (a+1)(b+1)(c+1).
If we want to find the positive divisors for an integer n, we just take the integers 1, 2, 3, . . . , n, divide n by each, and those that divide evenly make up the set of positive divisors for n.
The divisors (or factors) of a positive integer are the integers that evenly divide it
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The sum of the digits of a two-digit number is 7. When the digits are reversed, the number increases by 45. What is the original number?
original number: ⬜
The original number is 25.
We know that,
The sum of the original number is 7 --(i)
When reversed, the value of the number is increased by 45 --(ii)
Therefore, adding (i) and (ii), we get:
7 + 45 = 52
Also, 5 + 2 = 7
Since 52 is the reversed number,
Therefore, the original number is 25.
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A television is on sale for $75 off.
The price of the television with the sale is $300.
If you use the equation −75=300 to solve this problem, what does n represent?
In this equation, n represents the original price of the television before the sale.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions by using numbers, symbols, and operations. It is used to describe the relationship between different variables in a problem. Equations are usually written as a statement of equality, such as 2 + 2 = 4, where the left side of the equation (2 + 2) is equal to the right side (4). Equations can be used to solve for a single unknown value, or to determine the relationship between multiple variables.
In this equation, n represents the original price of the television before the sale.
This means that the original price of the television was $375.
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Making connections between arithmetic sequences and linear function
Use the graph or the formula to write the equation of the line in a slope intercept form
Arithmetic sequences are those in which the difference between each subsequent phrase is a fixed number. This is shown by writing the equation for a line as y = mx+c, where m denotes the slope and c the y-intercept.
What is the relationship between arithmetic sequences and linear functions?The origin is the place where the X and Y axes always meet. Point (0, 0) on the XY plane is where the origin is situated. The XY plane is divided into four distinct quadrants using symmetry and the origin.Our origin will not be in the specified place if we added negatives to the axes as in the example presented. This indicates that the XY plane's four quadrants are not properly separated.This means that, as seen in the provided illustration, we are unable to include negatives on the axes. It primarily involves incorrect notation. A linear function is an algebraic sequence. Where d represents the common difference and c is a constant, we write an=dn+c in place of y=mx+b.To learn more about arithmetic sequences refer to :
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What does it mean to translate coordinates?
A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.
Now, According to the question:
What does translation of coordinates mean?
A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.
Transformations of Graphs
Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically.
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-16x-32y=52 solve for y
Answer: I think 7/2?
Step-by-step explanation:
after a party there are parts of three pizzas remaining. there is 3/4 of a pepperoni pizza remaining 5/8 of a cheese pizza remaining and 11/12 of a sausage pizza remaining. the 5 friends who organized the party split the remaining pizza equally. What fraction of a whole pizza does each person get?
Adding all of the remaining pizzas, and dividing the total pizza into 5 equal fractions, the fraction of pizza that each person gets would be 11/24
What is a mixed number and how is it different from an improper fraction?A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number. It is different from an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4 is an improper fraction.
How do you convert a mixed number to an improper fraction?To convert a mixed number to an improper fraction, you must first multiply the whole number by the denominator of the fraction. Then add the result to the numerator. Finally, place the sum over the denominator. For example, to convert 3 1/2 to an improper fraction, you would first multiply 3 by 2 (the denominator of the fraction 1/2) to get 6, then add 1 (the numerator of the fraction 1/2) to get 7. So 3 1/2 is equivalent to 7/2 as an improper fraction.
So to find out the fraction of a whole pizza that each person gets out of the different remaining pizzas, first we need to all the remaining pizzas as shown below,
3/4 of pepperoni + 5/8 of cheese + 11/12 of sausage = 55/24
Now to equally divide this into 5 person, we need to divide this fraction by 5,
i.e 55/(24*5) = 11/24
Therefore, each person gets 11/24 of the whole pizza.
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g(x)=\sqrt{x} -5
what is the range and domain
Answer:
Function Domain and Range
g(x)=\sqrt{x} -5
what is the range and domain
To find the range of g(x), we can substitute a few values of x into the expression for g(x) to see what the output is. For example, when x = 0, g(x) = sqrt(0) - 5 = 0 - 5 = -5. When x = 1, g(x) = sqrt(1) - 5 = 1 - 5 = -4. When x = 2, g(x) = sqrt(2) - 5 = 1.4142 - 5 = -3.5858.
As we can see, the output of g(x) is always a negative number for any value of x in the domain. Therefore, the range of g(x) is the set of all negative real numbers, or (-infinity, 0).
So, the domain of g(x) is all real numbers x such that x >= 0, and the range of g(x) is all negative real numbers (-infinity, 0).
2 The displacement of a mass is given by the function
y = sin 3t. 3t is measured in radians.
The tasks are to:
a) Draw a graph of the displacement y against time t
for the time t = 0s to t = 2.s.
b)
Identify the position of any turning points and
whether they are maxima, minima or points of
inflexion.
c) Calculate the turning points of the function using
differential calculus and show which are maxima,
minima or points of inflexion by using the second
derivative.
Compare your results from parts b and c.
The graph is attached and the point of maximum as y"(π/6) < 0 and at point of minimum y"(π/2) > 0.
What is turning point and inflexion point?An inflection point is where a graph's curvature changes, from concave up to concave down or vice versa. It is also known as a turning point, flex, inflection, or "point of diminishing returns."
A concave down graph resembles an upside-down U or a cap, while a concave up graph resembles the letter U (or a "cup"). The intersection of a "cup" and a "cap" marks the inflection point.
Given displacement of mass by function,
y = sin(3t), where 3t is in radians,
the graph for t = 0 and t = 2 sec.
2: The position of turning point,
differentiate the equation we get,
y' = 3cos(3t)
the turning points are t = π/6 and t = π/2
y'(π/6) = y'(π/2) = 0
3: inflexion points,
again differentiate the equation we get,
y" = -9sin(3t)
and inflection at π/3
because y"(π/3) = 0
Maximum and minimum points are π/6 and π/2 respectively,
as the point of maximum t = π/6 as y"(π/6) < 0,
and point of minimum at t = π/2 as y"(π/2) > 0.
Hence the graph is attached and maximum at t = π/6, and minimum at t = π/2, and inflection at π/3.
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Ivan is a software salesman. His base salary is $2400, and he makes an additional $110 for every copy of History is Fun he sells.
Let P represent his total pay (in dollars), and let N represent the number of coples of History is Fun he sells. Write an equation relating P to N. Then use this
equation to find his total pay if he sells 24 coples of History is Fun.
The total pay when he sells 24 copies of Math exists Fun should be 3760.
What is meant by equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. A mathematical equation is a statement with two equal sides and an equal sign in between.
Numerical constants, symbolic names, mathematical operators, functions, and conditional expressions can all be found in expressions in some combination.
Calculation of the equation and the total pay:
His base salary is $2400, and he makes an additional $110 for every copy of Math is Fun he sells.
Here P means the total pay
So, here the equation be p = 2400 + 110 n
substitute the values in the above equation, we get
Now the total pay be
p = 2400 + 110(24)
simplifying the above equation, we get
= 2,400 + 2640
= 5040
The equation that should be related P to N should be considered as the 2400 + 110n.
Therefore, the total pay when he sells 24 copies of Math is Fun should be 5040.
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The total pay when he sells 24 copies of Math exists Fun should be 3760.
What is meant by equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. A mathematical equation is a statement with two equal sides and an equal sign in between.
Numerical constants, symbolic names, mathematical operators, functions, and conditional expressions can all be found in expressions in some combination.
Calculation of the equation and the total pay:
His base salary is $2400, and he makes an additional $110 for every copy of Math is Fun he sells.
Here P means the total pay
So, here the equation be p = 2400 + 110 n
substitute the values in the above equation, we get
Now the total pay be
p = 2400 + 110(24)
simplifying the above equation, we get
= 2,400 + 2640
= 5040
The equation that should be related P to N should be considered as the 2400 + 110n.
Therefore, the total pay when he sells 24 copies of Math is Fun should be 5040.
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help please!! this is for tonight, I don't know how to use the "undefined" please help
The equation of the line in slope-intercept form, with the point (4, -5) and an undefined rate of change is x = 4.
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope or rate of change.x and y represents the data points.c represents the y-intercept.In Mathematics, any line that has an undefined slope (rate of change) is a vertical line because it does not have a y-intercept. This ultimately implies that, a vertical line that is parallel to the y-coordinate (y-axis) would have an undefined slope (rate of change).
Generally speaking, the equation of a line that has an undefined slope (rate of change) is given by this mathematical expression;
x = a
Where:
a represents the x-intercept.
At point (4, -5), the required equation with an undefined slope (rate of change) is x = 4.
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How to convert log2 to log10?
To convert the log2 to log10, we can use the convert of base formula for logarithms. The change of base formula for logarithms is as written:
log b(x)=logc(x) / logc(b)
By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:
log2(x)=log10(x)/log10(2) = log(x)/log (2)
This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.
The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is presented as “log e e”.
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