Therefore , the solution of the given problem of linear equation comes out to be the plan will be equal at 21 visits.
A linear equation is precisely what?The algebraic equation y=mx+b stands in for a linear equation. The slope is m, and B is the y-intercept. The last phrase referred to a "simple formula with two elements" where both y and x are variables. Bivariate linear equations are calculations involving two variables. Here are a few examples: The outcomes are 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3. If the answer to a mathematical equation is in the form y=mx+b, where m denotes the slope and b the y-intercept, the equation is said to be linear.
Here,
Given :
Case 1: flat rate of $201 a month and you get unlimited visits.
and
Case 2:pay only $33 per month, but must pay $8 for each visit to the club.
Thus,
To find at what number of visits both plan be equal is
Let x be the number of visit,
We get,
Case 1: 201
Case 2: 33 + 8x
For equlaity:
=>33+ 8x =201
=>8x =168
=> x =168/8
=> x =21
Therefore , the solution of the given problem of linear equation comes out to be the plan will be equal at 21 visits.
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There is a 10% chance of rain tomorrow a spinner with 10 sections is spun to simulate the probability of rain where spinning a 1 indicates rain if the results are 3,6,1,8 and 3, then what is the difference in the experimental probability from the simulation and the prediction
The experimental probability is 30% higher than the predicted probability.
What is meant by experimental probability?
Experimental Probability: what actually occurs when the experiment is carried out. For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.
The spinner has 10 sections and a 10% chance of landing on the section representing rain. Therefore, the probability of rain predicted by the spinner is 0.1 or 10%.
From the simulation, the results are 3, 6, 1, 8, and 3. Out of these 5 spins, 2 of them landed on the section representing rain (1, 3). Therefore, the experimental probability of rain from the simulation is 2/5 or 40%.
The difference between the experimental probability from the simulation and the prediction is the difference between the two percentages, which is:
(experimental probability) - (predicted probability) = 40% - 10% = 30%
Hence, the experimental probability is 30% higher than the predicted probability.
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What does 4 more than mean?
Answer:
+4
Step-by-step explanation:
if x is your number, then x+4 is four more than
Answer:
Answer Below
Step-by-step explanation:
The phrase "4 more than" means 4 has been added onto a number. Eg:"Sue has 4 more sweets than Ann, means that however many sweets Ann has, Sue's number is bigger by 4.
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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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 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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You have 140 tomatoes and 13 onions left over from your garden. You want to use these
to make jars of tomato sauce and jars of salsa to sell at a farm stand. A jar of tomato
sauce requires 10 tomatoes and 1 onion, and a jar of salsa requires 5 tomatoes and 1
onion. You will make a profit of $2 on every jar of tomato sauce and a profit of $1.50 on
every jar of salsa sold. The owner of the farm wants at least three times as many jars of
tomato sauce as jars of salsa. How many jars of each should you make to maximize
profit?
3. A company produces two types of tables, T1 and T2. It takes 2 hours to produce the parts
of one unit of T1, 1 hour to assemble and 2 hours to polish. It takes 4 hours to produce
the parts of one unit of T2, 2.5 hour to assemble and 1.5 hours to polish. Per month, 7000
hours are available for producing the parts, 4000 hours for assembling the parts and 5500
hours for polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110.
How many of each type of tables should be produced in order to maximize the total
monthly profit?
1. To maximize the profit :
28 jars of salsa and
0 jars of tomato sauce should be made.
which make maximum profit of $42.
2. In order to maximize the total monthly profit
2300 units of T₁ type table and and
600 units of T₂ type table should be made
which provide maximum profit of $273000.
What is an Inequality?In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.
1. Let x be the numbers of jars of tomato sauce
Let y be the number of jars of salsa sauce
Profit P(x, y)=2x+1.5y
x≥0
y≥0
10x+5y≤140
x + y ≤13
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,13)
B at (0,28)
C at (14,0)
D at (15,0)
E at (15, -2)
Evaluate profit P(x, y) at each vertex
A at (0,13):P(0,13)=$19.5
B at (0,28):P(0,28)=$42
C at (14,0):P(14,0)=$28
D at (15,0):P(15,0)=$30
E at (15, -2):P(15,-2)=30-3=$27
The maximum profit of $42 is at vertex B.
Which means production of 28 jars of salsa and 0 jars of tomato sauce provides maximum profit of $42.
2. Let x be the number of tables of type T₁
and y the number of tables of type T₂
Profit P(x, y)=90x+110y
x≥0
y≥0
2x+4y≤7000
x+2.5y≤4000
2x+1,5y≤5500
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,0)
B at (0,1600)
C at (1500,1000)
D at (2300,600)
E at (2750,0)
Evaluate profit P(x, y) at each vertex
A at (0,0):P(0,0)=0
B at (0.1600):P(0,1600)=90(0)+110(1600)=176000
C at (1500,1000):P(1500,1000)=90(2500)+110(1000)=245000
D at (2300,600):P(2300,600)=90(2300)+110(600)=273000
E at (2750,0):P(2750,0)=90(2750)+110(0)=247500
The maximum profit of $273000 is at vertex D.
which means production of 2300 tables of type T₁ and 600 tables of type T₂ makes maximum profit.
1. Hence, maximum profit is made by making
28 jars of salsa and
0 jars of tomato sauce getting
$42 of profit.
2. Hence the company needs to produce
2300 tables of type T₁ and
600 tables of type T₂,
in order to maximize its monthly profit which is equal to $273000.
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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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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).
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer: 5$ for 52 days
Step-by-step explanation: (5 x 52) + 90 = 350
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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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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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.
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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1. For the three-part question that follows, provide your answer to each question in the given workspace.
Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Part A:
Evaluate the expression 4x² when
S
5
6
Part B:
1
Evaluate the expression 4x² when x =
2
Write the answer as a mixed number if necessary.
Write the answer as a mixed number if necessary.
Part C:
Show all of your work for Parts A and B to justify your answers.
Therefore , the solution of the given problem of function comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and
Domain :[ -∞,0 ] U [ 0,∞].
Function is what?
According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.
Here,
Part A:
=> 4/6x² - 5x²/4x
=> 8 - 15x + 3x³/12x²
=> 3x³- 15x +8 / 12x²
=> x(3x²- 15 ) + 8 / 12x²
Part B:
Domain : x ∈ R : x≠ 0
Part c:
The function domain at x= 0 Domain :[ -∞,0 ] U [ 0,∞]
Therefore , the solution of the given problem of equation comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and Domain :[ -∞,0 ] U [ 0,∞].
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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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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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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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Jack, Marta, Rand, Todd and 6 more students went apple picking. Every two of these 10 students pick a different number of apples. Combined, the ten students pick 45 apples. Suppose Jack and Marta pick a total of 16 apples; Marta and Rand pick a total of 15 apples; Rand and Todd pick a total of 13 apples. How many apples did Todd pick
So, Todd picked 1 apple.
We can use the information given to set up the following equations:
Let x be the number of apples Jack picked, and y be the number of apples Marta picked.
We know that x + y = 16 (Jack and Marta pick a total of 16 apples)
Let y be the number of apples Marta picked, and z be the number of apples Rand picked.
We know that y + z = 15 (Marta and Rand pick a total of 15 apples)
Let z be the number of apples Rand picked, and w be the number of apples Todd picked.
We know that z + w = 13 (Rand and Todd pick a total of 13 apples)
We know that the total number of apples picked is 45, therefore x + y + z + w = 45
We can use the equation x + y = 16 to express x in terms of y:
x = 16 - y
We can substitute this into the other equations
(16 - y) + y = 16
y + z = 15
z + w = 13
We can sum all the equations:
(16 - y) + y + y + z + z + w = 45
16 + 2y + 2z + w = 45
From the equation y + z = 15, we can substitute y = 15 - z
16 + 2(15 - z) + 2z + w = 45
16 + 30 - 2z + 2z + w = 45
46 + w = 45
w = 1
Therefore Todd picked 1 apple.
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-16x-32y=52 solve for y
Answer: I think 7/2?
Step-by-step explanation:
What is the definition of a solution give 3 examples of a solution?
A homogenous mixture of two or more components is referred to as a solution.
Solution Examples: Brass is an illustration of a solid solution. Liquid solutions include aqueous hydrochloric acid as an illustration (HCl in water). Air is an illustration of a gaseous solution.
1)When we combine salt (often table salt) and water, we create salt water.
2)By combining sugar and water, sugar water is created.
3)Mouthwash is made up of various chemicals that have been dissolved in water.
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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!
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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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
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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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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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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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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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]