The student's error is that 16 has to be prime factorized as (2)⁴ or 2 × 2 × 2 × 2.
What is Prime factorization?Prime factorization is defined as the method of writing a number as the product of two or more prime numbers.
Prime numbers are numbers which has only two factors, 1 and the number itself.
Given number is 16.
We have to factorize 16 as a product of prime factors.
Student wrote it as,
16 = 2 × 8
The error here is that 8 is not a prime number. We have to again factorize 8 to get the required factored form.
8 = 2 × 4
4 = 2 × 2
So combining all these,
16 = 2 × 2 × 2 × 2
So 16 can be prime factorized as 16 = 2 × 2 × 2 × 2.
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What is a table rule?
Therefore , the solution of the giving problem of tables is a number designating the type of rule, a set of -1 tokens, and a ranking of the rule.
Describe a table.A mathematical table is a collection of numbers that shows the outcome of a calculation using multiple inputs. data with numbers and descriptions that is arranged in rows and columns. The table and 10 pattern are easy to remember. The following is the order of the numbers:2,4,6,8,10,12,14,16,18,20. Value maps are used to show how different data pieces are related to one another. You can incorporate the values expression table into your science lecture. Scientists and researchers use tables of values to store data and seek for patterns in that data. Then, this pattern is used in forecasting.
Here,
Tokens from the address input sequence are mapped to a standardized output sequence using a set of rules found in the rules table.
A rule is described as a collection of input tokens, a set of output tokens, a set of -1 (terminator), a number designating the type of rule, a set of -1 tokens, and a ranking of the rule.
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34. Apply Math Models Olivia makes and sells
bracelets and necklaces. She can make up to
60 pieces per week. Write and graph a system
of inequalities that shows the combination of
bracelets and necklaces that she can make if
she wants to sell at least 30 items per week.
If necklaces sell for $8 each and bracelets sell
for $5 each, what is the most money she can
make in a week? Explain.
The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).
what is unitary method ?The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.
given
Assume that y is the number of necklaces and x is the number of bracelets.
Up to (less than or equal to) 60 pieces (bracelets and necklaces) can be produced by Olivia each week:
x+ y ≤60
Up to (less than or equal to) 40 bracelets can be made by Olivia each week:
x≤40(2)
Up to (less than or equal to) 40 necklaces can be created by Olivia each week.
y≤40(3)
Olivia aims to sell at least 30 products per week, preferably more.
x+y≥30(4)
It is possible to write x+y60 as yx+60 with a boundary of y=x+60. Since is used, we shade below the line and draw the line as solid. (red)
The vertical boundary of x40 is defined by x=40. Because is employed,, after which we darken the line's left side and draw the line as solid. (orange)
The horizontal boundary of y40 is defined by y=40. Because is utilized, we shade below the line and draw a solid line over it. (green)
The expression x+y30 can be written as yx+30 has a limit of y=x+30.
Because is utilized, we shade above the line and draw the line as a solid. (blue)
The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).
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Dante deposits $300 to open a savings account. He will earn 2% interest each year on his
money If he makes no deposits or withdrawals, how much money will Dante earn in interest
in 1 year? How much money will be in the account after 4 years?
When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.
what is amount ?aggregate attempting to determine the whole amount, time, or quantity. The amount at hand or under consideration is very active. the overall outcome, significance, or import. a third accounting, the principal, and the interest. There are word forms for quantities, amounting, and amounted. adaptable noun A thing's quantity is how much of it there is, how much you have, how much you need, or how much you can get. He needs that much money to make ends meet.
given
A= P( 1- rt )
A = 275 ( 1+ 300 )
A = 275( 1.4 )= $385
When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.
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Find the product of 1/2a and -8/3b.
using distributive law
PLS HELP FAST! At what value of x does the function f(x)=2(3)^(x) overtake the function g(x)=2x^(2)+4x?
x=2 is value of x does the function f(x).
An easy definition of a function?
As a set of inputs with one output for each, a function is defined as a relationship between them.
In plain English, a function is an association between inputs in which each input is connected to precisely one output. a unique relationship in which each input only results in one outcome. Where x is the input value, it is frequently expressed as "f(x)". as in f(x) = x/2 ("f of x equals x divided by 2") Each input "x" yields a single output "x/2," indicating that it is a function: • f(2) = 1.
X f(x) g(x)
1 6 6
2 12 16
3 18 30
4 24 48
We can see from this table that f(x) is greater than g(x) starting from x=2
Therefore I think x=2 is your answer.
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y-9+y-4 combining like terms (middle school)
By combining the like terms from the given expression we get 2y-13
what is an algebraic expression ?
Algebraic expression can be defined as the combination of constants , variables and operators.
Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.
Given ,
The expression ,
=y-9+y-4
=y+y-(9+4)
=2y-13
Hence , By combining the like terms from the given expression we get 2y-13.
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The parallelogram has an area of 20 square inches. What are the dimensions of the parallelogram, to the nearest hundredth of an inch?.
The dimensions of the parallelogram to the nearest hundredth of an inch are 6.54 in and 3.06 in.
A Parallelogram is a flat shape with opposite sides parallel and equal in length.
properties of Parallelogram
The opposite sides are parallel and equal in lengthOpposite angles are equal, Angle A and angle B add up to 180°, so they are called supplementary angles.Trigonometry would be used to determine the base and the length of the parallelogram.
Base: cos 40 = adjacent /hypotenuse
0.7660 = adjacent / 4
adjacent = 4 x 0.7660
adjacent = 3.06 inch
Length = area/base
Length= 20/3.06
Length= 6.54 in
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What is the additive inverse of 7 by 8?
The additive inverse of 7/8 is -7/8.
This can be seen when using the additive inverse formula. The additive inverse formula states that if a number is denoted as x, then the additive inverse would be -x. Therefore, when applied to 7/8, it would be -7/8. This can also be seen when adding the two numbers together. When 7/8 is added to -7/8, the sum is 0. This can be seen in the calculation below:
7/8 + (-7/8) = 0
7/8 - 7/8 = 0
0/8 = 0
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This relationship can also be shown in a table. Complete the equation that represents the relationship between n and w.
Answer: w=10n+8
Step-by-step explanation:
6x10+8=68
7x10+8=78
8x10+8=88
9x10+8=98
Help with question 3
The solution is [tex](27^2)^{ 1/5}[/tex] express as [tex]145 \frac{4}{5}[/tex] in simplest radical form.
How to calculate simplest radical form?A radical in mathematics is the opposite of an exponent, which is denoted by the symbol "√" and is also referred to as the root. It can either be a square root or a cube root, and the number before the symbol or radical is regarded as an index number or degree. This number cancels the radical and is represented as a whole number by an exponent.
step1:
extract form
27² =729
729/5= decimal form=145.8
step 2:
729/5=145.8
mixed form:
[tex]145 \dfrac{4}{5}[/tex]
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If a power is missing, then the coefficient of the term with that power is
Answer:
0
Step-by-step explanation:
if no term exists in an expression this means it has a coefficient of 0
Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
A) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
B) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
C) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
The two-way frequency table shows the number of blue and green parrots and parakeets in a rescue facility.
Green Blue Total
Parrot 17 16 35
Parakeet 20 28 48
Total 37 44 83
Find the probability that a randomly selected bird is a parakeet given that it is green.
The probability that a randomly selected bird is a parakeet given that it is green is 54.1%.
What is meant by probability?The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. The likelihood that the coin will land with the heads side up after being tossed into the air is described using the word probability.
Let,
A be the Parakee
B be the Green
To find the probability that a randomly selected bird is a parakeet given that it is green.
That means P(A|B)
The number of birds that are both parakeet and green is n(A∩B)=20
The number of birds that are green is n(B)=37
Hence, using the conditional probability formula P(A∣B) = [tex]\dfrac{n(A\bigcap B}{n(B)}[/tex]
P(A∣B) = [tex]\dfrac{n(A\bigcap B)}{n(B)}[/tex]
P(A∣B) = 20/37
P(A∣B) = 20/37 × 100%
P(A∣B) = 54.1%
Thus, the probability that a randomly selected bird is a parakeet given that it is green is 54.1%.
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Someone help me …
100 POINTS!!!
Answer:
$43
Step-by-step explanation:
165/5=33
33+10=43
Answer:
43
Step-by-step explanation:
165/5 =
33..
+10
43
Examine parallelogram RSTU below.
R
S
(6x-9)⁰
(3y-x)°
0
mZR-27⁰
(2y-1)⁰
Om2S-135°
OmZT=45°
OmZU-99⁰
(4x+39)⁰
Determine which of the following values are correct. Select three that apply.
Ox-15
Oy-23
U
T
Answer:
y = 23 , ∠ S = 135° , ∠ T = 45° are correct
Step-by-step explanation:
the opposite angles of a parallelogram are congruent , then
6x - 9 = 4x + 39 ( subtract 4x from both sides )
2x - 9 = 39 ( add 9 to both sides )
2x = 48 ( divide both sides by 2 )
x = 24 ≠ 15
and
3y - x = 2y - 1 , that is
3y - 24 = 2y - 1 ( subtract 2y from both sides )
y - 24 = - 1 ( add 24 to both sides )
y = 23 ← is correct
∠ R = 3y - x = 3(23) - 24 = 69 - 24 = 45° ≠ 27°
∠ S = 6x - 9 = 6(24) - 9 = 144 - 9 = 135° ← is correct
∠ T = ∠ R = 45° ← is correct
∠ U = ∠ S = 135° ≠ 99°
How many types has substitution?
Answer:
"Substitution comes in three flavors: nominal, verbal or clausal, depending on the item being substituted.
Step-by-step explanation:
Hope it helps!
Brody made 7/8 lb of granola he puts 1/4 lb of granola into each bag how many bags will he be able to fill completely
3.52bags will be filled completely with 7/8 lb of granola and 1/4 lb of granola
What is word problems?
Word Problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols. Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.
To get the number of bags, we simplify and use the quotient, that is:
We divide the quantity of granola over the number of bags
=(7 / 8 pounds) / (1 / 4 pounds)
=0.88/0.25
= 3.52 bags
Hence, The number of bags that will be filled completely is 3.52 bags
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how old am i if 400 reduced byy one half must subtracted from 257
You are 57 years old if 400 reduced by one half must subtracted from 257 is your age in the given arithmetic problem.
What is arithmetic?Mathematical arithmetic, which includes operations on numbers, is its foundation. Addition, subtraction, multiplication, and division are among these operations. The foundation of the subject "Maths" is laid by one of the crucial branches of mathematics: arithmetic.
Despite the fact that the subject involves numerous other modified operations, addition, subtraction, division, and multiplication are the three basic operations under the heading of arithmetic.
Let your age be x
[tex]$x=257-400\frac{1}{2}[/tex]
x = 257 - 200
x = 57
Hence, your age is 57 years old.
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Sunflower oil is a cooking ingredient that can be used as a substitute for olive. The density of sunflower oil is 0.925 grams per cubic centimeter. A farmer would like to sell bottles of sunflower oil that contain 370 grams of oil. What is the volume of the smallest container that holds 370 grams of oil?
The volume of the smallest container that holds 370 grams of oil is
400 cm³.
What is density?Density is mass per unit volume.
We have,
The density of sunflower oil = 0.925
Mass of sunflower oil = 370 grams
Now,
Density = Mass / Volume
So,
The volume of the smallest container that holds 379 grams of oil.
= Mass of the sunflower oil / Density of the sunflower oil
= 370 / 0.925
= 400 cm³
Thus,
The volume of the container that holds 379 grams of oil is 400 cm³.
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Lian wants to place wood flooring in his rectangular-shaped laundry room with the dimensions
show below. How much flooring does Lian need?
The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.
what is rectangle ?A rectangle is a polygon with four right angles in Euclidean plane geometry. You may also refer to it as an equiangular quadrilateral, meaning that all of its degrees are comparable. A straight angle could also be present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90-degree vertices with equal parallel sides make up a quadrilateral with the outline of a rectangle. As a result, it's also known as a georeferencing rectangle. A rectangle is also referred to as a parallelogram since its opposite sides remain parallel and equal.
given
are of floor = 12 * 12
= 144 ft2
The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.
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a) What sum amounts to Rs. 3,600 in 2 years at the rate of 10% p.a.
At a 10% annual growth rate, the cash equals Rs. 3,600 in two years. Rs. 3960.
What does total principal amount mean?The principal is the sum you borrowed and are required to repay, while the interest is what you pay. For the majority of borrowers, the total monthly payment you make to your mortgage company includes additional expenses like homeowners taxes and homeowner's insurance that may be placed in an escrow account.
According to the given information:
here principal(P)=3600, R=10%, n= 2 year
amount A=p(1+R/100)ⁿ
3600(1+10/100)²
3600*11/10
=3690
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there are 208 students going on the school field trip each bus can carry 32 students how many buses will be needed
Answer:
7 busses
Step-by-step explanation:
208students divided by the number of students per bus 32The answer is 6.5 you can't split a kid in half so you will need to take 7 bussesA website charges $3 for each movie you download. They also charge a one-time sign-up fee of $14.99. What is the output variable?
The Output Variable is Total cost represented by c(m).
What is domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given:
A website charges $3 for each movie you download.
They also charge a one-time sign-up fee of $14.99.
So, the input variable will be m which shows the number of movies.
and, the output variable will be c which shows the total cost.
Then, the equation models the cost c(m), is c(m)=3m+14.99
Now, putting the values for m = 0, 1, 2, ....
c(0)= 4.99, c(1)= 17.99, c(2)= 20.99
Hence, the output variable is total cost.
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Annie loved the first novel she read by Danielle Steel. Ms. Steel has just published a new novel, and it got great reviews. Therefore, it is likely that Annie would like that novel too.
Is this argument inductive or deductive?
If it is inductive, is it strong or weak?
If it is deductive, is it valid or invalid?
Annie loved the first novel she read by Danielle Steel. Ms. Steel has just published a new novel, and it got great reviews. Therefore, it is likely that Annie would like that novel too which means that the argument is inductive and it is a weak one.
What is an Inductive argument?This is a type of argument which is characterized by the arguer believing that the truth of the premises provides only good reasons to believe the conclusion is probably true.
In this scenario since Annie liked the author's previous books and the new one had great reviews then it is probably true that she would also like it and it is a weak one because assuming the premises are true,then it is probable for the conclusion to be false.
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Which of the following are quadratic equations? `(i)3x^2-5x+9=x^2-7x+3` (ii) `x+1/x=1` (iii) `x^2-3x=0`
Option (i) , (ii) and (iii) all represents quadratic equations as all of them is of degree 2 and coefficient of degree 2 is non-zero.
What is quadratic equation?Having the form a[tex]x^2[/tex] + bx + c = 0, quadratic equations are 2nd degree algebraic expressions. The meaning of the term "quad," is square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way.
Option i
3x^2-5x+9=x^2-7x+3
so the coefficent of degree 2 is 3-1 which is 2 which is non - zero value so this expression is a quadratic equation.
Option ii
x+ [tex]\frac{1}{x}[/tex] =1
=> [tex]x^2[/tex] -x +1=0
so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.
Option iii
[tex]x^2[/tex] -3x=0
so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.
so all the 3 option represents a quadratic equation.
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Find the slope of the line through the pair of points: (7,5)(-8,4)
Answer:1/15
Step-by-step explanation
formula = y2-y1/x2-x1;
x1=7;y1=5; x2=-8;y2=4
4-5/-8-7=-1/-15
=1/15
How do you find the perimeter of a concave pentagon?
The perimeter of a concave polygon may be calculated by summing the lengths of all its sides.
What is perimeter?A perimeter is a closed path that surrounds, encompasses, or outlines a two-dimensional shape or a one-dimensional length. The perimeter of a circle or ellipse is its circumference. The perimeter calculation has a variety of practical applications. The perimeter of an object is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length. A perimeter is the distance between the edges of a two-dimensional form. It is sometimes defined as the total of the object's side lengths. The perimeter of a shape is the algebraic sum of its side lengths. We have equations for the various forms in geometry.
Here,
The perimeter of a concave polygon may be calculated by summing the lengths of all its sides.
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From Belmont, how much farther is it to riverside than yardley?
On solving the provide question, based on the congruent triangles properties, we got to know that x= 76° and 90°.
what are congruent triangles?Congruent triangles are two triangles that are identical in terms of their size and form. The two congruent triangles remain congruent whether you rotate, flip, or flip one of them. If two triangles have the same number of sides, then their angles and congruence must match.
As a result, we can determine that two triangles are congruent if all three of their sides are equal. We also understand that if there is a side, an angle between the sides, and a third side that is congruent, the three sides are congruent. which means sides, corners, and sides.
For green -
=> x = 76° ( both side are same)
For orange -=> x = 90°
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What is the formula of XYZ ²?
Therefore , the solution of the given problem of quadratic equation comes out to be XYZ² equals to x² + y² + z² – 2 x y + 2 y z – 2 z x .
Describe a quadratic equation.A quadratic quadratic in a specific factor is x ax2+bx+c=0, that is a quadratic equation. a 0. The fact that this equation is of second order guarantees that it contains lease one solutions according to the First Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least the word in it should be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the quantitative coefficients or integers a, b, and c.
Here,
Given: XYZ ²
To find the value of XYZ ² ,
Thus,
=> XYZ ² = x² + y² + z² – 2 x y + 2 y z – 2 z x .
So, the solution for this XYZ² equals to x² + y² + z² – 2 x y + 2 y z – 2 z x .
Therefore , the solution of the given problem of quadratic equation comes out to be XYZ² equals to x² + y² + z² – 2 x y + 2 y z – 2 z x .
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Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
please help me please
Michael and Ashley bought same amount of turkey and ham.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Michael and Ashley each buy x pounds of turkey and y pounds of ham.
Michael purchased from store A.
Cost of turkey per pound at store A = $3
Cost of ham per pound at store A = $4
Michael spends $18 at store A.
3x + 4y = 18
Ashley purchased from store B.
Cost of turkey per pound at store B = $4.50
Cost of ham per pound at store B = $6
Ashley spends $27 at store B.
4.5x + 6y = 27
We get two linear equations,
3x + 4y = 18
4.5x + 6y = 27
Multiplying the first equation throughout with 4.5 and the second equation throughout with 3, we get,
13.5x + 18y = 81
13.5x + 18y = 81
Since both the equations coincide, Michael and Ashley bought same amount of Turkey and Ham.
Hence Michael and Ashley bought same amount of turkey and ham.
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