The least common denominator of the given fractions, can be found to be 72.
How to find the least common denominator ?The least common denominator of two or more fractions, is the least common multiple of the denominators of the fractions.
With the given fractions of 3 / 8 and 5 / 18 therefore, the least common denominator would be the least common multiple of 8 and 18.
The least common multiple of 8 and 18 is the value of 72 so this must be the least common denominator for the fractions.
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Which of the following relations is a function?
A.
(3, 4), (-5, 6), (3, 3), (-8, 2)
B.
(3, 0), (-5, 3), (5, 1), (-5, 5)
C.
(5, 1), (-5, 4), (3, 1), (5, 2)
D.
(3, 4), (-5, 2), (5, 1), (-8, 2)
The relation in this problem that is a function is given as follows:
D. (3, 4), (-5, 2), (5, 1), (-8, 2).
When does a relationship represents a function?To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.
The relationships that are not functions in this problem, along with the justification, are given as follows:
Relationship A: Input 3 is mapped to multiple outputs, 4 and 3.Relationship B: Input -5 is mapped to multiple outputs, 3 and 5.Relationship C: Input 5 is mapped to multiple outputs, 1 and 2.Hence the relationship that is a function is given by option D, as the inputs 3, -5, 5 and -8 are each mapped to a single output.
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An online music store charges $1.25 for each song after you pay a $25 subscription fee. write a function that represents the arithmetic sequence. how many songs
can you buy if you have $57 to spend?
If the 8th term of an arithmetic sequence is 25 and the 14th term is 43. Complete the explicit formula.
Answer:
Tn = 4 + (n – 1)3
is the arithmetic sequence for the nth term
Step-by-step explanation:
formula for an arithmetic sequence is
[tex]tn = a + ( n - 1)d[/tex]
where:-
Tn = nth term
a = first term
n = number of terms
d = common difference.
now back to the question
the 8th term of an arithmetic sequence is 25.
that will be written as
[tex]t8 = a \: + ( 8 - 1)d = 25[/tex]
[tex]a + (7 )d = 25 \: \: \: \: .....eqn1[/tex]
and the 14th term is 43
this will be written as
[tex]t14 = a + (14 - 1 )d = 43[/tex]
[tex]a + 13d = 43 \: \: \: \: .....eqn2[/tex]
subtract eqn 1 from 2
a – a, 13d – 7d, 43–25
[tex]6d = 18[/tex]
divide both sides by (6)
[tex] \frac{6d \\ }{6} = \frac{18}{6} [/tex]
d = 3
now that we know d = 3 let's substitute it in eqn 1 above.
a + 7d = 25
a + 7(3) = 25
a +21 = 25
a = 25 – 21
a = 4
now the normal arithmetic sequence given will be
[tex]tn = 4 + (n - 1 )3[/tex]
I hope this helps
HELP I ONLY HAVE TELL 12 QUICK I HAVE OTHER QUIZZES TOO
Answer:
by 5
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
The table below gives the annual sales (in millions) of a product.
The average rate of change in annual sales are as follows;
a) Between 2003 and 2004, the average rate of change of sales is -3 unit per year
b) The average rate of change between 2003 and 2006 is -9 units per year
What is the average rate of change of a set of values?The average rate of change of a set of values is the rate at which one variable changes with regards to the unit change in another variable, over an interval.
The values in the table are presented as follows;
The sales of a product in millions annually.
Year; 1998[tex]{}[/tex] 1999 2000 2001 2002 2003 2004 2005 2006
Sales; 174 [tex]{}[/tex] 201 222 237 246 249 246 237 222
The average rate of change between two data points, (x₁, y₁), and (x₂, y₂), can be obtained as follows;
[tex]Average \, rate \, of \, change= \frac{y_2-y_1}{x_2-x_1}[/tex]
a) The average rate of change between 2003 and 2004 is found using the formula for the average rate of change as follows;
[tex]Average = \frac{246-249}{2004-2003} =-3[/tex]
The average rate of change of annual sales of the product between 2003 and 2004 is -3 units per year.b) The average rate of change in sales of the product between 2003 and 2006 is found as follows;
Rate of change between 2006 and 2003; [tex]\frac{222-249}{2006-2003} =\frac{-27}{3} =-9[/tex]
The average rate of change in sales of the product between 2006 and 2003 is -9 unit per year.Please find attached the screen grab of the table in the attachment that specifies the annual sales of the product (in millions).
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An 80% confidence interval for a proportion is found to be (0.27 , 0.33). what is the sample proportion?
a. 0.29
b. 0.30
c. 0.31
d. 0.33
Answer: B
Step-by-step explanation:
1. The hypotenuse of a right triangle has length of 34cm. The sum of the lengths of the other two legs is 46cm. What are their lengths?
The length of the other two sides are 16 and 30.
What is right-angle triangle ?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. 90 degrees is the sum of the other two angles. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.
let one angle be x
the other angle be 46-x
as the sum of the angles is 46
x² + (46-x)² = 34²
2x² - 92x + 46² - 34² = 0
x² - 46x + 480 = 0
x² - 16x - 30x + 480 = 0
x(x-16) - 30 (x - 16) = 0
(x-30)(x-16) = 0
x = 30 or x = 16
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how many liters of a 15% alcohol solution must be mixed with 30 liters of a 40% alcohol solution to obtain a 30% solution
Answer: 20 liters
Step-by-step explanation:
Let the number of liters of 15% alcohol solution be [tex]x[/tex].
[tex]0.15x+30(0.4)=0.3(x+30)\\\\0.15x+12=0.3x+9\\\\12=0.15x+9\\\\0.15x=3\\\\x=20[/tex]
When you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.T/F?
It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.
In mathematics, an algorithm is a process, a description of a series of steps that may be used to solve a problem; however, they are now far more prevalent than that.
Although many areas of research (and daily life) employ algorithms, long division's step-by-step process is probably the most prevalent example.
Thus, It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.
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The ratios from parts A and B are equivalent. Write an equation by setting the ratios equal to one another.
Answer:
the solution is 9/2 = X24
help me with my maths homework please, thanks for your responses
On solving the provided question we can say that by factorization are
x(x-3) + 2(x-3) ⇒(x-3)(x+2) ⇒ x = 3, -2
what is factorization?A number or other mathematical object is factored, or written as the product of numerous factors—typically smaller or simpler things of the same kind—in mathematics. For instance, the integer 15 is factorized as 3 5, which is the factorization of the polynomial x2 – 4. Factorization in mathematics refers to the breakdown of a number into smaller numbers that are multiplied together to produce the original number. Factorization is the division of a number into its factors or factors. 12 is multiplied by 3 and 4 as an example.
the polynomial is as = x^2 + 14x + 48
by factorization are
x(x-3) + 2(x-3)
(x-3)(x+2)
x = 3, -2
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[tex]y^{2} =x^{2} +a^{2}[/tex]
make x the subject
suppose you want to estimate the percentage of college studentswho are using electronic cigarettes on a regular basis. you have permission to sample two colleges, grove city college and penn state university. grove city has an enrollment of 2,500 students and penn state has an enrollment of 45,000 students. what should the relative size of our samples be from each school if we want the two sampling distributions to have approximately the same standard deviation?
The correct option is A "Because the population sizes are so different, it's impossible to make the standard deviations equal by adjusting the two sample sizes ".
The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.
All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.
A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.
Complete question:
Suppose you want to estimate the percentage of college students who are using electronic cigarettes on a regular basis. You have permission to sample two colleges, Grove City College and Penn State University. Grove City has an enrollment of 2,500 students and Penn State has an enrollment of 45,000 students. What should the relative size of our samples be from each school if we want the two sampling distributions to have approximately the same standard deviation?
A. Because the population sizes are so different, it's impossible to make the standard deviations equal by adjusting the two sample sizes
B. We should take a larger number of Penn State students since there are more of them.
C. We should take a larger number of Grove City students since there are fewer of them.
D. We should take the same size samples from each school.
E. We should take samples that are exactly 10% of each school's enrollment.
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In the given figure, △ADE ∼ △ABC. Which triangle similarity theorem justifies
this similarity? Show proof toyour answer.
a. Using the figure below, name the three similar triangles.
b. Write the proportions that exist among corresponding parts of similar
By similarity theorem The three similar triangles are △CLB~△LUB~△CUL
(B) The proportions in corresponding parts of similar are in △CLB~△LUB: CL/LU=LB/UB=CB/LB and in △CLB~△CUL:CL/CU=LB/UL=CB/CL
What is similarity theorem?Triangle similarity in Euclidean geometry. According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.
In the given figure, △ADE~△ABC.
1. ∠D≅∠B
2. DE II BC converse of basic proportionality
3. ∠E ≅ ∠C corresponding angle are congruent
4. ∠DAE≅∠BAC reflexive property
5. △ADE ≅△ABC (AAA similarity theorem)
The three similar triangles are-
△CLB~△LUB~△CUL
The proportions that exist among corresponding parts of similar
→ In △CLB~△LUB
CL/LU=LB/UB=CB/LB
→ In △CLB~△CUL
CL/CU=LB/UL=CB/CL
→ In △LUB~△CUL
LU/CU=UB/UL=LB/CL
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n - 22 = 4 what is the answer in verbal expression
Cookie House charges different amounts for cookies based on how many cookies are purchased. If you only buy up to 5 cookies you are charged $2 per cookie. If you place an order for more than 5 cookies then you are only charged $1.50 per cookie.
Write a piecewise equation that represents the equation above.
Answer: A piecewise function is a function that is defined by multiple equations, each with its own domain. The equation for the situation can be represented as a piecewise function as:
f(x) = { 2x, 0<x<=5}
f(x) = { 1.5x, x>5}
Where f(x) is the cost of x number of cookies.
The first equation represents the cost of x number of cookies when x is between 0 and 5 (inclusive). The second equation represents the cost of x number of cookies when x is greater than 5.
So, the piecewise function that represents the cost of x number of cookies based on the given conditions is:
f(x) = { 2x, 0<x<=5}
f(x) = { 1.5x, x>5}
It means if you buy x number of cookies and if x is between 0 and 5 (inclusive) then you are charged $2 per cookie and if x is greater than 5 then you are only charged $1.50 per cookie.
Step-by-step explanation:
the product of three different positive integers is equal to $7^3$. what is the sum of the three integers?
The sum of the three integers is 57.
The term integer in math is known as the collection of whole numbers and negative numbers.
Here we have given that the product of three different positive integers is equal to 7³.
Here let us consider that x,y,z be three positive number.
Then based on the given is written as
=> xyz = 7³
When we expand the equation, then we get,
=> xyz = 343
Here we have expand the equation as,
=> xyz = 1 × 7 × 49
Then the equation written as
=> x + y + z = (1 + 7 + 49)
Then the sum equation is calculated as
=> x + y + z = 57
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Solve for X, Leave in simplest radical form.
Hope it helps.
If you have any query, feel free to ask.
Determine the area of each face of a cube with the given surface area.
a) 306.6 square meters
b) 450 square inches
Answer:
51.1 m² and 75 in²
Step-by-step explanation:
A cube has 6 congruent square faces
Given the surface area of the cube, that is the combined area of the 6 faces , then
divide the surface area by 6 for area of each face.
(a)
306.6 m² ÷ 6 = 51.1 m²
(b)
450 in² ÷ 6 = 75 in²
a) The area of each face of a cube 306.6 is 51.1 square units.
b) The area of each face of a cube 450 is 75 square units.
a) A cube has 6 faces
Area of each face is (side × side)
Area = side × side
So, total area is equal to 6 times the area of each side.
Area = 6 × (side × side)
Now,
306.6 = 6 (side)²
(side)² = 51.1
Therefore, the area of each face is 51.1 square units.
b) A cube has 6 faces
Area of each face is (side × side)
Area = side × side
So, total area is equal to 6 times the area of each side.
Area = 6 × (side × side)
now,
450 = 6 (side)²
(side)² = 75
Therefore, the area of each face is 75 square units.
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Last season , the Roswell hornets out scored their opponents 5:2 if their opponents scored 28 points , how many points did the hornets score ?
The hornets scored 70 points if they scored 5:2 when their opponents scored 28 points.
Therefore the answer is 70.
If the Roswell hornets outscored their opponents 5:2, this means that for every 5 points the hornets scored, their opponents scored 2 points.
If we know that the opponents scored 28 points, we can use this information to find out how many points the hornets scored.
We can set up the equation:
x/28 = 5/2
Where x is the number of points the hornets scored.
On solving the equation we get:
x = (5 × 28)/2
x = 5 × 14
x = 70
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please help will give brianliest The point (–3, –2) is a solution to 2(x + 1) > 3y – 2. True False
Answer:
True
Step-by-step explanation:
(3,2) is a solution to the equationExplanation:If (3 ,2) is a solution then it must 'satisfy' the equation. That is make it True.To determine this, substitute x = 3 and y = 2 into the left side of the equation and if the result is 12 then it is a solution.⇒(2×3)+(3×2)=6+6=12LHS = RHS hence (3,2) is a solution
If f(1)=3 and f(n)=f(n-1)^2+n then find the value of f(3)
Answer:
[tex]\sqrt{\sqrt{2} }[/tex]
Step-by-step explanation:
f(1)=3; f(1)=f(0)^2+1
f(0)=[tex]\sqrt{2}[/tex]=f(3)^2+0; f(3)^2=sqrt*2; f(3)=sqrt*sqrt2
An airplane is preparing to land at an airport. It is 45,600 feet above the ground and is descending at the rate of 3,200 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,500 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be?
Answer:
8 mins 20000feet
Step-by-step explanation:
let mins be x
45600-3200x = 2500x
so 45600= 5700
x=8
2500*8 = 20000
(2^-3x divided by 2^-2)^2=2^10
.
Greetings!!
Lool at the attachment
Jolon drew the figure that is shown below.
mc005-1 ( the graph see picture )
Jolon translated the figure left 5 units and down 4 units. What are the new coordinates of point C?
(–4, 0)
(0, 0)
(0, –3)
(1, –4)
Answer:
(0,-3)
Step-by-step explanation:
C( 5,1)
5 is the horizontal value. It is the distance from zero. If we go 5 units left we will be at 0
1 is the vertical value. Is is the distance above the x axis. If we go down 4 units, we will be at -3
(0,-3)
write an equation that represents how many grams of flour we need (fff) for some number of grams of sugar (sss).
We need 600 grams of flour to make the recipe with 400 grams of sugar.
What is a ratio?
A ratio is a mathematical comparison of two or more values or quantities. It is represented as a fraction, with the numerator representing the first value or quantity and the denominator representing the second value or quantity.
An equation is a mathematical statement that asserts the equality of two expressions. In this case, the recipe uses 300 grams of flour for every 200 grams of sugar. To write an equation that represents this relationship, we can use the variable "f" to represent the number of grams of flour and "s" to represent the number of grams of sugar.
The equation that represents this relationship is f = (3/2)s. The coefficient of the "s" variable is 3/2, which represents the ratio of flour to sugar in the recipe (3 parts flour to 2 parts sugar). This equation states that the number of grams of flour, represented by f, is equal to 3/2 times the number of grams of sugar, represented by s.
So, in other words, if we know the number of grams of sugar we need, we can use this equation to find out how many grams of flour we need. For example, if we need 400 grams of sugar, we can substitute that into the equation:
f = (3/2)s
f = (3/2) * 400
f = 600
Hence, We need 600 grams of flour to make the recipe with 400 grams of sugar.
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What is the difference between the best and worst credit score interest rates?
The difference between the best and worst credit score interest rates would be = 6.24%
What is an interest rate?An interest rate is defined as the particular amount of money an individual receives for a period of time due to an investment made.
The difference between the best and the worst credit score interest rates would be to substrate the best score from the worst score.
The best interest rate score = 3.65
The worst interest rate score = 9.89
Therefore the difference = 9.89 - 3.65 = 6.24 %
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consider a qubit to be in the state . what is the probability to find the spin projection along the x-axis (corresponding operator ) to be 1 ?
The probability to find the spin projection along the x-axis to be 1 is 0.5. The operator corresponding to the spin projection along the x-axis is X, and the expectation value of X in this state is 0.
This result is a consequence of the fact that operator X is a Hermitian operator, which means that its eigenvalues are real. The eigenvalues of X are ±1, so the probability of measuring a spin projection of 1 is ½. This is because the eigenstate corresponding to the eigenvalue 1 is |+⟩, which is a superposition of |0⟩ and |1⟩.
Similarly, the eigenstate corresponding to the eigenvalue -1 is |-⟩, which is also a superposition of |0⟩ and |1⟩. Thus, the qubit is equally likely to be found in either the |+⟩ or the |-⟩ state, and so the probability of measuring a spin projection of 1 is 0.5.
In summary, since the qubit is in a superposition of the two computational basis states, the expectation value of any Hermitian operator is 0, and the probability of measuring a spin projection of 1 is 0.5.
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Height in meters 15 30 45 60 75 90 105 Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598 1. Determine a function that could be used to model the data in the table. Make sure to use h for height and d for distance.
1. a function that could be used to model the data in the table. Make sure to use h for height and d for distance is d = -0.425h + 39.25
2. If the balloon is 800 meters high, the farthest distance that you would be able to see is 48 km
3. at the height of 67 does the balloon have to rise for the building to be visible.
The table in the question shows a relationship between the height of a balloon and the distance away from the balloon that can be seen. Using this data, a linear function can be determined that models this relationship. The function is d = -0.425h + 39.25, where h is the height of the balloon in meters and d is the distance in kilometers. Using this function, if the balloon is 800 meters high, the farthest distance that can be seen is 48 km, which is the y-intercept of the equation.
Inversely, if a building is 16 km away from the balloon, the height the balloon must rise for the building to be visible is 67 m. This can be determined by substituting 16 for d in the equation and solving for h. Overall, the linear function d = -0.425h + 39.25 models the relationship between the height of the balloon and the distance away from the balloon that can be seen. The equation can be used to determine the height of the balloon needed to see a certain distance or the distance away from the balloon that can be seen when the balloon is at a certain height.
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Height in meters 15 30 45 60 75 90 105 , Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598
1. Determine a function that could be used to model the data in the table. Make sure to use h for height and d for distance.
2. If the balloon is 800 meters high, what is the farthest distance that you would be able to see? Round the answer to the nearest whole number
3. Round answer to the nearest whole number A building is 16 km away. What height does the balloon have to rise for the building to be visible?
the expression $x^2 3x - 28$ can be written as $(x a)(x - b),$ and the expression $x^2 - 10x - 56$ written as $(x 2b)(x c)$, where $a$, $b$, and $c$ are integers such that $c > 0.$ what is the value of $2c - a$?
The required value of the expression 2c - a is 1.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
So, we have:
x²+3x-28
x²+7x-4x-28 [28=7×2×2, 7-(2×2)=7-4=3]
x(x+7)-4(x+7)
(x+7)(x-4)$
In light of the fact that x2+3x-28 can be expressed as (x+a)(x-b).
in order to compare (x+7)(x-4) and (x+a)(x-b).
As a result, a = 7 and b = 4.
Similarly,
x²-10x-56$
x²-14x+4x-56 [ 56= 7×2×2×2, - (7×2)+(2×2) = -14+4=10]
x(x-14)+4(x-14)
(x-14)(x+4)
Given that (x+2b)(x+c) can be used to represent x2-10x-56.
Consequently, compare (x-14)(x+4)and (x+2b)(x+c).
Now, c=4 [∵c>0].
Then,
2c-a
(2×4)-7
8-7
1
Therefore, the required value of the expression 2c - a is 1.
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