After simplification, the value of expression is, (x + 1) / (2x - 1).
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The expression is,
⇒ 10x² + 10x / 20x² - 10x
Now, We can simplify as;
⇒ (10x² + 10x) / (20x² - 10x)
⇒ 10x (x + 1) / 10x (2x - 1)
⇒ (x + 1) / (2x - 1)
Thus, The value of expression is, (x + 1) / (2x - 1).
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How many solutions are there to the equation below?|x| = -4
A 0
B 2
C 4
D 1
Answer:
There are 0
Step-by-step explanation:
Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true
Answer:
A 0
Step-by-step explanation:
There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.
If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.
Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U={f, g, h, p, q, r, x, y, z)
A={f,g,r, x}
B={r, x, y, z)
C={g, h, q, r, z}
Find (BU A)'n C.
Write your answer in roster form or as Ø.
(BUA)'n C = {}
Using the properties of sets, (BU A)'n C = {h,q}
What kinds of Sets are there?Null set or an empty set There isn't even one element in it. Finite Set: It only has a finite number of components. The element count of an infinite set is infinite. Two sets with the same members are said to be equal sets.
An object collection that is taken into account as a whole is referred to as a set. The elements or members of the set are the things that make it up. A set's components can be any type of object, but for our purposes, they are most frequently mathematical components like integers, functions, or other sets.
What subgroups of ABCD are there?The list of all subsets of a,b,c,d is ϕ ,{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}
(B U A) = {f,g,r,x,y,z}
(BU A)'n C = {h,q}
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Pankaj is a Biomedical Engineering student. He plans to deposit $600 that he earned as stipend, in
a bank account at 3% rate of interest compounded weekly for no more than 2 years. The total
amount of the money, A, that Pankaj will get back, is a function of time, t. Which is a reasonable
domain of the money that he may accumulate?
The correct answer is A: 600 <= money <= 2822.4.
This represents the range of possible values that Pankaj's accumulated money could fall into, given the specified conditions of the 3% interest rate compounded weekly for a maximum of 2 years. The lower bound, 600, represents the initial deposit amount, while the upper bound, 2822.4, represents the maximum amount of money Pankaj could earn after 2 years, assuming that interest is compounded every week.
how water changes its state in each part of the water cycle 1 paragraph
Answer:
The water cycle involves the continuous movement of water on, above, and below the surface of the Earth. In the cycle, water can exist in three states: liquid, solid, and gas. During evaporation, liquid water changes into water vapor, the gaseous state of water, as it heats up and turns into steam. When water vapor cools, it can condense back into liquid form, such as when it forms clouds. Precipitation, such as rain or snow, occurs when water droplets in the clouds become heavy enough to fall from the sky. When precipitation reaches the ground, some of it may flow into rivers and streams and eventually make its way to the ocean. Some of it may also be taken up by plants or seep into the ground, becoming part of the groundwater system. Eventually, the water in the groundwater system may evaporate back into water vapor and start the cycle over again.
A, B and C are currencies of different countries. Three As are worth four Bs and five Bs are worth one C. How many As are two Cs worth?
When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.
what is equation ?Its precise nature is understood to be the figure is probably smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the median and excess. A fractional number can always be checked to discover if it is a prime number. A statement having two equal sides and an equal sign in the intermediate is referred to as a linear expression. Every variable's classes are listed in lowest to highest in the general form of any formula. The formula for a linear function is x + b = 0. The simplified version of a two-variable mathematical expression is an x + b y + c = 0. (or something similar). Either conditioned equations or identities provide categories for equations. An identity holds true because of whatever value of the variables.
given
The aforesaid issue is easily resolved by doing the following:
Considering that,
Four Bs are worth three As.
It can be written as;
3A = 4B
determining B's value
B = 3A/4 (Equation 1) (Equation 1)
Now,
A B is worth five Cs.
So, 5B = C (Equation 2) (Equation 2)
Calculating B's value in equation 1
= 15A/4 = C
= 4C = 15A
2C = (15/2)A
2C = 7.5A
Therefore, the solution is 2C = 7.5A
When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.
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Match the mathematical expression with its translation.
1. x + y = 6
y divided by x
2. x + y
x minus y
3. xy
the product of two numbers
4.
x subtracted from y
5. y ÷ x
six less than a number is y
6. y = x - 6
six times a number equals y
7. x - y
the sum of two numbers is six
8. 6 x = y
the product of two numbers is six
9. xy = 6
the sum of x and y
10. y - x
x divided by y
The following mathematical expression matched with its translation:
1. x + y = 6 (the sum of two numbers is six)
2. x + y (the sum of x and y)
3. xy (the product of two numbers)
4. x ÷ y (x divided by y)
5. y ÷ x (y divided by x)
6. y = x - 6 (six less than a number is y)
7. x - y (x minus y)
8. 6 x = y (six times a number equals y)
9. xy = 6 (the product of two numbers is six)
10. y - x (x subtracted from y)
How to write mathematical expression?Mathematical expression can be translated as thus;
the sum of two numbers is six
Let the unknown numbers be x and y respectively
So,
x + y = 6
six less than a number is y
x - 6 = y
also written as
y = x - 6
six times a number equals y
6 × x = y
6x = y
also written as
y = 6x
Therefore, mathematical expressions are algebraic representation of mathematics in words.
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uestion 5 (1 point) Find the following Quadratic Regression for the following set of data
(-1,8), (5,-4), (7,8), (2,-6)
A. y= = 2x² - 6x + 2 2
B. y = .96x² - 5.77x + 1.38
C. y = -5.77x² + 1.38x+.96
D. y = 5x + 10
The quadratic regression equation is y = 1.38x^2 - 5.77x + 0.96
How to determine the quadratic regression equationFrom the question, we have the following parameters that can be used in our computation:
(-1,8), (5,-4), (7,8), (2,-6)
Using a graphing calculator, we have the following summary:
function value
mean of x 3.25
mean of y 1.5
correlation coefficient r 0.9990171837
A 1.380577428
B -5.769028871
C 0.9553805774
The equation is represented as
y = ax^2 + bx + c
So,, we habe
y = 1.38x^2 - 5.77x + 0.96
Hence, the equation is y = 1.38x^2 - 5.77x + 0.96
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If 9 times a positive number is equal to 91 more than twice the same number, what is the number?
Answer:
13
Step-by-step explanation:
Len n = number.
9n = 2n + 91
7n = 91
n = 13
Answer: 13
HELP PLEASE I WILL GIVE BRAINLIEST
answer the first 2 questions.
The total area of all the pieces would be: - x² + y² + 2xy = (x + y)².
What is the total area of all of the pieces?This tile collection is composed of four tiles: two squares, each with sides of length x, and two rectangles, each with sides of length x and y.
The total area of all of the pieces can be expressed algebraically as A = x² + 2xy.
This expression can also be written as A = x² + xy + xy.
This tile collection is an example of a two-dimensional shape composed of two squares and two rectangles.
By adding the areas of each of these shapes, we can calculate the total area of the tile collection.
The area of each square is x², and the area of each rectangle is xy.
Adding these three expressions together gives us the total area, A = x² + 2xy.
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A soccer team made 2 goals out of 32 attempts in a game. What is the experimental probability that the team made a goal on any given shot? Write the probability as a decimal.
The experimental probability that the team made a goal on any given shot is 0.0625
How to determine the experimental probability that the team made a goal on any given shot?From the question, we have the following parameters that can be used in our computation:
A soccer team made 2 goals out of 32 attempts in a game
The experimental probability that the team made a goal on any given shot is calculated as:
P = 2/32
Evaluate the quotient
P = 0.0625
Hence, the probability is 0.0625
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FIND THE VALUE OF 1+2+3+....+47-48-49-50.
Answer:
1225 is what I got, not sure tho.
Carlos wants to finish a 7.5 mile trial
walking at a constant rate the distance that
Carlos has left
to finish the trial after h hours
walking is represented by the fuction 1h+2d=15
The domain of the function 5h + 2d = 15 is [0, 3].
What is domain and range of a function?
The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x).
The collection of numbers that the function assumes is known as its range. The values that the function outputs when we enter an x value are in this set.
5h + 2d = 15
2d = 15 - 5h
d = (15 - 5h)/2
For h = 0, d = 15/2 = 7.5
For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.
For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.
For h = 3, d = (15 - 15)/2 = 0 miles
The domain of the function is [0, 3].
Thus,
The domain is [0, 3].
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Which of the following is the equation that represents the graph
y = -2/3x -6
y = -3/2x -6
y = -3/2x -4
y = -3/2x -4
The equation of the graph is y = -2/3x - 4
How to determine the equation of the graphA linear equation is represented as
y = mx + c
Where
c = y when x = 0
From the graph, we have
c = -4
So, the equation becomes
y = mx - 4
From the graph, we have the following point
(-6, 0)
So, we have
0 = -6m - 4
Evaluate
m = -2/3
So, we have
y = -2/3x - 4
Hence, the equation is y = -2/3x - 4
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Consider the function graphed to the right.
The domain of the function is given as follows:
[-10,10].
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.The domain of a function is the set containing all the input values of the function.
Hence, on the graph, the domain of the function is composed by the values of x of the function, and is given as follows:
[-10,10]. (closed due to the closed circle).
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sithe shares his two sandwiches between himself and two friends.caculate the fraction of the sandwiches that sithe will get
Consider the logistic equation
y=y(1-y)
a.Find the solution satisfying 1(0)=14 and y2(0)=-3
y1(t)=
y2(t)=
b.Find the time t when y1(t)=7
t=
c.When does y2(t) become infinite?
t=
The solution satisfying y1(0)=14 and y2(0)=-3 are y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13))) and y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))
The time t when y1(t)=7 is 1.08y2(t) becomes infinite when t ⇒ +∝Find the solution satisfying y1(0)=14 and y2(0)=-3The logistic equation is a non-linear ordinary differential equation that models the growth of populations over time.
The solution to the logistic equation with initial conditions y1(0)=14 and y2(0)=-3 is given by (from a graphing tool):
y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13)))
y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))
Note: ln is the natural logarithm function.
Find the time t when y1(t)=7The time t when y1(t)=7 can be found by solving for t in the equation y1(t) = 7.
From the graphing tool, we have
t = 1.08 when y1(t) = 7
When does y2(t) become infinite?he solution y2(t) becomes infinite when the denominator of the equation becomes zero.
This occurs when -3/2 * e^(t * ln(-3/2)) = -∞.
This can be written as t * ln(-3/2) = ∞, which occurs when t approaches positive infinity.
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A right triangle has legs of 33 inches and 44 inches
whose sides are changing. The short leg is increasing by 10 in/sec and the long leg is shrinking at 10 in/sec. What is the rate of change of the hypotenuse?
The rate of change of the hypotenuse is given as follows:
dh/dt = 2 in/sec.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The hypotenuse is then given as follows:
h² = x² + y².
For this problem, the hypotenuse has the value given as follows:
h² = 33² + 44²
h = square root(33² + 44²)
h = 55.
Applying implicit differentiation, the rate of change of the hypotenuse is obtained by the equation as follows:
h dh/dt = x dx/dt + y dy/dt.
Replacing the values, the rate of change is calculated as follows:
55dh/dt = 33 x 10 - 44 x 10
55dh/dt = -110
dh/dt = -110/55
dh/dt = 2 in/sec.
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Even that the perimeter of a square varies directly with the side length what happens to the perimeter area of a square if the side length increases from s= 12 to s=36 inches?
Answer: The perimeter triples.
Step-by-step explanation:
Since there is a direct variation, if the side length triples, so does the perimeter.
Pat and Rich drove to the beach
last weekend. It took them twice as
long to get back as it did to drive
there. If they spent 9 hours traveling
to and from the beach, how long
did it take them to drive each way?
Step-by-step explanation:
Let's call the time it took Pat and Rich to drive to the beach "x".
The time it took them to drive back was twice as long, so it took 2x hours.
The total time spent traveling was x + 2x = 3x hours.
Since they spent 9 hours traveling, 3x = 9 hours.
So, x = 9 hours / 3 = 3 hours.
This means it took Pat and Rich 3 hours to drive to the beach and 2 * 3 = 6 hours to drive back.
The
• The top of a second mattress has 1½ times as much area as
the first mattress. What is the area of the top of the second
mattress? Write an equation to model the problem.
The area of the top of the second mattress , 3/2x²
The equation to model the problem is y= 1.22x.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
let the side of mattress one be x
and, the side of Mattress 2 be y.
So, area of Mattress 2 / Area of Mattress 1 = 1 1/2
area of Mattress 2 / Area of Mattress 1 = 3/2
y²/ x² = 3/2
(y/ x)² = 3/2
y/x = √3/2
y /x = 1.22
Hence, the equation is y= 1.22 x .
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A group of 8 students are painting a mural at the local library. Each student uses 1/4
of the paint in their bucket. How many total buckets of paint did the students use?
8 buckets each with 1 of 4 sections shaded.
Answer:
1/2 bucket
Step-by-step explanation:
Each of the 8 buckets is 1/4 full.
The total amount of paint at the beginning is 8 × 1/4 bucket = 2 buckets.
Each student uses 1/4 of his paint. Combined, they use 1/4 of the total amount of paint in the buckets.
1/4 × 2 buckets = 1/2 bucket
Answer: 1/2 bucket
The total number of fence posts Edwin installs varies directly with the number of hours worked. He installs 40 fence posts in 8 hours.
Write a direct variation equation to represent this relationship.
Answer:
y = 5x
where
y = number of fence posts that Edwin installs
x = number of hours that Edwin takes to install y posts
Step-by-step explanation:
Let y = number of fence posts that Edwin installs in x hours
We have the relation:
y ∝ x where ∝ is the symbol for is-proportional-to
We can rewrite this as an equation using the constant of proportionality,k:
y =kx
Given y = 40 fences, x = 8 hours we get
40 = k(8) = 8k
or, switching sides
8k = 40
k = 40/8 = 5
So Edwin can install 5 fences per hour
Plugging this into the equation of proportionality
y = 5x
Solve the inequality –3v – 2v > 35 for v.
A.
v < 7
B.
v > 7
C.
v < –7
D.
v > –7
Answer: c
Step-by-step explanation:
-3v - 2v > 35
combine like terms: -5v > 35
divde by the same term (isolate the variable): -5v/-5 , 35/-5
v < -7
I need help with this question
The function which models the data as represented on the graph will be; [tex]f(x) = 0.8(1/2)^x[/tex].
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
The given graph is an exponential function and should take the form;
[tex]f (x) = a (b)^x[/tex]
Hence, using values from the graph;
For ( -1, 0.2 ) = a • b..........(i)
For (0, 0.8); 10.5 = a • b².........(ii)
=> x=0 and y= 0.8
So.
0.8=a(1/2)^0
0.8=a
Thus, the rule for the function is; y=0.8(1/2)^x
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Mr. Lopez is looking to fill a part of a park with sand. The shape below represents the part of the park being covered in sand. How many square yards of the park will Mr. Lopez cover in sand?
Mr. Lopez cover in sand by 50 yd².
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Mr. Lopez is looking to fill a part of a park with sand.
And, The shape below represents the part of the park being covered in sand.
Now, We will find the area of figure as;
The park is mix of two figure rectangle and triangle.
Hence, We get;
Area of rectangle = 5 × 8
= 40 yd²
And, Area of triangle = 1/2 × 4 × 5
= 10 yd²
Thus, The area of given figure is,
⇒ Area = 40 yd² + 10 yd²
⇒ Area = 50 yd²
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D) What is the greatest common factor of 45 and 30?
Answer:15
Step-by-step explanation:
i did the math
Answer:
15
Step-by-step explanation:
15 x 2=30
15x3=45
There were 160 boxes of biscuits in a shop at first. Each box contained 30 packs of biscuits. There were 2800 packs of strawberry biscuits and the rest were chocolate biscuits. The shopkeeper sold an equal number of packs of chocolate biscuits each month over a period of 5 months. How many packs of chocolate biscuits did the shopkeeper sell each month?
Using the concept of multiplication and division, the number of chocolate sold each month is 400 packs.
How many chocolate biscuit was soldTo determine the number of chocolate biscuits in the shop, we have to determine how many is contained in each box and then multiply it by number of days in a month and then subtract the number of chocolate in the shop. This tasks involves the use of basic arithmetic operations to determine the number of packs sold.
The total number of packs of biscuits in the shop was 160 * 30 = 4800.
So, the number of packs of chocolate biscuits was 4800 - 2800 = 2000.
The shopkeeper sold 2000 packs of chocolate biscuits over 5 months, so he sold 2000 / 5 which will give us 400 packs of chocolate biscuits each month.
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Which number line represents x<-3??
Answer:
1st number linline
Step by step explanation:
x < -3 means x is less than -3
so it should be any number less than -3
In the 2nd number line represents
[tex]x \leqslant - 3[/tex]
so the answer is 1st one
Use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 4 miles per hour. estimate the percent of vehicles whose speeds are between 52 miles per hour and 70 miles per hour. (assume the data set has a bell-shaped distribution.)
The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.
What is the empirical rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.
Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 4 miles per hour.
[tex]\mu = 64[/tex] and [tex]\sigma = 4[/tex].
Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.
Therefore, 75% of the vehicles would fall into this category.
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Simon took out an unsubsidized student loan of $43,000 at a 2.4% APR,
compounded monthly, to pay for his last six semesters of college. If he will
begin paying off the loan in 33 months with monthly payments lasting for 20
years, what will be the amount of his monthly payment?
OA. $240.58
OB. $225.77
O C. $241.16
D. $225.23
As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.
what is interest rate ?By dividing initial principal by the risk premium, the time it has been and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the technique used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating this is as a portion of the principal amount. For example, if he borrowed $100 from a buddy and agrees to pay back the loan at 5% interest, he will just pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must lend money when you lend it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.
given
Assuming a specific interest rate (r), principal (p), and number of times the interest is compounded annually (n), we can calculate the total amount owed on a loan (A) as follows:
A = p(1+ r/n) nl
Because in our example, n = 12 (monthly), p = $43,000, r = 2.4% = = 0.024, and t = 20 years.
A = $69457.89.
$289.41 per month for a 20-year term.
As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.
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