The fraction is [tex]\frac{3}{5}[/tex]
Let's take the fraction as [tex]\frac{a}{b}[/tex]
According to the first statement,
If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1.
[tex]\frac{a + 1}{b - 1}[/tex] = 1
a + 1 = b -1
a + 2 = b
b = a + 2........(1)
According to the second statement
If we only add 1 to the denominators, it becomes 1/2.
[tex]\frac{a}{b+1}[/tex] = 1/2
2a = b + 1
b = 2z -1 .........(2)
Equating both the equation (1) and (2)
2a - 1 = a + 2
2a - a = 2 + 1
a = 3
Now substitute the value of a in equation (1)
b = 3 + 2
= 5
Therefore the fraction is [tex]\frac{a}{b}[/tex] = [tex]\frac{3}{5}[/tex]
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on monday ramon bought 5 zip disks. two days later the price of the discs were decreased by 1.50 per disk. leticia bought ten disks at the sale price and paid 22 more than ramon paid for 5 disks. what was the original price of a disk
The original price of a zip disk is; $1.4
How to Solve Algebra Word Problems?Let cost of zip sticks bought by Ramon be x. Thus;
Cost that Ramon paid = 5x
Now, we are told that 2 days later the price increased by $1.5 per disc. Thus, new cost = x + 1.5
Leticia bought ten disks at the sale price and paid 22 more than ramon paid for 5 disks. Thus, equation here is;
10(x + 1.5) = 5x + 22
Expand the bracket to get;
10x + 15 = 5x + 22
10x - 5x = 22 - 15
5x = 7
x = 7/5
x = $1.4
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Examine the following graph of y=1/4x+2.
If the point (−4,b) is on this line, what is the value of b?
Enter your answer as the correct value, like this: 42
Answer:
b = 1
Step-by-step explanation:
they are asking what is y when x is -4. We can look on the graph and see that when x = -4, when is 1. It is the point (-4,1).
We can also see it algebraically. We can replace x with -4 and solve for y
y = 1/4 x + 2
y = 1/4((-4) + 2
y = -1 + 2
y = 1
In a survey the ratio of students who prefer muffins to bagels is 4 to 5 if the number of students surveyed who prefer muffins is 420 how many prefer bagels
In a survey where the ratio of students who prefer muffins to bagels is 4 to 5 and 420 prefer muffins, 525 students prefer bagels.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
It can be expressed in different ways:
1) Use the ":" to separate the values : a : b
2) Use the word "to" : a to b
3) Write it in fraction: a / b
On the other hand, proportion is the equality of two ratios, such that
a : b = c : d
Given a proportion, the product of its means must be equal to the product of its extremes. That is:
ad = bc
If the ratio of students who prefer muffins to bagels is 4 to 5, and 420 students prefer muffins, the proportion can be written as:
4 : 5 = 420 : n
where n = number of students who prefer bagels
Solving for n,
4n = 5(420)
4n = 2100
n = 525
number of students who prefer bagels = 525
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Find the equation of the linear function represented by the table below in slope-intercept form. x y -1 -1 2 14 5 29 8 44
The equation of the linear function represented by the table below in slope-intercept form is y = 5x + 4
Linear equationsThe equation of a line in point-slope form is expressed as y = mx + b
where
m is the slope
b is the intercept
Using the coordinate points (-1,-1) and (2, 14)
Slope = 14+1/2+1
slope = 15/3
Slope = 5
For the intercept;
14 = 5(2) + b
14 = 10 + b
b = 4
The y-intercept is at the point (0,4)
Determine the equation
y = mx + b
y = 5x + 4
Hence the equation of the linear function represented by the table below in slope-intercept form is y = 5x + 4
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Find the distance between points A and B. A = (3,-7) B = (3,1)
The distance between points A and B is 8 units.
We have been given two points A and B.
The coordinates of the points are A = (3,-7) B = (3,1)
We need to find the distance between points A and B.
Let d be the distance between points A and B.
Using distance formula,
d = √[(3 - 3)² + (1 - (-7))²]
d = √[0² + 8²]
d = √8²
d = 8 units
Therefore, the distance between points A and B is 8 units.
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Evaluate the expression when h = 5.
2h+h-2 (3) =
Answer:
Step-by-step explanation:
For every "h" plug in "5", then follow the order of operations
2h+h-2(3)
2(5)+5-2(3)
10+5-6
15-6
=9
The answer is 9
Solve 6^x + 2 = 10 for x using the change of base formula log, y = log y log b
The answer for "x" in 6^(x+2) = 10 is -0.715
The logarithm is the inverse function of exponentiation in mathematics. That is, the logarithm of a given integer x is the exponent to which another set number, the base b, must be increased in order to create x.Firstly, we use the change of base formula. The base must be 6 because the "x" variable is a power of it.6^(x+2) = 10Taking a log with base 6 on both the sidesThen, we can use the property logarithm power rule:(x + 2) log6 = log10(x + 2)(1) = (log10)/(log6)x + 2 = 1/log6x + 2 = 1.285x = 1.285 - 2x = -0.715To learn more about logarithm, visit :
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\large \frac{2\cdot3^{-4}}{5^{-2}}
Adam wrote: \large \frac{2\cdot5^2}{3^4}
Nick wrote: \large \frac{5^2}{2\cdot3^4}
Shane wrote: \large \frac{2\cdot3^4}{5^{^2}}
Who is correct and why?
a
Adam is correct because the negative exponent moves the base to the other side of the fraction bar and makes the exponent positive.
b
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
c
Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
d
Shane is correct because all that needs to be done is to make the negative exponents positive.
Answer:the answer is A:nick is correct
Step-by-step explanation:
Based on the fraction given of [tex]\large \frac{2\cdot3^{-4}}{5^{-2}}[/tex], the correct person is c. Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
Why is Nick correct?When a number is being taken to the negative power, then it can be rewritten as a fraction where the number becomes the denominator and the numerator becomes 1.
The number, 2.3⁻⁴ can be written as:
= 1/2.3⁴
The number 5⁻² can be written as:
= 1 / 5²
When these numbers are divided we get:
= 1/2.3⁴ ÷ 1 / 5²
= 1/2.3⁴ x 5²/1
= 5² / 2.3⁴
= [tex]\large \frac{5^2}{2\cdot3^4}[/tex]
In conclusion, Nick was correct.
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the given equation is either linear or equivalent to a linear equation. solve the equation. (if there is no solution, enter no solution. if all real numbers are solutions, enter reals.)
The given equation has one solution which is x = 6 (which is a REAL number).
What is a solution of linear equation?Linear Equation Solutions are the values of a variables in linear equations that give all possible solutions. Linear equations represent real-world problems by involving unknown quantities with in form with one or more variables.
Some key concepts regarding the solution of linear equation are-
Linear equation solutions are the points where the lines or planes indicating the linear equations intersect or meet. A solution set of a linear equation system is the collection of all possible solutions' values for the variables. While solving linear equations, for example, one can depict the solution of such a system of simultaneous linear equations by having drawn two linear graphs and locating their intersection point.Now, for the given question;
The linear equation is -
4x + 9 = 33
Solving this;
4x = 33 - 9
4x = 24
x = 24/4
x = 6
Therefore, the solution of the given linear equation is (x=6), where 6 is the real number.
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The complete question is-
The given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter NO SOLUTION. If all real numbers are solutions, enter REALS.)
4x + 9 = 33
Solve the following:
32 ÷ 4 + 4 x 8 = ?
A. 42
B. 32
C. 96
D. 40
Answer:
Step-by-step explanation: 40 see attachment
If it costs $9.50 to buy a
movie ticket, what is the
most number of tickets
someone can buy for
$40.00? How much money
is left over?
PLEASE SHOW WORK
The number of tickets that can be bought with $40 is 4 tickets
How to calculate the number of tickets ?It costs $9.50 to buy 1 tickets
The number of tickets that will be bought with $40 can be calculated as follows
= 40/9.50
= 4.2
Hence 4 tickets will be bought with $40
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The planet XYZ travels about the star ABC in an orbit that
is almost circular. Assume that the orbit is a circle with
radius 94,000,000 mi. Assume there are 24 hours in one
day on planet XYZ.
(a) Assume that XYZ planet year is 346 days, and find the
angle formed by XYZ's movement in one day.
(b) Give the angular speed in radians per hour.
(c) Find the linear speed of XYZ in miles per hour.
please help me!!!
Answer:
v = 2.33 10⁷ mi / h
Explanation:
For this exercise we must observe that the velocity module is constant, so we can use the kinematic relation v = d / tThe distance traveled in each orbit is the length of the circle L = 2π rThe time it takes in orbit is called period (T)Let's reduce the quantities r = 8.9 10⁷ mi t = 24 h (3600s / 1 h) = 86400 sWe replace v = 2π r / TLet's calculate v = 2π 8.9 10⁷/86400 v = 6.47 10³ mi / s v = 6.47 10³ mi / s (3600 s / 1h) v = 2.33 10⁷ mi / h
a simple dart target has two concentric circles. the larger circle has a radius of 4. the smaller circle has a radius of 2. the scoring should correspond to the relative difficulty of hitting the inner circle and the outer ring. how many more points should a player receive for landing a dart in the inner circle, as opposed to the outer ring? the player should receive 2 π times as many points. the player should receive 3 times as many points. the player should receive 9 times as many points. the player should receive 4 π times as many points.
The points awarded for striking the inner circle ought to be tripled.
What is the inner circle?
The face region of the circle determines the likelihood of landing an outrage there.The formula for calculating a circle's area is: inner circle for the exterior circle, apply the formula to subtract the inner circle's value to determine the remaining area.The formula for the area of a(one) circle is an inner circle for the external circle, use the formula also abate the value of the inner circle, to find the remaining area, which means that the area of the external circle is 3( three) times larger, making it 3( three) times more likely to hit the external circle.
Thus, The points awarded for striking the inner circle ought to be tripled.
[tex]\pi r^2 A =\pi 2^2 = 12.566 A\\[/tex]
so,
[tex]\pi 4^2 - 12.566 = 3(three)[/tex]
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Which of the following numbers is rational?
A. 2√5
B. √25
C. 2pi
D. 25pi
Answer:
B
Step-by-step explanation:
_/25 can be rooted to 5. 5 is rational.
a. It is linear because it has a constant rate of change.
b. It is linear because it does not have a constant rate of change.
c. It is not linear because it has a constant rate of change.
d. It is not linear because it does not have a constant rate of change.
c. It is not linear because it has a constant rate of change.
Answer:
D
Step-by-step explanation:
this is showing a quadratic
A,b,c or d I don’t know which one to pick
Answer:
b
Step-by-step explanation:
the answer is b because 50 + (11 x 9) = 149
75 + (8 x 9) = 147
Therefore, franks fiesta is less expensive for parties of 9 or more
which ratio has the unit rate of 4
[tex]2\frac{1}{2} ~~ : ~~ \cfrac{5}{8}\implies \cfrac{5}{2} ~~ : ~~ \cfrac{5}{8}\implies \cfrac{ ~~ \frac{5}{2} ~~ }{\frac{5}{8}}\implies \cfrac{5}{2}\cdot \cfrac{8}{5}\implies 4 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}~~ : ~~1\implies \cfrac{ ~~ \frac{1}{8}~~ }{1}\implies \cfrac{1}{8} ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]
[tex]4~~ : ~~1\frac{1}{4}\implies 4~~ : ~~\frac{5}{4}\implies \cfrac{4}{ ~~ \frac{5}{4} ~~ }\implies \cfrac{4}{1}\cdot \cfrac{4}{5}\implies \cfrac{16}{5}~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}~~ : ~~3\frac{1}{2}\implies \cfrac{7}{8}~~ : ~~\cfrac{7}{2}\implies \cfrac{ ~~ \frac{7}{8}~~ }{\frac{7}{2}}\implies \cfrac{7}{8}\cdot \cfrac{2}{7}\implies \cfrac{1}{4}~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]
[tex]4\frac{1}{3}~~ : ~~3\implies \cfrac{13}{3}~~ : ~~3\implies \cfrac{ ~~ \frac{13}{3}~~ }{3}\implies \cfrac{13}{3}\cdot \cfrac{1}{3}\implies \cfrac{13}{9} ~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ 2~~ : ~~\cfrac{1}{2}\implies \cfrac{2}{ ~~ \frac{1}{2} ~~ }\implies \cfrac{2}{1}\cdot \cfrac{2}{1}\implies 4 ~~ \checkmark[/tex]
Caroline is the youngest of four siblings whose ages are consecutive odd integers. If
the sum of their ages is 96, find Caroline's age.
Caroline's age is 21 years which is an odd integer.
Integers are a subset of real numbers.
Integers are rational numbers except decimals and fractions.There are 3 types of integers positive , negative and Zero.Positive integers are 3, 6, 789 ...Negative integers are -87, -345, -234 ...Zero integers is 0It is given that Caroline is the youngest of 4 siblings and all of their ages are odd consecutive integers.
Let us consider the age of Caroline's age to be x years(x is an odd integer).
She is the youngest so the sibling's age who is just older than Caroline is given by x+2 which is also another odd integer.
Ages of the other two siblings will be x + 4 , x + 6 .
Now sum of their ages is 96.
Therefore: x + (x+2) + (x+4) + (x+6) =96
or, 4x + 12 = 96
or, 4x = 84
or, x = 21 (odd integer)
Carline's age is 21 years.
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Please answer the questions in the photo [ Brainliest + points ]
Answer:
8 is 69
9 is 68
t is 99 i think
z is 80 i think
3)
1 1/3
is fractions between which set of numbers?
A) 1.3 and 1.4
B) 1.2 and 1.3
□ C) 1.1 and 1.2
□ D) 1.4 and 1.5
None of the above, since the improper fraction 4/3 is identical to the mixed number 1 1/3.
There are various types of fractions, including proper and improper fractions as well as mixed numbers. Mixed numbers: Sometimes converting a mixed number into an incorrect fraction is advantageous or required. If you answer equations that contain both mixed numbers and fractions, you must take this step.
Divide the full integer by the denominator of the fraction (3). (1). 3 x 1 = 3. The product you obtained in the previous step (3) after adding the fraction's numerator (1) is equal to four. 1 + 3 = 4.This turns becomes the improper fraction's numerator. As with the proportion in the mixed number, the denominator remains constant.
Hence, the set of numbers 1 1/3 fraction is 4/3.
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Multiply the total (36.45) by 0.07 to find the tax. Then find the total, including tax.
Answer:
39.0015
Step-by-step explanation:
36.45 x 0.07 = 2.5515
36.45 + 2.5515 = 39.0015
I need help and i WILL OFFER 100 POINTS and make you a BRAINLIEST or try
Answer:
782.5
Step-by-step explanation:
First off, we have to somewhat follow the order of PEMDAS.
1) Simplify the exponents
[tex]\frac{(7.3 * 1000000) + (2.4 * 10000000)}{(4 * 10000)}[/tex]
2) Multiply what's in the parenthesis
[tex]\frac{7,300,000 + 24,000,000}{40,000}[/tex]
3) Now we have to add what's on the top bracket
[tex]\frac{31,300,000}{40,000}[/tex]
4) After all the simplifying is done, we have to divide
31,300,000 ÷ 40,000 = 782.5
I hope this helped you :)
Step-by-step explanation:
you can ask questions for clarification
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answer:
(x – 4)² + y² = 36
(x + 6)² + y² = 144
Step-by-step explanation:
All other questions are parabolas!
which expression is equivalent to 4(23)? 4(20 3) 4 left parentheses 20 plus 3 right parenthesis 4(2 13) 4 left parentheses 2 plus 13 wright parentheses 4(20 30) 4 left parentheses 20 plus 30 right parenthses 4(2 3)
4 • 23 = 92 so the correct answer is a 4(20+3).
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
For example, x + y is an expression, where x and y are terms having an addition operator in between.
Expressions can be simplified to form an answer. For example, 3+6-2 is an expression that can be simplified to 7. There are two different ways to simplify arithmetic expressions and algebraic expressions. We use the bracket open division multiplication addition subtraction rule which means the operations are performed in the given manner to simplify them.
For example, 2x+5x results in 7x, whereas 7ab-b is an expression that has two unlike terms, which cannot be added.
Checking for all the options:
option a) 4 (20+3)=4 * 23 = 92
option b) 4 (2 + 13) = 4 * 15 =60
option c) 4 (20 + 30) = 4 * 50 =200
option d) 4 (2 + 3) = 4 * 5 = 20
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Graph the line that represents the equation y= - 2/3 x + 1
I will give out brainlist
help [please]
Answer:
Step-by-step explanation:
Hi
in a random sample of 7 residents of the state of california, the mean waste recycled per person per day was 1.7 pounds with a standard deviation of 0.36 pounds. determine the 99% confidence interval for the mean waste recycled per person per day for the population of california. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
The critical value that should be used in constructing the confidence interval is ( 1.592, 1.807 ).
Given that;
Number of residents, n = 7
Z*- value of 90% confidence level equals z* = 0.79
Mean x = 1.7 and deviation σ = 0.36
What is the standard deviation?
Standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean.
Now,
Number of residents, n = 7
Z*- value of 90% confidence level equals z* = 0.79
Mean x = 1.7 and deviation σ = 0.36
The confidence interval for mean waste recycled per person is
[tex](x-z^{*} \frac{sigma}{\sqrt{n} } ; x+z^{*} \frac{sigma}{\sqrt{n} } )[/tex]
[tex](1.7 - 0.79*\frac{0.36}{\sqrt{7} } ; 1.7 + 0.79*\frac{0.36}{\sqrt{7} })[/tex]
[tex](1.592, 1.807)[/tex]
Hence, the critical value that should be used in constructing the confidence interval is ( 1.592, 1.807 ).
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The record high temperature in Green Bay, Wisconsin is 104 degrees, the record low
temperature is -36 degrees.
What is the difference between the record high and record low temperatures?
Which contributions did Galileo make to the model of the solar system? Select two options.
0 A mathamatical model for the orbits of the planet.
0 scientifically accurate data on planetary orbits
0 data that showed that planets reflected sunlight simular to earths moon
0 the idea that stars are suns that do not move
0 observations of the moons of jupitar rotating rotating around the gas giant.
WHOEVER ANSWERS GETS 1,000 YEARS OF GOOD LUCK. IF YOU CAN'T TELL, IM DESPERATE
Answer: It should be 3 and 5
Step-by-step explanation: I hope this helps <33
4–3n≥10
someone want 50 points?
Answer:
n <(_) -2
Step-by-step explanation:
We can start by doing this linearly.
First subtract 4 on both sides
-3n >(_) 6
Then divide both sides by -3. You have to switch the sign because you are dividing by a negative number.
n <(_) 6
Consider this system of inequalities.
x + y ≤ –3
y < StartFraction x Over 2 EndFraction
Which graph shows the solution for this system?
The line x + y ≤ –3 will be solid and shaded below the graph and the line y < x/2 will be dashed and shaded below the graph.
Graphing linear inequalities.Inequalities is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
When graphing the inequalities x + y ≤ –3, the line will intersects the y-axis at the coordinate point (0, -3) and the line will be solid and shaded below the graph.
When graphing the inequalities y < x/2, the line will intersects the y-axis at the coordinate point (0, 0) and the line will be dashed and shaded below the graph.
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