Waiting time follows an exponential distribution with mean
μ=60
μ=60 seconds. This implies λ=1μ=160λ= μ1= 601
Let X be the waiting time. for first we have to calculate the probability of customers who wait less than 30 secs.
a. X is less than 30 seconds, then we have to find ,
P(X<X1)=1−e−λX1⇒P(X<30)=1−e−λ×0
=1−e−160×30 =1−e−12=1−0.6065
=0.3935P(X<X 1)⇒
P(X<30)
=1−e −λX 1=
1−e −λ×30 1−e − 601×30 =
1−e − 21
=1−0.6065
=0.3935
b. X is more than 120 seconds, then we have to find less than 120 sec
b. X is more than 120 seconds
P(X>X1)=1−P(X<X1)=1−(1−e−λX1)⇒P(X>120)=1−(1−e−λ×120=e−60×120=e−2=0.135
P(X>X 1)⇒P(X>120)=1−P(X<X 1)=1−(1−e −λX 1)=1−(1−e −λ×120= − 601×120 =e −2=0.135
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Anna is ordering a taxi from an online taxi service. She has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far she travels. She wrote an equation to represent her total cost, y=3+2. 3xy=3+2. 3x, where yy represents the total cost in dollars and cents, and xx represents the number of miles she travels. What could the number 3 represent in the equation?.
Answer:
The number 3 represents the fixed cost in the equation which is the flat charge.
What is the image point of (0,1) after translation right 5 and up 5 units?
Answer: (5,6)
Step-by-step explanation: 5 units right is adding 5 to your X. 5 units up is adding 5 to your Y.
For left and down, you'd subtract 5. For instance, "What is the image point of (8,9) after a translation of 5 units left, and 5 units down. The answer would be (3,4)
2.0 2.8
2.5 1.1
3.0 –0.8
3.5 –1.2
4.0 –0.3
4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
The zeros of the polynomial function should be between
(2.5, 1.1) & (3.0 -0.8) and (4.0, -0.3) & (4.5, 0.7)How to know the zeros of the polynomial functionThe zeros of a polynomial function is the point where the polynomial crosses the x axis
At this point, the y axis has a value of zero. This point can be seen on the graph easily as the graph will show the x intercept,
For the table, examining the values of the y coordinate to see where the signs change will help to know where the zero will lie.
The table shows that the y values changed sign at 1.1 to -0.8 and -0.3 to 0.7 and hence the zeros will lie between (2.5, 1.1) & (3.0 -0.8) and (4.0, -0.3) & (4.5, 0.7)
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13) An airline know from experience that the ditribution of the number of uitcae that
get lot each week on a certain route i approximately normal with μ = 15. 5 and σ = 3. 6. In one year, how many week would you expect the airline to loe between 10 and 20
uitcae?
The probability of losing 10 to 20 suitcase between a week is 0.8313 by the airline company.
Given what we know,
μ = 15. 5 and σ = 3. 6
Additionally, the weekly distribution of missing baggage along a particular route is roughly average.
z =( x - μ ) / σ
Therefore,
z(20) = (20-15.5)/3.6
= 1.25
P(x < 20)
= P(z < 1.25)
= 0.8944
Therefore, the probability that during a given week the airline will lose between 10 and 20 suitcases = 0.8313
The ratio of good outcomes to all possible outcomes of an event is known as the probability.
The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results
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NEED help asap!!help me
Answer:
132 square inches
Step-by-step explanation:
The surface area of a pyramid is the sum of the areas of all of its faces. Since the base of the pyramid is a square with an edge length of 6 inches, the area of the base is 36 square inches (6 inches x 6 inches).
To find the surface area of the pyramid, you also need to find the area of the lateral faces of the pyramid. The lateral faces of a pyramid are the triangular faces that are not the base. The lateral faces of a pyramid are all congruent, meaning that they are all the same size and shape.
To find the area of a lateral face of the pyramid, you can use the formula for the area of a triangle: A = 1/2bh, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.
In this case, the base of the triangle is 6 inches (the edge length of the base of the pyramid) and the height of the triangle is 8 inches (the slant height of the pyramid). The area of each lateral face of the pyramid is therefore 1/2 x 6 inches x 8 inches = 24 square inches.
Since there are 4 lateral faces on the pyramid, the total area of the lateral faces is 4 x 24 square inches = 96 square inches.
To find the surface area of the pyramid, add the area of the base to the area of the lateral faces: 36 square inches + 96 square inches = 132 square inches. Therefore, the surface area of the pyramid is 132 square inches.
Bernard was going on an 3.5 kilometre bushwalk. He needs 1.2 litres of water for every 1.4 kilometres he walks. He only has 500 mL water bottles. How many water bottles will he need to take to make sure he has enough water for his walk?
The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL
The number of water bottles = 6
What is an 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.
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 data ,
Let the number of water bottles required be = A
Now , the equation will be
The total distance of the bush walk = 3.5 km
Bernard's requirement of water for every 1.4 km = 1.2 L of water
So , Bernard's requirement of water for every 3.5 km = ( total distance of the bush walk / 1.4 ) x 1.2 L
Substituting the values in the equation , we get
Bernard's requirement of water for every 3.5 km = ( 3.5 / 1.4 ) x 1.2 L
Bernard's requirement of water for every 3.5 km = 2.5 x 1.2 L
Bernard's requirement of water for every 3.5 km = 3 L
Now , the amount of water one water bottle can hold = 500 mL
The value of 3 L = 3000 mL
So , the number of water bottles required to hold 3 L = 3000 / amount of water one water bottle can hold
Substituting the values in the equation , we get
The number of water bottles required to hold 3 L = 3000 / 500
The number of water bottles required to hold 3 L = 6 water bottles
Therefore , the value of A is 6 water bottles
Hence , The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL
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how to divide 3.5 by 70
calculator is going to be the most accurate
reteaching 5-5 using proportional Reasoning (PLEASE HELP)
1. The cost 7 Books is $10. 85
2. He can lay 336 bricks
3. n= 1
4. n= 1
5. n= 18
6. n= 5
7.n= 3
8. n=6
9. n= 6
10. n= 2
11.n= 12
12. n= 66
13. n= 10
14. n= 5
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
1. The cost 7 Books is = 7.75/ 5 x 7
= $10. 85
2. He can lay = 144/3 x 7
= 336 bricks
3. 4/24 = n/6
6 x4 = 24n
n= 1
4. 30/5 = 6/ n
30 n = 30
n= 1
5. n/6 = 27/ 9
9n = 162
n= 18
6. 50/ 70= n/7
n= 5
7. 14/7 = 6/n
2n= 6
n= 3
8. n/15= 2/5
n=6
9. 4/10 = n/ 15
n= 6
10. 4/200 = n/ 100
n= 2
11. 6/n= 5/10
n= 12
12. 32/22 = 96/ n
n= 66
13. 6/3 = n/5
n= 10
14. 2/n = 4/ 10
n= 5
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Find the length of the segment. Write the mixed number in simplest form.
Answer:
[tex]1 \, \dfrac{3}{8}[/tex]
Explanation:
It's 1/8 less than 1 1/2.
[tex]1 \, \dfrac{1}{2} - \dfrac{1}{8} = 1 \, \dfrac{4}{8} - \dfrac{1}{8} = 1 \, \dfrac{3}{8}[/tex]
At the city museum, child admission is $5.60 and adult admission is $9.50. On Friday, 170 tickets were sold for a total sales of $1228.90. How many child tickets were sold that day?
The number of child tickets sold is 99.
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, the cost of a child ticket and the cost of an adult ticket are $5.60 and $9.50 respectively.
Let the number of child tickets sold and the number of adult tickets sold be s and a, then
s + a = 170
a = 170 - s
The total cost of s child tickets and a adult tickets is:
5.6s + 9.5a = 1228.90
Substitute a= 170 -s into the above equation:
5.6s + 9.5(170 - s) = 1228.90
5.6s + 1615 - 9.5s = 1228.90
3.9s = 386.1
s = 99
Hence, the number of child tickets sold is 99.
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A bookstore took in $167 on sale of 5 copies of a new cookbook and 3 copies of a new novel. The next day it took in $89 on the sales of 3 copies of the cookbook and 1 copy of the new novel. What was the price of each book.
Hint: use elimination or substitution
The price is $14 for each novel and $25 for each Cookbooks when a bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook.
Given that,
A bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook. Three cookbook copies and one copy of the brand-new book were sold the next day, bringing in $89 for the company.
We have to find what the cost of each book was.
We know that,
A bookstore took in$ 167 on the sale of 5 copies of a new cookbook and 3 copies of a new novel.
The next day it took in $ 89 on the sale of 3 copies of the cookbook and 1 copy of the novel.
What is System of equation?An algebraic expression-based system of equations is a collection of relationships between several unknown variables.
Now,
Let x= cookbook and y= novel.
So,
On first day, 5x + 3y = 167----->equation(1)
On second day, 3x + 1y = 89----->equation(2)
These equations must be solved in order to determine the cost of each book.
From equation(2), we get;
y = 89 - 3x
Now we use this x solution to solve our first equation.
We get;
5x + 3(89-3x) = 167
5x + 267 - 9x = 167
267-167 = 9x - 5x
100 = 4x
x = 25
So, The price is $25 for the each Cookbooks.
Now, By substituting $25 for x in the second equation, we must get the value of y.
y=89-3(25)
y=89-75
y=14
So, The price is $14 dollars for each novel.
So,
Therefore, The price is $14 for each novel and $25 for each Cookbooks when a bookstore made $167 on the sale of 3 new novels and 5 copies of a new cookbook.
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A cone has a radius of 8 m and a height of 30 m. What is the volume of the cone in terms of pi?
Answer:
640[tex]\pi[/tex]
Step-by-step explanation:
The formula for a cone is [tex]\pi r^2*h/3[/tex].r meaning Radius and h meaning Height.Your looking for the answer in terms of [tex]\pi[/tex] so you would take the [tex]\pi[/tex] out of the equation making it [tex]r^2*h/3[/tex].Insert your values in their respective locations, r becoming 8, and h becoming 30.Solve your equation of [tex]8^2*30[/tex]/3 getting 640.Add [tex]\pi[/tex] to the end.Answer:
640π
Step-by-step explanation:
The formula for a cone volume is
[tex]V = \pi r^{2} \frac{h}{3} \\\\V = \pi 8^{2} \frac{30}{3} \\\\V = \pi 64 * 10 \\\\V = 640\pi[/tex]
Khalil earns $106.50 for 6 hours of work. If he makes a constant hourly wage, which table represents the relationship between the number of hours he works and his total earnings.
The table that represents the relationship between the number of hours Khalil works and his total earnings is Table A.
How to represent the table?The ratio connecting two given values in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
Mathematicians use the constant of proportionality to determine whether a relationship is direct or indirect and what kind of proportionality it is. Equations involving ratios and proportions can be resolved with the aid of the proportionality constant.
It should be noted that the information given relates to a constant of proportionality. In this situation, Khalil earns $106.50 for 6 hours of work.
The amount that will be earned per hour will be:
= Amount earned / Number of hours
= $106.50 / 6
= $17.67
In this case, 7 hours will be:
= $17.67 × 7
= $123.7
The correct option is A.
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Please help:
given that ∠QRS and ∠EFG are supplementary angles, find M∠QSR and M∠EFG
PLS ANSWER ASAP 50 POINTS!!
Determine if you can use the hypotenuse-leg congruency property to prove the triangles are congruent.
A. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if a leg of one triangle is congruent to a leg of the other triangle.
B. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
C.Yes, the hypotenuse-leg congruence property can be applied.
D. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the triangles are right triangles.
No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
What is hypotenuse?
The side opposite to the right angle is always the hypotenuse of a right triangle . It is also the longest side in a right triangle.
what is hypotenuse-leg congruence property?
HL (hypotenuse-leg) congruence Property: The hypotenuse-leg congruence property only applies to the right triangles.
According to hypotenuse-leg congruence property, in any two right angle triangles if the length of the hypotenuse of both the triangles are same and the length of one leg of the triangle is the same in both then the triangles are congruent in nature.
In the given case , leg of one triangle is congruent to a leg of the other triangle and also the triangles are right triangles but the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
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Point O is the incenter of ΔABC.
Point O is the incenter of triangle A B C. Lines are drawn from the point of the triangle to point O. Lines are drawn from point O to the sides of the triangle to form right angles and line segments O Q, O R, and O S. Angle Q A O is (2 x + 6) degrees, angle O A S is (4 x minus 12 degrees), and angle Q B O is (3 x minus 15) degrees.
What is m Angle Q B O?
5°
9°
12°
24°
Answer:
12
Step-by-step explanation:
12 .........
What is 1+1
A. 2
B. 3
C. -24,000
D. Some ridiculous number
Answer:
a
Step-by-step explanation:
ik my math
suppose that three in ten adults own an answering machine. a researcher selects a random sample of 38 adults, and is interested in the number of people in the sample will own an answering machine. a) find the probability that in a sample of 38, exactly 15 people own an answering machine. b) find the probability that in a sample of 38, at most 15 people own an answering machine.
A sample of 38 adults who has own an answering machine,
a) The probability that in a sample of 38, exactly 15 people own an answering machine is 0.061.
b) The probability that in a sample of 38, at most 15 people own an answering machine is 0.92381.
We have three in ten adults own an answering machine . That is probabilty of success, p = 3/10
Sample size, n = 38
Using Binomial Probability distribution,
X ~ Binom( 38, 0.3)
where X is random variable of adults has own an answering machine.
P(X= x) = ⁿCₓ (p)ˣ1-p)⁽ⁿ⁻ˣ⁾
The probability that in a sample of 38, exactly 15 people own an answering machine. , P(X= 15)
= ³⁸C₁₅(0.3)¹⁵ )(1 - 0.3)²³
= 38!/15!23! (0.3)¹⁵5(0.7)²³
= 0.06075 ~ 0.061
so, P(X= 15) = 0.061
b) The probability that in a sample of 38, at most 15 people own an answering machine, P(X<= 15)
Now, P(X≤ 15) = P( X= 1 ) + P(X= 2) + ... + P(X= 15) or 1 - P(X>15)
= 0.923814121
Hence, required probabilities
are 0.061 and 0.9238.
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Please someone help me in 1985, there were 285 cell phone subscribers in the small town of glenwood. the number of subscribers increased by 75% per year after 1985. Find out the number of subscribers in 2008?
If the number of subscribers increases by 75% each year, then the number of subscribers each year is 175% the number of the previous year. So we need to multiply by 1.75 each year to get the next years number.
Since 2008 is 23 years after 1985, we'd have to multiply the 1985 number by 1.75 twenty-three times:
285 (1.75)^23 ≈ 110,845,988
That seems a bit crazy, since Glenwood is a small town, but so is a 75% growth each year for 23 years.
how many miles can you drive, if your car gets 25.00 miles per gallon and you have 12.00 gallons of gas?
3 × 10² miles can you drive, if your car gets 25.00 miles per gallon and you have 12.00 gallons of gas.
What is distance?Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
Given that,
car gets 25.00 miles per gallon.
In 1 gallon car covers 25 miles distance.
In 12 gallon the car will cover = 25 × 12 miles distance
= 300 miles distance.
Thus, distance covered in 12 gallons = 300 miles.
= 3 × 10² miles.
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Pregunta rápida, que responderían cuando alguien dice: "sigue soñando :)"
Answer:
Si es un chiste, me reiría. Pero si es un insulto, agradecería que se preocuparan por mí.
Step-by-step explanation:
A rectangular box has dimensions 40 cm by 35 cm by 30 cm.
calculate the largest number of cubes of length 10 cm that can be placed inside the box.
The largest number of cubes that can be placed in the rectangular box is 42
How to find the cubes the box can containThe problem is solved by solving for the volume of the rectangular box and dividing by the given size of cube
The formula for the volume of rectangular box is given by
= length * width * height
= 40 * 35 * 30
= 42000 cm³
A cube of length 10 cm has a volume of 1000
= 10 * 10 * 10 = 1000
the largest number of cubes of length 10 cm that can be placed inside the box.
= 42000 / 1000
= 42
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Convert 1400 pounds into kilograms. Round your answer to the nearest whole number.
Answer:
635 kg
Step-by-step explanation:
1 pounds = 0.453592 kg
1400 = 0.453592 x 1400
=635.0288
=635 kg
Find the measure of each angle indicated.
Answer:
answer is 124 degree ....
In 1995, the standard bus fare in a city was $0.25. In 2022, the standard bus fare was $3.25. Find the percent
increase. (Round to the nearest tenth of a percent.)
Answer: 1200 percent increase
Step-by-step explanation:
Increase = New Number - Original Number
divide the increase by the original number and times 100
3.25-0.25=3
3/0.25=12*100
1200 percent
Find the distance between each pair of parallel lines with the given equations Y=7. Y = -1
The distance between the two parallel lines with the equations y = 7 and
y = -1 is 8 units
What is the distance of a line between 2 points?
The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Given data ,
Let the equation of line be y = 7 and y = -1
Now , the slope of both the lines is 0
Slope m = 0
And the y intercept of the equation 1 or line 1 is = 7
So , the point is ( 0 , 7 )
And the y intercept of the equation 2 or line 2 is = -1
So, the point is ( 0 , -1 )
Now , the distance between the points ( 0 , 7 ) and ( 0 , -1 ) is given by the equation ,
[tex]Distance D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
Substituting the values in the equation , we get
Distance D = √ ( 7 - ( - 1 ) )²
Distance D = √ ( 8 )²
Distance D = 8 units
Therefore , the value of D is 8 units
Hence , The distance between the two parallel lines with the equations y = 7 and y = -1 is 8 units
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Solve each system by eliminantion: -5x+3y=6 x-y=4
Answer: x = -9 , y = -13
Step-by-step explanation:
Multiply the second equation by 5, then add the equations together.
(−5x+3y=6)
5(x−y=4)
Becomes:
−5x+3y=6
5x−5y=20
Add these equations to eliminate x:
−2y=26
Then solve −2y=26 for y:
−2y = 26
Divide both sides by -2
y= -13
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
−5x+3y=6
Substitute−13 for y in −5x+3y=6:
−5x+(3)(−13)=6
−5x−39=6 (Simplify both sides of the equation)
−5x−39+39=6+39 (Add 39 to both sides)
−5x=45
Divide both sides by -5
x = -9
hope it help
you can proof it in the first equation if you want
find the range for 46 22 46 49 45 39 40 42 41 39 40 36
Answer: 27
Step-by-step explanation: 46 22 46 49 45 39 40 42 41 39 40 36
The range is calculated by subtracting the lowest value from the highest value.
So the lowest number is 22 and the highest is 49.
Then we subtract 22 from 49 to find the range.
How do you write 142/00 as a percentage
Answer: 14200%
Step-by-step explanation:
To convert 142 to percent multiply 142 by 100. The result is 14200 percent, or, using the percent sign, 14200 %.
Put simply, to change 142 to % move the ″.″ two places to the right.
Check out the next plus one section on how to express 142 as a percent. And, in case you have a number different from 142, then use our decimal to percent calculator above.
If our calculator has been of help to you make sure to bookmark it now. Besides 142 into percent, it can convert any decimal to percent and vice versa.
What is 142 as a Percent?
You already know the answer to what is 142 as a percent. Ninety-one as a percent is 14200%.
If you have been looking for 142 as %, 142 in %, 142 in percentage or what is 142 as a percentage then you have also found what you have been looking for.
Note that you can find many decimal to percent conversions, including 142 in percentage, by using the search form in the sidebar.
Enter, for instance, 142 to percents.
BTW: Similar conversions include, for example:
147 as a percent
148 as a percent
149 as a percent
Next we explain how do you write 142 as a percent.
Write 142 as a Percent
To write 142 as a percent multiply 142 by 100 to obtain 14200. Then append the percent sign (%). To learn about the spacing check out the reference section of decimal to percent.
In a table and in texts with space restrictions you write 14200%, whereas in a running text, like this one, you write it spelled out as 14200 percent in American English, and 14200 per cent else.
Particularly in the UK, the abbreviations pc, pct., and pct are also used sometimes, e.g. 14200pc.
These days, the old forms 14200 per centum and per cent followed by a period, 14200 per cent., are hardly seen anymore and can be considered obsolete in daily life.
There is no difference in meaning between the two-word per cent and percent. Choosing between 14200 per cent and 14200 percent is merely a matter of preference.
142 as a Percentage
142 as a percentage of certain number x can be calculated by dividing 142 by x, and multiplying the result by 100. For example, 142 as a percentage of 10 = (142 / 10) x 100% = 1420%.
Feel free to use our decimals to percents calculator below. Enter 142 in the number field, then insert your value in the field labelled “% of”.
To start over, press reset first.
At this stage the 142 in percent conversion will be conducted automatically. Observe that the result is rounded to ten decimal places.
[tex]142/100[/tex] can be written as [tex]142[/tex][tex]%[/tex]%.
The Latin word "per centum," which means "by the hundred," was the source of the English word "percentage." Fractions with a denominator [tex]100[/tex] are called percentages.
A percentage is a certain number or part of every hundred. It is a fraction with a denominator [tex]100[/tex], and the symbol for it is "%."
Finding the percentage of a whole in terms of [tex]100[/tex] is what percentage calculation refers to.
There is no dimension to percentages. As a result, it is known as a dimensionless number.
A fraction or a decimal can also be used to represent a percentage.
Therefore, the answer is [tex]142[/tex]%.
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The correct question is :
How do you write 142/100 as a percentage?
I need your assistance please
Answer:
subtraction property of equality
Step-by-step explanation: