If the number y is divided by x, the quotient is p and the remainder is r , then the relation between x,y,p,r is given by the expression [tex]y=xq+r[/tex] .
What is Euclid's Division Lemma ?
The Euclid's Division Lemma states that for two positive integers , a and b , then there exist unique integers q and r such that : [tex]a=bq+r,\; \; where \; 0\leq r < b[/tex] ;
here , the number y is divided by x , that means , the divisor is "x" , the dividend is "y" ,
the quotient is denoted by "q" ;
and the remainder is denoted by "r" ;
So , According to Division Lemma :
we can write ; the relation between x,y,p,r as ⇒ [tex]y=xq+r[/tex] , where [tex]where \; 0\leq r < x[/tex] .
Therefore , the relation between x,y,p,r is [tex]y=xq+r[/tex] .
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e wants a green paint that requires 3 parts blue paint to 2 parts yellow paint. if he needs a total of 10 gallons to paint the whole house, how many gallons of blue paint does he need?
The gallons of blue paint he needs to make the green paint is 6 gallons.
This is a problem in ratios. Let's look into what we know.
Volume of green paint needed = 10 gallons
Parts of blue paint needed = 3
Parts of yellow paint needed = 2
Total number of parts = parts of blue paint + parts of yellow paint
3 + 2 = 5
So fraction of blue paint needed = parts of blue paint / total parts
= 3/5
Volume of blue paint needed = [tex]\frac{3}{5}[/tex] × 10
= 6 gallons
Volume of yellow paint needed = [tex]\frac{2}{5}[/tex] ×10
= 4 gallons.
So we need 6 gallons of blue paint and 4 gallons of yellow paint to make 10 gallons of green paint.
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A gas occupies 4.23 l at 2.25 atm. What is the volume at 3.46 atm?
a. 1.84 l
b. 2.75 l
c. 6.50 l
d. 32.9 l
e. 0.364 l
A gas occupies 4.23 l at 2.25 atm. 2.75 L is the volume at 3.46 atm. This can be solved using the concept of Boyle's law.
What is Boyle's law?Boyle's law gives the relationship between pressure and volume of gas.
It states that at constant temperature pressure in inversely proportional to volume.
PV = k
where P - pressure V - volume and k - constant
P₁V₁ = P₂V₂
Given that,
initial pressure (P₁) = 2.25 atm
final pressure (P₂) = 3.46 atm
initial volume (V₁) = 4.23 L
final volume (V₂) = ?
where parameters for the first instance are on the left side and parameters for the second instance are on the right side of the equation
substituting the values in the equation
2.25 atm x 4.23 L = 3.46 atm x V
V = 2.75 L
Thus, the final volume is 2.75 L
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work out the area of this shape
Answer:
[tex]72cm^{2}[/tex]
Step-by-step explanation:
9/3=3
12/3=4
(4x9)+(4x6)+(4x3)=
=36+24+12
=[tex]72cm^{2}[/tex]
describe how honesty might be measured and defined using an operational definition. check all that apply.
Honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty, ranking their fellow participants in terms of honesty, conducting a polygraph test to assess physiological responses when presented with specific questions, and conducting interviews to assess how forthright people are in their answers.
An operational definition of honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty. This would allow participants to self-assess their own level of honesty and provide a baseline for comparison. By observing how often people tell the truth in a given situation, one can measure the level of honesty of a person.
Additionally, a polygraph can be used to measure physiological responses when asking a series of specific questions. This can provide a more accurate measurement of a person’s honesty in comparison to a self-reported scale.
Lastly, conducting interviews with participants can help to assess how forthright people are in their answers. This allows for a more in-depth assessment of honesty by allowing interviewers to observe and assess the sincerity of participants’ answers.
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The cost of a council tax bill increased by 5%.
The council tax bill increased by £62.
Work out the cost of the council tax bill before the increase
Answer:
To work out the cost of the council tax bill before the increase, we can use the formula:
Original cost = New cost / (1 + increase percentage)
We know that the council tax bill increased by 5% and the increase is £62. So the new cost of the council tax bill is £62 more than the original cost.
We can use the formula above to find the original cost:
Original cost = £62 / (1 + 0.05)
Original cost = £62 / 1.05
Original cost = £59.04
So the cost of the council tax bill before the increase was £59.04.
Tavon wants to plant these flowers in
his flower beds. His large flower bed will
hold 3/4 of the flowers. He will plant the
remaining flowers in his small flower bed.
How many flowers will Tavon plant in his
small flower bed?
Answer: 1/4
Step-by-step explanation: He plants 3/4 of the flowers in one garden. There are 1/4 left. 4/4 - 3/4= 1/4
What output force is generated when an input force of 630 n is applied to a machine with a mechanical advantage of 3? 21 n 189 n 210 n 1,890 n
The force that a simple machine applies to an object is known as output force. The mechanical advantage exceeds one if the output force exceeds the input force.
How does the output force function?A basic machine's output force is indeed the pressure it puts on an item. The mechanical advantage exceeds 1 when the output force exceeds the input force. Output force minus input force equals the mechanical advantage ratio. Work is made easier by increasing the mechanical advantage.
A 630 N input force is therefore necessary.
a 3 percent mechanical advantage
It can be represented mathematically as follows:
M=f 1/f 2
the output force F1 is
The input force is F2,
and thus
F1=1890 N and 3=F1/630 N
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Answer:
the answer is D. 1,890 N!!!
Convert a pressure of 1379 torr to atm
Conversion of pressure of 1379 torr to atm= 1.814474
What are unit Conversion ?Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.
Additionally, choosing the right number of significant digits and rounding may be necessary during the process.
The multi-step process of unit conversion involves multiplying or dividing by a numerical factor.
Weight, distance, and temperature can all be measured in a variety of ways.
Temperature is expressed in degrees Celsius, weight is expressed in kilos, and distance is measured in kilometers.
Imagine you are on vacation in India and are informed that the two cities are 100 kilometers apart.
Hence, Conversion of pressure of 1379 torr to atm= 1.814474
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3/20 plus 3/5=[tex]3/20 plus3/5[/tex]
what is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?
The probability that 3 hearts are chosen if 7 cards are selected from a well-shuffled deck of 52 playing cards is [tex]\\& =0.175823334\end{aligned}[/tex]
A probability simple definition is what?The probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging between 0% to 100% can be used to describe probabilities.
A probability may it be negative?Although a quasiprobability distributed enables a negative probability, called quasiprobability, for some events, the probability of the result of an experiment is never negative. These distributions may be applicable to conditional probability or unobservable occurrences.
The number of choosing cards out of 52 is = ⁵²C₃
Number of ways of choosing 3 cards of heart out of 13 cards and 4 out of remaining 39 cards = ¹³C₅ × ³⁹C₃
Probability of choosing 5 hearts = ¹³C₃ × ³⁹C₄ / ⁵²C₃
[tex]\begin{aligned}\frac{13 \times 2 \times 11 \times 13 \times 19 \times 3 \times 9}{26 \times 17 \times 10 \times 7 \times 2 \times 47 \times 46} & =\frac{23523786}{133784560} \\& =0.175823334\end{aligned}[/tex]
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Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = - 16t^2 + 2120, where s is the distance from the ground in feet and t is the time in seconds. Approximately how long would it take the object to reach the ground? Round your answer to the nearest tenth.
it would take the object approximately 11.51 seconds to reach the ground.
What is time?Generally, Time is a concept used to describe the progression of events, or the duration of those events. It is often measured in units such as seconds, minutes, hours, days, and years.
Time can also be described as a continuum, with past events on one end and future events on the other.
Time is a fundamental aspect of the universe and is closely related to concepts such as causation, change, and entropy.
The time it would take the object to reach the ground can be found by setting the distance from the ground, s, to 0 and solving for t.
0 = -16t^2 + 2120
t^2 = (2120/16)
t = [tex]\sqrt{(2120/16)}[/tex]
t = approximately 11.51 seconds
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a standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. the deck is randomly arranged. what is the probability that the top card is red and the second card is black?
The probability of the top card being red and the second card being black is P(A and B) = 0.0650.
The probability that the top card is red and the second card is black can be calculated using the formula P(A and B) = P(A) x P(B)
Let A be the event of the top card being red and B be the event of the second card being black.
The probability of the top card being red is P(A) = (26/52), since there are 26 red cards in the deck.
The probability of the second card being black is P(B) = (26/51), since there are 26 black cards left in the deck after taking away the red card from the top.
Therefore, the probability of the top card being red and the second card being black is P(A and B) = (26/52) x (26/51) = (169/2612) = 0.0650.
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What is the volume of the composite solid? Use 3.14 for pie and round your answer to the nearest cm3. cylinder height is 2.5 radius : 3 inches, cone is height of 3 inches and radius of inches.
(A) 471 cm3
(B) 733 cm3
(c) 707 cm3
(D) 1099 cm3
The volume of the composite solid 28.26 cm³
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The volume is the space occupied for a solid figure.
For the composite:
Volume of composite = volume of cylinder + volume of cone
For cylinder:
height is 2.5, radius : 3 inches
Volume of cylinder = π * radius² * height = π * (3)² * 2.5 = 70.65 cm³
For cone:
height is 3, radius : 3 inches
Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (3)² * 3 = 28.26 cm³
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a fruit stand has to decide what to charge for their produce. they need \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. they also need \$7.30$7.30dollar sign, 7, point, 30 for 111 apple and 222 oranges. we put this information into a system of linear equations. can we find a unique price for an apple and an orange? choose 1 answer: choose 1 answer: (choice a) a yes; they should charge \$3.30$3.30dollar sign, 3, point, 30 for an apple and \$2.00$2.00dollar sign, 2, point, 00 for an orange. (choice b) b yes; they should charge \$2.00$2.00dollar sign, 2, point, 00 for an apple and \$3.30$3.30dollar sign, 3, point, 30 for an orange. (choice c) c no; the system has many solutions. (choice d) d no; the system has no solution.
The Price of an Orange is $2 and the price of an Apple is $3.3.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
Let us assume that,
Apple price = A $
Orange price = B $
$5.30 for 1 apple and 1 orange
=> A + B = 5.30 Equation 1
$7.30 for 1 apple and 2 oranges.
=> A + 2B = 7.30 Equation 2
Equation 2 - Equation 1
=> B = 2
Thus, the Price of an Orange = $2
A + 2 = 5.30
=> A= $3.30
Price of Apple = $3.3
Therefore, The Price of an Orange is $2 and the price of an Apple is $3.3
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in how many ways can $8$ different people be seated around a round table with $8$ places? two sections are considered equivalent if one can be rotated to form the other.
As per the permutation, there are 5040 number of different ways are available for seating.
The term permutation in math is known as a mathematical calculation of the number of ways a particular set can be arranged
Here we know that there are 8! ways that you can arrange 8 people.
Now here we have to imagine a specific arrangement.
Here we have consider that everyone get up and move one seat to their right.
Then in that arrangement was counted separately from the first one in the 8!
Here have to know that it’s really the same since if each person looks to their left and their right and here they’re sitting next to the same person. Then here there are 8 such “identical rotations” for each possible seating arrangement so the total number of seating's is calculated as,
=> 8! / 8
=> 7! = 5040.
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Write the function of the graph in f(x)=a∙b^x form.
The exponential function graphed is given as follows:
y = 2^x.
How to model an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the parameters are given as follows:
a is the initial value.b is the rate of change.When x increases by one, the output is multiplied by 2, hence the parameter b is given as follows:
b = 2.
The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:
a = 1.
Hence the function is defined as follows:
y = 2^x.
Missing InformationThe graph is given by the image presented at the end of the answer.
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a statistical survey shows that only 2% of secretaries know how to use the highly sophisticated word processor language tex. if a certain mathematics department prefers to hire a secretary who knows tex, what is the least number of applicants that should be interviewed so as to have at least a 50% chance of finding one such secretary? math stack
To have a 50% chance of probability finding a secretary who knows Tex, at least 50 out of 100 applicants should be interviewed.
In order to determine the least number of applicants that should be interviewed to have a 50% chance of finding one secretary who knows the word processor language Tex, we can use the binomial probability formula. This formula states that the probability of finding at least one success out of a certain number of trials is given by P(X ≥ 1) = 1 – P(X = 0). Assuming that there are 100 applicants, the probability of finding at least one secretary who knows Tex is given by 1 – (98/100)^50, which is approximately 0.5. Therefore, at least 50 out of 100 applicants should be interviewed to have a 50% chance of finding a secretary who knows the language Tex.
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lost luggage a department of transportation report about air travel found that airlines misplace about 5 bags per 1000 passengers. suppose you are traveling with a group of people who have checked 22 pieces of luggage on your flight. can you consider the fate of these bags to be bernoulli trials? explain.
The fate of the 22 checked bags can be considered the Bernoulli trials.
A Bernoulli trial is a random experiment with two possible outcomes, often referred to as a "success" or "failure." In the context of the lost luggage problem, success would be a checked bag that is not misplaced, and failure would be a checked bag that is misplaced.
For a set of trials to be considered Bernoulli trials, the following conditions must be met:
The trials must be independent, meaning that the outcome of one trial does not affect the outcome of another trial.The probability of success (a bag not being misplaced) must be constant across all trials.The trials must have only two possible outcomes: success or failure.In this case, the fate of the 22 checked bags can be considered Bernoulli trials if the following conditions are met:
The bags are checked in separately, so the outcome of one bag does not affect the outcome of another bag, therefore they are independent trials.The probability of a bag being misplaced is given as 5 bags per 1000 passengers, which is constant across all passengers, including the group of 22 passengers.The trials have two possible outcomes: a bag is misplaced or a bag is not misplaced.Therefore, the fate of the 22 checked bags can be considered Bernoulli trials.
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please help! I will give you 15 brainy point
Answer:
V = 17 m3
Step-by-step explanation:
The area of the base (triangular) is multiplied by the height, resulting in the volume
[tex]V=\frac{(2)(1)}{2} (17)=(\frac{2}{2})(17)=(1)(17)=17[/tex]
Hope this helps
What is the best approximation of the solution to the system to the nearest integer values?
A. (1, 3)
B. (3, 4)
C. (2, 3)
D. (3, 2)
The best estimate of the system solution to the nearest integer values is (2,3).
What is coordinate points?The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis. A point's Cartesian coordinates (also known as rectangular coordinates) are a pair of integers (in two dimensions) or a triplet of numbers (in three dimensions) indicating signed distances from the coordinate axis. A point's coordinates are a pair of integers that define its precise location on a two-dimensional plane. Remember that the coordinate plane contains two axes that are perpendicular to each other, known as the x and y axes.
Here,
This question is asking us what the coordinates are for the point of intersection. Since the point is not directly on the grid lines, we must approximate.
The point is closest to the value "2" on the x axis.
The point is closest to the value "3" on the y axis.
This means the correct point is (2,3).
The best approximation of the solution to the system to the nearest integer values is (2,3).
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Halona walks 1.93 kilometers to a neighbor's house in 23 minutes. assuming she walks at a constant speed,write a proportion that represents how many kilometers pls hurry :)
The proportion that represents kilometers Halona walks is 193 kilometers in 2300 minute, that is 193/ 2300.
1 kilometer / x minutes = 1.93 kilometers / 23 minutes
Let x be the kilometers Halona walks in 1 minute. If she walks at a constant speed, as speed is rate of distance covered in unit time
x kilometer / 1 minute = 1.93 kilometers / 23 minutes
So the proportion is:
x kilometer / 1 minutes = 1.93 kilometers / 23 minutes
x kilometer / 1 minutes = 193/ 2300
This proportion represents how many kilometers Halona walks per minute. To find her speed in kilometers per hour, we can multiply the proportion by 60 minutes/hour.
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(WILL GIVE BRAINIEST) A collage artist makes art out of real-life objects. She has three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. If she makes a triangle out of the pieces will it be right, acute or obtuse triangle?
If the artist makes a triangle from three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. The triangle will not be a right triangle because the values are not Pythagorean triple
What is Pythagorean triple?Pythagorean triples are b² + a² = c² where b, a and c are all positive integers.
These triples are represented as (b, a, c).
Here, b is perpendicular (or right angel) to a, a is the base and the hypotenuse of the right - angled triangle is labeled .
The most known and smallest triplets are (3, 4, 5).
In the problem, the values 4 inches, 5 inches and 7 inches cannot make a Pythagorean triple since
c² = 4² + 5²
c² = 16 + 25
c² = 41
c = √41 ≠ 7
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Find the z-score for the value 66, when the mean is 51 and the standard deviation is 1.
The z score for the value 66, when the mean is 51 and the standard deviation is 1 is 15.
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Z score shows by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that:
mean = 51, standard deviation = 1. For a value of 66:
z = (66 - 51) / 1 = 15
The z score is 15.
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you have some quarters and pennies worth $3.75 and 39 coins altogether. how many of each coin do you have?
There are 14 quarters and 25 number of pennies
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that some quarters and pennies worth $3.75
0.25x+0.01y=3.75
There are 39 coins altogether
x+y=39
x=39-y
Now plug in x value in 0.25x+0.01y=3.75
0.25(39-y)+0.01y=3.75
9.75-0.25y+0.01y=3.75
9.75-0.24y=3.75
9.75-3.75=0.24y
6=0.24y
Divide both sides by 0.24
25=y
x+y=39
x=14
Hence, there are 14 quarters and 25 number of pennies
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A room is 20 m long and 14 m broad. It has one door measuring 1 m by 1.7 m and one window measuring 1.8 m by 1.8 m . The cost of painting the walls of the room at the rate of $ 15 per m 2 is $ 12165.9 . Find the height of the room.
Answer:
13.75 m.
Step-by-step explanation:
We can start by calculating the total area of the walls of the room by subtracting the area of the door and window from the total area of the room.
The total area of the room is 20m * 14m = 280 m^2
The area of the door is 1m * 1.7m = 1.7 m^2
The area of the window is 1.8m * 1.8m = 3.24 m^2
The total area of the walls is 280m^2 - 1.7m^2 - 3.24m^2 = 275.06 m^2
Now that we have the total area of the walls, we can divide it by the cost of painting per m^2 to find the height of the room.
The cost of painting per m^2 is $12165.9 / 275.06 m^2 = $44.32/m^2
So we can find the height of the room by dividing the cost by the rate of painting, $12165.9 / $44.32/m^2 = 275.06 m^2 / (20m * h) = 275.06 / 20 = 13.75m
Therefore, the height of the room is approximately 13.75 m.
PLS HELP IMMEDIATELY!!
Answer:
56 adult tickets were sold that day
Step-by-step explanation:
let a represent number of adult tickets sold and c number of child tickets sold , then
a + c = 122 → (1)
9.1a + 5.7c = 885.8 → (2)
from (1) subtract c from both sides
c = 122 - a
substitute c = 122 - a into (2)
9.1a + 5.7(122 - a) = 885.8
9.1a + 695.4 - 5.7a = 885.8
3.4a + 695.4 = 885.8 ( subtract 695.4 from both sides )
3.4a = 190.4 ( divide both sides by 3.4 )
a = 56
that is 56 adult tickets were sold that day.
Given the data set red, red, blonde, blonde, blonde, blonde, brown, black which of the mean, median or mode would you use to describe the typical or central value in this date set? Why?
A. None of these as this data set is quantitative.
B. The median as there are outliers at the high end of the data set causing the mean to be skewed high.
C.The mode as this data set is qualitative and the mean and median require quantitative data.
D. The mean as this data set has no outliers causing the mean to be skewed.
c. The mode is the best measure to describe the typical or central value in this data set.
The data set consists of qualitative values, which means they are not in numerical form and cannot be used to calculate the mean or median. The mode is the best measure to describe the typical or central value because it identifies the value that occurs most often in the data set.
In this case, the value that occurs most often is ‘blonde’, which would be the mode. The mean and median cannot be used because they require quantitative data, such as numerical values, to be calculated.
Additionally, the data set does not have outliers, which would cause the mean to be skewed. By using the mode, we can accurately describe the typical or central value of this data set.
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I just need to know the which one is the answer out of (1-4) questions. Please help??
Answer:
1/ 14^4
Step-by-step explanation:
Rules of Exponents
We know that a^-b = 1/a^b
14^-4 = 1/ 14^4
Answer:
[tex]{14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]
Step-by-step explanation:
To find the answer for this, you have to follow the negative rule of exponents.
That is,
1) If the number with a negative power is in it's numerator, the number with a negative exponent should be put to the denominator and make the power positive.
2) If the number with a negative power is in it's denominator, the number with a negative exponent should be put to the numerator and make the power positive.
Here, we have follow the rule 1.
Ex:
[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]
Accordingly, let us find the answer for the question.
[tex] {14}^{ - 4} = \frac{1}{ {14}^{4} } [/tex]
A car costs £12000 when bought. It's value depreciates by 10% of the previous years value for 1 year and then at 7.2% for the next 10 years. How much will the car be worth in 5 years time?
Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.
here,
rate = 10%
Time = 1 year
Principle = 12000
=>SI = PRT/100
=> SI = 10*1*12000/100
=> SI = 1200
and
=> After 1 year = 12000 -1200 = 10800
and
for five years
=> SI = PRT/100
=> SI = 10800 * 7.2 * 4 / 100
=> SI = 3110.4
After 5 year = 10800 - 3110.4 = 7,689.6
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Five numbers have a median of 8, a mode of 4, a mean of 9 and a range of 11.
Find the five numbers.
Let x1, x2, x3,x4,x5 be 5 nos in increasing order.
Median of 5 nos =[(5-1)/2 +1 ] th value =
3rd value = 8
x3 = 8 ........(0)
Range = Max - Min = x5 - x1
x5 - x1 = 11
x5 = 11 + x1. .......(1)
Mean = sum of values/ no. of values
(x1+x2+x3+x4+x5)/5 = 9
x1+ x2 +8 +x4+ 11+x1 = 45 _____(using (1) and (0))
2*x1 + x2 + x4 = 45-8-11
2*x1+ x2 + x4 = 22-------------(2)
Now mode = value that occurs most number of times
Mode = 4. -------(3)
Using (3) in (2) we get
2*x1 + 4 + 4 = 22
2*x1 = 14
x1 = 7
From (1)
x5 = x1+ 11 = 7+11= 18
So
x1 = 7, x2 = 4, x3 = 8, x4 = 4, x5 = 18
