Answers
Answer:
BANK A
I=5700.825
T.P=25190.83
BANK B
I=3274.32
P=22764.32
Related Questions
Write 8/5 as a mixed number.
Answers
Answer:1 3/5
Step-by-step explanation:
All you have to do is we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.
Answer:1 3/5
Step-by-step explanation: 8/5-5/5= 3/5 so that leaves you with 1 3/5
A train travels 1 kilometre in 1 minute 20 seconds At this rate, how many kilometres will the train travel in 1 hour?
Answers
The train will travel for approximately 50 kilometres in 1 hours.
How to find the time in hours the train covers?The train travels 1 kilometre in 1 minute 20 seconds.
At this rate the number of kilometres the train will travel in 1 hour can be calculated as follows;
Therefore, lets convert 1 minutes and 20 second to hours.
20 seconds = 0.333333 minutes
Hence,
60 minutes = 1 hour
1.33333 minutes = ?
cross multiply
time in hours = 1.3333 / 60
time in hours = 0.02222221666
Therefore,
0.02 hours = 1 km
1 hours = ?
number of kilometres the train will travel in 1 hours = 1 / 0.02 = 50 km
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The perimeter of a rectangle is 72 inches. Its length is 6 inches greater than twice its width. Write and solve a system of equations that represents this situation.
f(x) =
g(x)=
solution:
Answers
Answer:
Step-by-step explanation:
first up, the perimeter is 4 side added up. so we do 72/4= which equals 18. we need to apply the 6 to the sides so we do 6/2=3 18/3=15 f=15 18+3= 21 one side is 15 & the other side is 21 to double check, 21+15*2= 72
True or false
a consumer has a budget of 90 monetary units and (s)he is considering buying two products: flowers (x) and chocolate (y). the price of x is 3 and the price of y is 5. if the price of x, px, increases to 5 the vertical intercept remains the same, while the slope will be flattened (smaller). true
false
question 2
0. 25 points
if px increases to 5 both the vertical intercept and the slope remains the same. true
false
question 3
0. 25 points
if py increases to 6 the vertical intercept change and the slope will be flattened (smaller). true
false
question 4
0. 25 points
if py increases to 6 the vertical intercept will be the same and the slope will be steeper
Answers
Answer:
false
Step-by-step explanation:
question 4
0. 25 points
if py increases to 6 the vertical intercept will be the same and the slope will be steeper
Please help need it in the next 5 mins
Answers
Answer:
y = 4x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
here m = 4 , then
y = 4x + c ← is the partial equation
to find c substitute (2, 9 ) into the partial equation
9 = 8 + c ⇒ c = 9 - 8 = 1
y = 4x + 1 ← equation of line
If 1200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Answers
If 1200 square centimeters of material is available to make a box with a square base and an open top,
The largest possible volume of the box is V = 4000cm^3.
We have 1200 cm^2 worth of material. This represents the surface area of a box with a square base and an open top.
the dimensions of the box.
Square base implies the length and width are the same.
Let x = length/width.
The box has a height as well.
Let h = height
the surface area ; S.
S = (area of base) + (area of 4 walls)
The area of the base is x^2
The area of one of the walls is length times height, or xh. Since there are 4 of them, it would be 4 times xh, or 4xh.
S = x^2 + 4xh
And we know that S = 1200cm^2, so
x^2 + 4xh = 1200
Let's solve for h.
4xh = 1200 - x^2
h = (1200 - x^2) / (4x)
we require the volume formula.
V = (length) x (width) x (height)
And we know all of these.
V = (x)(x)(h)
V = (x^2) h
putting h = (1200 - x^2) / (4x) in the formula
V = (x^2) ( 1200 - x^2)/(4x)
We get a cancellation,
V = x(1200 - x^2)/4
V = (1/4)x (1200 - x^2)
This will be our volume function, V(x).
V(x) = (1/4)(x)(1200 - x^2)
To maximize V(x), we must first take the derivative and then make it 0. Using the product rule (and ignoring the constant 1/4), we have
V'(x) = (1/4) [ (1200 - x^2) + (x)(-2x) ]
Simplify,
V'(x) = (1/4) [ 1200 - x^2 - 2x^2 ]
V'(x) = (1/4) [ 1200 - 3x^2 ]
V'(x) = (1/4) [ 3(400 - x^2) ]
V'(x) = (3/4) [ 400 - x^2 ]
To maximize, make V'(x) = 0, and solve for x.
0 = (3/4) [ 400 - x^2 ]
0 = 400 - x^2
x^2 = 400
x = +/- 20
Therefore,
x = { 20, -20 }
However, since x represents a dimension, it can never be negative, and we must discard the negative solution. That means
x = 20.
This tells us that the maximum volume occurs when x = 20. However, the question is asking WHAT the largest volume of the box is. Solving this is as simple as plugging x = 20 into our volume function, V(x).
V(x) = (1/4)(x)(1200 - x^2)
Therefore,
V(20) = (1/4) (20) (1200 - 20^2)
V(20) = (1/4) (20) (1200 - 400)
V(20) = (1/4) (20) (800)
V(20) = (20/4)(800)
V(20) = 5(800)
V = 4000cm^3
Hence the answer is, the largest possible volume of the box is V = 4000cm^3.
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if a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is . a. .20 b. 0 c. .03125 d. .50
Answers
The probability of getting all heads when flipping a coin four times is 1/16.
(HHHH), (HHHT), (HHTH), (HHTT), (HTHH), (HTHT), (HTTH), (HTTT), (THHH), (THHT), (THTH), (THTT), (TTHH), (TTHT), (TTTH), (TTTT) are some examples of spaces.
There were 16 total outcomes.
Probability going out of control
HHHH P(A) = P(getting all heads) = 1/16
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Answer fast please!! will give brainiest
Answers
Answer:
8
Step-by-step explanation:
you divide so you can get the average
Answer:
in average she makes 8 friend in a week.
Step-by-step explanation:
You divide 80 by 9 that is 8 remaining 1, so yeah.
There were 500 lions in an African nature
reserve. 3 years later there were 864 lions in
the same nature reserve.
a) Work out the percentage increase per year,
assuming that the number of lions increased
by the same percentage each year.
b) Use your answer to part a) to predict the
number of lions in the nature reserve after
another year.
Round your answer to the nearest integer.
Answers
The percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.
Given that, there were 500 lions in an African nature reserve. 3 years later there were 864 lions in the same nature reserve.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the percentage increase per year be x.
a) According to the question,
500(1+x)³=864
⇒ (1+x)³=864/500
⇒ (1+x)³=1.728
⇒ 1+x= 1.2
⇒ x =0.2
In percentage 20%
b) [tex]500(1+0.2)^1[/tex]
= $600
Hence, the percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.
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define the semantics (inference rule) of the if statement: {p} if (e) s1 else s2 {q}. hint: one way to prove it is to do a case analysis. if e is true, the whole statement is equivalent to what? if e is false, the whole statement is what? formulate it as an inference rule.
Answers
The inference rule is ({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q}).
In the given question, we have to define the semantics (inference rule) of the if statement: {P} if (E) S1 else S2 {Q}.
A way of inferring the veracity of one assertion based on the significance of other assertions is known as an inference rule.
(S1, S2, ........, Sn)/S
According to the rule, if S1, S2,..., and Sn are real, then S's validity can be derived.
Given,
{P} if (E) S1 else S2 {Q}
The inference rule is
We know that if if E and P are true then it is S1 with postcondition {Q} or if E and P is false then it is else part that is S2 with postcondition {Q}
i.e. {E and P} S1 {Q},{not E and P} S2 {Q}
So the inference rule is:
({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q})
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This item has two parts: Part A and Part B. Use the information to complete Part A and Part B.
Two populations of bacteria increased at exponential rates. The table shows the bacteria population size for sample A, A(x), after x weeks.
x 0 1 2 3 4
A(x) 100 300 900 2,700 8,100
The graph shows the bacteria population size for sample B, B(x) = 500(2)x, after x weeks.
Part A
Which bacteria sample had a smaller initial population? What was that value?
Sample A; 100 bacteria
Sample A; 300 bacteria
Sample B; 2 bacteria
Sample B; 500 bacteria
Part B
Compare the population of each sample on the 5th week. Which sample was larger and by how much?
Sample A; 24,300
Sample A; 8,300
Sample B; 40,300
Sample B; 16,000
Answers
A. The bacteria sample that had a smaller initial population is;
Sample A; 100 bacteria.
B. The sample that was larger in the 5th week was;
Sample A; by 8,300.
How to solve Exponential functions?
An exponential function is defined by the general expression;
y = abˣ
where;
a is initial value.
b is rate of change.
For Sample A, the values of the above parameters are given as;
a = 100
b = 3
Thus, the exponential function is:
f(x) = 100(3)ˣ
In the 5th week, the population will be calculated as;
f(5) = 100 * 3⁵
f(5) = 24300.
For Sample B, the exponential function is expressed as:
g(x) = 500(2)ˣ
In the 5th week, the population will be;
g(5) = 500 * 2⁵
g(5) = 16000.
The difference of the larger population in Sample A and the smaller population in Sample B is;
24300 - 16000 = 8300.
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In the diagram below of triangle ABC,
D is the midpoint of AC and E is the
midpoint of BC. If DE = 34 - 6x,
and AB = 28 - 4x, what is the measure
of DE?
A
Answer:
DE =
Submit Answer
D
C
E
B
Answers
Using midpoint theorem the value of DE is 4.
What is midpoint theorem?
According to the midpoint theorem, "The line segment of a triangle linking the midpoint of its two sides is said to be parallel to its third side and is also half the length of the third side."
Here using midpoint theorem we know that ,
=> DE = 1/2 AB
Here DE=34-6x and AB=28-4x.
=> 34-6x=1/2(28-4x)
=>68-12x=28-4x
=> 12x-4x=68-28
=> 8x = 40
=> x =5.
Now put x=5 into DE then,
=> DE=34-6(5)=34-30 = 4.
Therefore using midpoint theorem value of DE is 4.
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A 0. 2 kg red ball is thrown horizontally at a speed of 4 m/s from a height of 3 m. A 0. 4 kg green ball is thrown horizontally from the same height at a speed of 8 m/s. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is.
Answers
The ratio of time that the red ball reaches the ground when compared with the green ball is 2:1
By using the equations of motion we first find the acceleration and time of both the balls using [tex]v^{2} -u^{2} =2as[/tex] and [tex]v=u+at[/tex]
where,
v=final velocity,
u=intial velocity,
a=acceleration,
s=height,
t=time
For the red ball,[tex]v^{2} -u^{2} =2as[/tex], v=4m/s, u=0m/s, s=3m by substitiuting in the equation we get ,
[tex]4^{2} -0^{2} =2*a*3[/tex],
acceleration=a=16/6=8/3,
[tex]v=u+at[/tex] by substituting we get,
4=0+8/3*t,
time taken by the red ball to reach ground t=3/2
For the green ball,[tex]v^{2} -u^{2} =2as[/tex], v=8m/s, u=0m/s, s=3m by substituting in the equation we get ,
[tex]8^{2} -0^{2} =2*a*3[/tex],
acceleration=a=64/6=32/3,
[tex]v=u+at[/tex] by substituting we get,
8=0+32/3*t,
time is taken by the green ball to reach ground t=3/4
and their ratio of time red ball/green ball=(3/2)/(3/4)=2/1,
hence time to reach the ground is independent of their mass
therefore, the ratio of time that the red ball reaches the ground when compared with the green ball is 2:1
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Rite Aid sells 8 ounces of shampoo for $0.89 and Walgreens sells 12 ounces for $1.47 which is the better buy?
Answers
8 ounces for $1.47. It comes out to $0.07 per ounce compared to $0.12 per ounce.
Answer:Rite aid
Step-by-step explanation:
8 ounces for $1.47. It comes out to $0.07 per ounce compared to $0.12 per ounce.
the side lengths of the state flag of Michigan are in the ratio 4:7. if the flag is 28 feet long, what is its height?
Answers
If the side lengths of the state flag of Michigan are in the ratio 4:7. when the flag is 28 feet long the height will be 49 feet
How to calculate the height of the flagThe height of the flag is calculated using the scale factors, 4 : 7
if 4 is equivalent to 28 what would 7 be
4 / 7 = 28 / ?
4 * ? = 7 * 28
? = 7 * 28 / 4
? = 49 feet
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Find the product in simplest form.
1. 13 × 11 (1 point)
019¹
011
4
081
4
0152/12
4
Answers
Answer:
19 1/4
Step-by-step explanation:
1 3/4 × 11 = 7/4 × 11/1 = 77/4 = 19 1/4
You have $20 and you make $5 an hour at your job. Your brother has $10 and makes $10 an hour at his job. Write and solve an equation to find out how many hours it will take for you and your brother to have the same amount of money.
Answers
Answer:
Let h = number of hours.
[tex]20 + 5h = 10 + 10h[/tex]
[tex]4 + h = 2 + 2h[/tex]
[tex]4 = 2 + h[/tex]
[tex]h = 2[/tex]
In 2 hours, we will have the same amount of money.
Help right now please!
Andrew believes that the probability that he will win the tennis match is 39% What
is the probability that he will lose the match?
Answers
Answer:
39%
Step-by-step explanation:
Given m \| nm∥n, find the value of x.
Answers
The value of x is 6.67 degrees.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
The (5x + 9)° angle on line m and the (7x - 9)° angle on line n are corresponding angles.
We have given that Line m and Line n are parallel.
t line is the transversal line on the two parallel lines, line m and line n.
We see that,
(5x + 9)° angle on line m is corresponding to the (7x - 9)° angle on line n.
So,
(5x + 9)° + (7x - 9)° = 180
12x = 180
x = 80 /12
x = 6.67
Thus, The value of x is 6.67 degrees.
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Makayla spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 5750 feet. Makayla initially measures an angle of elevation of 16^{\circ} ∘ to the plane at point AA. At some later time, she measures an angle of elevation of 31^{\circ} ∘ to the plane at point BB. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
Answers
The distance the plane traveled from point A to point B is 10952 feet approx.
To solve this we have to use the Pythagoras theorem.
Given that the plane is at a constant height which can be supposed as the perpendicular (i.e 5750 feet) for the triangle which the plane , ground and the makayla make.
Now when the plane is at the A point then the angle of the elevation is 16°, so the distance from the makayla the plane is :
tanθ = P/B,
B(distance of makayla to plane on ground at point A) = P/tanθ ,
B = 5750 / tan 16°,
B = 5750/ 0.28;
B1 = 20535 feet approx
Similarly when the plane reach at the point B then the angle of the elevation is 31° then the distance from the makayla and the plane would be different, which will be :
tanθ = P/B,
B(distance of makayla to plane on ground at point B) = P/tanθ ,
B = 5750 / tan 31°
B = 5750 / 0.6
B2 = 9583 feet approx
now the distance traveled by the plane is B1 - B2 :
which is 20535 - 9583
10952 feet approx
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Answer:10483
Step-by-step explanation:
5 A pole 5 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Zoe measures the distance from
the pole to the stake and from the pole to the tower, as shown in the diagram below.
Find the length of the guy wire, to the nearest foot.
Answers
The length of the guys wire to the nearest foot is 56 feet.
How to find the length of the guy wire?The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.
The situations forms a right angle triangle.
Therefore, the length of the guy wire can be found as follows:
Using trigonometric ratios, we can find the angle the guy wire made with the ground.
tan ∅ = opposite / adjacent
tan ∅ = 5 / 1
∅ = tan ⁻¹ 5
∅ = 78.690067526
∅ = 78.69°
Therefore, let's find the length of the guy wire using the angle.
cos 78.69° = adjacent / hypotenuse
0.1961172908 = 11 / h
h = 11 / 0.1961172908
h = 56.088884361
Therefore,
length of the guy wire = 56 feet
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the initial pressures for bicycle tires when first filled are normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. a random sample of 15 tires is drawn from this population. what is the probability that the mean tire pressure of the sample is less than 69 psi?
Answers
the probability that the mean tire pressure of the sample is less than 69 psi 0.2030
The formula of the z-score is z = (x - μ)/σ, where
x is the score
μ is the mean
σ is the standard deviation
given,
a mean of 70 pounds per square inch
μ = 70
the standard deviation of 1.2 psi.
σ = 1.2
the sample is less than 69
x=69
so on substituting
z=(69-70)/1.2
z=-1/1.2
z=-0.83
The value corresponding to the z score is 0.2030 i.e 20.30%
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URGENT
Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $55 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2575. How long did each mechanic work?
Answers
The first mechanic worked 20 hours and the second mechanic worked 5 hours
The work charge of first mechanic = $115 per hour
The work charge of second mechanic = $55 per hours
Total number of hours they worked = 25 hours
The total amount they charged = $2575
Consider the number of hours that first mechanic work as x and second mechanic as y
Then the equations will be
x + y = 25
x = 25 -y
The second equation
115x + 55y = 2575
Here we have to use substitution method here
115(25-y) + 55y = 2575
2875 - 115y +55y = 2575
2875 -60y = 2575
60y = 2875 - 2575
60y = 300
y = 300 / 60
y = 5 hours
Then x = 25 - y
= 25 -5
= 20 hours
Hence, the first mechanic worked 20 hours and the second mechanic worked 5 hours
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there are 280 counters in a bag
1/2 of the counters are red
2/5 of the counters are yellow
the rest are green
work out the number of green counters in the bag
Answers
Answer:
84 counters
Step-by-step explanation:
⅖ + ½ = 7/10
10 - 7 = 3
280 ÷ 10 × 3 = 84
Answer:
28
Step-by-step explanation:
1/2×280=140(red counters)
2/5×280=112(yellow counters)
140+112=252
280-252=28(green counters)
If 120% of a is equal to 80% of b, then what is a+b?
Answers
After simplifying the percentage, if 120% of a is equal to 80% of b, then a+b is 5.
In the given equation,
If 120% of a is equal to 80% of b, then we have to find the value of a+b.
We firstly express the statement in the algebraic equation.
It is given in the statement that 120% of a.
We write it as 120%×a.
From the statement, 80% of b.
We write its as 80%×b.
Both are equal to each other.
So the expression should be
120%×a=80%×b
Divide by 12% on both side
120%/120% ×a=80%/120% ×b
Simplifying
a=80%/120% ×b
As we know that % means 100 but both number 80 and 120 have % sign. So the % sign emitted.
So a=80/120 ×b
Divide by b on both side
a/b=80/120 ×b/b
a/b=80/120
Simplifying the ration
a/b=2/3
Hence, the value of a=2 and b=3.
Now finding the value of a+b.
a+b = 2+3
a+b = 5
Hence, if 120% of a is equal to 80% of b, then a+b is 5.
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What is the solution of the following system?
Use the substitution method.
{y+7=3x6x−2y=12
Responses
The only solution is (14, 12) .
The only solution is , begin ordered pair 14 comma 12 end ordered pair, .
The only solution is (12, 14) .
The only solution is , begin ordered pair 12 comma 14 end ordered pair, .
There is no solution.
There is no solution.
There are an infinite number of solutions.
Answers
The given system of equations has no solution.
What is substitution method?
In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this procedure before the variable's value is substituted in the second equation.
Consider, the given system of equations,
y + 7 = 3x ..(1)
6x - 2y = 12 ..(2)
From equation (1),
y = 3x - 7.
Substitute value of (y) in inequation (2),
6x - 2(3x - 7) = 12
6x - 6x - 14 = 12
-14 = 12
It is not possible to solve -14 = 12.
Therefore, the given system of equations has no solution.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
9.34 billions of pounds
Hope that helps ;)
Thando divided 1572 by a certain number,and got an answer of 104,remainder 12 what number did she divide 1572
Answers
The number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
The dividend = 1572,
The quotient = 104,
The reminder = 12
Calculate the divisor by the following formula,
Dividend = Divisor × quotient + Reminder
Substitute the values,
1572 = Divisor × 104 +12
Divisor = 15
Therefore, the number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.
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Evaluate the function. f(x)=-x^{2}+3x+11 Find f(−1)
Answers
The function f(x) = [tex]-x^2 + 3x +11[/tex] of the value is 7.
Given,
In the question:
The function is given as:
f(x) = [tex]-x^2 + 3x +11[/tex]
To find the f(-1)
Now, According to the question:
The function is :
f(x) = [tex]-x^2 + 3x +11[/tex]
To put the value of x = -1 in above function's equation:
f(x) = [tex]-x^2 + 3x +11[/tex]
f(-1) = [tex]- (-1)^2 + 3(-1) +11[/tex]
Solve the equation:
Determine the sign:
f(-1) = -1 -3 +11
Calculate the sum or difference:
f(-1) =7
Hence, The function f(x) = [tex]-x^2 + 3x +11[/tex] of the value is 7.
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an urn contains two red balls and three white balls. if a ball is chosen at random, what is the probability that it is white?
Answers
If an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white ball is 3/5
The number of red balls = 2 balls
The number of white balls = 3 balls
Total number of balls = 2 + 3
= 5 balls
The probability = Number of favorable outcomes / Total number of outcomes
Number of favorable outcomes = Number of white balls = 3
Total number of outcomes = 5
The probability = 3/5
Hence, if an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white is 3/5
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