The probabilities obtained from z-scores found from the specified mean and standard deviation (approximate values) are;
a. Normal distribution
X ~ N(16, 2.5)
b. 0.19089
c. 15.04 and 16.96
What is the z-score of a raw score from a dataset?The z-score is a measure of the number of standard deviation a data point or raw score is from the mean.
a. The distribution of X with a mean and standard deviation of 16 and 2.5 years is a normal distribution, therefore; X ~ N(16, 2.5)
b. The probability that an indoor cat dies when it is between 16.9 and 18.5 can be found as follows;
The z-scores for the two ages are;
z-score for 16.9 years z = (16.9 - 16)/2.5 = 0.36
z-score for 18.4 years z = (18.4 - 16)/2.5 = 0.96
The standard normal table can be used to find the area under the standard normal curve as follows;
P(z < 0.36) = 0.64058
P(z < 0.96) = 0.83147
Therefore; P(0.36 < z < 0.96) = 0.83147 - 0.64058 = 0.19089
The probability that the age at which an indoor cat dies is between 16.9 and 18.4 years is about 0.19089
c. The z-score that corresponds to the lower and upper bounds of the middle 30% of the standard normal distribution, can be found as follows;
The middle 30% is symmetrical about the mean, we get;
The lower bound is the z-score for which 35% of the distribution are located, and 35% are upper bound is the z-score for which 35% of the distribution are located to the right. Using an online calculator, we get;
The lower bound z-score = -0.385
The upper bound z-score = 0.385
The raw score values are therefore;
z = (x - μ)/σ
x = zσ + μ
The lower bound value for X = 16 + 2.5 × -0.385 = 15.0375 ≈ 15.04
The upper bound value for X = 16 + 2.5 × 0.385 = 16.9625 ≈ 16.96
The ages between which the middle 30% of indoor cats dies are therefore about 15.04 and 16.96 years
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A three-column table is given.
Part A C D
Part 14 28 63
Whole B 40 90
What is the value of B in the table?
a factory makes lightbulbs. the probability that a bulb is defective is 1/9. if 400 lightbulbs are tested, about how many are expected to be defective
Answer:
45.
Step-by-step explanation:
so every 1/9 lightbulbs are defective, so make that L/400, (L for amount of defective bulbs).
Take the total, 400, and divide it by 9, which equals 44.4444444444. Evaluate 44.4444444444/400 and you get 0.11111111111. Evaluate 1/9, and you get 0.11111111111. So they are equivalent. But you cant have 44.4444444444 lightbulbs defective, because you can't have a lightbulb 40% defective, it either works, or doesn't work. So, round your answer up, and you get 45 total defective lightbulbs if they make 400.
Evaluate, 7×2+(7+3×(5-2)÷4×2
Answer:
19m75
Step-by-step explanation:
Solution:
To evaluate the expression 7×2+(7+3×(5-2)÷4×2), we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Step 1: First, we need to simplify the expression inside the parentheses.
5-2 = 3
3÷4 = 0.75
3×0.75 = 2.25
7+2.25 = 9.25
Step 2: Next, we need to simplify the multiplication and division from left to right.
3×2 = 6
0.75×2 = 1.5
Step 3: Finally, we need to simplify the addition and subtraction from left to right.
7×2+9.25+6-1.5 = 19.75
Therefore, the value of the expression 7×2+(7+3×(5-2)÷4×2) is 19.75.
sarah was cutting fabric for a quilt. she cut 5 pieces that were 19 1/8 inches long. when she finished cutting she had a piece that was 2 1/4 inches long. how long was the piece she cut for the quilt.
The length of the fabric Sarah cut for the quilt is 97.875 inches.
To determine the length of the fabric Sarah cut for the quilt, we need to add up the lengths of the individual pieces she cut.
Number of pieces cut: 5
Length of each piece: 19 1/8 inches
Length of the remaining piece: 2 1/4 inches
To find the total length, we can multiply the length of each piece by the number of pieces and add the length of the remaining piece.
Length of each piece = 19 1/8 inches = 19 + 1/8 inches = 19.125 inches
Length of the remaining piece = 2 1/4 inches = 2 + 1/4 inches = 2.25 inches
Total length = (Length of each piece) [tex]\times[/tex] (Number of pieces) + Length of the remaining piece
Total length = 19.125 inches [tex]\times[/tex] 5 + 2.25 inches
Total length = 95.625 inches + 2.25 inches
Total length = 97.875 inches
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On a coordinate plane, a point is 4 units to the left and 1 unit down.
For the point shown:
The x-coordinate is
.
The y-coordinate is
.
The point is in quadrant
.
.
The point has an x-coordinate of -4 and a y-coorindate of -1, and it is on the third quadrant.
In which quadrant is the point?First, remember that for a point (x, y):
if x >0, y > 0, then the point is in quadrant I.if x <0, y > 0, then the point is in quadrant II.if x < 0, y < 0, then the point is in quadrant III.if x >0, y < 0, then the point is in quadrant IV.For the point that is 4 units to the lefft and 1 unit down (of the origin) it is written as:
(-4, -1)
Then we can see that this point is on the quadrant III.
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Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?
Answer: (x² - 5)(x - 7)
Step-by-step explanation:
Grouping the terms, we have:
(x^3 - 7x^2) + (-5x + 35)
Now, let's factor out the common factors from each pair:
x^2(x - 7) - 5(x - 7)
Notice that we have a common factor of (x - 7) in both terms. We can factor it out:
(x^2 - 5)(x - 7)
Therefore, the resulting expression after factoring by grouping is (x^2 - 5)(x - 7).
please help with the questions on the photo
a. The relative frequency of landing on the number 4 is 0.24
b. The relative frequency of landing on a prime number is 0.20
What is relative frequency?Relative frequency is the ratio of the frequency of a particular event in a statistical experiment to the total frequency.
This means to find the relative frequency of a particular outcome of an event, we divide the frequency of the event with the total frequency.
Here, the total frequency is
= 14+9+6+12+4+5
= 50
a. The frequency of 4 is 12
therefore the relative frequency of landing on 4 =
12/50 = 0.24
b. A prime number is a number that can only be divided by itself. Therefore 3 and 5 are the prime numbers in the outcome.
landing on 3 = 6/50 = 0.12
landing on 5 = 4/50 = 0.08
On a prime number = 0.12 + 0.08
= 0.20
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Use the scenario below to determine the correct values of n, p, q and x of the binomial distribution.
Suppose that in a certain video game there is a 1.9% item drop rate of frozen rain after defeating a Frigid Element.
What is the probability that 2 frozen rains will drop if 20 Frigid Elements are defeated?
n=
p=
q=
X =
The probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.
q = 1 - p
q = 1 - 0.019
q = 0.981
X: The number of successful outcomes.
In this scenario, we can model the situation using a binomial distribution. Let's determine the values of n, p, q, and X:
n: The number of trials or attempts.
In this case, the number of trials is the number of Frigid Elements defeated, which is given as 20.
n = 20
p: The probability of success on a single trial.
The probability of a frozen rain item dropping after defeating a Frigid Element is given as 1.9%, which can be expressed as 0.019.
p = 0.019
q: The probability of failure on a single trial.
The probability of failure is the complement of the probability of success. Therefore:
q = 1 - p
q = 1 - 0.019
q = 0.981
X: The number of successful outcomes.
We want to find the probability of 2 frozen rains dropping, so X is 2.
X = 2
Now that we have determined the values, we can calculate the probability using the binomial distribution formula. The formula for the probability mass function of the binomial distribution is:
P(X = x) = [tex](nCx) * (p^x) * (q^(n-x))[/tex]
where nCx represents the binomial coefficient, which is the number of ways to choose x successes out of n trials.
Using this formula, we can substitute the values into the equation:
P(X = 2) = [tex](20C2) * (0.019^2) * (0.981^(20-2))[/tex]
Calculating the binomial coefficient:
(20C2) = (20!)/(2!(20-2)!)
= (20 * 19 * 18!)/(2 * 18!)
= (20 * 19)/(2 * 1)
= 190
Now substituting the values:
P(X = 2) = [tex]190 * (0.019^2) * (0.981^18)[/tex]
Now we can calculate the probability:
P(X = 2) ≈ 0.2713 or 27.13% (rounded to two decimal places)
Therefore, the probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.
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Given the diagram below, find the value for x. Enter a number only.
Answer:
x=4
Step-by-step explanation:
angles on a straight line always add up to 180°
so...
25x+20+15x=180°
simplify the left side of the equation
40x+20=180°
take away 20
40x=160°
divide by 40
x=4
In sampling distributions the mean is consistently _____ the population mean
A. Lower than
B. Higher than
C. Identical to
D. Unrelated to
In sampling distributions, the mean is consistently identical to the population mean. (Option C)
This concept is a fundamental property of sampling distributions and is rooted in the principles of probability and statistical theory. A sampling distribution is a theoretical distribution that represents the possible values of a statistic (such as the mean or proportion) calculated from different samples drawn from the same population. The mean of a sampling distribution is an average of the sample means, and it provides an estimate of the population mean.
When random samples are drawn from a population, the mean of each sample will vary due to random sampling variability. However, as the sample size increases, the distribution of sample means tends to converge around the population mean. This phenomenon is known as the Central Limit Theorem.
According to the Central Limit Theorem, as sample sizes become large (typically n > 30), the sampling distribution of the mean becomes approximately normal, with a mean that is identical to the population mean. In other words, on average, the sample means will be equal to the population mean. This property holds true regardless of the shape, spread, or other characteristics of the population distribution.
Therefore, the correct answer is C. Identical to.
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what is one and half right angle
Answer: 135°
Step-by-step explanation:
1 and 1/2 right angle.
1 right angle is 90°
1/2 of a right angle = 45°
so 1 and 1/2= 90+45=135°
f(x)=x-1. Find the inverse of f(x).
Answer: D
Step-by-step explanation: X is being subtracted by 1 so it will now add 1 in the inverse
What terms do not apply to a rhombus
The terms that do not apply to a rhombus are:
Right angle: A rhombus does not have any right angles. Its angles are typically acute or obtuse, but never right angles.
Perpendicular sides: In a rhombus, the opposite sides are parallel to each other, but they are not perpendicular. Perpendicular sides are characteristic of rectangles and squares.
The terms that do not apply to a rhombus are:
Right angle: A rhombus does not have any right angles. Its angles are typically acute or obtuse, but never right angles.
Perpendicular sides: In a rhombus, the opposite sides are parallel to each other, but they are not perpendicular. Perpendicular sides are characteristic of rectangles and squares.
Congruent angles: While the opposite angles in a rhombus are equal to each other, the adjacent angles are not necessarily congruent. Congruent angles are a characteristic of rectangles and squares.
Right triangle: A rhombus does not contain any right angles, so it cannot be classified as a right triangle. A right triangle is a triangle that has one right angle.
Equilateral: A rhombus is not an equilateral polygon. An equilateral polygon has all sides of equal length, while a rhombus has all sides equal in length but does not require all angles to be equal.
It's important to note that a rhombus is a quadrilateral with opposite sides that are parallel and equal in length, but it does not possess the characteristics mentioned above.
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A 5-inch candle burns down in 10 hours. After how many hours will it have burned 3 1/4 inches?
[tex]\begin{array}{ccll} inches&hours\\ \cline{1-2} 5&10\\[1em] 3\frac{1}{4}&x \end{array}\implies \cfrac{5}{ ~~ 3\frac{1}{4} ~~ }=\cfrac{10}{x}\implies \cfrac{5}{~~ \frac{ 13 }{ 4 } ~~}=\cfrac{10}{x}\implies \cfrac{20}{13}=\cfrac{10}{x} \\\\\\ 20x=130\implies x=\cfrac{130}{20}\implies x=\cfrac{13}{2}\implies x=6\frac{1}{2}[/tex]
Two numbers are in the ratio 10: 16. When 4 is added to each, the ratio of resulting numbers is 4 to 6. Find the numbers
The two numbers are 20 and 32.
Let's assume the two numbers in the ratio 10:16 are 10x and 16x, where x is a common factor.
According to the given information, when 4 is added to each number, the ratio becomes 4:6. This means that the new numbers are (10x + 4) and (16x + 4).
To find the numbers, we can set up an equation based on the given ratios:
(10x + 4) / (16x + 4) = 4/6
To simplify the equation, we can cross-multiply:
6(10x + 4) = 4(16x + 4)
Expanding both sides:
60x + 24 = 64x + 16
Bringing like terms together:
60x - 64x = 16 - 24
-4x = -8
Dividing both sides by -4:
x = 2
Now that we have the value of x, we can substitute it back into the original ratios to find the numbers:
The first number = 10x = 10 * 2 = 20
The second number = 16x = 16 * 2 = 32
Therefore, the two numbers are 20 and 32.
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Answer:
Let the two numbers be 10x and 16x.
When 4 is added to each, the resulting numbers are (10x + 4) and (16x + 4).
According to the problem, the ratio of (10x + 4) to (16x + 4) is 4:6.
We can write this as:
(10x + 4)/(16x + 4) = 4/6
Cross-multiplying, we get:
6(10x + 4) = 4(16x + 4)
Simplifying the equation, we get:
60x + 24 = 64x + 16
48 = 4x
x = 12
Therefore, the two numbers are:
10x = 120
16x = 192
So the two numbers are 120 and 192.
Find the derivative of f(x) = 6x + 1 at x = 2
The derivative of f(x) = 6x + 1 at x = 2 is 6, obtained through the limit definition of the derivative.
To find the derivative of f(x) = 6x + 1 at x = 2, we can use the formula for the derivative of a function: f'(x) = lim(h → 0) [f(x + h) - f(x)]/h
We substitute x = 2 into the formula to get: f'(2) = lim(h → 0) [f(2 + h) - f(2)]/h
We plug in f(x) = 6x + 1: f'(2) = lim(h → 0) [(6(2 + h) + 1) - (6(2) + 1)]/h
Simplifying the expression:
f'(2) = lim(h → 0) [(12 + 6h + 1) - (12 + 1)]/h
= lim(h → 0) (6h)/h = lim(h → 0) 6
The limit of 6 as h approaches 0 is simply 6. Therefore, the derivative of f(x) = 6x + 1 at x = 2 is f'(2) = 6.
The derivative of f(x) = 6x + 1 at x = 2 is 6.
In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.
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Use the table, along with dimensional analysis to convert the given square unit indicated.
14cm^2 to in^2
To convert 14 cm² to in² using dimensional analysis, we can use the following conversion factors:
1 cm = 0.393701 in (exact conversion factor)
1 in = 2.54 cm (exact conversion factor)
We want to convert cm² to in², so we need to use the conversion factor that relates cm² to in². This is:
1 cm² = (0.393701 in)² = 0.15500031 in² (approximate conversion factor)
To set up the dimensional analysis, we start with the given quantity and multiply it by the appropriate conversion factors so that the units cancel out and we are left with the desired units. We can set it up as follows:
14 cm² * (0.15500031 in² / 1 cm²) = 2.17000434 in² (approximate answer)
Therefore, 14 cm² is approximately equal to 2.17000434 in².
You deposit $2000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 25 years?
Answer:
157908.83
Step-by-step explanation:
RD formula is :
[tex]P(1+\frac{r}{m} ) [(1+\frac{r}{m} )^{N} -1 }]{\frac{m}{r}[/tex]
where P: Principal / rd amount = $2000
r : interest = 8% = 0.08
m : no. of times compounded in a year = 1 (compounded annually)
N : time = 25 years
Amt =
[tex]2000(1+\frac{0.08}{1} ) [(1+\frac{0.08}{1} )^{25} -1 }]{\frac{1}{0.08}[/tex]
[tex]= 2000(1.08) [1.08^{25} -1 }]{\frac{1}{0.08}[/tex]
= 157908.83
Solve the formula Ax+ By= C for x.
Solve for x
Answer:
A) [tex]x=\frac{C-By}{A}[/tex]
Step-by-step explanation:
[tex]Ax+By=C\\Ax=C-By\\x=\frac{C-By}{A}[/tex]
need help please ion get it
Answer:
Step-by-step explanation:
d
In the quadrilateral below, angles DAB and BCD are the same size. What is the size of angle DAB? A D 226° 38° B
The size of angle DAB in the quadrilateral is 48°.
How to find the size of angle DAB?The sum of the interior angles of a quadrilateral is 360°. We can say:
[tex]\angle \text{A} +\angle\text{B} + \angle\text{C} + \angle\text{D} = 360^\circ[/tex]
[tex]\angle \text{A} +38^\circ + \angle\text{C} + 226^\circ = 360^\circ[/tex]
[tex]\angle \text{A} + \angle\text{C} + 264^\circ = 360^\circ[/tex]
[tex]\angle \text{A} + \angle\text{C} = 360^\circ- 264^\circ[/tex]
[tex]\angle \text{A} + \angle\text{C} = 96[/tex]
Since angles DAB and BCD are the same size. This implies ∠A = ∠C. Thus:
[tex]\angle\text{A} + \angle\text{A} = 96[/tex]
[tex]2\angle\text{A} = 96[/tex]
[tex]\angle\text{A} = \dfrac{96}{2}[/tex]
[tex]\angle\text{A} = 48^\circ[/tex]
Therefore, the size of angle DAB is 48°.
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A piece of buttered toast falls to the floor 26 times. The toast landed buttered side up 9 times. Which statement below is correct?
A. The experimental probability that the toast lands buttered side up is 17/26.
B. A simulation could be carried out using odd digits to represent the buttered side landing up and even digits representing the buttered side landing down.
C. The experimental probability that the toast lands buttered side down is 17/26.
D. The theoretical probability that the toast lands buttered side up is 9/26.
Answer:
D. The theoretical probability that the toast lands buttered side up is 9/26.
Forgive me if im wrong....
Step-by-step explanation:
State the expression for finding Tn the n th term in the sequence what is the Tn
The 8th term of the given Sequence is 26.
A sequence is a list of numbers arranged in a particular order. It can be finite or infinite. The nth term of a sequence is represented by Tn.
It can be found using the formula: Tn = a + (n-1)d, where a is the first term, d is the common difference and n is the number of terms being considered.
If we know any three of the terms, we can use the formula to find the fourth term. Let's consider an example to understand this concept better. Example: Find the 8th term of the sequence 5, 8, 11, 14,...Solution:
We can see that the first term of the sequence is 5. Also, the common difference between the terms is 3. Using the formula Tn = a + (n-1)d, we get:T8 = 5 + (8-1)3T8 = 5 + 21T8 = 26
Therefore, the 8th term of the given sequence is 26.
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What is different about multiplying and dividing two signed numbers?
Multiplying two signed numbers results in a product, and the sign of the product depends on the signs of the multiplied numbers.
Multiplying and dividing two signed numbers differ in terms of the rules and properties that apply to each operation. Here are the key differences:
1. Product vs. Quotient:
When multiplying two signed numbers, the result is called the product. It represents the total of repeated addition or combining equal groups. For example, multiplying -3 by -4 gives a product of 12.
When dividing two signed numbers, the result is called the quotient. It represents the ratio or partitioning of one quantity into equal parts. For example, dividing 12 by -4 gives a quotient of -3.
2. Signs of the Result:
In multiplication, the sign of the product depends on the signs of the multiplied numbers. If the signs are the same (both positive or both negative), the product is positive. If the signs are different (one positive and one negative), the product is negative. For example, (-3) * (-4) = 12, and (-3) * 4 = -12.
In division, the sign of the quotient depends on the signs of the dividend and divisor. If both numbers have the same sign, the quotient is positive. If the numbers have different signs, the quotient is negative. For example, 12 / (-4) = -3, and (-12) / (-4) = 3.
3. Properties:
Multiplication has properties like the commutative property (changing the order of the factors doesn't change the product) and the associative property (changing the grouping of factors doesn't change the product). For example, (-3) * (-4) = (-4) * (-3) = 12.
Division, on the other hand, has specific properties like the division property of zero (dividing any number by zero is undefined) and the division property of one (dividing a number by one leaves the number unchanged). For example, 12 / 1 = 12.
In summary, multiplying two signed numbers results in a product, and the sign of the product depends on the signs of the multiplied numbers. Dividing two signed numbers results in a quotient, and the sign of the quotient depends on the signs of the dividend and divisor. Additionally, multiplication has properties like commutativity and associativity, while division has properties specific to the division operation.
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Sara and Steve each bought a pair of pants and some socks .The pants that they purchased cost the exact same amount and the pair of socks are also the same amount.
Sara paid $60 for one pair of pants and two pairs of socks
Steve paid $75 for one pair of pants and three pairs of socks
What was the cost of 1 pair of pants?
Equations
1P+2S=60
1P+3S=75
Answer:
These are two linear equations with two unknowns, P (price of pants) and S (price of socks). You can solve them by using either substitution or elimination methods.
Let's use the elimination method.
First, let's subtract the second equation from the first:
1P + 2S - (1P + 3S) = 60 - 75
After simplifying this, we get:
-1S = -15
Dividing both sides by -1, we find:
S = 15
Now, we can substitute S = 15 into the first equation to find the price of pants (P):
1P + 2(15) = 60
1P + 30 = 60
Subtract 30 from both sides to get:
1P = 60 - 30
1P = 30
So, the price of one pair of pants (P) is $30.
A new city park will have a path from the southeast corner to the northwest corner. The shape of the park is rectangular. With the information given, determine how many yards long the path will be. The rectangles length is 50 yd and the width is 120 yd
The length of the path is 130 yards
How to determine the value
To determine the value of the path, c, we need to know the Pythagorean theorem
Using the Pythagorean theorem which states that the square of the longest leg of a triangle is equal to the sum of the squares of the other two sides of the triangle.
In this case, we have that;
c² = length² + width²
Substitute the values from the information given, we have that;
c² = 50²+ 120²
Find the squares, we get;
c² = 2500 + 14, 400
add the values, we get;
c² = 16900
c = 130 yards
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One month Jina rented 6 movies and 2 video games for a total of $30. The next month she rented 3 movies and 5 video games for a total of $36. Find the
rental cost for each movie and each video game.
Rental cost for each movie:
$11
Rental cost for each video game: $
X
Ś
Answer:
Rental cost for each movie = $3.25
Rental cost for each video game = $5.25
Step-by-step explanation:
We can find the rental cost for each movie and each video game using a system of equations where:
M represents the rental cost for each movie,and V represents the rental cost for each video game.First equation:
Since Jina rented 6 movies and 2 video games for a total of $30, our first equation is given by:
6M + 2V = 30
Second equation:
Since Jina also rented 3 movies and 5 video games for a total of $36, our second equation is given by:
3M + 5V = 36
Method to solve: Elimination:
We can solve this with eliminate. First, we need to multiply the second equation by -2. Then, we must add the two equations to eliminate the Ms and solve for V:
Multiplying the entire second equation by -2:
-2(3M + 5V = 36)
-6M - 10V = -72
Adding the two equations:
6M + 2V = 30
+
-6M - 10V = -72
(6M - 6M) + (2V - 10V) = (30 - 72)
-8V = -42
Solving for V:
(-8V = -42) / -8
V = 5.25
Thus, the rental cost for each video game is $5.25.
Solving for M:
We can now find M by plugging in 5.25 for V in any of the two equations in our system.
Let's use the first equation:
Plugging in 5.25 for V in 6M + 2V = 30 to solve for M:
6M + 2(5.25) = 30
(6M + 10.50 = 30) - 10.50
(6M = 19.50) / 6
M = 3.25
Thus, the rental cost for each movie is $3.25.
Find the value of x.
Answer:
x=7
Step-by-step explanation:
Assuming the angles to be congruent, then 7 and x are both congruent sides, which makes the figure an isosceles triangle. Therefore, x=7 as well.
A bag contains 7 red, 12 white and 4 green balls. Three balls are drawn randomly. What probability that (a) 3 balls are all white (b) 3 balls are one of each color (c) 3 balls are same color
a). Probability (3 balls are all white) = 220/1771 = 0.124
b). Probability of drawing one ball of each color = 336/1771 = 0.19
c). Probability of drawing 3 balls of the same color = 259/1771 = 0.146
Therefore:(a) Probability of drawing 3 white balls:
Total number of balls = 7 red + 12 white + 4 green = 23 balls
Number of favorable outcomes = selecting 3 white balls = 12C3 = (12!)/(3!(12-3)!) = 220
Total number of possible outcomes = selecting 3 balls from 23 = 23C3 = (23!)/(3!(23-3)!) = 1771
So, Probability of drawing 3 white balls = Number of favorable outcomes / Total number of possible outcomes
P(3 white balls) = 220/1771 = 0.124
b). Probability of drawing one ball of each color:
Number of favorable outcomes = selecting 1 ball of each color = 7C1 × 12C1 × 4C1 = 7 × 12 × 4 = 336
Total number of possible outcomes (as calculated above) = 1771
Probability of drawing one ball of each color = Number of favorable outcomes / Total number of possible outcomes
P(1 ball of each color) = 336/1771 ≈ 0.19
C. Total number of favorable outcomes = 35 + 220 + 4 = 259
Total number of possible outcomes (as calculated above) = 1771
Probability of drawing 3 balls of the same color = Number of favorable outcomes / Total number of possible outcomes
P(3 balls of the same color) = 259/1771 = 0.146
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Tenjing bought two television at rs 52000 he is sold one of them at 10% profit and another at 10% loss if the selling price of both the television are same find its total gain or loss percentage in the transaction
the transaction results in a net gain.Net gain percentage = Net gain / Total cost price × 100%=(2SP - 52000) / 52000 × 100%Now, we can use the above expressions to calculate the total gain or loss percentage in the transaction.
Let's assume that the cost price of the first television set is CP1 and that of the second is CP2. As per the given information, the total cost price of both television sets is 52000 rupees.
Therefore, CP1 + CP2 = 52000Assuming the selling price of both television sets is the same, let's assume it to be SP for convenience. Selling price is defined as the price at which a product is sold to the customer. Therefore, the selling price of both television sets will be SP.
Now, we have to calculate the net gain or loss percentage in the transaction.Gain or loss is calculated as the difference between the selling price and cost price.
Gain or loss on the first television set is 10% of CP1, and the gain or loss on the second television set is 10% of CP2. Therefore,Gain or loss on the first television = 10/100 × CP1 = 0.1CP1Loss or gain on the second television = 10/100 × CP2 = 0.1CP2The selling price of both television sets is the same.
Therefore,Selling price of the first television = SPSelling price of the second television = SPThe selling price of both television sets combined is:Selling price of both television sets = SP + SP = 2SPNow, let's calculate the net gain or loss percentage in the transaction.
Net gain or loss = Selling price - Cost price= (SP + SP) - (CP1 + CP2)= 2SP - 52000Now, we need to determine whether the transaction resulted in a gain or a loss. We know that the gain or loss on the first television is 0.1CP1, and the gain or loss on the second television is 0.1CP2.
Let's consider two
cases:Case 1: When CP1 < CP2 (the cost price of the first television is less than that of the second television)In this case, the gain on the first television is less than the loss on the second television, as 0.1CP1 < 0.1CP2. Therefore, the transaction results in a net loss.
Net loss percentage = Net loss / Total cost price × 100%=(2SP - 52000) / 52000 × 100%
Case 2: When CP1 > CP2 (the cost price of the first television is greater than that of the second television)In this case, the gain on the first television is greater than the loss on the second television, as 0.1CP1 > 0.1CP2.
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