a) The probability of a defect is 0.0668.
b. The process standard deviation can be reduced to 0.0062.
c. The advantage of reducing process variation is more efficient and reliable production process, as it reduces the need for inspection and rework.
Probability is the measure of the likelihood of an event occurring. It is used in various fields such as finance, engineering, and manufacturing to analyze and predict outcomes.
One company that utilizes probability in its production process is Motorola. In this scenario, Motorola uses the normal distribution, also known as the Gaussian distribution, to determine the probability of defects in their production process.
The normal distribution is a probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. The mean represents the center of the distribution, while the standard deviation represents the spread of the distribution.
a. To determine the probability of a defect, we need to find the area under the normal distribution curve to the left or right of ounces. This area represents the probability of a defect occurring. We can use a standard normal distribution table or a calculator to find this area. The probability of a defect to four decimal places is approximately 0.0668.
If the production run is for 100 items, then the expected number of defects would be 0.0668 x 100 = 6.68. Since we cannot have fractional defects, we would round this number to the nearest whole number, which is 7.
b. If the process standard deviation is reduced to, then the probability of a defect will decrease. This is because a smaller standard deviation means the distribution is less spread out, and therefore, fewer items will fall outside the control limits.
To find the new probability of a defect, we would follow the same process as in part a. The probability of a defect to four decimal places is approximately 0.0062.
c. The advantage of reducing process variation is that it results in a larger distance between the mean and the control limits. This means that there is less chance of items falling outside the control limits, which in turn, reduces the probability of defects. This leads to a more efficient and reliable production process, as it reduces the need for inspection and rework. Additionally, it can lead to cost savings and improved customer satisfaction.
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Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
Of the positive integers less than 2021, how many can be written
as a difference of two powers of 2?
Answer:
61
Step-by-step explanation:
You want the number of positive integers less than 2021 that can be written as the difference of two powers of 2.
Powers of 22^12 = 4096 and higher powers cannot produce integers less than 2021 when other powers of 2 are subtracted. Hence we're looking for pairs of powers that are 2^11 and smaller.
2^11 = 2048, which is 27 more than 2021. This means a number in range can be generated only by subtracting a power of 2 from 2^11 that is 2^5 = 32 or greater.
CombinationsThere are 66 pairs (combinations) of numbers in the range 0 to 11. Except for the 5 pairs (11, 0), (11, 1), (11, 2), (11, 3), (11, 4), they all represent pairs of powers of 2 that will have a unique difference less than 2021.
There are 61 positive integers less than 2021 that can be written as the difference of powers of 2.
Given: ABCD is a parallelogram and AD is perpendicular to BD
Prove: AB congurent to BC
Answer:
...here is the answer...
The bank would exchange 1.6 Canadian dollars for one US dollar. How many Canadian dollars would the bank exchange for $160 US dollars?
The number of Canadian dollars the bank exchange for $160 US dollars is 100.
What is money?Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.
A current medium of exchange in the form of coins and banknotes.
Given that, the bank would exchange 1.6 Canadian dollars for one US dollar.
Here, there are $160 US dollars.
So, number of Canadian dollars
= 160/1.6
= 100
Therefore, the number of Canadian dollars the bank exchange for $160 US dollars is 100.
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How to Solve this question ??
The coordinates of the fourth vertex of the parallelogram are (1, -3).
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Three vertices are located at these coordinates: (-1, 2), (1, 2), and (-1,-3).
we have three points in the coordinate plane, we can use the concept of vector addition to find the fourth point.
The vectors connecting the first and second points, and the first and third points can be determined as follows:
v₁ = (1,2) - (-1,2) = (2,0)
v₂ = (-1,-3) - (-1,2) = (0,-5)
The fourth point will be located at the vector sum of the first point and the vector formed by adding v₁ and v₂.
v₃ = v₁ + v₂ = (2,0) + (0,-5) = (2,-5)
So, the fourth point will be located at:
(-1,2) + (2,-5) = (1,-3)
Thus, the coordinates are (1, -3).
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help me solve this question and show the steps how to do it
The equivalent expression to 14^6 is given as follows:
[(14^5)^3]/14^9.
How to obtain the equivalent expression?When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.
The power of power exponential rule states that when a single base is elevated to multiple powers, the powers are multiplied.
Then the expression with the desired value of 14^6 is obtained as follows:
(14^5)^3 = 14^(5 x 3) = 14^15.14^15/14^9 = 14(15 - 9) = 14^6.More can be learned about simplification of expressions at https://brainly.com/question/30142908
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The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool
Answer:
Step-by-step explanation:
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The actual distance between the basketball court and the pool is 37.5 feet
Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.
The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.
We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:
3 inches / 5 feet = 22.5 inches / x
We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:
3 inches x x = 5 feet x 22.5 inches
3x = 112.5
x = 37.5 feet
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Complete Question:
The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?
how to solve the first order linear differential equation
The solution to the given differential equation is y = e⁽ˣ³⁾⁽²⁸ˣ ⁺ ᶜ⁾, where C is a constant.
To solve the first-order linear differential equation of the form y' + p(x)y = q(x), where p(x) and q(x) are functions of x:
Find the integrating factor (IF) = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾
Multiply both sides of the equation by the IF.
Apply the product rule to the left side and simplify the right side.
Integrate both sides with respect to x.
Solve for y.
Using this method, for the given equation:
y' - 3x²y = 28e⁽ˣ³⁾
Find the integrating factor (IF):
IF = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾ = e⁽⁻³/¹ * ∫ˣ²ᵈˣ⁾ = e⁽⁻ˣ³⁾
Multiply both sides by the IF:
e⁽⁻ˣ³⁾y' - 3x²e⁽⁻ˣ³⁾y = 28
Apply the product rule to the left side and simplify the right side:
d/dx (e⁽⁻ˣ³⁾y) = 28
Integrate both sides with respect to x:
e⁽⁻ˣ³⁾)y = 28x + C, where C is the constant of integration.
Solve for y:
y = e⁽ˣ³⁾(28x + C)
Therefore, the solution to the given differential equation is y = e⁽ˣ³⁾(28x + C), where C is a constant.
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Complete question:
How to solve the first order linear differential equation
Y'- 3x²y=28eˣ³
With the given budget, what’s the farthest distance a truck can travel from the warehouse to the retail outlet?
Russell surveyed 16 students at his school and found that 4 of them planned to take orchestra as their next elective. If Russell surveys 12 more students, how many of them are probably planning on taking orchestra as an elective, based on past data?
Answer:
3 students are probably planning on taking orchestra as their next elective.
Step-by-step explanation:
Russell's results of the 16 surveyed students tells us that (4/16), or 25%, of the students planned on taking orchestra as their next elective. If we assume this sampling is valid for other students (i.e., the sampled students were chosen at random and are believed to be representative of the rest of the students), we may use the same percentage for the next 12 students:
(12 students)*(25%) = 3 students are probably planning on taking orchestra as an elective.
A scuba diver dives 36 feet and
stops to look at a school of fish.
Then he dives down another 26 feet
How deep is the scuba diver now?
Answer:
62 Feet
Step-by-step explanation:
26+36=62
6 + 6 = 12
20 + 30 = 50
12 + 50 = 62
Answer:
The scuba diver is 62 feet deep.
Step-by-step explanation:
We know the scuba diver has dived 36 feet. When he stops to look at the school of fish, he doesn't dive down any further and stays at 36 feet. He then dives down another 26 feet
All we would need to do is add 36 and 26, which would give you your answer of 62.
Which scatter plot most likely has a line of best fit represented by y = 3x + 1?
The graph showing the line of best fit for the function y = 3x + 1 is attached below
What is line of best fitThe line of best fit is a line that is used to represent the relationship between two variables in a scatterplot. It is a line that passes through the center of the data points in the scatterplot in such a way that the total distance between the line and the data points is minimized. The line of best fit can be used to make predictions about the value of one variable based on the value of another variable. There are several methods to obtain the line of best fit, including the method of least squares, which finds the line that minimizes the sum of the squares of the differences between the observed values and the values predicted by the line.
In the problem given, the line of best fit the line of best fit can be plotted on a graph using a graphing calculator.
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in forecasting, there is more than one use for linear regression. what are they? check all that apply.
Casual relationship forecasting and Time series forecasting uses linear regression in forecasting.
Linear regression is a statistical tool used in forecasting to model the relationship between a dependent variable and one or more independent variables. Some of the common uses of linear regression in forecasting are:
Predictive modeling: Linear regression can be used to build a predictive model that estimates the value of the dependent variable based on the values of the independent variables..Trend analysis: Linear regression can be used to analyze the trend of the dependent variable over time.Forecast accuracy evaluation: Linear regression can be used to evaluate the accuracy of a forecasting model by comparing the predicted values to the actual values of the dependent variable. Causal analysis: Linear regression can be used to identify the causal relationship between the independent variables and the dependent variable. .Therefore, linear regression is a versatile tool in forecasting, with many useful applications for predicting future values, analyzing trends, evaluating accuracy, and identifying causal relationships.
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The complete question is :
In forecasting, there is more than one use for linear regression. What are the? Check all that apply.
1. Causal relationship forecasting
2. Time series forecasting
Find the volume of the composite solid. Round your answer to the nearest tenth. The volume is about cubic centimeters
The volume of the composite solid with cube and hemisphere is equal to 646.0 cubic centimeters ( nearest tenth ).
In the attached figure:
Composite figure consists of two figures:
Cube and hemisphere
Side length of the cube = 8cm
Diameter of the hemisphere = 8cm
Radius of the hemisphere 'r' = 8cm / 2
= 4cm
Volume of the cube = ( side length )³
⇒ Volume of the cube = (8)³
⇒ Volume of the cube = 512 cubic centimeters
Volume of the hemisphere = ( 2/3 )πr³
⇒ Volume of the hemisphere = ( 2/3 ) × 3.14 × ( 4 )³
⇒ Volume of the hemisphere = 133.97 cubic centimeters
Volume of the composite figure
= Volume of the cube + volume of the hemisphere
= 512 + 133.97
= 645.97 cubic centimeters
= 646.0cubic centimeters
Therefore, the volume of the composite solid is equal to 646.0cubic centimeters ( nearest tenth ).
The above question is incomplete, the complete question is:
Find the volume of the composite solid. Round your answer to the nearest tenth. The volume is about cubic centimeters.
Figure is attached.
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Each marble bag sold by Chau's Marble Company contains 2 red marbles for every 3 blue marbles. If a bag has 18blue marbles, how many red marbles does it contain?
Answer:
12 red marbles.
Step-by-step explanation:
No step by step explanation.
1. Which equation has a quotient of 1 1/5?
A 5÷6=
B 6÷5=
C 4÷5=
D 5÷4=
Answer:
none of them do
Step-by-step explanation:
5/6=0.83
6/5=1.2
4/5=0.8
5/4=1.25
11/5=2.2
850 Miles on 25 Gallons. How many miles per gallon?
Answer:
34 miles per gallon
Step-by-step explanation:
850/25 = 34
A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 62. 7 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.
The density and mass are related to each other with the formula -
Density = mass/volume
So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.
Volume of hemisphere = 2/3πr³, where r represents radius.
Volume = 2/3×π×5³
Performing multiplication, division and taking cube
Volume = 261.8 feet³
Now, mass = density × volume
Mass = 62.7 × 261.8
Performing multiplication
Mass = 16,414.86 pounds
Rounding off
Mass = 16,415 pounds
Thus, the mass of liquid will be 16,415 pounds.
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Aldo debe escoger una camisa y un par de pantalones para su atuendo de hoy. Puede escoger entre 2 camisas y 3 pares
de pantalones. ¿Cuántos diferentes atuendos puede crear?
The number of different outfits that Aldo can create from the shirts and the pairs of pants are 6 outfits.
How to find the number of outfits ?In this case, Aldo has 2 options for his shirt and 3 options for his pants. To find the total number of outfits, we can multiply these numbers together:
= Number of shirts x Number of pairs of pants
= 2 x 3
= 6 outfits
Therefore, Aldo can create 6 different outfits by choosing a shirt and a pair of pants from the available options.
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12 pack can of soda is 8. 25 what is the price per can
The price per can of a 12 pack of soda is 8.25. the price per can of a 12 pack of soda is 0.6875.
To calculate this, we can use the following formula: Price per Can = Total Price of 12 Pack / 12 Price per Can = 8.25 / 12 Price per Can = 0.6875 Therefore, the price per can of a 12 pack of soda is 0.6875. To better understand the price per can of a 12 pack of soda, it is important to understand the concept of unit pricing. Unit pricing is the cost of a single item compared to a larger quantity. When shopping, it is beneficial to look at the unit pricing of items to ensure that you are getting the best deal. For example, if a 12 pack of soda is 8.25 and a 6 pack of soda is 4.00, then the unit price of the 12 pack is lower, which means it is a better deal. By understanding unit pricing, you can make the most cost-efficient decisions when shopping.
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y=x^2 6 units to the left 2 units up
The translation of the graph is represented by y = -6(x+2)² - 7.
What is translation ?A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
Given that the graph of y= x² translated left 2 units and up 8 units. The translated equation is:-
Start with y = x².
Shift 2 units left to get y = (x+2)².
Vertically stretch to get y = 6(x+2)².
Reflect across x-axis to get y = -6(x+2)².
Shift 7 units down to get y = -6(x+2)² - 7.
Hence, the translation of the graph is represented by y = -6(x+2)² - 7.
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The question is incomplete so solved for,
Suppose the graph of y= x^2 translated left 2 units, and up 8 units
Can someone help me please with this question
Answer:
x=-2log10(12)
Step-by-step explanation:
12x10^x/2=1/12
x/2=-log10(12)
x=-2log10(12)
Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister that she has to pay back before she can start saving.
This relationship can be shown by a linear function. Below is a table showing how many hours Yvette has worked (input), and how much money she's saved (output).
Hours Worked (x) Amount Saved (y)
0 -$25
4 $14
8 $53
12 $92
16 $131
Which of the following statements are true regarding the graph of this linear function? Select all that apply.
Group of answer choices-
The slope of the line, 25, is the amount of money she makes per hour of work.
The slope of the line, 9.75, is the amount of money she starts with having worked 0 hours.
The y-intercept of the line, 0, is the amount of money she starts with, since she's worked 0 hours.
The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
The slope of the lines, 9.75, is the amount of money she makes per hour of work.
The slope of the line is 9.75 and the y-intercept is -25.
What is a linear function?Two distinct but related concepts are referred tο by the phrase "linear function": A polynomial function of degree zero οr one that has a straight line as its graph is referred tο as a linear function in calculus and related fields.
Given: Yvette is saving mοney to buy holiday gifts. She will save the money she makes at her part-time job. Hοwever, she borrowed $25 from her sister which she has to pay back befοre she can start saving.
Let the linear functiοn that models the given situation be y = ax + b. Here, a and b are constants. We can use this infοrmation to find the values of a and b.
We put x = 0 & y = -25 into y = ax + b
b = -25
Substitute the value of b intο y = ax + b
y = ax -25...(1)
Nοw we put x = 4 and y = 14 in equatiοn(1) and we get
14 = 4a - 25
4a = 39
a = 9.75
Substitute the value of a in equatiοn (1):
y = 9.75x - 25
Cοmpare the above function with the slοpe-intercept form of a line y = mx + c
m = 9.75, c = -25
Hence, the slοpe οf the line is 9.75 and the y-intercept is -25.
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The temperature at noon was $-4\degree$ C. By midnight, the temperature dropped $8\degree$ C. Which expression represents the temperature at midnight?
The temperature at midnight would be -4°C - 8°C since the temperature at noon was -4°C and at midnight it dropped 8°C.
The temperature at midnight would be -4°C minus 8°C, which can be expressed as:
-4°C - 8°C = -12°C
Therefore, the temperature at midnight would be -12°C.
Temperature is a measure of the degree of hotness or coldness of a body or an environment. It is a physical quantity that expresses the amount of thermal energy in a substance or a system, typically measured using a thermometer in units such as Celsius (°C) or Fahrenheit (°F). In general, the higher the temperature, the more thermal energy is present in the system, and the lower the temperature, the less thermal energy is present.
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Solve the compound inequality and graph its solution:8r-3 ≥7r - 7 or 2r + 4≤ r-3
Answer:
Step-by-step explanation:
o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.
For the first inequality: 8r - 3 ≥ 7r - 7
Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r
Combining like terms: 15r - 3 ≥ 14r
Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0
Combining like terms: r - 3 ≥ 0
Adding 3 to both sides: r ≥ 3
For the second inequality: 2r + 4 ≤ r - 3
Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r
Combining like terms: 4 ≤ -r - 3
Adding r and 3 to both sides: 4 + r + 3 ≤ -r
Combining like terms: 7 ≤ -r
Multiplying both sides by -1: r ≤ -7
The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.
To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7:
Divide ₹1750 into 2 parts such that if one part be lent out at 15% per annum for 2 years and the other part at 16% per annum for 3 years, the total interest is 624.
The amount of lent out at 15% and 16% will be ₹1,200 and ₹550, respectively.
What is simple interest?Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,
The formula for interest is written as,
I = (PRT)/100
Divide ₹1750 into 2 parts such that if one part is lent out at 15% per annum for 2 years and the other part at 16% per annum for 3 years, the total interest is 624.
Let 'x' be the amount of lent out at 15%. Then the amount of lent out at 16% is (₹1750 - x). Then the equation is given as,
(x · 0.15 · 2) + [(1750 - x) · 0.16 · 3] = 624
Simplify the equation, then we have
(x · 0.15 · 2) + [(1750 - x) · 0.16 · 3] = 624
0.30x + 840 - 0.48x = 624
0.18x = 216
x = ₹1,200
Then the value of (₹1750 - x) is given as,
₹1750 - x = (₹1750 - ₹1,200)
₹1750 - x = ₹550
The amount of lent out at 15% and 16% will be ₹1,200 and ₹550, respectively.
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Latanya plans to repaint some classroom bookcases. She has 5 3/5 gallons of paint. All of the bookcases are the same size and each requires 1/2 gallon of paint. What is the maximum number of complete bookcases she can paint?
With her 5 3/5 gallons of paint, Latanya can paint up to 11 full bookcases.
What does the equation's solution consist of?Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is a solution to the problem. Solving an equation is locating its solution or solutions.
Let's first translate 5 3/5 gallons of paint into an incorrect fraction:
5 3/5 = (5 x 5 + 3)/5 = 28/5
Next, we can find the number of bookcases she can paint by dividing the total amount of paint by the amount needed for each bookcase:
28/5 ÷ 1/2
= 28/5 x 2/1
= 56/5
=11 1/5.
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8x = 3y +3
- 24x +9y=3
parallel perpendicular or neither
The two lines have the same slope and different y-intercepts, thus, the lines are parallel.
What is the relation between the two linear equations?Here we want to find the relation between the two lines:
8x = 3y + 3
-24x + 9y = 3
First, we need to write these two as lines in the slope-intercept form. We will get:
3y = 8x - 3
y = (8/3)*x - 3/3
y = (8/3)*x - 1
And the other one:
9y = 3 + 24x
y = (3/9) + (24/9)*x
y = (1/3) + (8/3)*x
So, we can see that both lines have the same slope (and different y-intercept), thus, the lines are parallel lines.
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If Pakistani rupee (y) is a function of UAE dirham (x), write a function for y in terms of x. Draw the conversion graph between these two currencies by taking UAE dirham along x-axis.
The function for the Pakistani Rupee (y) in terms of UAE Dirhams (x) can be represented as, y = 71.59 x.
What are Function?A function is defined as a relation from a set A to a set B for which an element in set A maps to one and only one image in set B.
Usually the set A consists of the independent variable and set B consists of dependent variable.
We have to find a function relating the conversion of Pakistani rupees and UAE dirhams.
Let y denotes Pakistani Rupees and x denotes the UAE dirhams.
We know that,
1 UAE dirham = 71.59 Pakistani Rupees
So,
2 dirhams = 2 × 71.59 = 143.18 rupees
In this way,
x dirhams = 71.59 x rupees
So, we can write this as,
y = 71.59 x
Hence the required function is y = 71.59 x.
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each of two persons tosses three gair coincs. what is the probability that they obtain the same numbre of heads
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
1/8
The probability of getting a head or a tail when flipping a coin is 1/2.
Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.
The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.
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