The required number of elements in set A and set B as per given elements of A, B , and A ∪ B is equal to |A ∩ B| = 3.
Number of elements in set A, |A| = 97
Number of elements in set B, |B| = 16
Total number of elements in set A or set B, |A ∪ B| = 110
Use the formula for the size of the union of two sets,
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A| represents the number of elements in set A,
|B| represents the number of elements in set B,
And |A ∩ B| represents the number of elements in the intersection of sets A and B.
Rearrange the formula to solve for |A ∩ B|,
|A ∩ B| = |A| + |B| - |A ∪ B|
⇒|A ∩ B| = 97 + 16 - 110
⇒|A ∩ B| = 3
Therefore, the number of elements in sets A and B have 3 elements in common.
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helpppp
need the answer asap
The key features of the graph are (a) x-int = 5 and y-int= 5, HA; y = 0.5 and VA: x = 0.5 and hole = (-2, 7/5)
Identifying the key features of the graphThe x-intercept of a graph is the point at which the graph intersects the x-axis while the y-intercept of a graph is the point at which the graph intersects the y-axis.
From the given graph, we have the intercepts to be
x-intercept = 5 and y-intercept = 5
The horizontal asymptote of a graph is a horizontal line that the graph approaches as x approaches positive or negative infinity
While the vertical asymptote is a vertical line that the graph approaches as x approaches a certain value.
From the given graph, we have the asymptote to be
Horizontal; y = 0.5 and Vertical: x = 0.5
A hole in a graph refers to a point on the graph where the function is undefined but can be made continuous by removing the point and filling the gap with a single point.
From the given graph, we have the hole to be
Hole = (-2, 7/5)
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What exponential function can be used to determine the number of transistors in a car that doubles every TWO years? The number starts at 4100. For this function to work, we should be able to find the amount of transistors in a car after 5 years (or any odd number of years)
Answer:
[tex]f(t) = 4100( {2}^{ \frac{t}{2} }) [/tex]
Find the measure of DE 2x+7 4(x-3)
The measure of DE is 8x. This was found by using the distance formula to calculate the length of the side.
What is measurements ?Measurements are the process of comparing an unknown quantity to a known reference value in order to estimate the size, quantity, distance, weight, or other characteristics of that unknown quantity. Measurements are used in science and engineering to quantify the properties of objects, or to compare objects to each other. Measurements are also used in everyday life to help make decisions and assess the impact of changes.
To find the measure of DE, we must first calculate the length of the side. We can do this by using the distance formula. The distance formula is used to calculate the length of a line between two points in a plane. The formula is given as d = √(x2 - x1)2 + (y2 - y1)2.
For the side DE, we can use the coordinates (2x+7, 4(x-3)). The first point is (2x+7, 4(x-3)) and the second point is (2x+7, 4(x+3)). We can substitute these points into the distance formula to calculate the length of DE.
The formula becomes d = √[(2x+7 - 2x+7)2 + (4(x+3) - 4(x-3))2]
Simplifying, we get d = √[(0)2 + (8x)2]
d = √[64x2]
d = 8x
Therefore, the measure of DE is 8x.
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a nurse annual gross salary is $29460 he contributes 2% of his salary to a medical scheme.His contribution to the medical scheme is a non taxable allowance
(a) The total amount of the nurse's annual salary that is not taxed is $6644. (b) His annual taxable salary is $22,226.8. (c) The tax he pays annually is $5856.7.
(a) To find the total amount of the nurse's annual salary that is not taxed, we need to add up all of the non-taxable allowances:
$37 x 12 (months) = $444 for national insurance
$3000 for personal allowance
$1800 for his wife
$1400 for his children
Total non-taxable allowances = $444 + $3000 + $1800 + $1400 = $6644
Therefore, the nurse's total non-taxable salary is $6644.
(b) To find the nurse's annual taxable salary, we need to subtract his non-taxable allowances from his gross salary:
Annual taxable salary = $29,460 - 2% x $29,460 - $6644
Annual taxable salary = $29,460 - $589.2 - $6644
Annual taxable salary = $22,226.8
Therefore, the nurse's annual taxable salary is $22,226.8.
(c) To calculate the nurse's annual tax, we need to apply the income tax rates:
Tax on first $4000 at 20% = $800
Tax on remainder at 25% = 0.25 x ($22,226.8 - $4000) = $5056.7
Total annual tax = $800 + $5056.7 = $5856.7
Therefore, the nurse pays an annual tax of $5856.7.
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Complete question is attached below
approximately what percentage of americans consume alcoholic beverages regularly? group of answer choices 50 percent 25 percent 10 percent 75 percent
There are 75 percent of Americans consume alcoholic beverages regularly. so, the correct answer is D).
According to a 2021 survey conducted by the National Institute on Alcohol Abuse and Alcoholism, approximately 75% of adults in the United States reported that they had consumed alcohol in the past year.
However, it's important to note that this does not necessarily mean that they consume alcohol regularly. The percentage of Americans who consume alcoholic beverages regularly may vary depending on how "regularly" is defined and the specific population being studied.
So, the correct option is D).
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Here is an equation that is true for all values of x: 5(x + 2) = 5x + 10. Jenny
saw this equation and says she can tell 20(x + 2) + 31 = 4(5x + 10) + 31 is
also true for any value of x. How can she tell? Explain your reasoning.
Answer:
20(x + 2) = 20x + 40 = 4(5x + 10)
please help me out
x-2/x+3≤0
Answer:
Step-by-step explanation:
What is the area of the regular polygon?
(Round to one decimal place as needed)
PLS PLS PLS HELP THIS IS DUE TODAY (geometry btw)
The area of the polygon is 6. 9m²
How to determine the area of the polygonFrom the information given, we have that the regular polygon takes the shape of a triangle.
The formula for calculating the area of a triangle is expressed with the equation;
A = 1/2bh
Such that the parameters in the formula are;
A is the area of the triangle.b is the base of the triangle.h is the height of the triangle.Area of a equilateral triangle is;
= √3/4a²
Then,
= √3/4 (4)²
= √3 × 4
= 6. 9m²
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Triangle FDE is a rotation.
For given triangles, Condition 3 and 6 are true.
What is a triangle's definition?
A triangle is a closed two-dimensional shape with three straight sides, three angles, and three vertices (or corners). It is formed by connecting three non-collinear points in a plane with straight lines. The sum of the interior angles of a triangle is always 180 degrees, and each exterior angle is equal to the sum of its two adjacent interior angles. Triangles can be classified based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.
Now,
As we can see that ΔABC is rotated 90° clockwise to make
ΔDEF.
So, the angles follows these conditions
∠F=∠A
∠E=∠C
∠D=∠B
hence,
Condition 3 and 6 are true.
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PLEASE HELP ME
Let f(x) and g(x) be polynomials as shown below.
f(x)= a0 + a1x + a2x^2 ... + anx^n
g(x)= b0 + b1x + b2x^2 ... + bmx^m
Which of the following is true about f(x) and g(x)?
The answer is A. f(x) and g(x) are closed under addition because when added, the result will be a polynomial.
What is addition?Addition is denoted using the plus sign (+) or a plus symbol. Addition can be used to find the total in a group of numbers, to combine two or more numbers, or to compare two numbers.
When two polynomials f(x) and g(x) are added, the result is also a polynomial. The degree of the resultant polynomial is equal to the highest degree of the two added polynomials.
Thus, when a polynomial is added to another polynomial, the result will always be a polynomial.
This is true because when two polynomials are added, the resulting polynomial will have the same form as the two polynomials that were added.
In other words, the sum of two polynomials will have the same coefficients and powers of x as the two polynomials that were added.
Therefore, f(x) and g(x) are closed under addition because when added, the result will always be a polynomial.
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what is the slope of these pionts ( 7,-2) (1,-6)
Answer:
m = 2/3
Step-by-step explanation:
Given two points on a line, we can find the slope, m, of a linear equation using the slope formula:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point and x2 and y2 are the other point.
The order of the points don't matter as long you pair the points already together (e.g., if you choose 7 as x1, you have to choose -2 as y2, and if you choose 1 as x1, you have to choose -6 as y2).
Thus, if we allow the first point to be x1 and y2 and the second point to be x2 and y2, our slope is:
[tex]m=\frac{-6-(=2)}{1-7}\\ \\m=\frac{-6+2}{-6}\\ \\m=\frac{-4}{-6}\\ \\m=\frac{2}{3}[/tex]
A field has a walkway surrounding it by 3 sides. The total width/base of the area, both the field and walkway, is 300m while the total length is 200m. The area of the field is 30,000m and the total area is 60,000m. The thickness/width of the walkway is x, what does x equal?
Answer:
x = 15.
Therefore, the width of the walkway is 15m.
Step-by-step explanation:
Let's represent the width of the walkway by "x".
We know that the total width/base of the area (including the walkway) is 300m, so we can set up the equation:
length of field + 2(width of field) + 2(width of walkway) = 300
Substituting the given values, we get:
200 + 2w + 2x = 300
Simplifying the equation, we get:
2w + 2x = 100
We also know that the area of the field is 30,000m, so we can set up the equation:
length of field x width of field = 30,000
Substituting the given values, we get:
200w = 30,000
Simplifying the equation, we get:
w = 150
Finally, we know that the total area (including the walkway) is 60,000m, so we can set up the equation:
(length of field + 2x) x (width of field + 2x) = 60,000
Substituting the values we've found so far, we get:
(200 + 2x) x (150 + 2x) = 60,000
Expanding the equation, we get:
300x^2 + 1000x - 45,000 = 0
Solving for x using the quadratic formula, we get:
x = 15 or x = -30/100
Since x can't be negative, we can discard the negative solution and conclude that x = 15.
Therefore, the width of the walkway is 15m.
What is the answer?
The sequence of transformation that makes the shapes congruent is rotation then transformation
From the question, we have the following parameters that can be used in our computation:
The figures
From the figure, we have the shapes to have different orientation but same size
This means that one of the shapes is rotated to form the other
In this case, the rotation is a 90° clockwise
Followed by the rotation is a translation transformation
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Jenna mixed two shades of purple paint. For Purple People Eater, she used 3 pints of red paint for every 5 pints of blue paint. For Purple Majesty, she used a blue to red paint ratio of 7 to 4 . Compare the ratios of red paint to blue paint.
The ratio for Purple People Eater can be expressed in fraction form as
.
The ratio for Purple Majesty can be expressed in fraction form as
.
To compare these fractions, rewrite them with a common denominator of
.
The ratio of red paint to blue paint in Purple People Eater is
the ratio in Purple Majesty.
Answer:
Step-by-step explanation:
The ratio for Purple People Eater can be expressed in fraction form as
✔ 3/5
.
The ratio for Purple Majesty can be expressed in fraction form as
✔ 4/7
.
To compare these fractions, rewrite them with a common denominator of
✔ 35
.
The ratio of red paint to blue paint in Purple People Eater is
✔ greater than
the ratio in Purple Majesty.
slope of line graphed on photo
The slope of the line passing through (0,3) and (1,-1) is -4.
What is slope of the line?
The slope of a line is a measure of its steepness or incline. It describes how much the line rises or falls as it moves horizontally.
To find the slope of the line passing through (0,3) and (1,-1), we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the coordinates of the two points.
Plugging in the given coordinates, we get:
m = (-1 - 3)/(1 - 0)
m = -4/1
m = -4
Therefore, the slope of the line passing through (0,3) and (1,-1) is -4.
The slope of a line can be positive, negative, zero, or undefined (when the line is vertical). A positive slope means that the line is increasing as it moves to the right, while a negative slope means that the line is decreasing as it moves to the right. A slope of zero means that the line is horizontal, and an undefined slope means that the line is vertical.
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Complete question is: Slope of the given line passing through (0,3) and (1,-1) is -4.
cooling towers are used to remove or expel heat from a process. a cooling tower's walls are modeled by where the measurements are in meters. what is the width of the cooling tower at the base of the structure? round your answer to the nearest whole number.
The width of the cooling tower at the base of the structure is 100 meters, rounded to the nearest whole number.
Given that the cooling tower's walls are modeled by where the measurements are in meters and the width of the
cooling tower at the base of the structure is required, we can find the width by using the formula for the area of a
trapezoid. The area of the trapezoid represents the area of the base of the cooling tower.
Area of a trapezoid = 1/2 × (a + b) × h
where a and b are the lengths of the parallel sides of the trapezoid and h is the height or perpendicular distance
between the parallel sides.
In this case, the parallel sides of the trapezoid are not given, but we are given the height of the cooling tower, which is
100 meters. We also know that the area of the base of the cooling tower is 10,000 square meters.
Therefore, we can use the formula for the area of a trapezoid to find the sum of the lengths of the parallel sides of the
trapezoid, which will give us the width of the cooling tower at the base.
Area of a trapezoid = 1/2 × (a + b) × h
10,000 = 1/2 × (a + b) × 100
100 = (a + b)/2
200 = a + b
Width of cooling tower at the base = (a + b)/2
Width of cooling tower at the base = 200/2
Width of cooling tower at the base = 100 meters
Therefore, the width of the cooling tower at the base of the structure is 100 meters, rounded to the nearest whole number.
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Hii, can someone help me solve this? Thankyou
1)
a) the mean is µ = 2.5.
b) the variance is σ² = 1.25.
c) Standard Deviation σ = 1.12
2)
a) the mean is µ = 6.40.
b) the variance is σ² = 2.12
c) Standard Deviation σ = 1.46.
1) To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: (See attached table I)
Sum | 1 | 2.5
Therefore, the mean is µ = 2.5.
To find the variance (σ²), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products:
See table II
Sum | 1 | | 5 | 1.25
Therefore, the variance is σ² = 1.25.
Finally, to find the standard deviation (σ), we can take the square root of the variance:
σ = √(σ²) = √(1.25) ≈ 1.12.
2)
To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: See table III...
Sum | 1.00 | 6.40
Therefore, the mean is µ = 6.40/1.00 = 6.40.
To find the variance (σ^2), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products: See table IV
Sum | 1.00 | | 40.80 | 2.1200
Therefore, the variance is σ² = 2.1200.
Finally, to find the standard deviation (σ), we can take the square root of the variance:
σ = √(σ²) = √(2.1200) ≈ 1.46.
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rectangle below has an area of 160 inches2. Which of the following statements about the shape
below is not true?
A The base of the figure is 20 inches in length.
B the formula A=b/8 could be used to determine the area
C the formula b=160/8 could be used to determine the length of the base
D The formula 160(b)(8) could be used to determine the length of the base
Answer: The statement that is not true is D.
Explanation:
We know that the area of the rectangle is 160 square inches. Let's assume that the length of the base is b inches. Then, the height of the rectangle would be 160/b inches (since area = base x height).
Now, we can check the given statements:
A. The base of the figure is 20 inches in length.
We do not know the length of the base, so we cannot say for sure whether this statement is true or false.
B. The formula A=b/8 could be used to determine the area.
This statement is false. The correct formula for the area of a rectangle is A = b x h.
C. The formula b=160/8 could be used to determine the length of the base.
This statement is true. We can solve for b as:
b = A/h = 160/(160/b) = 8
So, the length of the base is 8 inches.
D. The formula 160(b)(8) could be used to determine the length of the base.
This statement is false. The given formula does not make sense in the context of the problem, and it does not allow us to determine the length of the base.
Step-by-step explanation:
Are these triangles identical? Explain your reasoning
No, the triangles are not identical
What are identical triangles?Identical triangles are two triangles that have the exact same
shape and size.In other words, all corresponding sides and angles are congruent (equal).
Identical triangles can be thought of as the same triangle, just in different positions or orientations in space.
The triangles are similar triangles but not identical triangles as the sides are not equal
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give branliest
you have to split the equation to get the answer for absolute value.
|x-5|=2
Step-by-step explanation:
When x -5 is a positive
x -5 = 2
x = 7
when x -5 is a negative
x-5 = -2
x = 3
x + 2xyz
9x3y2
18x2 + 5ab − 6y
4x4 + 3x2 − x − 4
The expressions when factorized are x(1 + 2yz), 9x^3y^2 and 6(3x^2 − 2y) + (5ab + 6y)
Factorizing the expressionsFactorization of X + 2xyz:
We can factor out x from the given expression to get:
x(1 + 2yz)
Therefore, the factorization of X + 2xyz is x(1 + 2yz).
Factorization of 9x3y2:
The given expression, 9x3y2, is already in its simplest form and cannot be factorized further.
Factorization of 18x2 + 5ab − 6y:
We can use the grouping method to factorize the given expression:
(18x2 − 12y) + (5ab + 6y)
6(3x2 − 2y) + (5ab + 6y)
Therefore, the factorization of 18x2 + 5ab − 6y is 6(3x2 − 2y) + (5ab + 6y).
Factorization of 4x4 + 3x2 − x − 4:
Cannot be factorized
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Mario has 45 red chips, 12 blue chips, and 24 white chips. What is the probability that Mario randomly selects a red chip or a white chip?
Step-by-step explanation:
To find the probability of Mario randomly selecting a red chip or a white chip, we need to first determine the total number of red and white chips he has.
Total number of red and white chips = 45 + 24 = 69
Therefore, the probability of Mario randomly selecting a red chip or a white chip is:
P(red or white) = (number of red chips + number of white chips) / total number of chips
P(red or white) = (45 + 24) / (45 + 12 + 24)
P(red or white) = 69 / 81
P(red or white) = 0.85
So the probability of Mario randomly selecting a red chip or a white chip is 0.85 or 85%.
Answer: 0.8519 ≈ 85%
Step-by-step explanation:
To find the probability, we will divide wanted outcomes by total possible outcomes. See below.
[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{number of red or white chip}}{\text{total number of chips}} =\frac{45+24}{45+12+24}= \frac{69}{81}[/tex]
= 0.8519 ≈ 85%
The probability that Mario will randomly select a red or white chip is 0.8519 or about 85%.
Balance Nancy's budget by putting what remains each month into a savings account. She can save
The amount that Nancy can save each month and put in the savings account is $10.
What is savings?Savings are funds that are not used right away but are instead set aside for unforeseen expenses or future needs. It is the gap between one's earnings (income) and their outlays (expenditures) (the amount of money spent). Regular income, investment profits, tax refunds, and gifts are just a few of the several ways that people might support their savings. You may save money in a variety of ways, such as by creating a budget and eliminating wasteful spending, opening a savings account, buying stocks or bonds, and making contributions to retirement plans like 401(k)s or IRAs.
The total income earned by Nancy is:
30 + 50 + 25 + 35 = $140
The total expenses are:
40 + 60 + 30 = $130
The amount remaining after expenses is:
Savings = 140 - 130 = $10
Hence, the amount that Nancy can save each month and put in the savings account is $10.
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To get from home to her friend Ryan's house, Shannon would have to walk 7 kilometers due north. To get from home to her friend Emmy's house, Shannon would have to walk 2 kilometers due east. What is the straight-line distance between Ryan's house and Emmy's house? If necessary, round to the nearest tenth.
Answer: approximately 7.3 kilometers.
Step-by-step explanation:
Using the Pythagorean theorem, we can write:
x^2 = 7^2 + 2^2
x^2 = 49 + 4
x^2 = 53
Taking the square root of both sides, we get:
x = sqrt(53)
Using a calculator or estimating, we find:
x ≈ 7.3 km
So the straight-line distance between Ryan's house and Emmy's house is approximately 7.3 kilometers.
7. Higher Order Thinking The manager of a restaurant wants to choose a different side dish for the special each week. She surveys customers about side dish preferences and records the results in the table shown at the right. How can she use 10 index cards to simulate choosing a side dish?
This method ensures that the side dish selection reflects customer preferences while incorporating an element of randomness.
Hi! To simulate choosing a side dish using 10 index cards, the manager can follow these steps:
1. Assign a number to each side dish based on the survey results.
2. Determine the probability of each side dish being chosen according to customer preferences.
3. Based on the probabilities, allocate the appropriate number of index cards to each side dish (e.g., if a dish has a 30% chance of being chosen, it would be assigned 3 out of the 10 index cards).
4. Write the side dish name or its assigned number on the allocated index cards.
5. Shuffle the index cards and randomly draw one card each week to determine the special's side dish.
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the amount of medication, in milligrams, in a patient's bloodstream after t hours, can be represented by the following function: m of t equals 88 over the quantity 1 plus e to the x plus 7 tenths power end quantity what is the rate of change for the amount of medication in the patient's bloodstream after 4 hours?
Answer:
about -0.79 mg/hour
Step-by-step explanation:
You want the rate of change of the amount of medication in a patient after 4 hours if the amount after t hours is modeled by y=88/(1+e^(t+0.7)).
Rate of changeThe rate of change is found by taking the derivative of the function with respect to time. Let u = 1+e^(t+0.7). Then du/dt = e^(t +0.7).
The function can be written ...
y = 88/u = 88·u^-1
so its derivative is ...
dy/dt = (-88·u^-2)·du/dt
dy/dt = -88(e^(t +0.7))/(1 +e^(t +0.7))^2
At t=4The value of the rate of change at t=4 is ...
dy/dt = -88(e^(4 +0.7))/(1 +e^(4 +0.7))^2 ≈ -88(109.95)/(1 +109.95)^2
dy/dt ≈ -0.78602 ≈ -0.79 . . . . . . mg/h
The rate of change in the amount of medication is about -0.79 mg/h.
Solve by substitution method 2x+7y=11 and x-3y=5
Answer:
Step-by-step explanation:
[tex]x = \frac{68}{13}[/tex]
[tex]y = \frac{1}{13}[/tex]
To solve the system of equations by substitution method, we can use one equation to solve for x or y, and then substitute that expression into the other equation to solve for the other variable.
From the second equation, we have:
x - 3y = 5
Solving for x, we get:
x = 3y + 5
Now we can substitute this expression for x into the first equation and solve for y:
2x + 7y = 11
2(3y + 5) + 7y = 11
6y + 10 + 7y = 11
13y = 1
y = 1/13
Now that we have solved for y, we can substitute this value back into one of the original equations to solve for x:
x - 3y = 5
x = 3y + 5
x = 3(1/13) + 5
x = 5 6/13
Therefore, the solution to the system of equations is:
x = 5 6/13 and y = 1/13.
The base of a rectangular pyramid has side has side 5 ft and 7 ft. the height of the smaller triangular face is 4 ft. Do you have enough information to find the surface area of the pyramid? Explain
A rectangular pyramid is a pyramid with a rectangular base and four triangular faces that meet at a single point at the top, called the apex. It is a three-dimensional solid with five faces, including the base, and is a type of pyramid with a rectangular base.
Do you have enough information to find the surface area of the pyramid?No, we do not have enough information to find the surface area of the rectangular pyramid.
To find the surface area of a rectangular pyramid, we need to know the lengths of all four sides of the base, as well as the slant height and height of each triangular face.
In this case, we only have two sides of the rectangular base (5 ft and 7 ft) and the height of one of the triangular faces (4 ft). We do not have enough information to find the length of the other two sides of the base or the slant height and height of each triangular face.
Therefore, we cannot find the surface area of the rectangular pyramid with the given information.
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can someone please help thank you
The probability of choosing a password with no Y's and O's is 20/30 = 2/3, or approximately 0.667. The two probabilities are the same, so neither is greater than the other.
Describe Probability?Probability is a measure of the likelihood or chance that an event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
In mathematical terms, probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 0.5, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
To calculate the probability of choosing a password with no Y's or no O's, we need to first count the number of valid passwords without Y's or O's and then divide it by the total number of possible passwords.
Number of valid passwords without Y's:
There are 5 choices for the first character (B, R, O, G, P), since Y is not allowed.
There are 4 choices for the second character (any of the remaining 5 letters except Y), since we cannot repeat the first letter.
So the total number of valid passwords without Y's is 5 x 4 = 20.
Number of valid passwords without O's:
There are 5 choices for the first character (Y, B, R, G, P), since O is not allowed.
There are 4 choices for the second character (any of the remaining 5 letters except O), since we cannot repeat the first letter.
So the total number of valid passwords without O's is 5 x 4 = 20.
The total number of possible passwords is the number of ways to choose 2 characters out of 6, without repetition. This is given by the formula:
6P2 = 6! / (6 - 2)! = 6 x 5 = 30
Therefore, the probability of choosing a password with no Y's is 20/30 = 2/3, or approximately 0.667.
Similarly, the probability of choosing a password with no O's is also 20/30 = 2/3, or approximately 0.667.
The two probabilities are the same, so neither is greater than the other.
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Leonardo da Vinci wrote, "When each of two squares touch the same circle at four points, one is double the other." Explain why the statement is true.