The number of one-to-one functions from f from the set {1,2,... , n} to the set {1,2,... , n} so that f(x) = x for some 1 ≤ x < n and f(n) ≠ n is \((n-1) * (n-1)! * n * (n-1)^{(n-1)}\).
To count the number of one-to-one functions satisfying the given conditions, we can break it down into two cases:
Case 1: f(x) = x for some 1 ≤ x < n
In this case, we have (n-1) choices for the value of x. Once we select x, we can assign any value from {1, 2, ..., n} except x to f(n) since f(n) ≠ n. So, there are (n-1) choices for f(n). The remaining (n-2) elements can be assigned to any of the remaining (n-2) elements. Thus, the number of such functions for this case is (n-1) * (n-1)!
Case 2: f(n) ≠ n
In this case, we have n choices for the value of f(n) since it can take any value from {1, 2, ..., n-1}. For the remaining (n-1) elements, we have (n-1) choices for each element since f(x) cannot be equal to x. Thus, the number of such functions for this case is \(n * (n-1)^{(n-1)}\).
To find the total number of functions satisfying both cases, we need to multiply the number of functions from each case. Therefore, the total number of such functions is:
Total = \((n-1) * (n-1)! * n * (n-1)^{(n-1)}\)
Note: The symbol "!" denotes the factorial function, which means multiplying all positive integers from 1 to that number. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
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Help please!! Anything helps
The missing lengths of right triangles are listed below:
Case 1: AB = 3√3, AC = 6√3
Case 2: DE = √2, DF = 2
Case 3: GI = 5√2, GH = 5
Case 4: JL = 14, KL = 7√3
Case 5: OP = 10√3, MP = 20
How to calculate missing sides in special right triangles
In this problem we must determine the missing sides of special right triangles by means of Euclidean geometry. There are two special right triangles: (45 - 90 - 45), (30 - 60 - 90)
Right triangle 45 - 90 - 45
The length of the hypotenuse is √2 times the length of any leg.Right triangle 30 - 60 - 90
The length of the short leg is 0.5 times the length of the hypotenuse.The length of the long leg is 0.5√3 times the length of the hypotenuse.The length of the long leg is √3 times the length of the short leg.Now we proceed to find the missing lengths:
Case 1
AB = BC / √3
AB = 3√3
AC = BC / 0.5√3
AC = 6√3
Case 2
DE = √2
DF = 2
Case 3
GI = 5√2
GH = 5
Case 4
JL = 7 / 0.5
JL = 14
KL = 7√3
Case 5
OM = 10
MP = 20
OP = 10√3
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The vertices of a square are located at (0, 2), (2, 0), (0, -2), and (-2, 0).
Select all transformations that will carry this square onto itself.
A reflection across the line y = x
B reflection across the line y = -X
C reflection across the x-axis
D 45° rotation about the origin
E 90° rotation about the origin
Answer:
Step-by-step explanation:
A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.
A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.
However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.
A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.
Therefore, the correct answers are C, D, and E.
(-3)+(-10)+(-17)+....... as far as the 11th term
Answer: The answer is y=-7x. yeah
4x +2y= -18 Standard to Slope Intercept Form
Answer:y=-2x-9
Step-by-step explanation:
Slope intercept form is y=mx+b
4x+2y=-18
Subtract 4x from both sides:
2y=-4x-18
Divide the entire thing by 2:
y=-2x-9
In an
an inter- barangay basket ball lesove,
The team from Baranggay Cullat tage has won
12 out of 25 aames a winning percentage of
48% How
manly games should they win in a
row to improve their with peocentage to 60%
Probability
Answer:
8 games in a row
Step-by-step explanation:
If they win 8 games in a row, there winning percentage will be 20/33, which is equal to about 60%.
25=q+14 pls help me thanks!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
q= 11
Step-by-step explanation:
25-14= 11
Answer:
q= 11
Step-by-step explanation:
25=q+14
25-14=q+14-14
11=q
hope it's helpful ❤❤❤
THANK YOU.
Ryan is practicing his shot put throw. The path of the ball is given approximately by the function H(x) = -0.01x² + .66x +5.5, where H is measured in feet above the ground and is the horizontal dista
Answer:
The highest peak when x= 33 and the ball reaches a height of 16.39 ft
Step-by-step explanation:
The peak is obtained at x= -b/2a
x= -0.66 / 2(-0.01)
x = -0.66/(-0.02)
x= 33
The highest is reached when x=33 :
-0.01(33)^2 +0.66*33 +5.5 = 16.39 ft
The ball finally touches the ground again when -0.01x² + .66x +5.5 = 0
and the starting height is when x=0 => -0.01(0)^2 + 0.66(0) +5.5 = 5.5 ft
He started his throw at 5.5 ft
20 points someone who actually knows what they doing lol❤️
Answer:
77°
Step-by-step explanation:
We can use: \((c*9/5)+32=f\) to convert Celsius to Fahrenheit.
'c' - Celsius
'f' - Fahrenheit
Replace 'c' with 25:
\((25*9/5)+32=f\\45+32=f\\\boxed {77 = f}\)
25° Celsius is 77° Fahrenheit.
Answer:
77
Step-by-step explanation:
You spin the spinner and flip a coin. Find the probability of the compound event is not spinning 5
The probability of the compound event of spinning a 5 and flipping heads is 1/12.
Assuming that the spinner is fair and each outcome is equally likely, the probability of spinning a 5 is:
P(spinning 5) = number of ways to get 5 / total number of outcomes
P(spinning 5) = 1 / 6
Now, assuming that the coin is fair and has an equal probability of landing on heads or tails, the probability of flipping heads is:
P(flipping heads) = number of ways to get heads / total number of outcomes
P(flipping heads) = 1 / 2
To find the probability of the compound event of spinning 5 and flipping heads, we multiply the probability of spinning 5 by the probability of flipping heads:
P(spinning 5 and flipping heads) = P(spinning 5) x P(flipping heads)
P(spinning 5 and flipping heads) = (1/6) x (1/2)
P(spinning 5 and flipping heads) = 1/12.
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The complete question:
You spin the spinner and flip a coin. Find the probability of the compound event. The probability of spinning number 5 and flipping heads is__.
And spinner sample space is {1, 2, 3, 4, 5, 6}
HELP ILL GIVE BRAINLIEST
Answer:
y= -3x + 5
Step-by-step explanation:
The slope of the line is m=−3
m=−3.
The equation of the line in the slope-intercept form is y=−3x+5y=−3x+5.
The equation of the line in the point-slope form is y−5=−3xy−5=−3x.
If the scale factor of two similar cylinders is 4:7,
what is the volume ratio?
A. 64:343
B. 12:21
C. 16:49
D. 256:2,401
Answer:
the answer is A. 64:343.
Step-by-step explanation:
The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding side lengths. Since the scale factor of the two cylinders is 4:7, the ratio of their corresponding radii is 4:7 and the ratio of their heights is also 4:7.
So, the ratio of their volumes is (4/7)^3 = (64/ 343) = 64:343
So, the answer is A. 64:343.
Two sides of a triangle have lengths 5 and 12. Which inequalities represent the
possible lengths for the third side, x?
The inequality that represent the possible length of the third side is
7 < x < 17
According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the measure of the third side of the triangle.
We have been given measure of two sides which are 5 and 12. Then the possible length for the third side has two condition
Let the third side be x unit.
First condition, x + 5 > 12
x > 7
Second condition, 12+ 5 > x
17 > x
Hence the inequality that represent the possible length of the third side is
7 < x < 17
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PLEASE HELP!!!Which is an equation in point-slope form for the line that passes through the points (−1,4) and (3,−4)?
100 POINTS!!!!!
Answer:
y - 4 = - 2(x + 1)-------------------------
GivenPoints (-1, 4) and (3, - 4)Find the slopem = (- 4 - 4)/(3 - (-1)) = - 8/4 = - 2Use one of the points and the point-slope formy - y₁ = m(x - x₁)y - 4 = - 2(x - (-1)) ⇒ y - 4 = - 2(x + 1)After a dicount of 25 percent the aving on a pair of roller blade wa $12. 0. What wa the ale price?
The sales price is $36.
We have been told that the discount on the pair of rollerblades is 25%. It has also been told that the discounted price is $12.0. Now, first, we need to find the original price of the rollerblades. Let the original price of the rollerblades be = $x.
Now - x/100 * 25 = $12
- x/100 = 12/25
- 25x = 1200
- x = $48
Now, in order to find the sale price, we need to -
= Original price - Discounted price
= $48 - $12
= $36
Hence, the price of the rollerblades after putting in a 25% discount is $36.
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Type the correct answer in each box.
x f(x)
-1
1
2
3
3
6
5
7
7 8
The values in the table define the function f (x). The value of f-¹ (3) is
Reset
Next
, and the value of f¹ (8) is
The values of the inverse functions are f-¹ (3) = -1 and f-¹ (8) = 7
How to determine the values of the inverse functionsFrom the question, we have the following parameters that can be used in our computation:
x f(x)
-1 3
1 6
2 5
3 7
7 8
Using the above as a guide, we have the following:
f-¹ (x) means that we calculate the value of x from the table when y = x in the function notation
So, we have
f-¹ (3) = -1 and f-¹ (8) = 7
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Find 3 1/4 - 4 1/2 show your work!
Answer: 3 1/4 + 2 1/3 = 67/
12
= 5 7/
12
≅ 5.5833333
Step-by-step explanation:
The table below lists the populations and the areas for the 10 U.S. states having the least population density (number of people per square mile). Which of these countries has a population density less than the average population density of the 10 U.S. states listed in the table?
Choose all that are correct.
A. Laos, which has an area of 89,112 square miles and a population of 6,368,481.
B. Saudi Arabia, which has an area of 829,995 square miles and a population of 27,019,731.
C. Canada, which has an area of 3,560,217 square miles and a population of 33,098,932.
D. Iceland, which has an area of 38,707 square miles and a population of 299,388.
E. Turkey, which has an area of 297,591 square miles and a population of 70,413,958.
A. A, B, and C
B. B, D, and E.
C. A and C
D. C and D
The correct answer is option C: A and C. The average population density is 12,199,895 / 1,566,231 ≈ 7.793 people per square mile.
To solve the problem, we need to first find the average population density of the 10 U.S. states listed in the table.
The total population of these states is:
584,080 + 624,779 + 713,635 + 799,063 + 1,068,778 + 1,359,146 + 1,568,662 + 1,792,147 + 1,826,341 + 1,853,304 = 12,199,895
The total area of these states is:
97,818 + 104,100 + 109,889 + 121,298 + 146,435 + 178,040 + 192,174 + 212,818 + 236,058 + 268,601 = 1,566,231
The average population density is then:
12,199,895 / 1,566,231 ≈ 7.793 people per square mile
Now, we can compare the population densities of the countries listed in the answer choices to the average population density of the 10 U.S. states.
A. Laos has a population density of 71.5 people per square mile, which is less than the average population density of the 10 U.S. states. Therefore, this option is correct.
B. Saudi Arabia has a population density of 32.5 people per square mile, which is less than the average population density of the 10 U.S. states. Therefore, this option is not correct.
C. Canada has a population density of 9.3 people per square mile, which is less than the average population density of the 10 U.S. states. Therefore, this option is correct.
D. Iceland has a population density of 7.7 people per square mile, which is equal to the average population density of the 10 U.S. states. Therefore, this option is not correct.
E. Turkey has a population density of 236.6 people per square mile, which is greater than the average population density of the 10 U.S. states. Therefore, this option is not correct.
Therefore, the correct answer is option C: A and C.
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Factor the algebraic expression. 7x+63
Step-by-step explanation:
7x+63
= 7 (x +9)
Hope it helps ya
Answer:
7(x+9)
Step-by-step explanation:
7 times what = 63?
7*9 = 63 so lets pull out a 7 from the expression
7x+63 = 7(x+9)
Brainlist!
Show all steps and I will make you Brainlist.
Answer:
The height of the tree to the nearest foot is 75.
Step-by-step explanation:
The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.
tangent = opposite/adjacent
\(\frac{tan(59)}{1} = \frac{h}{45}\)
h = tan(59) * 45
h ≈ 74.89
To the nearest foot, 74.89 is 75 ft.
A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 41 miles north of the transmitter to a second city 42 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter
On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
city - north at (0,65)
city-east at (59,0)
Slope is m=(-65/59)
\(B= y - mx = 65 - (-65/59)(0) = 65\)
The equation of the line between the cities is y = (-65/59)x + 65
\(x^2 + ( (-65/50)x + 65) )^2 = 47^2\)
the intersection points are:
(20.698, 42.197) and (43.998,16.527)
The transmitter is within range between those to points along the line.
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An equation is a math sentence. Which letter(s) represent only an expression, not a complete math sentence? (Could be more than one answer.)
1. 3y=14
2. x-6
3. a/7=6
4. 3 + 5b
5. 12=0.8(5) + c
6. 6/p + 0.5-2/3(p)
Answer:
2, 4, 6 are expressions
Step-by-step explanation:
A math sentence has a verb: "is equal to" It could also be some other, similar phrase, such as "is less than" or "is not equal to," for example.
An expression has no verb!
x - 6 Say it out loud. See? No verb. It's like saying "that evil neighbor of mine" without saying anything more. Yes? Did what? Is what? Compares to what?
A company has recently been hiring new employees. Today the company has 33% more employees than it did a year ago. If there are currently
53,200 employees, how many employees did the company have a year ago?
Answer:
Sorry , I might be wrong : 35664
Step-by-step explanation:
So, first, we can find 33% of 53,200
That is 17,556
Then, we can subtract 17556 from 53,200
We get 35664
name four fractions whose values are between 1/4 and 3/4
Answer:
ok don't panic it's organic
Answer:
\(\frac{1}{3} , \frac{1}{2} , \frac{3}{8} , \frac{5}{8}\)
Step-by-step explanation:
15PTS PLEASE HELP ASAP!
(dont write random answers pls)
look at the pic attached:
Answer:
-1.75
Step-by-step explanation:
We know that the midpoint formula is [for the x-coordinate per say] x = 1/2x1 + 1/2x2. If we want to find a point that lies 1/4th of the way we use x = 3/4x1 + 1/4x1. How? Because the point lies 1/4th from one endpoint and 3/4th from the other.
x = 3/4x1 + 1/4x2,
x = 3/4(-3) + 1/4(2) = -9/4 + 2/4 = -7/4
= - 1.75
--- There is an easier way to do it though, but it is really vague so you should not use it. We can form a triangle with MN being the hypotenuse. What would the length of the legs be? They would be 6 and 5. Now let's form a triangle 1/4th of that. 6/4 = 1.5 and 5/4 = 1.25. If you look at the diagram, start from point N move up 1.5 units and over 1.25 forming our mini triangle. You can see the x-axis has a value of -1.75.
Dumisani earn 42 480 per month. He splits his earnings in the ratio 7:5. And then saves the lesser amount. How much does he save
If Dumisani earn $42480 per month and he splits his earnings in the ratio 7:5, then he saves $17,700 per month.
A ratio is a way of comparing two quantities or values. It expresses the relationship between two numbers or values in terms of their relative sizes or amounts.
To split Dumisani's earnings in the ratio 7:5, we need to divide his earnings into 7 + 5 = 12 equal parts.
Each part is therefore:
42480 ÷ 12 = 3,540
Dumisani saves the lesser amount, which is in the ratio of 5 parts to 7 parts.
So he saves:
5 × 3,540 = $ 17,700
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Work out £55.30-£34.10
Answer:
21.2£
Step-by-step explanation:
Answer:
21.2£
Step-by-step explanation:
yw can I get brainiest tooo
29. LMNK is a parallelogram. What are the values of x and y on the labeled
diagonals?
A X = 4, y = 4
B x = 5, y = 2
C x = 9, y = 3
D x = 8, y = 11
To solve for x and y, we would need additional information, such as the length of one of the sides of the parallelogram or the measure of one of the angles.
Without this information, there are multiple possibilities for the values of x and y that could form a parallelogram. Therefore, the answer is none of the given options.
To better understand why additional information is needed, consider that a parallelogram has two pairs of parallel sides. This means that opposite sides are congruent and parallel to each other.
Without knowing the length of any of the sides or the measure of any of the angles, we cannot determine the lengths of the diagonals or the relationship between x and y.
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In 2015 there were 759 laptops at lightning high school starting a 2016 the school box 75 more laptops at the end of each year the function t(x) equals 75X +759 can be used to determine the total number of laptops at the school X years after 2015 what is the projected total number of laptops at lightning high school at the end of 2020
Answer:
Step-by-step explanation:
Given the following :
Number of laptops in 2015 = 759
t(x) = 75x + 759 ; model to determine number of laptops at the school. X years after 2015.
Number of laptops in the school in 2020:
Write the equation of the line that passes through the points (3, -7) and (-6, -13)
Answer:
-18 y + 91 y = 73 y
(3, -7) y (-6, -13)
{-18 y, 91 y}
I'll send you a pic of the equation
g(h(0)):
\(\begin{gathered} g\lbrack h(x)\rbrack=(x^2-1)+4 \\ g\lbrack h(0)\rbrack=0^2-1+4 \\ g\lbrack h(0)\rbrack=3 \end{gathered}\)answer: g[h(0)]=3