The permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3
How to prove the equation?We have:
[tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex]
Apply the following permutation formula
[tex]^{n}P_r = \frac{n!}{(n- r)!}[/tex]
So, we have:
[tex]\frac{(n + 1)!}{(n + 1 - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]
Evaluate the difference
[tex]\frac{(n + 1)!}{(n - 2)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)!}[/tex]
Expand
[tex]\frac{(n + 1)!}{(n - 2)(n - 3)!} - \frac{n!}{(n - 3)!} = 3 * \frac{n!}{(n - 2)(n - 3)!}[/tex]
Multiply through by (n - 3)!
[tex]\frac{(n + 1)!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]
Expand
[tex]\frac{(n + 1) * n!}{(n - 2)} - n! = 3 * \frac{n!}{(n - 2)}[/tex]
Divide through by n!
[tex]\frac{(n + 1)}{(n - 2)} - 1 = \frac{3}{(n - 2)}[/tex]
Take the LCM
[tex]\frac{n + 1 - n + 2}{(n - 2)} = \frac{3}{(n - 2)}[/tex]
Evaluate the like terms
[tex]\frac{3}{(n - 2)} = \frac{3}{(n - 2)}[/tex]
Both sides of the equations are the same.
Hence, the permutation equation [tex]^{n+1}P_3 - ^nP_3= 3 * ^nP_2[/tex] is true for all integers n ≥ 3
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graph the line with slope -1/2 passing through the point (5,-3)
Step-by-step explanation:
The graph is shown in the image above.
Answer: Draw a line through the two points (5,-3) and (7,-4)
See the diagram below.
=======================================================
Explanation:
Start at (5,-3). Then move down 1 and to the right 2 units to arrive at (7,-4)
The motion of "down 1, right 2" is from the slope of -1/2
slope = rise/run = -1/2
rise = -1 = go down 1 unit
run = 2 = go 2 units to the right
Two points are the minimum amount needed to draw any line. Plot the two points (5,-3) and (7,-4) and draw a straight line through them as shown in the diagram below. I used GeoGebra to make the graph. Desmos is another tool you could use.
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
[tex]\sqrt{4x-3}=5[/tex]
Answer:
x = 7
Step-by-step explanation:
[tex](\sqrt{4x-3} )^{2} =5^{2}[/tex]
[tex]4x-3=25[/tex]
[tex]4x=25+3[/tex]
[tex]x=\frac{28}{4}[/tex]
[tex]x=7[/tex]
Hope this helps
What is the equation of the line that passes through the point (6,-4) and has a slope
of-?
Answer:
y = -x + 2
Step-by-step explanation:
*Assuming the slope given is -1*
Applying point-slope formula :
y - (-4) = -1 (x - 6)y + 4 = -x + 6y = -x + 2P(Ω)
P(A)
0.4
0.1
P(B)
0.2
0.3
Answer:
i dont even have the first one on my computer
Step-by-step explanation:
Dan went on a drive. He modeled the relationship between the distance he drives D (in kilometers) and the remaining fuel in his tank C (in liters) as C=40-0.1D. He wanted to graph the relationship for the entire distance of his drive, which was 100 kilometers. What mistakes did Dan make when drawing the graph?
Answer:
B
Step-by-step explanation:
the entire distance was 100 km, but the other 200 km on the x axis is unnecessary
Answer:
A
Step-by-step explanation:
khan acadamy
There are 39 adults and 26 children registered for a seminar. the seating is to be arranged so each row has the same number of people. all of the people in a row must be in the same age group. how many rows of seats are needed to seat the greatest possible number of participants in each row?
The number of rows of seats needed to seat the greatest possible number of participants in each row is 5
What is Highest Common Factor ?The highest common factor is the highest number that divides the numbers given.
On the basis of given data
Total number of children = 26
Total number of adults = 39
The highest common factor of both the number is 13 ,
Therefore the highest possible number of people that can sit in one row so that the number is in constant in all the rows.
So 2 rows of children of 13 each and
3 rows of adult of 13 each
Which makes the total number of rows = 5
Therefore the number of rows of seats needed to seat the greatest possible number of participants in each row is 5
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For what values of x does f(x) = 0?
O-4, 0, 2
O-2, 0, 4
O-5, 0, 17
O-17, 0,5
The values of x does f(x) = 0 will be -4,0,2.Option A is corect.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The graph shows the cubic polynomial equation found as;
⇒(x+4)(x)(x-2)
The points f(x) = 0 is;
⇒(x+4)(x)(x-2)
⇒(-4+4)(0)(2-2)
⇒0
The values of x does f(x) = 0 will be -4,0,2.
Hence, option A is corect.
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This image of a physics problem shows a block resting on a ramp, . ∠P is the angle between the ramp and the horizontal, and is oriented vertically. Which quantity is equal to cos W?
A. sin p
b. cos p
c. 1 - sin p
d. 1 - cos p
Based on the image description, the quantity that is equal to cos W is sin P.
What is the image about?The image is known to be showing an object on a ramp. Based on it, we can therefore take the angle a to the complementary angle of angle w.
Note that the angle w and angle b are said to be the same via alternate interior angles. Therefore, the quantity that is equal to cos W is sin P.
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Colin walked a distance of 15m in 6 hours. Work out Collin's average speed. Give your answer in miles per hour
2.5 miles/hour
Simply 15/6
Answer:
Colin walks an average speed of 2.5 miles per hour.
Step-by-step explanation:
15/6= 5 miles/2 hours
2.5
You toss a coin and roll a number cube. Find P(heads and an even number.)
Answer:
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number)
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number) = P(head) × P(even number)
P(even number)Assuming a fair coin and a fair die:
P(even number)Assuming a fair coin and a fair die:P(head)
P(even number)Assuming a fair coin and a fair die:P(head) =50%
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number)
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50%
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number)
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number) =50%×50%=25%
Find the percent of the area under the density curve where xxx is more than 333.
Answer:
25%
Step-by-step explanation:
Got it right on khan
Answer:
60%
Step-by-step explanation:
its right on khan
In a group of 20 pupils, 3 play the flute only.
6 play the piano only.
6 play both instruments.
A student is chosen at random.
What is the probability the student plays neither instrument?
Please answer in fractional form!!
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given information:
Total number of pupils = 203 pupils play the flute6 pupils play the piano only6 play both instrumentsWe can assume that 3 pupils play the flute only as we have also been told that 6 pupils play both instruments.
To calculate the probability that a randomly chosen pupil plays neither instrument, first determine how many pupils do not play an instrument by subtracting the number of pupils who do play an instrument from the total number of pupils:
⇒ total number of pupils - pupils who play instruments
⇒ 20 - (3 + 6 + 6)
⇒ 20 - 15
⇒ 5
Therefore, 5 pupils do not play the piano and/or flute.
To calculate probability:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore:
[tex]\implies \textsf{Probability of a pupil playing neither instrument} = \dfrac{5}{20}=\dfrac{1}{4}[/tex]
express 80 as a product of its prime factors, write the prime numbers in accending order
Answer:
80 as a product of prime numbers can be expressed as 2×2×2×2×5
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195, how long was the repairman there? answers a: 2 hours b: 2.5 hours c:4 hours d: 3 hours
The time spent by the repairman there will be 3 hours so the correct answer is option D.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195.
The time will be calculated as:-
Total amount = $195
Now the fixed consulting cost will be $60 and will be deducted from the
total amount.
Variable cost = 195 - 60 = 135
The $45 per hour charge so for $145 the time will be:-
Time = 135 / 45
Time = 3 Hours
Therefore the time spent by the repairman there will be 3 hours so the correct answer is option D.
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3 erasers cost $4.41. Write a proportion that would solve for the cost of 4 erasers.
Answer:
$5.88
Step-by-step explanation:
3 erasers ⇒ $4,41
4 erasers ⇒ $A
A = 4 erasers * $4.41 / 3 erasers
A = $ 5.88
Answer:
see below
Step-by-step explanation:
Proportion:
4.41 is to 3 erasers as 'x' is to 4 erasers:
4.41 /3 = x / 4 <======this is your proportion
or rearrange
4 * 4.41/3 = x
(this results in x = $ 5.88 for 4 erasers )
f(x) = x+3 f ( x ) = x + 3
Answer + Step-by-step explanation:
y = mx + b where m is the slope and b is the y-intercept
y = x + 3 where m = 1 is the slope and b = 3 is the y-intercept
Table of some points:
| x | 0 | 1 | 2 | 3 |
| y | 3 | 4 | 5 | 6 |
when x = 0, y = 0 + 3 and y = 3
when x = 1, y = 1 + 3 and y = 4
when x = 2, y = 2 + 3 and y = 5
Graph:
x(x+3)-2(-5x+1)x=x^2-3(4-2x)
The answer is no solution
Explanation:
it depends on how you interpret what's written. The way I initially interpreted it*, I was able to use the quadratic formula to find :
[tex]x=\frac{1}{4}-i\frac{\sqrt{455}}{20},\:x=\frac{1}{4}+i\frac{\sqrt{455}}{20}[/tex]
*I interpreted it as: [tex]x\left(x+3\right)-2\left(-5x+1\right)x=x^2-3\left(4-2x\right)[/tex]
but I don't want to say that this is your correct answer, because there are multiple interpretations (like a lot of interpretations)
{this is mostly in response to other answers}
If teens have about 80h a month of leisure time, how much time would they spend each activity a month?
Answer:
depends on how many actives there are and maybe on if they preferred one over another it would get more time
Step-by-step explanation:
Which expression is equivalent to 2 (14x-37+28x+12.2-5y-17.5)?
A. 84x-16y-10.6
B. 28x-6y-10.6
C. 42x-8y-5.3
D 84x-16y-5.3
Answer:
A. 84x - 16y - 10.6
Explanation:
[tex]\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)[/tex]
[tex]\sf \rightarrow 2 (42x-8y-5.3)[/tex]
apply distributive method: a(b + c) = ab + ac
[tex]\sf \rightarrow 2 (42x) -2(8y)-2(5.3)[/tex]
[tex]\sf \rightarrow 84x -16y-10.6[/tex]
Can someone help please?
Thank you.
Answer:
B and C are the answers.
Step-by-step explanation:
3b+b = 4b because the value of B or any variable is 1 so 3 +1 is four and 4b is our answer.
2(2b) the brackets tell the number before brackets should be multiplied and 2 × 2 is 4 so the answer is 4b
A circle has a diameter with endpoints (-7, 1) and (-3, 7).
What is the equation of the circle?
r2 = ( x - 3) 2 + ( y + 4) 2
r2 = ( x + 3) 2 + ( y - 4) 2
r2 = ( x + 5) 2 + ( y - 4) 2
r2 = ( x - 5) 2 + ( y + 4) 2
Divide 140 in the ratio 2:5
Answer:
40 : 100
Step-by-step explanation:
→ Find the sum of the ratio
2 + 5= 7
→ Divide 140 by the answer
140 ÷ 7 = 20
→ Multiply each part of the ratio by 20
40 : 100
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
One leg of a right triangle is 2 inches and the hypotenuse is 6 inches.
Find the area of the triangle.
_[tex]\sqrt{x} \\[/tex]
We can see that the area of the triangle is: 5.65in².
What is a triangle?A triangle is actually known to be a shape that has three sides, three angles and three vertices. It's also known as a plane shape.
In order to find the area of the triangle, we will use Pythagorean Theorem: c² = a² + b².
Where c = hypotenuse = 6in.
b = 2in.
6² = a² + 2²
36 = a² + 4
a² = 36 - 4 = 32
a = √32
Area of the triangle = ½ × base × height.
Where base = √32
height = 2
Thus: A = ½ × √32 × 2
A = √32 = 5.65in².
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Which expression is equivalent to \frac{r^9}{r^3}
Answer:
[tex]\sf r^6[/tex]
Step-by-step explanation:
Exponent law:[tex]\boxed{\bf \dfrac{a^m}{a^n}=a^{m-n}}[/tex]
In exponent division, if bases are same, subtract the powers.
[tex]\sf \dfrac{r^9}{r^3}=r^{9-3}=r^{6}[/tex]
Y=-5x +6 Y= 3x -2 Find the solution to the system of equations
X = _____
Y= _____
Answer:
x=1, y=1. (1, 1).
Step-by-step explanation:
y=-5x+6
y=3x-2
------------
-5x+6=3x-2
-5x-3x+6=-2
-8x+6=-2
-8x=-2-6
-8x=-8
8x=8
x=8/8=1
y=3(1)-2=3-2=1
Which equations are true?
Select all that apply
A) -x + (-x) =0
B) x - (-x) = 0
C) None of the above.
The correct answer from the task content is; Choice C; None of the above.
Which of the equations are true?The equations can be evaluated as follows;
A) -x + (-x) =0
-x -x = -2x......Not True
B) x -(-x) = 0
x + x = 2x .....Not True.
On this note, it follows that none of the equations is true.
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In the figure below, if line r is parallel to line s, m
Answer:
Step-by-step explanation:
I'm not sure exactly what you're trying to ask
but r and s are parallel
and I'm assuming the 3rd line is line m, line m is not parallel to any line
and angles A and B are equal
Suppose y varies directly as x², and y = 160 when x = 4. Find y when x = 6.
Finding the constant of proportionality :
y = kx²160 = k(4)²k = 10Finding y when x = 6 :
y = 10(6)²y = 10(36)y = 360The value of y is 360 when x = 6.
Approximate the area under the curve y = x^2 from x = 0 to x = 3 using a Right Endpoint approximation with 6 subdivisions.
Will mark brainliest
Subdivide the interval [0, 3] into 6 subintervals of equal length, ∆x = (3 - 0)/6 = 1/2. Then the partition is
[tex]\left[0,\dfrac12\right] \cup \left[\dfrac12,1\right] \cup \left[1,\dfrac32\right] \cup \cdots \cup \left[\dfrac52,3\right][/tex]
The right endpoint of the [tex]i[/tex]-th subinterval is
[tex]r_i = \dfrac12 + (i-1)\times\dfrac12 = \dfrac i2[/tex]
with [tex]i\in\{1,2,3,\ldots,6\}[/tex].
Then the area under the [tex]y=x^2[/tex] on the interval [0, 3] is approximately
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \sum_{i=1}^6 (r_i)^2 \Delta x = \frac18 \sum_{i=1}^6 i^2[/tex]
Recall that
[tex]\displaystyle \sum_{n=1}^N n^2 = \frac{N(N+1)(2N+1)}6[/tex]
Then the approximate value of the area is
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \frac{6\times7\times13}{48} = \boxed{\frac{91}8}[/tex]
The actual value of the area is 9, so this approximation is an overestimation, as is always the case when using a right endpoint sum for an increasing function.
Now that you have x² - 8x 16 = 9 16, apply the square root property to the equation.
The square root property to the equation will be (x – 4)² = 25. And the solutions will be the negative 1 and 9.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have
The equation is given below.
x² – 8x + 16 = 9 + 16
Then the equation can be written as
(x – 4)² = 25
x – 4 = ±5
x = 4 ± 5
x = -1, 9
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