Write an
explicit formula for an, the nth term of the sequence 8, -4, 2, ....
By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence.
What does "sequence" in mathematics mean?A sequence is a list of objects that is in order in mathematics. (or events). Similar to a set, it has members. (also called elements, or terms). The length of the sequence is the number of many ordered elements (potentially infinite).
Given :
The ratio between consecutive terms in the above sequence is not constant, hence it is not a geometric sequence. The series does, however, appear to rotate between positive and negative numbers.
The explicit formula for the nth term in this sequence is as follows:
a = (-1)^(n+1) * 2^(n-2) (n-2)
By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence. For instance, when n is 1, we obtain:
n = 2 results in:
so forth.
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HELP PLSSS....The table shows the result of spinning a color spinner (purple, blue, yellow, and green) in an experiment. PART A: Using the results in the table, what is the experimental probability of a spinner landing on purple (P) in Experiment A? Write your answer as a fraction and as a decimal.
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
part A)
the table shows that in 10 attempts
Blue was hit 5 times
Yellow was hit 2 times
Green was hit 2 times
Purple was hit 1 time
so the experimental probabilities are
Blue 5/10 = 1/2 = 0.5
Yellow 2/10 = 1/5 = 0.2
Green 2/10 = 1/5 = 0.2
Purple 1/10 = 0.1
part B)
the theoretical probability of Purple with an equally spaced spinner of 4 colors is 1/4 = 0.25
According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 200 executives are randomly surveyed.
a. What is the probability that fewer than 90 of the executives believe employees are most productive on Tuesdays?
b. What is the probability that more than 100 of the executives believe employees are most productive on Tuesdays?
c. What is the probability that more than 82 of the executives believe employees are most productive on Tuesdays?
Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 4 decimal places, the tolerance is +/-0.005.
Therefore , the solution of the given problem of probability comes out to be there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.
Define probability.The primary goal for every procedure's criteria-based methods is to ascertain the probability that a statement is true or that a specific event will occur. Chance can be represented by any number range between 0 and 1, where 0 usually represents probability and 1 usually reflects degree of certainty. A probability illustration displays the possibility that a specific event will take place.
Here,
a.
=> P(X < 90) = F(89)
We can determine: Using a computer or a spreadsheet
=> Binom.dist(89, 200, 0.48, TRUE) = 0.0016 when
=> P(X 90) = F(89) (rounded to 4 decimal places)
Therefore, there is a 0.0016 percent chance that fewer than 90 of the executives agree that workers are most effective on Tuesdays.
b.
=> P(X > 100) = 1 - P(X < 100) = 1 - F(100)
We can determine: Using a computer or a spreadsheet
=> Binom.dist(100, 200, 0.48, TRUE)
=> 0.0668 for P(X > 100) = 1 - F(100) = 1 - (rounded to 4 decimal places)
Therefore, there is a 0.0668 percent chance that more than 100 executives agree that Tuesdays are when workers are most effective.
c.
=> P(X > 82) = 1 - P(X < 82) = 1 - F(82)
We can determine: Using a computer or a spreadsheet
=> Binom.dist(82, 200, 0.48, TRUE) = 0.7569, P(X > 82) = 1 - F(82) = 1
Therefore, there is a 0.7569 percent chance that more than 82 executives agree that Tuesdays are when workers are most effective.
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A sequence is defined by t_1 = 1 and t_2 = 2, and t_3=(2k+1)/k^2, and t_4=(3k+1)/2k^3, and t_5=(k+1)/2k^2, and t_6=1 and t_7=2 and t_8=(2k+1)/k^2, and t_9=(3k+1)/2k^3 and t_n = [kt_(n−1)+ 1] /[k^2 t_(n−2)] for n ≥ 3, where k is a positive integer. Determine the value of t_2023 in terms of k.
[tex]t_2023[/tex] will be equal to the expression[tex]: t_2023 = [k*t_2022 + 1] / [k^2 * t_2021][/tex]. in terms of k.
The sequence given is defined by the recurrence relation: [tex]t_n[/tex] = [tex][kt_(n−1)+ 1] /[k^2 t_(n−2)] for n ≥ 3,with t_1 = 1[/tex] and [tex]t_2[/tex] = 2, and [tex]t_3=(2k+1)/k^2[/tex], and [tex]t_4=(3k+1)/2k^3[/tex], and [tex]t_5=(k+1)/2k^2[/tex], and [tex]t_6[/tex]=1 and [tex]t_7[/tex]=2 and [tex]t_8=(2k+1)/k^2, t_9=(3k+1)/2k^3[/tex]. To find the value of [tex]t_2023[/tex], we need to find the values of the previous two terms, [tex]t_2022[/tex] and [tex]t_2022[/tex] . We can do this by using the recurrence relation, starting at n = 3 and going up until n = 2022.
Therefore,[tex]t_2022 = [k*t_2021 + 1] / [k^2 * t_2020][/tex].
Similarly, [tex]t_2021 = [k*t_2020 + 1] / [k^2 * t_2019[/tex]].
We can now plug in the values of [tex]t_2021[/tex] and [tex]t_2020[/tex], which can be found by continuing to work backwards in the recurrence relation until n = 9, and then we have the initial conditions of the sequence. Once we have the values of [tex]t_2021[/tex] and [tex]t_2021[/tex] , we can substitute them into the recurrence relation for[tex]t_2023[/tex] to get the desired result. Therefore, [tex]t_2023 = [k*t_2022 + 1] / [k^2 * t_2021].[/tex]
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The dimensions of a rectangle are 14 centimeters by 48 centimeters. Find, in centimeters, the length of the diagonal of the rectangle
We can use the Pythagorean theorem to find the length of the diagonal of the rectangle. The Pythagorean theorem states that in a right triangle with legs of length a and b and hypotenuse of length c, we have:
a^2 + b^2 = c^2
In this case, the rectangle has dimensions of 14 centimeters by 48 centimeters, so we can let the length and width of the rectangle be the legs of a right triangle, and the diagonal be the hypotenuse. Then:
a = 14 cm b = 48 cm c = ?
We can plug these values into the Pythagorean theorem and solve for c:
14^2 + 48^2 = c^2 196 + 2304 = c^2 2500 = c^2 c = sqrt(2500) c = 50
Therefore, the length of the diagonal of the rectangle is 50 centimeters.
Answer:
50 cm
Step-by-step explanation:
the equation is d=sqrt(w^2+l^2)
so you get sqrt(14^2+48^2) which equals 50.
Determine the quantity of fuel that was utilized by the water tanker in March
The quantity of fuel that was utilized by the water in March is 230.4 liters.
Fuel capacity of the tanker = 460 liters
Fuel consumption rate = 5 km/ℓ
Total distance covered per full tank = fuel capacity * fuel consumption rate = 460 x 5 = 2,300 km
Number of full tanks required to make one round trip = distance per round trip / total distance covered per full tank = 18/2300
=0.0078
Number of round trips made in March 2022 = 1/0.0078 x 2
= 64.1
Total distance covered = number of round trips * distance per round trip
= 64 x 18
= 1,152 km
Therefore, the total distance covered by the water tanker = 1,152 km
Quantity of fuel utilized = total distance covered / fuel consumption rate
= 1152/5
= 230.4 liters.
Therefore, The quantity of fuel that was utilized by the water in March is 230.4 liters.
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Your question is incomplete. The complete question is:
The water source is at a distance of about 18 km (return trip) from the construction site. The water tanker has a fuel capacity of 460 liters. The rate of fuel consumption of the Mercedes water tanker averages 5 km/t. The prices of fuel per liter in March and June 2022 appear below:
MARCH 2022 FUEL PRICES
DIESEL
50 ppm
COST
R19,55
JUNE 2022 FUEL PRICES
DIESEL
50 ppm
Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022.
If f(x) = x3, what is the equation of the graphed function?
A nonlinear function on a coordinate plane passes through (minus 4.5, minus 5), (minus 3, minus 2), (minus 2, minus 1), and (minus 1, 6)
A. y = f(x − 3) − 2
B. y = f(x + 3) – 2
C. y = f(x + 2) − 3
D. y = f(x − 2) + 3
The equation of the graphed function, which is composed of translations to f(x) = x³, is given as follows:
B. y = f(x + 3) - 2.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The turning point of f(x) = x³ is at the origin, while for the graphed function it is at point (-3,-2), hence the translations are given as follows:
3 units left -> x = x + 3.2 units down -> y = y - 2.Hence the graphed function is defined as follows:
B. y = f(x + 3) - 2.
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How many numbers less than or equal to 120 are co-prime with 120? (co-prime as in they have no common factors with 120.)
Answer:
We know that 120 can be factored as 2^3 * 3 * 5, so its totient function value can be found as follows:
φ(120) = φ(2^3) * φ(3) * φ(5)
= 2^2 * 2 * 4
= 16
Therefore, there are 16 numbers less than or equal to 120 that are relatively prime to 120
A horizontal number line labeled from negative 4 to positive 1 with tick marks every one fourth unit. There is a point one tick mark to the left of negative 3. A horizontal number line labeled from negative 4 to positive 1 with tick marks every one fourth unit. There is a point one tick mark to the left of negative 3. What point is marked on the number line?
The point one tick mark to the left of negative 3 on the number line is -3.25.
Number lines are horizontal straight lines in math where the intervals between the integers are equal. A number line can be used to show all of the numbers in a sequence. At both ends, this line continues indefinitely.
Each tick mark on the number line represents one-fourth of a unit, so the distance between negative 4 and negative 3 can be divided into 4 parts, each with a length of one-fourth of a unit. Starting from negative 4, the tick marks would be labeled as -4, -3.75, -3.5, -3.25, -3, and so on. Therefore, the point one tick mark to the left of negative 3 is at -3.25 on the number line.
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URGENT! WILL MARK BRIANLIEST!!!!
The caterpillar touches 15 points with two integer coordinates, including the start point (-3, -4) and the end point (25, 38).
What is co-ordinate geometry ?
Coordinate geometry is a branch of mathematics that deals with the study of geometry using the principles of algebra. In coordinate geometry, geometric figures are represented using algebraic equations and analyzed using techniques from algebra and calculus.
The caterpillar moves from (-3, -4) to (25, 38) in a straight line. We can find the equation of the line passing through these two points using the slope-intercept form of the equation of a line:
y - (-4) = (38 - (-4))/(25 - (-3)) * (x - (-3))
y + 4 = 42/28 * (x + 3)
y = 3/2 * x + 19
The caterpillar touches a point with two integer coordinates whenever x and y are both integers. To find these points, we can substitute integer values for x and solve for y. Since the slope of the line is 3/2, every time x increases by 2, y increases by 3.
Starting from x = -3, we can list the integer values of x that the caterpillar touches:
-3, -1, 1, 3, 5, ..., 25
For each value of x, we can compute the corresponding value of y using the equation of the line:
y = 3/2 * x + 1
For example, when x = -3, y = 3/2 * (-3) + 19 = 14.5, which is not an integer. When x = -1, y = 3/2 * (-1) + 19 = 17.5, which is also not an integer. However, when x = 1, y = 3/2 * 1 + 19 = 20, which is an integer. Similarly, we can find the integer values of y for all the other values of x.
Therefore, the caterpillar touches 15 points with two integer coordinates, including the start point (-3, -4) and the end point (25, 38).
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Question 1 (3 points) Saved If A and B are independent events
with P(A) = 0.4 and P(B) = 0.25, then P(A ∪ B) = Question 1
options: 0.65 0.55 0.10 Not enough information is given to answer
this quest
The value of the probability P(A ∪ B) if the events are independent events is 0.55
How to determine the value of the probabilityThe formula for the probability of the union of two events is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Since the events A and B are independent, the probability of their intersection is simply the product of their individual probabilities:
P(A ∩ B) = P(A) × P(B)
Substituting the given values, we have:
P(A ∩ B) = 0.4 × 0.25 = 0.1
Now we can use the formula for the union:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
So, we have
P(A ∪ B) = 0.4 + 0.25 - 0.1
This gives
P(A ∪ B) = 0.55
Therefore, the probability of the union of events A and B is 0.55.
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Ray is measuring fabric for the costumes of a school play. He needs 12. 5 meters of fabric. He has 30. 5 centimeters of fabric. How many more centimeters of fabric does he need?
Answer:
1219.5 more centimeters of fabric
Step-by-step explanation:
First, we need to convert 12.5 meters to centimeters, since the given amount of fabric is in centimeters.
12.5 meters = 12.5 x 100 centimeters/meter = 1250 centimeters
Now we can find the difference between what Ray needs and what he has:
1250 centimeters - 30.5 centimeters = 1219.5 centimeters
Therefore, Ray needs 1219.5 more centimeters of fabric.
Brainliest will be rewarded+ 100 points!!
Take a screen shot of the work and do the work on the ss
Answer: When do you need it done?
Step-by-step explanation: ?
Answer:
Step-by-step explanation:
x+y=17
x-y = 7
From equation 2, x = 7 + y
put this in equation 1.
(7+y) + y = 17
7+2y = 17
2y = 10
y = 5.
We said that x = 7+y
thus, x = 7 + 5
x = 12.
2x+2y=36
2(x+y) = 36
Thus, x + y = 18.
x+y = 18
x-y=6 using elimination (literally simplifying this)
2x = 24 (y-y=0. ELIMINATED!)
x = 12
When x = 12,
x+y=18
12+y=18
y=6.
3x = y
x + y = 20
From 1, y = 3x.
x + (3x) = 20
4x = 20
x = 5.
when x = 5,
y = 3x
y = 3(5)
y = 15.
x+y = -4
xy = -21
from 1, x = -4-y
=> y(-4-y)= -21
-y²-4y = -21
Therefore,
y² + 4y -21 = 0
y= 3 or -7.
When y = 3,
x + 3 = -4
x= -7.
When y = -7,
x + (-7) = -4
x-7=-4
x = 3.
Hope these help! :)
*fingers cracking*
help, please !!
Abiana wants to get to the opposite corner of a rectangular park that is $3/4$ miles wide and $1$ mile long.
If she rides her scooter, it only takes her $8$ minutes to travel $1$ mile, but she has to go around the park. If she walks, it takes her $20$ minutes to travel $1$ mile, but she can cut directly across the grass.
Which mode of transportation is faster, assuming she travels at a constant speed?
Answer: Scootering is faster
Step-by-step explanation: If it takes 20 minutes to go around walking going through the middle would technically split the time in half and 20 divided by 2 is 10 which is more than 8 therefore scootering is faster.
Kay is standing near 200-foot-high radio tower.
Answer:
265 ft
Step-by-step explanation:
its asking what is the hypotenuse
"SOHCAHTOA"
sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent
use
soh because it has hypotenuse in it
sine equals opposite over hypotenuse
sine 49 = 200 / x
x & sine 49 can switch
x = 200/sin(49°)
x = 200/0.7547
x = 265.005962634
x = 265
using pythagorean theorem other leg is 173.85 or 174
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When the result of (5x^(2)+x-7)(x-4)-(2x^(3)+5x^(2)-6) is expressed as a polynomial in the form ax^(3)+bx^(2)+cx+d, what is the value of b ?
After expanding the polynomial (5x² + x - 7)(x - 4) - (2x³ + 5x² - 6), b = -24
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
Since we have the polynomial (5x² + x - 7)(x - 4) - (2x³ + 5x² - 6) and we want it expressed as a polynomial in the form ax³ + bx² + cx + d, to find the value of b, we proceeda s follows.
(5x² + x - 7)(x - 4) - (2x³ + 5x² - 6)
Expanding the brackets, we have that
(5x² + x - 7)(x - 4) - (2x³ +5x² - 6) = 5x³ - 20x² + x² - 4x - 7x + 28 - (2x³ + 5x² - 6)
= 5x³ - 20x² + x² - 4x - 7x + 28 - 2x³ - 5x² + 6
Collecting like terms, we have
= 5x³ - 2x³ - 20x²- 5x² + x² - 4x - 7x + 28 + 6
= 3x³ - 24x² - 11x + 34
So, comparing 3x³ - 24x² - 11x + 34 with ax³ + bx² + cx + d, we have that
b = - 24
So, b = -24
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(1 point) A tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. (a) What is the amount of salt in the tank initially
The initial amount of salt in the tank is 60 kg, calculated using the formula M = ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank.
Initially, the tank contains 60 kg of salt and 2000 liters of water. The amount of salt in the tank can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The density of salt is 2270 kg/m3. Assuming the tank has a constant volume, the mass of the salt in the tank is 60 kg.
The amount of salt in the tank changes due to the addition of pure water and mixing of the solution. The amount of salt in the tank at any given time can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The rate at which the salt is added to the tank is equal to the rate at which the salt-water solution is drained from the tank.
Therefore, the rate of change of the mass of the salt in the tank is equal to 8 liters/minute of pure water entering the tank minus 4 liters/minute of salt-water solution draining from the tank. Thus, the amount of salt in the tank initially is 60 kg.
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if n(r' intersection s') + n(r' intersection s)=3, n(r intersection s)=4 and n(s' intersection r)=7
We can use the principle of inclusion-exclusion to find n(U), which states that for two sets A and B:
n(A union B) = n(A) + n(B) - n(A intersection B)
We can apply this to three sets r, s, and their complements r' and s':
n(U) = n(r union s)
= n(r) + n(s) - n(r intersection s)
= [n(r intersection s') + n(r intersection s)] + [n(s intersection r') + n(s intersection r)] - n(r intersection s)
= [(4 + n(r' intersection s)) + (n(r intersection s') + 7)] - 4
= n(r' intersection s) + n(r intersection s') + 3
= 7 + 3 + 3
= 13
Therefore, n(U) = 13.
Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
The solution of the system of equations from the graph is x = 2.
What is point of intersection?The point of intersection formula is used to determine where two lines meet, or the point at which they intersect. In Euclidean geometry, the intersection of two lines can be either an empty set, a point, or a line. Two lines must meet certain requirements in order to intersect, including being in the same plane and not being skew lines. The intersection of these lines may be determined using the intersection formula.
The solution of the system of equations can be determined from the graph by determining the point of intersection between the two lines.
From the graph we observe that the point of intersection of the two lines is at (0, 2).
Hence, the solution of the system of equations is x = 2.
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I NEED HELP ON THIS QUICKLYY WILL GIVE BRAINLIESTTT PLEASE HELP!!!
x is the number of HD Big View television produced daily.
y is the number of Mega Tele box television produced daily.
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox television takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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What's the 5th term?
Answer:
what term?
Step-by-step explanation:
Explain the question.
A fish tank contains 90 litres of water, rounded to 1 significant figure.
30 litres of water, rounded to 1 significant figure, are removed from the
tank.
Work out the upper bound of the volume of water left in the fish tank.
Give your answer in litres.
The upper bound of the volume of water left in the fish tank is 60 liters.
What exactly is a litre of water?33.81 fluid ounces make up one litre (US).
One litre of water would fill about one-fourth of a gallon water bottle. Also, you should be aware that there are two different kinds of ounces used globally to measure water volume: (1 litre = 33.814 US ounces).
The maximum allowable mistake can be added to the actual value to determine the upper bound of the amount of water still in the fish tank.
The maximum error for 90 litres, rounded to one significant figure, is half of the value of the last significant figure, or 5. Hence, the actual value of 90 litres might be either 85 or 95.
The largest potential inaccuracy for 30 litres, rounded to one significant figure, is likewise 5. Hence, the actual value of 30 litres might be 25 or 35.
We subtract the lower bound of the withdrawn volume from the higher bound of the original volume to determine the upper bound of the volume of water still present in the tank.
The upper bound of the volume of water left in the fish tank can be found by adding the half of the absolute uncertainty to the measured value of 60 liters (90 - 30):
Upper bound = 60 + 0.5 x 1 = 60.5 liters (rounded to 1 significant figure)
Therefore, the upper bound of the volume of water left in the fish tank is 60 liters.
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Consider the function f(x)=3x-2
If f(g(x))=x and g(f(x))=x, what is g(x)?
Answer:a
Step-by-step explanation:its simple
Help asap
Given g(x) = -x +5
h(x) = 3x² - 2
Find g(h(x))
A -3x³ +9x +3
B 3x² + 30x + 73
C 3x² 30x + 73
D- 3x² +7
After answering the provided question, we can conclude that Therefore, the answer of quadratic equation is D) [tex]$-3x^{2}+7$[/tex]
What is quadratic equation?A quadratic equation is x ax² + bx + c = 0, so it's a single variable quadratic polynomial. a 0. Because this regression is of second order, the Fundamental Principle of Algebra helps to ensure that it includes at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic calculation.
This means there is at least yet another word that must be squared. The formula "ax² + bx + c = 0" is a common solution for quadratic equations. where a, b, and c are arithmetical coefficients or constants. where the parameter "X" is unidentified.
To find g(h(x))
[tex]$\begin{array}{l}{{h(x)=3x^{2}-2}}\\ {{g(h(x))=g(3x^{2}-2)}}\\ {{g(3xA^2))=-3x^2-2}+5}}\\ {{g(h(x))=-3x^{2}+7}}\end{array}$[/tex]
Therefore, the answer is D) [tex]$-3x^{2}+7$[/tex]
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Which describes a possible dependent variable for the given independent variable?
The number of hours you study for a test
1. Your test score
2. The number of students in your study group
3. How many students are taking the test T
4.T he time the test starts
Answer:
1
explanation in head
A computer must print all natural numbers between 0 and 1,000,000. It can print 9 digits per second. How many seconds will it take to print all these numbers?
Consider two natural numbers n,k and p where 0≤k≤p≤n a. Prove that:
P(n+1,k)=P(n,k)+kP(n,k−1) b. Prove that: C(n,k)C(n−k,p−k)=C(p,k)C(n,p)
`C(p,k) * C(n-p,k)`
a. Proof: We will apply the same method we used in formula (1) in our class notes on this question. For this purpose, we choose a set containing `n + 1` elements. It contains all elements of the set of `n` elements and another element `y` that has not been included in the set of `n` elements.Let the number of sets of `n` elements that contain `k` particular elements `a` be `P(n, k)`. To count the number of sets of `n + 1` elements that contain `k` elements, we use the concept of permutations with repetition, such as -{n + 1} can be placed in any of the `k` places of the k-element subsets of `{1, 2,...,n}`, or it can be one of the remaining `n-k+1` elements in each of the `P(n,k)` sets that contain `k` elements.Let us use `A` to denote the set of sets of `n` elements that do not contain the element `y` and `B` to denote the set of sets of `n` elements that contain the element `y`. Then, `P(n+1,k)=|A|+|B|=P(n,k)+(n−k+1)P(n,k−1)`.b. Proof: To count the number of `k` element subsets from a set of `n` elements, we use `C(n, k)`.Let us consider two sets, `A` and `B`, where `|A|=n-k` and `|B|=p-k`. We want to choose `k` elements from these two sets such that the number of subsets we get from `A` is `x` and the number of subsets we get from `B` is `y`. In the set `A`, we select `x` elements by choosing `k-x` elements from the remaining `n-k` elements. Similarly, in the set `B`, we select `y` elements by choosing `k-y` elements from the remaining `p-k` elements.Thus, the total number of ways of choosing `k` elements from `A` and `B` is given by `C(n-k, x) * C(p-k, y)`. The total number of ways of choosing `k` elements from `n` elements is given by `C(n, k)`. Therefore, the total number of ways of choosing `k` elements from `n` elements such that `x` elements are chosen from `A` and `y` elements are chosen from `B` is `C(n-k, x) * C(p-k, y) * C(n, k)`.To get the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B`, we must sum over all possible values of `x` and `y`. Thus, the total number of ways of choosing `k` elements from `n` elements such that `k` elements are chosen from `A` and `p-k` elements are chosen from `B` is given by: `C(p,k) * C(n-p,k)` which is the required result.
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Which ordered pairs are in a proportional relationship with (0. 2, 0. 3)?
A
(1. 2, 2. 3)
B
(2. 7. 4. 3)
C
(3. 2, 4. 8)
D
(3. 5, 5. 3)
E
(5. 2, 7. 8)
A proportional connection exists when two values may be expressed as y = kx, where k is a constant. To discover which ordered pairings have a proportionate connection with (0.2, 0.3).
We must find a value of k for each pair that makes this equation true. Let us begin with option A: (1.2, 2.3). If we wish to represent this combination as y = kx, we must discover the value of k that results in 2.3 = k. (1.2). When we solve for k, we get: k = 2.3 / 1.2 ≈ 1.92 As a result, (1.2, 2.3) does not have a proportionate connection with (0.2, 0.3) since the value of k is different for both couples. This procedure can be repeated for each of the others. options. Option B: (2.7, 4.3) yields: k = 4.3 / 2.7 ≈ 1.59 Option C: (3.2, 4.8) yields: k = 4.8 / 3.2 = 1.5 Option D: (3.5, 5.3) yields: k = 5.3 / 3.5 ≈ 1.51 Option E: (5.2, 7.8) yields: k = 7.8 / 5.2 = 1.5 As a result, alternatives C and E are proportional to (0.2, 0.3) since they can be represented in the form y = kx with the same k value. k = 1.5 in both situations.
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ABCD is a parallelogram and CE stands on AD, DF stands on AB. If AD = 20 metre, CE = 8 metre, AB = 16 metre, find DF
In the parallelogram ABCD the value of DF is 13.33 metres or DF = 40/3 metres (rounded to two decimal places).
In the parallelogram ABCD, we can draw a diagonal AC that splits the parallelogram into two congruent triangles, namely, △ABC and △ADC.
Let x be the length of DF. We can use similar triangles to find x.
Notice that △BCE and △DFE are similar triangles, since they share the same angle at E and the angles at B and D are congruent due to opposite angles in a parallelogram. Therefore, we can write the following proportion:
BC/CE = DF/FE
Substituting the given values, we have:
16/8 = x/(20-x)
Simplifying this equation, we get:
2 = x/(20-x)
2(20-x) = x
40 - 2x = x
3x = 40
x = 40/3
Therefore, DF = 40/3 meters or 13.33 meters (rounded to two decimal places).
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how long will it take for the battery to run down one sixth of its capacity of 3600 Milli Ampere hours
Answer:
6 hours
Step-by-step explanation:
[tex]\frac{1}{6}[/tex] of Total battery life = [tex]\frac{1}{6} * 3600 = 600[/tex]milliamps
Assuming the battery takes 100 Milliamps per hour,
Time = Battery Capacity / Current hours
Time = 600 / 100 Mah = 6H