Answer:
3*3*3 or 3^3
Step-by-step explanation:
27/3=9/3=3
so 3*3*3 or 3^3
Show that [n-r] nPr =nP[r+1]
Using the relationship of permutation and combination, we can say that the relation [tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex] holds true.
What is Permutation?
The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics include permutations in some form or another. They frequently appear when various orderings on certain finite sets are taken into account.
What is Combination?
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations may be counted in simpler situations. The combination is the taking together of n items, k at a time, without repetition. The words k-selection or k-combination with repetition are frequently used to describe combinations when repetition is permitted.
In the given question:
To proof:
[tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex].
Let's Proof the relation:
Using the basic relation of permutation and combination, we have;
[tex]$\begin{aligned}(n-r+1){ }^n P_{r-1} &=(n-r+1) \frac{n !}{(n-r+1) !} \\ &=(n-r+1) \frac{n !}{(n-r+1)(n-r) !} \\ &=\frac{n !}{(n-r) !}={ }^n P_r \end{aligned}$[/tex]
Hence, Proved.
Therefore, we can say that the relation [tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex] holds true.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola is f(x) = 7(x-3)^2+5.
Given:
The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.
If the parabola has same shape then its a values are same.
so f(x) = 7x^2
here a = 7
so the equation with vertex (3,5) also has a value is 7.
(h,k) = (3,5)
f(x) = a(x-h)^2+k
= 7(x-3)^2 + 5.
Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.
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Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Sidney wants to take group fitness classes at a nearby gym, but needs to start by selecting a
membership plan. With the first membership plan, Sidney can pay $36 per month, plus $2 for
each group class she attends. Alternately, she can get the second membership plan and pay
$35 per month plus $3 per class. If Sidney attends a certain number of classes in a month,
the two membership plans end up costing the same total amount. How many classes per
month is that? What is that total amount?
If Sidney attends
Submit
classes per month, each membership plan costs $
The system of equation to describe the situation below is x= 1.
What is equation?
an equation is a formula that is to expresses the equality of two expressions, by the connecting them with in the equals sign.
The process of equting one thing with another is called the equation of science with objective.
Sol- Based on the given condition-
The formulate is- 36+2x=35+3x
Rearrange variables to the left side of the equation
2x-3x=35-36
Combine like terms
-x= 35-36
Calculate the sum or difference
-x=-1
Devide both side of the equation by the coefficient of variable we get
X=1
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Two parallel lines are cut by a transversal as shown below.
Suppose m4=124°.
Answer:
156°
Step-by-step explanation:
m5 = m7 (vertical angles)
m4 + m5 = 180 (supplementary)
m5 = 180 - 124 = 156
So measure of both angle 5 and 7 is 156
how is solving an equation that includes cubes similar to solving an equation that includes squares? how is it different?
The difference in solving equations with cubes and squares is of one additional step of reducing the cubic equation to a quadratic equation. In this way, a quadratic equation (variable raised to power 2) is separated from the given cubic equation.
For example, x3+3x2+x1+3=0 can be reduced to (x+3) and (x2+1), where the later one is a quadratic equation. This step is never part of a squared equation’s solution.
The similarity is from here onwards. Quadratic equations are solved similarly in both cases. Although there are multiple possibilities for roots differing from each other in nature. But once a quadratic equation is developed, the solution from there onwards is mostly generic.
You can refer to the following formula for solving quadratic equations efficiently:
x= -bb2-4ac2a
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What are the roots of this polynomial? f(x) = (x+9)(x-9)(x+10)?
The solution for the given polynomial are x = -9, 9 and -10.
What is polynomial?
Polynomials are algebraic expressions that contain coefficients and variables. Variables are sometimes known as indeterminates. Mathematical operations like addition, subtraction, multiplication, and positive integer exponents can be performed on polynomial equations but division by variables cannot.
Given polynomial:
(x+9)(x-9)(x+10)
Equating it wit zero,
we get solutions as:
x = -9, 9, -10
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A student has these scores on their assignments. The teacher is considering dropping a lowest score. What effect does eliminating the lowest value, 0, from the data set have on the mean and median? 0, 40, 60, 70, 75, 80, 85, 95, 95, 100
The effect of eliminating the lowest value, 0, from the data set have on the mean and median of the data set is;
There is a difference of 7.5 between the mean without 0 and mean with 0There is a difference of 2.5 between the median without 0 and median with 0What is mean and median?The mean of a given data is the sum of all observations divided by the number of observations
The median of a given set of data refers to the middlemost observation, obtained after arranging the data in ascending or descending order.
Given data:
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
a) Mean without '0' = (40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100) / 9
= 700/9
= 77.777
Median without '0' = 40, 60, 70, 75, 80, 85, 95, 95, 100
= 80
Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100 / 10 = 70
Median with '0' = 0, 40, 60, 70, 75, 80, 85, 95, 95, 100
= (75 + 80) / 2
= 77.5
So therefore,
Difference in mean = Median without '0' - Mean with ' 0'
= 77.77 - 70
= 7.7
Difference in median = Median without '0' - Median with '0'
= 80 - 77.5
= 2.5
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Dakota found a vintage skateboard from the 1980s in her parents' garage. The owner of the local skate shop told her the skateboard is currently worth $380 and will increase in value by about 7% each year. Write an exponential equation in the form y=a(b)x that can model the skateboard's value, y, in x years. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = To the nearest dollar, how much will the skateboard be worth in 7 years?
1. An exponential equation modeling the skateboard's value, y, in x years is y = 380 x 1.07ˣ.
2. The value of the skateboard will be worth $610.28 in seven years.
What is an exponential equation?An exponential equation is a mathematical function that depicts an equation with variable exponents.
The exponential function is always written in the form of y = abˣ.
Where a = the constant or initial value, b = the continuous growth rate, and x or t = the time variable.
Y represents the value that we are looking for after the growth rate has been applied for several (t) years.
The current worth of the skateboard = $380
Annual increase = 7% = 0.07
Number of years = 7 years
Y = 380 x 1.07⁷
= 380 x 1.606
= 610.28
= $610.28
Thus, in seven years, using the exponential equation, the skateboard will be worth $610.28.
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On Friday night, Clara ate a pizza for dinner and had 1/5 of the pizza left over. On Saturday, she ate 2/3 of what was left. How much of the pizza did Clara eat on Saturday? Write your answer as a fraction or as a whole or mixed number.
Answer:
Clara ate 2/15
Step-by-step explanation:
1/5 equals 3/15
Help Im begging Brainliest Help!!!!!!
A 3−4−5 right triangle is the base of a prism that is 10 inches tall. How many cubic inches of sand could fill the solid?
Answer:
60 [tex]in^{2}[/tex]
Step-by-step explanation:
Volume = the area of the base times the height.
Base:
[tex]\frac{lengthxwidth}{2}[/tex]
[tex]\frac{3x4}{2}[/tex]
6 multiply this by the height of 10
Volume = 60 [tex]in^{3}[/tex]
Answer:
60 cubic inches of sand-------------------------------
The volume of the prismV = Bh, B- area of base, h- heightArea of baseB = 1/2×3×4 = 6 in²Find the volumeV = 6×10 = 60 in³Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
Answer:yes
Step-by-step explanation:
for every week he gets 3 cars so it can only incre ment by 3. (1,3) (2,6) (3,9) and so on.
Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
The cars are 315 miles apart 1.5 hours after they start moving. Use the answer
from part (c) to write an equation.
To rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $5.80 per hour. The math club wants to spend less than $72.20 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for .
The possible amount of time for which they could rent the meeting room is 1, 2, and 3 hours.
In the question,
It is given that,
Reservation fee is $49.
Additional fee is $5.80 per hour.
The math club can spend maximum of $72.20.
The inequality will be:
49 + 5.8*t < 72.20
5.8*t < 23.2
t < 4
Hence, the possible amount of time for which they could rent the meeting room is 1, 2, and 3 hrs.
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Mason is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Mason will earn $30 every time one of his songs is played in a commercial and he will earn $80 every time one of his songs is played in a movie. Mason earned a total of $470 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Mason's songs were played. Define the variables that you use to write the system.
Answer:
Get the roundend answer to 10
Step-by-step explanation:
Jane received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.39 per pound. After buying the coffee, she had $28.05 left on her card. How many pounds of coffee did she buy?
Answer:
85 ggoooofffffyyy
Step-by-step explanation:
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
The required expression of the reflection of the point is (-x, y).
Given that,
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4) is to be determined.
The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
A line segment has endpoints at (–4, –6) and (–6, 4) and an image with endpoints at (4, –6) and (6, 4) is produced the equation of the reflection is given as,
(x, y) ----> (-x, y)
Thus, the required expression of the reflection of the point is (-x, y).
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Use the Commutative and Associative Properties to find the expression
equivalent to (-3.3x + (-3.2)) + (5.7x + (−1)).
-3.3x + (-3.2) + 5.7x + (-1)
(-3.3x (-1)) + ((-3.2)x - 5.7)
(-3.3x + (-3.2)) + (5.7x- (-1))
(-3.3x + 5.7x) + ((-3.2) + (-1))
The expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is -3.3x + 5.7x) + ((-3.2) + (-1))
The commutative property of addition states that any change in the order of the numbers being added does not affect the sum.
a + b = b + a
The given expression is (-3.3x + (-3.2)) + (5.7x + (−1))
on simplifying we get, -3.3x - 3.2 + 5.7x - 1 = 2.4x - 4.2
Upon checking the options provided
-3.3x + (-3.2) + 5.7x + (-1)
= 2.4x - 4.2
(-3.3x (-1)) + ((-3.2)x - 5.7)
-9 - 6.7
-3.3x + (-3.2)) + (5.7x- (-1))
2.4x - 2.2
(-3.3x + 5.7x) + ((-3.2) + (-1))
2.4x - 4.2
Therefore, the expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is -3.3x + 5.7x) + ((-3.2) + (-1))
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Please help me with this!!!
The Probability of an odd number = 0.5.
What is Probability?
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using probability, we can calculate everything from the possibility of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. The formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two occurrences coming together, are essential to understand in order to properly appreciate this field of mathematics.
In the given question, we have:
The odd numbers on the given spin are 1,3,5,7 and 9;
So, The number of odd numbers is 6;
That is, n(odd) = 6;
and,
Total number of Spin = 12;
So, The probability of an odd number = [tex]\frac{odd number}{total number}[/tex]
The probability of an odd number = [tex]\frac{6}{12}[/tex]
Hence, The Probability of an odd number = 0.5.
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Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
–4, –3, –2, –1, ...
Answer:
[tex]a_{n}[/tex] = n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
- 3 - (- 4) = - 2 - (- 3) = - 1 - (- 2) = 1
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 4 and d = 1 , then
[tex]a_{n}[/tex] = - 4 + 1 (n - 1) = - 4 + n - 1 = n - 5
I need what x equals
Answer: x=143
Step-by-step explanation: the ratio is 1:13 so 11*13=143
Answer: Don't take my word wait until someone else says something.
Step-by-step explanation: i think it is 134 or around that.
a student cycles for x hours at 12km/h and y hours at 16km/h.altogether, tge student cycles 66km in 5 hours. find x and y
Answer:
x = 3.5 hours
y = 1.5 hours
Step-by-step explanation:
There are two unknowns, x and y, both in umits of hours. We need at least two equations before we start trying to solve this with substitution. Looking at the information, this should be possible.
First, we know that Speed x Time = Distance.
The distance covered by the cyclyst would be the sum of (12km/h)*x and (16km/h)*y, where x is the time, in hours, for the slower speed and y for the faster. Together, the student travels 66 km.
The total distance of 66 km would be comprised of the two distances 12x and 16y:
12x + 16y = 66 km
For the second equation, we know that the total time is 5 hours. That would be the sum of x and y:
x + y = 5 hours
We now have 2 equations, so we stand a good chance of finding the answer. Pick one of the equations and isolate one of the variables to one side. Let's choose x + y = 5 hours, since that is easy to rearrange:
x = 5-y
Now take the first equation and substitute the definition of x from above (5-y):
12x + 16y = 66
12(5-y) + 16y = 66
60-12y + 16y = 66
4y = 66-60
4y = 6
y = (6/4) or 1.5 h
The time spent at 16 km/h was 1.5 hours.
Use this value of y in either equation to find x. Let's use x+y=5, since that will be easier:
x+y = 5 for y = 1.5
x+1.5 = 5
x = 3.5h
The time spent at 12 km/h was 3.5 hours
Find x. Round your answer to the nearest tenth of a degree.
Answer:
~62.35°
Step-by-step explanation:
To find the degree of an angle from side lengths, use reverse trigonometric function.
arcsin, arccos, arctan / [tex]sin^-1, cos^-1, tan^-1[/tex]
Because we have adjacent and opposite, lets use arctan.
Set up the equation.
[tex]x = arctan\frac{21}{11}[/tex]
Use a calculator to solve.
a die is rolled 2 times .what is the probability of getting a number 6 two times. what is the probability of not getting 6 at all?
The probability of not getting 6 at all is 11/36
Define probability.The term "probability" is most commonly used to refer to the likelihood that a specific event (or set of events) will occur, expressed as a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.
Given,
A die is rolled 2 times
6 was on the first roll, but there was no 6 on the second,
6 came up on the second roll but not the first.
2 sixes
A) It is evident that 1/6 of the time you will roll a six.
B) There is a 5/6 chance of not getting a six on a single roll.
1/6x5/6 + 5/6x1/6 + 1/6x1/6
= 5/36 + 5/36 + 1/36
= 11/36
The probability of not getting 6 at all is 11/36
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One type of plant root splits 4 times while growing in the ground. The number of new roots after each split can be modeled by the function f(x)=3x, where x is the number of times the root splits. What is the domain of f(x)? CLEAR CHECK All positive integers All positive integers less than or equal to 4 All integers All positive integers greater than or equal to 4
The domain of the function represented as .f(x) is (b) All positive integers less than or equal to 4
How to determine the representation of the domain?The equation of the function is given as
f(x) = 3x
Where
x = Number of splits
f(x) = number of new roots in each split
From the question, we have
Splits = 4
This means that the maximum value of x is 4
The other values of x would be
x = 1, 2, 3, 4
This can be represented as
0 ≤ x ≤ 4
The interpretation of the above notation is all positive values less than or equal to 4
Hence, the domain value is option (b)
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Is x + 1/y = 7 a linear equation?
[tex]x + \frac{1}{y} = 7[/tex]
The equation ; x + 1/y = 7 as given in the task content is a linear equation.
What are linear equations?It follows from the task content that the equation given in the task content is to be identified as linear or not.
Since the given equation is; x + 1/y = 7;
It is noteworthy to know that a linear equation is one in which case, the greatest exponent of the variable is; 1.
Therefore, since the greatest exponent of a variable in the given equation is 1; it follows that the equation is a linear equation.
Hence, the equation given in the task content; x + 1/y = 7 is a linear equation.
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Over which of the following intervals would the function h(x)=|x-2|+6 be decreasing only?
We have an absolute value function that opens upwards. The interval where it is decreasing only is:
(-∞, 2)
Over which interval is the function decreasing only?All absolute value equations of the form:
y = |x - a| + b
have graphs that open upwards, and a vertex in the point (a, b).
While ones of the form:
y = -|x - a| + b
have graphs that open downwards, and again, a vertex in the point (a, b).
In this case we have one that open upwards:
h(x)=|x-2|+6
With a vertex at (2, 6)
The function will be decreasing on the left side of the vertex, so the interval where the function is only decreasing is:
(-∞, 2)
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If RS = 7, ST = 3x, and RT = x + 9, what is RT?
The required value of RT is 10 units when RS = 7, ST = 3x, and RT = x + 9.
What is a Line Segment?A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.
The figure given below shows a line segment RT, where the length of line segment RT refers to the distance between its endpoints, R and T.
RS = 7, ST = 3x, and RT = x + 9
R______________S______________T
⇒ RT = RS + ST ....(i)
Substitute the values of RS = 7, ST = 3x, and RT = x + 9,
⇒ x + 9 = 7 + 3x
⇒ 3x - x = 9 - 7
⇒ 2x = 2
⇒ x = 1
Substitute the values of x = 1 in RT = x + 9
So RT = 1 + 9 = 10
Hence, the value of RT is 10 units.
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if a seed is planted, it has a 95% chance of growing into a healthy plant. if 9 seeds are planted, what is the probability that exactly 3 don't grow?
If 9 seeds are planted, what is the probability that exactly 3 don't grow will be 1/5832000 as 5% chance are there that plant will not grow.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The chances of seed to be not growing is 1–0.95 =0.05.
For 3 seeds not to grow being simultaneous occurring events have the probability = 0.05×0.05x0.05=0.000125
As 9 seeds being planted the probability of selecting 1 out of 9 is (1/9).
So for 3 mutual occurring case is (1/9)×(1/9)x(1/9)= 1/729
So the probability will be (1/729)×1/8000=1/58,32,000
The likelihood that exactly 3 seeds out of 9 will not germinate is 1/5832000, or 5%, so there is a chance that the plant won't grow.
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Write a letter to your friend wishing him success
Answer:
Hello _____,
You are a pig, a fatty, a dunce, and a monkey. Also, you smell like a diseased pustule on the butt of a wildebeest.
Cordially,
_____
Step-by-step explanation:
super bowl xlvi was played between the new york giants and the new england patriots in indianapolis. due to a decade-long rivalry between the patriots and the city's own team, the colts, most indianapolis residents were rooting heartily for the giants. suppose that 90% of indianapolis residents wanted the giants to beat the patriot. what is the probability that, of a sample of 100 indianapolis residents, at least 15% were rooting for the patriots in super bowl xlvi?
The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.
By using the normal distribution method, a mean u and standard deviation σ,
The ratio of people who wants the Giants to eat patriots is p = 0.90,
The assumed sample size denoted by n is 100,
and their distribution's mean is u = 0.90,
by using the standard deviation formula is
σ = √(p(1 - p) ÷ n),
σ = √(0.90(1 - 0.90) ÷ 100),
σ = 0.03,
we get that the standard deviation is σ = 0.03
Here the probability that at least 15% of 100 Indianapolis residents encouraged the Patriots in the gaint match Super Bowl XLVI is
P(X > 0.15) = 1 - P((X - u) ÷ σ) > (0.90 - 0.15) ÷ 0.03))
The significant value of X,
X - u ÷ σ = Z
we get,
P(X > 0.75) = (Z<5)-1
P(X < 0.75) = 1.293 - 1
P(X < 0.75) = 0.293
By solving we get, The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.
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