find both the number combinations in the number of permutations for 9 objects taken 7 at a time
Answers
Answer
There are 36 combinations and 181440 permutations
Explanation
The number of combinations of n object taking r at a time is given by the formula;
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]From the question, n = 9 and r = 7, then substitute these values into the formula
[tex]^9C_7=\frac{9!}{7!(9-7)!}=\frac{9!}{7!\text{ }2!}=\frac{9\cdot8\cdot7!}{7!\times2}=\frac{72}{2}=36[/tex]The number of permutations of n object taking r at a time is given by the formula;
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations
[tex]^9P_7=\frac{9!}{(9-7)!}=\frac{9!}{2!}=\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2!}{2!}=181440[/tex]Therefore, there are 36 combinations and 181440 permutations
Related Questions
Karen is driving her moterhome. It uses 3 gallons of gas for every 24 milesComplete the table below showing the number of gallons used and the distance traveled.
( The table is 3,24 6, ? 7,? ? , 72 and 10, ?)
Answers
Answer: 6, 48 and 7, 56 and 9, 72 and 10,80
Step-by-step explanation:
Find the area of the pool. Write as a polynomial.
Pool
6x
3x-5
Answers
F(4) if f(x) = 3 x -1
Answers
Answer:
f(4) = 11
Step-by-step explanation:
f(x) = 3 x -1
Let x = 4
f(4) = 3*4 -1
= 12-1
= 11
f (x) = 3x - 1
f (4) = 3 × 4 - 1
f (4) = 12 - 1
f (4) = 11
Hope Helpful :-;
7. If Antonio makes x dollars per regular hours, and his boss tells him that he is
going to get paid over time at double time, write an equation to find his hourly
rate if he makes $1578.5 working 55 hours this week.
Answers
The equation for the hourly rate is 55x = 1578.5
For double hourly rate for overtime, it is 55 x 2x= 1578.5
Given
Antonia makes X dollars for regular hours
And 2x dollars for over time
Since he works 55 hours this week he works 8 hours a day
Hence the equation is as follows
55x = 1578.5
x= $28.7
In case of double payment during overtime
He gets double amount as following equation
55 x 2x
55 x 2(28.7) = $3157
Hence the equation to find his hourly rate is 55x = 157.85
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1) The compound interest of a sum of money is Rs 13310 and in 4 years is Rs 14641. Find the rate of interest and sum.
Answers
The rate of interest is 10% and the sum is Rs 10,1000.
What is compound interest?The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.
The compound interest formula is given by
Compound Interest = Amount – Principal
Here, the amount is
[tex]A=P(1+\frac{r}{100} )^{n}[/tex] where,
A = amount
P = principal
r = rate of interest
n = time (in years)
Given:
C.I. of a sum of money in 3 years = Rs 13310
C.I. of a sum of money in 4 years = Rs 14641
Let the principal be P and the rate of interest be r%
Then, according to the question,
For 3 years:
[tex]13310=P(1+\frac{r}{100} )^{3}[/tex] ..... (1)
For 4 years:
[tex]14641=P(1+\frac{r}{100} )^{4}[/tex] ..... (2)
Dividing equation (2) by (1), we obtain
[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]
⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]
⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]
⇒[tex]r=\frac{100}{10}[/tex]
⇒ r = 10%
Now, substituting r in equation (1),
[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]
⇒[tex]13310=P(\frac{1331}{1000} )[/tex]
⇒P = Rs 10,000
Therefore, the rate of interest is 10% and the sum is Rs 10,1000.
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please help meeee!!! :c
Function A
f(x) = x − 9
Function B
graph of line going through ordered pairs negative 1, negative 3 and 2, 3
Which equation best compares the slopes of the two functions?
Slope of Function B = 2 x Slope of Function A
Slope of Function A = Slope of Function B
Slope of Function A = 2 x Slope of Function B
Slope of Function B = − Slope of Function A
Answers
The equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
Given,
The function A, f(x) = x - 9
We have to find slope of Function B
The function is in the form of y = mx + b
Here, m is the slope.
y = x - 9
m is 1 and b is -9
Now, lets consider the graph of line passing through points (-1, -3) and (2, 3)
That is,
(x₁, y₁) = (-1, -3)
(x₂, y₂) = (2, 3)
Now we can find the slope of the line:
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-3)) / (2- (-1))
m = (3 + 3) / (2 + 1)
m = 6/3
m = 2
That is, the slope of function B is 2
Here,
Slope of function A is 1.
That is, slope of function B is twice the slope of function A.
Therefore, the equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
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PLEASE HELP!: I'm so confused about what equations to write for the problem. All I need is the equations and I can solve it alone! I'll give brainly!
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal, and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
Answers
Using simple interest, the amounts invested into each account are given as follows:
Paper returns: $3,500.Metal returns: $1,500.Glass returns: $3,000.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = P(1 + rt)
In which:
P is the initial amount.r is the interest rate, as a decimal.The amount of interest after t years is given by:
I(t) = Prt
You invest $8,000 in 3 investment accounts, hence:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
From the rates of the account, we have that:
[tex]I_1 = 0.02P_1[/tex][tex]I_2 = 0.04P_2[/tex][tex]I_3 = 0.05P_3[/tex]The amount invested in the glass account was double the amount invested in the metal account, hence:
[tex]P_3 = 2P_2[/tex]
The yield was a total of $280 at the end of one year, hence:
[tex]I_1 + I_2 + I_3 = 280[/tex]
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
From the first and the third equations, we have that:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
[tex]P_1 + 3P_2 = 8000[/tex]
[tex]P_1 = 8000 - 3P_2[/tex]
Hence the amount of the metal investment can be found as follows:
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]
[tex]0.08P_2 = 120[/tex]
[tex]P_2 = \frac{120}{0.08}[/tex]
[tex]P_2 = 1500[/tex]
Hence the other investments are given as follows:
Paper: 8000 - 3 x 1500 = $3,500.Glass: 2 x 1500 = $3,000.More can be learned about simple interest at https://brainly.com/question/20690803
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n(x) = -1-x+4
n(-2) =
n(0)=
n(5)=
Answers
Step-by-step:
n(x) = -1 - x + 4
n(-2) = -1 - (-2) + 4
= -1 + 2 + 4
= 5
___________________________
n(0)= -1 - 0 + 4
= 3
___________________________
n(5)= -1 - 5 + 4
= -2
18x-51=9(4x+5)-6(3x-10)
Answers
[tex]18-51=36x+45-18x-60\\18x-51=36x-18x+45-60\\18x-51=18x-15\\18x-18x=-15+51[/tex]
∴ 18x-18x≠-15+51
THERE IS NO SOLUTION FOR THIS EQUATION
Suppose f(x)=4[[x-1]].
Find: f(1.7),f(-3.4), and f(9.8).
Answers
Answer:
I believe it should be
f(1.7) = 2.8
f(-3.4) = -17.6
f(9.8) = 35.
Step-by-step explanation:
Simply plug-in the different numbers for x.
If f(x) = 4x6 + x² + 4, then what is the remainder when f(x) is divided by x -1?
Answers
Answer:
9
Step-by-step explanation:
[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]
The equation y = 0.43x + 50 models the cost y of renting a car if the car is driven x
miles.
According to the model, what is the best estimate of the cost for renting a car if you
plan to drive 489 miles? Please round your answer to the nearest dollar.
Answers
By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.
What do we mean by equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.
Now, solve for y when the value of x is 489.
y = 0.43x + 5y = 0.43(489) + 5y = 210.27 + 5y = $215.27Rounding off: y = $215
Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.
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the ratio of 26,000 bytes to 48,000 bytes can be written in fractional form as
Answers
Answer:
26000:48000
26000/48000
26/48(cancel the zeros)
13/24
fractional form=13/24
for a sequence of events in which the first event can occur n 1 ways, the second event can occur n 2 ways, the third event can occur n 3 ways, and so on, the events together can occur a total of n 1 times n 2 times n 3 times ... ways. this is called .
Answers
The most appropriate choice for Independent event and multiplicative counting rule will be given by
This is known as multiplicative counting rule.
What is Independent event and multiplicative counting rule?
Event that is not dependent on any other event is called independent event.
Let A and B be two independent events.
P(A∩B) = P(A) [tex]\times[/tex] P(B)
If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.
Here,
Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on
Also assuming that the events are independent
The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways
This is known as multiplicative counting rule.
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i need help with this i just need the answer.
Answers
We have to find the length of FH.
We know that G is on the line, and we know the length FG and GH, so we can represent this as:
We then, we can apply the rule that states that the length of a segment is equal to the length of the segments that are part of it:
[tex]FH=FG+GH=10+5=15[/tex]Answer: FH = 15
round to the underlined digit:
Answers
Answer:
c because if the number next to the underlined is above 5 u round up under 4 u round down
Step-by-step explanation:
Answer: c. 76
Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.
Divide
-36
-8
Enter your answer as a mixed number, in simplified form, in the box.
Answers
the answer is this
4 4/8.
1. 5- (-8) =
2. -3 1/2 - 4 1/2 =
3. -7 - 4 =
4. -0.5 - 3.5 =
Answers
Answer:
1. 5- (-8) = 13
2. -3 1/2 - 4 1/2 = -7 1/2
3. -7 - 4 = -11
4. -0.5 - 3.5 = -4
Step-by-step explanation:
1. 5- (-8) =
5 + 8
13
2. -3 1/2 - 4 1/2 =
-7 1/2
3. -7 - 4 =
-11
4. -0.5 - 3.5 =
-4
Mrs. argueta needed to fill up her gas tank. gas cost $3.66 per gallon and she needed 9 1 2 gallons. how much did it cost mrs. argueta to fill up her tank?
Answers
Answer:
$3337.92
Step-by-step explanation:
$3.66 x 912 = $3337.92
Someone please help me!!! ( I'll mark brainliest )
Answers
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
find the number of sides of a regular polygonwhose exterior angle measure 18°
Answers
Answer:
20
Step-by-step explanation:
The sum of the exterior angles of a polygon add to 360. 360 divided by 18 is 20.
How do you do these?
Solve for s.
6/s = 2
Answers
Answer:
s=3
Step-by-step explanation:
So you have the equation: [tex]\frac{6}{s}=2[/tex]
If we multiply both sides by this "s" value we should maintain equality, and it conveniently cancels out our division by "s" on the left side giving us the following equation: [tex]6=2s[/tex]
The only "operation" on the value "s" is the coefficient of 2, which is multiplying the value of "s" by 2.
To undo this multiplication of 2, we simply divide by 2, since 2/2 = 1, and now we have a coefficient of 1 for the "s", which is the same as isolating "s"
But we want to divide both sides by 2 to maintain equality, so let's write out our expression
[tex]\frac{6}{2}=\frac{2s}{2}\implies3=\frac{2}{2}*s\implies 3=s[/tex]
We can double check this by plugging in this value for "s" in the original equation: [tex]s=3, \ \frac{6}{s}=2\implies \frac{6}{3}=2\implies 3=3[/tex] which is indeed true, so we have our solution!
You cut a 90-foot rope into 6 pieces of equal length. What is the length of
each piece?
Answers
Answer:
Length = 15
Step-by-step explanation:
The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation
90 feet / 6 pieces
Which equals
90 feet / 6 pieces = 15 feet/piece (15 feet per peice)
Hope this helps :)
Find the value of x if T is the midpoint of segment XY. Segment XT = 3x-14, Segment XY = 8x-56
Answers
The value of x if T is the midpoint segment XY is 14.
How to find the mid point of a segment?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints.
The midpoint is halfway between the two end points.
Therefore, the end point of the segment is XY.
The midpoint is T.
Hence,
XY = XT + YT
XT = 3x - 14 = YT
XY = 8x - 56
Let's find the value x.
Therefore,
8x - 56 = 3x - 14 + 3x - 14
8x - 56 = 6x - 28
8x - 6x = -28 + 56
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
Therefore, the value of x is 14
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Which expression is equivalent to t
3(x+24)?
A-2/3x+24
B-2/3x+16
C -2/3x-16
D 2/3x-16
Answers
Because of -2 the answer is c
help asap please and thank u
Answers
Answer:
y = 5, 3
x = 155, 171
(y = 5, x = 155)
(y = 3, x = 171)
Step-by-step explanation:
(8y - 15) = (y²)
-8y + 15 -8y + 15
--------------------------------
y² - 8y + 15 = 0
(y - 5) (y - 3) = 0
--------------
y = 5, 3
----------------------------------------------------------------------------------------------------------
y² + x = 180
(5)² + x = 180
25 + x = 180
-25 -25
--------------------
x = 155
(3)² + x = 180
9 + x = 180
-9 -9
------------------
x = 171
----------------------------------------------------------------------------------------------------------
I really hope this helps!
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Answers
We can conclude that the probability of the randomly selected person does not use any facility is 0.
What is probability?Simply put, the 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. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the selected person does not uses any facility:
According to the given data, we can easily say that all the people use some or the other facility.So, there are 0 people present who do not use the facility.Then, the probability that the selected person does not use any facility will be 0.Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.
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i need help with this, thanks
Answers
Answer: 11
Step-by-step explanation:
8x + 7 = 9x - 4
7 = x - 4
11 = x
Please answer the question in the photo
Answers
Answer:
u= 30
Step-by-step explanation:
the sum of all angles on a triangle is 180* so u add the others (120+30)
that brings it to 150 then 180-150=30*
Bob makes some fruit punch that contains apple and mango juice in a 1:5 ratio. If he uses 15 pints of the mango juice how many pints of apple juice will he need
Answers
he needs 3 pints of mango
Answer:3
Step-by-step explanation:
If the ratio is 1:5 that means that the number of pints of apple juice is multiplied by 5 to get the nimber of pints of mango juice