Answers
Answer:
[tex]36[/tex]
Step-by-step explanation:
The expression [tex]_nC_k[/tex] is used to denote the number of ways you can choose [tex]k[/tex] things from a set of [tex]n[/tex] things. It is equal to:
[tex]_nC_k=\binom{n}{k}=\frac{n!}{k!(n-k)!}[/tex]
In this case, [tex]n=9[/tex] and [tex]k=2[/tex], so:
[tex]\implies \frac{9!}{2!(9-2)!}=\frac{9!}{2!7!}=\boxed{36}[/tex]
You can also think of it like this:
[tex]_9C_2[/tex] is saying 9 choose 2. We are choosing 2 things from a set of 9 things, where order doesn't matter. For the first thing we choose, there are 9 options. Then 8 options, 7, and so on. Since we're only choosing two things, there are [tex]9\cdot 8=72[/tex] permutations. However, the order of which we choose each thing does not affect what we've chosen overall (e.g. If we're choosing two donut flavors original and strawberry, it doesn't matter which flavor I choose first, because I'm still getting the same two flavors). Therefore, we must divide this by the number of ways we can arrange two distinct values, which is [tex]2![/tex]. Our answer is thus [tex]\frac{72}{2!}=\frac{72}{2}=\boxed{36}[/tex]
=========================================================
Explanation:
We have 9*8 = 72 different permutations. This is if we used the nPr formula with n = 9 and r = 2.
Notice the countdown from 9 to 8. This is because we don't reuse the same element twice.
Since order doesn't matter with nCr, we will divide by 2. This is because something like AB is the same as BA. So we go from 72 to 72/2 = 36
The value 36 is found in Pascal's Triangle in the row that has 1,9,... at the start of it. Start at the left hand side and count exactly 3 spaces to the right, and you should land on 36.
Related Questions
How many solutions does the system have?
4x−6y=−24
2x−3y=−6
Answers
Answer:
none
Step-by-step explanation:
if we plot it, it's clear, but you might also spot that the plotted lines will be parallel in the equation
because x and y in line two are the same multiple of these in line one (both values are just the half)
plotted with desmoes
✨Please help me :) ✨
Answers
Answer:
Jaden would have to save $25 each week for next 6 weeks to get the $290 bike.
Step-by-step explanation:
What do we know:
He has $140 to start withHe saves $25 each weekHis bike costs $290What are we solving for;
We are solving for x (number of weeks it would take Jaden to buy a $290 bike), when y = 290Equation would be:
y = 25x + 140So for Jaden to buy a $290 bike, y would have to be replaced with 290, and solve for x;
y = 25x + 140=> 290 = 25x + 140
=> 290 - 140 = 25x
=> 150 = 25x
=> 150 / 25 = x
=> 6 = x
Therefore, Jaden would have to save $25 each week for next 6 weeks to get the $290 bike.
Hope this help!
Share $150 among John, Mary, and Sarah so that each of the two girls receives twice as much as John. Calculate the amount of money Jon received.
Answers
please answer and explain the link below
Answers
Answer:
2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFunctionsFunction NotationCalculus
Limits
Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Definition of a Derivative: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
f(x) = 2x - 5
Step 2: Differentiate
[Limit] Substitute in x [Function f(x)]: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - f(x)}{\triangle x}[/tex][Limit] Substitute in function: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - (2x + 5)}{\triangle x}[/tex][Distributive Property] Distribute 2: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2x + 2\triangle x + 5] - (2x + 5)}{\triangle x}[/tex][Distributive Property] Distribute negative: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{2x + 2\triangle x + 5 - 2x - 5}{\triangle x}[/tex][Subtraction] Combine like terms: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{2\triangle x}{\triangle x}[/tex][Division] Simplify: [tex]\displaystyle \lim_{\triangle x \to 0} 2[/tex]Evaluate limit [Limit Rule - Constant]: [tex]\displaystyle 2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
What’s the answer for this
Answers
Answer:
4) y + 3 = 6x
Step-by-step explanation:
The y-intercept of your graph is (0, -3)
Putting 4) in standard form:
y = 6x - 3 the y-intercept is also (0, -3)
Identify the slope and y-intercept for the line y = -2x -3.
Answers
Answer:
The slope is -2 and the y intercept is -3
Step-by-step explanation:
y = -2x -3
This equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is -2 and the y intercept is -3
Stella earned $72 working 9 hours. How much will she earn in 23 hours?
Answers
Answer: Stella would earn $184 in 23 hours.
Step-by-step explanation: First we need to find the unit rate so start by dividing by 9
[tex]\frac{72}{9} =8\\\frac{9}{9}=1[/tex]
Now we know every hour Stella will earn $8. We can now multiply the amount for 1 hour by 23 to get the amount for 23 hours.
8x23=184
1*23=23
Now we can see that Stella would earn $184 for working 23 hours.
What is a solution of -8x+5>=11
A.-1/2
B.3
C.0.25
D.-1
Answers
Answer:
i got -2
Step-by-step explanation:
1 step; 8*x-5-(11)=0
2 step; 8x - 16 = 8 • (x - 2)
3 step; Solve : 8 = 0
4 step; Solve : x-2 = 0
final part Add 2 to both sides of the equation :
x = 2
Use the tangent ration to find the height of the tree. Round to next whole number.
Answers
Answer:
74.8925767 rounded to 75
Step-by-step explanation:
Which function graph is shown
Answers
Answer:
A) y=3cos(-x)
Step-by-step explanation:
Because the amplitude of the graph is 3, this eliminates options C and D as their amplitudes are different. With the period of the graph being 2π, B cannot be correct because that would have a period of π/2. Therefore, A is correct.
can someone help me solve the inequality-2x+4>8 with the steps? Thanks
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\rm{-2x + 4 > 8}[/tex]
[tex]\large\textsf{SUBTRACT 4 to BOTH SIDES}[/tex]
[tex]\rm{-2x + 4 - 4 > 8 - 4}[/tex]
[tex]\large\textsf{CANCEL puts 4 - 4 because that gives you 0}[/tex]
[tex]\large\textsf{KEEP: 8 - 4 because that helps solve for the x-value}[/tex]
[tex]\rm{8 - 4 = \boxed{\bf 4}}[/tex]
[tex]\rm{NEW\ EQUATION: -2x > 4}[/tex]
[tex]\large\textsf{DIVIDE -2 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{-2}{-2}>\dfrac{4}{-2}}[/tex]
[tex]\mathsf{CANCEL\ out: \dfrac{-2}{-2}\ because\ that\ gives\ you\ 1}[/tex]
[tex]\mathsf{KEEP: \dfrac{4}{-2} \ because \ it \ helps \you \ compare\ to \ the \ x-value }[/tex]
[tex]\mathsf{\dfrac{4}{-2} = \boxed{\bf -2}}[/tex]
[tex]\rm{\bold{x < -2 }}[/tex]
[tex]\rm{It\ is \ an\ O PENED \ circle \ shaded \ to \ the \ left \ side \ of \ the \ number \ line}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: } \mathsf{\bf x < -2}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Put commas and write the following numbers in Indian system of
numeration
a) 2345678
b) 5678090
Put commas and write the following numbers in International system of
numeration
a) 234589
b) 9807062
Answers
1. Indian System:-
(a) 23,45,678
(b) 56,78,090
2. International System:-
(a) 234,589
(b) 9,807,062
what is the mean absolute deviation for 3 3 4 5 5 4
Answers
Answer as a fraction = 2/3
Answer in decimal form = 0.667 (approximate)
=======================================================
Explanation:
The first thing we need is to find the mean. Add up the values to get 3+3+4+5+5+4 = 24. Then divide by n = 6 since there are 6 values.
24/n = 24/6 = 4
The mean is 4
Now subtract the mean from each value
3-4 = -13-4 = -14-4 = 05-4 = 15-4 = 14-4 = 0Apply absolute value to each result so that the difference is not negative.
We get this new list: {1, 1, 0, 1, 1, 0}
Now compute the mean of that new list to get the final answer
1+1+0+1+1+0 = 4
4/n = 4/6 = 2/3 = 0.667 approximately
Answer:
hi how are you
Step-by-step explanation:
hope you are good
someone help me answer these two
Answers
Range (9,0) to (6,3)
Not a function because two inputs cannot share the same output
2. Domain (1, 50) to (5, 200)
Range (1,50) to (5, 200)
Yes it is a function
find hcf and LCM of 40 ,60 and 80
Answers
hear here is your answer in attachment attach
Answer:
Step-by-step explanation:
40 = 2*2*2*5
60 = 2 * 2 * 3 * 5
80= 2 * 2 * 2 * 2 * 5
LCM = 2 * 2 * 2 * 2 * 5 * 3 = 240
HCF = 2*2*5= 20
Given the linear equation 5x+3y-9=0. Write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines
Answers
Answer:[tex]5x+3y+1=0[/tex]
Step-by-step explanation:
Given
The linear equation is [tex]5x+3y-9=0[/tex]
The other linear equation parallel to the given line can be represented by
[tex]5x+3y+c=0[/tex]
Here, c can take any value . for example c=1, line becomes
[tex]\Rightarrow 5x+3y+1=0[/tex]
10 points!
If you are going to answer, actually answer!
Answers
Answer:
1/27
Explanation:-
(1/3)^3=(1x1x1)/(3x3x3)=1/27
Answer:
0.03703703703 or
²/27
sorry i am late but still hope I helped
Step-by-step explanation:
On Saturday, the fruit and juice bar was selling 27 glasses of fruit punch an hour. By 7 p.m., they had sold 243 glasses. If their goal was to sell more than 324 glasses of fruit punch, find the number of hours, h, they must stay open past 7 p.m. to make their goal.
Answers
Answer: 3 hours
Step-by-step explanation:
the answer this can be solved by the function:
324 = 27x + 243
-243 -243
27x = 81
/27 /27
x = 3 hours past 7.
henry who is 3 years younger than sandra is 14 write an equation to represent sandras age
Answers
what is the slope that passes through the points : (-2,9) and (4,-7)
Answers
Use the slope formula below:
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
The m-term represents the slope.
The formula is the changes of two y-points over the changes of two x-points. We are given two points. Substitute both points in the formula.
[tex] \large{m = \frac{9 - ( - 7)}{ - 2 - 4} } \\ \large{m = \frac{9 + 7}{ - 6} \longrightarrow \frac{16}{ - 6} } \\ \large{m = \frac{8}{ -3 } \longrightarrow - \frac{8}{3} }[/tex]
Therefore the slope is -8/3
Answer
the slope is -8/3Hope this helps! Let me know if you have any doubts.
Answer:
y = -8 / 3x + 11/3
Step-by-step explanation:
Using the slope formula:
[tex]slope = y = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}[/tex]
1. Select one point to be [tex](x_{1} ,y_{1} )[/tex] and the other [tex](x_{2} ,y_{2} )[/tex]
I chose (-2, 9) to be [tex](x_{1} ,y_{1} )[/tex] and (4, -7) to be [tex](x_{2} ,y_{2} )[/tex]
2. Plug the values into the formula:
[tex]y = \frac{-7-9}{4-(-2)} \\\\y= \frac{-16}{6} \\\\y = \frac{-8}{3}[/tex]
3. Finding the c-value by plugging in one of the points into the equation
y = mx + c
9 = -8/3 (-2) + c
9 = 16/3 + c
c = 11/3
4. y = -8/3x + 11/3
help me solve for m<4 and m<5 and x
Answers
Answer:
x = 18
Angle 4 = 31 degree
Angle 5 = 59 degree
Step-by-step explanation:
According to the question, angle 3 is 90 degree and the sum of angle 4 and 5 is equal to the angle 3 as they are vertically opposite angles.
Angle 4 + angle 5 = 90 degree
Angle 4 = 2 x - 5
angle 5 = 4 x - 13
So, according to the question,
2 x - 5 + 4 x - 13 = 90
6 x - 18 = 90
6 x = 108
x = 18
So, angle 4 = 2 (18) - 5 = 31 degree
So, angle 5 = 4 (18) - 13 = 59 degree
Each student gets a bag with 6 celery sticks in it. Dwayne eats 4 of his celery sticks. Write the fraction of celery sticks Dwayne eats. Dwayne thinks he ate 2 3 of his celery sticks. Is he correct?
Answers
I will give brainiest
Answers
Answer:
B
Step-by-step explanation:
The graph shows the absolute value parent function. Which statement best describes the function?
A. The function is positive when x > 0.
B. The function is always positive.
C. The function is positive when x< 0 and when x > 0
D. The function is positive when x< 0
PLEASE HELPPP!!!!
Answers
The function of the absolute value is always positive the correct answer would be option (B).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
For example, |5| is 5 because it is 5 units away from 0. Also, |-5| is also 5 because -5 is 5 units from 0.
We have to determine the statement best describes the function.
We have been given that the graph represents the absolute value parent function.
Since the parent function's graph with an absolute value that is always positive.
Therefore, the graph of the absolute value parent function would be always positive.
Hence, the correct answer would be option (B)
Learn more about the absolute value here:
brainly.com/question/1301718
#SPJ2
Which of the following equations will be the graph of a parabola?
y = 5x + 12
y = x^2 - 2x + 3
3x^5 - 6x^3 + 4x + 12
y = 2 ⋅ 3^x
Answers
Answer:
Y=x^2 -2x + 3
Step-by-step explanation:
it's quadratic like:-)
B.
If m ZACB = 180°, and mZACD = 55°, then
mZDCB = [?]
Enter
Answers
Answer:
125
Step-by-step explanation:
/_ ACB = 180
/_ ACD = 55
/_ ACB is made up of /_ACD and
/_ DCB
Hence, /_ ACB = /_ ACD + /_ DCB
*We then plug in the known values*
180 = 55 + /_ DCB
We now solve for the missing angle
Subtract 55 from both sides
125 = /_ DCB
Please help me ASAP and i mean ASAP
Answers
Answer:
no
Step-by-step explanation:
no
I NEED HELP ASAP IM STRESSJNG OUT
Answers
Answer:
A
Step-by-step explanation:
Using the Sine rule in Δ ABC
∠ B = 180° - (30 + 50)° = 180° - 80° = 100° ( sum of angles in triangle ) , then
[tex]\frac{13}{sin100}[/tex] = [tex]\frac{BC}{sin30}[/tex] ( cross- multiply )
BC × sin100° = 13 × sin30° ( divide both sides by sin100° )
BC = [tex]\frac{13sin30}{sin100}[/tex] ≈ 6.6 ( to the nearest tenth )
Help me to do exercise no 5
Answers
Answer:
Step-by-step explanation:
a) x + 20 = 70 Vertically opposite angles are congruent
b) 2x - 50 = x + 20 Vertically opposite angles are congruent
c) 3x - 10 + 140 = 180 Linear pair
Answer:
(a) 70= x+20 (vertical angles are equal)
70 - 20=x
50=x
(b) x +20 = 2x -50 (vertical angles are equal)
20 + 50 = 2x - x
70 = x
(c) 140 +3x -10=180 (angles on the straight line)
130 +3x = 180
3x = 180 - 130
3x = 50
x= 50/3
Helpppp meeeeeeeeeee
Answers
Answer:
1
[tex] = \frac{45}{100} \times 75 \\ = 33.75[/tex]
2.
[tex] \frac{150}{100} \times 36 \\ = 54[/tex]
3.
[tex] \frac{850}{100} \times 255 \\ = 21675[/tex]
