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Find the binomial coefficient
( 11)
(6)
Evaluate using Pascal's Triangle
4_C_1
Answers
Answer:
462; 4------------------------------
The binomial coefficients can be found using Pascal's triangle.
Remember the rows are numbered starting from the second one on the top, and the first element is skipped in every row.
For the first one, follow the 11th row and 6th column, it is number 462, and for the second one follow the 4th row and 1st column, this is number 4, see the attached for both.
Calculation of the binomial coefficient is as follows:
[tex]\[ \binom{11}{6} = _{11}C_6=\cfrac{11!}{6!(11-6)!}=\cfrac{6!*11*10*9*8*7}{6!5!} =\cfrac{11*10*9*8*7}{5*4*3*2} =462[/tex][tex]\[ \binom{4}{1} = _4C_1=\cfrac{4!}{1!(4-1)!} =\cfrac{4!}{3!} =\cfrac{3!*4}{3!} =4[/tex]
Related Questions
A student purchased 9 binders for $11.07.
Solve the equation to determine the cost, in dollars, for each binder.
$
Answers
Answer:
$1.23
Step-by-step explanation:
9 binders for 11.07, where x = num of binders
9x = 11.07 [Divide both sides by 9]
x = $1.23
Answer:
each binder costs $1.23
Step-by-step explanation:
$11.07 divided by 9 equals $1.23
A chi-square test was conducted to investigate whether there is an association between a person's favorite flavor of ice cream and their favorite toppings. Each of 200 randomly selected customers at an ice cream parlor was asked to pick their favorite flavor from vanilla, chocolate, chocolate chip, or none of these. They were also asked to pick their favorite topping from chocolate sauce, peanuts, crumbled cookies, crushed candies, or none of these. The hypothesis test had a test statistic of 24.97 with an associated p-value of 0.015. If the significance level of the test was a = 0.05, which of the following is the correct decision for this hypothesis test?
A. There is not convincing statistical evidence to suggest an association between favorite ice cream flavor and favorite topping.
B. There is convincing statistical evidence to suggest an association between favorite ice cream flavor and favorite topping.
C. There is convincing statistical evidence to suggest there is not an association between favorite ice cream flavor and favorite topping.
D. There is proof that a person's favorite ice cream topping is dependent on the person's favorite ice cream flavor.
E. There is proof that a person's favorite ice cream topping is independent of the person's favorite ice cream flavor.
Answers
Answer:
B
Step-by-step explanation:
I hope it is correct :)
Answer:
The answer is definitely B
Step-by-step explanation:
I just did this question on my test.
23 Points | Brainliest | Pre Calc Question | Thanks so much ahead of time.
Find the sum of the first 12 terms of the sequence. Show all work for full credit.
1, -4, -9, -14, . . . (2 points)
Answers
Answer:
1, -4, -9, -14, -19, -24, -29, -34, -39, -44, -49, -54 = -318
Step-by-step explanation:
Answer:
The Answer is -318.
Step-by-step explanation:
1 + (-4) + (-9) + (-14) + (-19) + (-24) + (-29) + (-34) + (-39) + (-44) + (-49) + (-54)
Question 7 (3 points)
Cris borrowed $10,000 at an interest rate of 6% compounded daily. What is her approximate balance at the end of 4 years?
A $14,100
B $14,400
C $11,800
D $13,500
E $12,700
Answers
Side A=3 cm
Side B=?
Side C( Hypotenuse)=6 cm
Find missing side of right triagle using Pythagorean Theorem
a
3 cm
3 square root (5) cm
3square root (3) cm
6 cm
Answers
Answer:
3sqrt3 cm
Step-by-step explanation:
6^2-3^2
36-9=27
sqrt27 = 3sqrt3
Answer:
c. 3 square root ( 3 ) cm
Step-by-step explanation:
C^2 = A^2 + B^2
A^2 = C^2 - B^2
= 6^2 - 3^2
= 36 - 9
A^2 = 27
A = 3√3 cm
evaluate 3 + jk + k ^3 when j = 2 and k = 6
Answers
hope this helps!
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter. To the nearest meter, how many meters are in 318 inches? Enter the answer in the box.
Answers
Explanation:
the slope of (3, 12) and (4, 16)
Answers
Answer:it’s 1/4
Step-by-step explanation:
What's the distance between (4,-2) and (4,3)
Answers
Answer:
5 units
Step-by-step explanation:
(4, -2 ) ; [tex]x_{1}=4[/tex] and [tex]y_{1} = -2[/tex]
(4 , 3) ; [tex]x_{2} = 4[/tex] and [tex]y_{2}=3[/tex]
distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\[/tex]
[tex]= \sqrt{(4-4)^{2}+(3-[-2])^{2}}\\\\= \sqrt{0+(3+2)^{2}} \\\\=\sqrt{5^{2}}\\\\= 5 units[/tex]
Which function defines (g•f)?
f(x)= log(5x)
g(x) = 5x + 4
A. (g•f)(x)= 5x log(5x) + 4log(5x)
B. (g•f)(x) = 5x + 4 + log(5x)
C. (g•f)(x) = 5x – 4 – log(5x)
D. (g•f)(x) = 5x log(5x) + 4
Answers
Answer:
A
Step-by-step explanation:
A. (g•f)(x)= log(5x) ( 5x + 4)=5x log(5x) + 4log(5x)
The function 5x log(5x) + 4log(5x) defines (g•f)
We have given that,
A. (g•f)(x)= 5x log(5x) + 4log(5x)
B. (g•f)(x) = 5x + 4 + log(5x)
C. (g•f)(x) = 5x – 4 – log(5x)
D. (g•f)(x) = 5x log(5x) + 4
We have to determine which function defines (g•f)
Where f(x)=log(5x) and g(x)=5x+5
What is the multiplication function?
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
A. (g•f)(x)= log(5x) ( 5x + 4)=5x log(5x) + 4log(5x)
(5x+4)(log(5x))=5x(log(5x))+4(log(5x))
Therefore the option A is correct.
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which equations are equivalent of requirements -1/4(x)+3/4=12? select all that apply.
the answer: B,C,E (for people who don’t have brainly plus) <3
you can use this to get points if you’d like
Answers
179=-9x+8
How do I break it down to slove this problem
Answers
Answer:
x = -19
Step-by-step explanation:
first isolate x by subtracting 8 on both sides:
179 = -9x + 8
-8 -8
=> 171 = -9x
then divide -9 on both sides to solve for x:
=> x = 171 ÷ -9 = -19
hope it helps ;)
1/2 minus 2/3
I have trouble with fractions
Answers
Answer:
-1/6
Step-by-step explanation:
Hope this helps down below! Pls mark brainliest
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(12×33)−(23×22)=?
Complete the multiplication and the equation becomes
36−46=?
The two fractions now have like denominators so you can subtract the numerators.
Then:
3−46=−16
This fraction cannot be reduced.
Therefore:
12−23=−16
Solution by Formulas
Apply the fractions formula for subtraction, to
12−23
and solve
(1×3)−(2×2)2×3
=3−46
=−16
Therefore:
12−23=−16
Leanna opens a savings account with an initial balance of $100. She then deposits $50 each month. Use an equation, a table, and a graph to explain the relationship between the amount of money in the account, a, and the number of months since Leanna opened the account, m.
Part A Write an equation to represent the problem. Explain how the value of a changes as m increases.
Part B Make a table to show the relationship between m and a. Find 5 ordered pairs.
Part C Use your table from Part B to draw a graph to represent the situation.
Please answer all questions
Answers
See the attached picture:
HELP ME WITH 6-10 PLS
Answers
6. = 0.0000004834
7. = 0.0000506
8. = 0.00098
9. = 64580000
10. = 1398600000
What is the period of this function
Answers
Answer:
B
Step-by-step explanation:
Period equals pi/2
(10 pts) A four-lane freeway (two lanes in each direction) is located on rolling terrain and has 12-ft lanes, no lateral obstructions within 6 ft of the pavement edges, and there are 2 ramps within 3 miles upstream of the segment midpoint and 3 ramps within 3 miles downstream of the segment midpoint. A weekday directional peak-hour volume of 1800 vehicles (familiar users) is observed, with 700 arriving in the most congested 15-min period. Ifa level of service no worse than C is desired, determine the maximum number of heavy vehicles that can be present in the peak-hour traffic stream.
Answers
Answer:
309
Step-by-step explanation:
To determine the estimated free-flow speed
[tex]FFS = 75.4 -f_{LW}-f_{LC} - 3.22 TRD^{0.84}[/tex]
From the table "Adjustment for lane width," which corresponds to a lane width of 12 feet. As a result, [tex]f_{LW}[/tex] equals 0 mi/h.
Take the meaning from the table "Adjustment for right-shoulder lateral clearance," which corresponds to 6 feet of right shoulder lateral clearance and two lanes in one direction.
The [tex]f_{LC} = 0 mi/h[/tex]
[tex]FFS = 75.4 -0-0-3.22 ( \dfrac{5}{6})^{0.84}[/tex]
[tex]= 72.64 \ mi/h[/tex]
[tex]\simeq 73 \ mi/h[/tex]
Determine the peak-hour factor
[tex]PHF = \dfrac{V}{V_{15}\times 4} \\ \\ =\dfrac{1800}{700\times 4}\\ \\ = 0.6429[/tex]
Now, Find the heavy-vehicle adjustment factor.
[tex]v_P = \dfrac{V}{PHF\times N \times f_{HV}\times f_P} --- (1)[/tex]
Take the value for the 15-minute passenger car equivalent flow rate from the table "LOS requirements for freeway segments" for the FFS and LOS C conditions. The free-flow speed is estimated to be 73 miles per hour
[tex]v_p = 1735+ \dfrac{73-70}{75-70}(1775-1735)[/tex]
[tex]v_p = 1759 \ pc/h/In[/tex]
Think about for familiar users the value of f_p = 1.00
Replace all of the values obtained in (1)
[tex]v_p = \dfrac{V}{PHF \times N\times f_{HV}\times f_p}[/tex]
[tex]1759 = \dfrac{1800}{0.6429\times 2 \times f_{HV}\times 1}[/tex]
[tex]f_{HV} = \dfrac{1800}{0.6429\times 2 }\times \dfrac{1}{1759}[/tex]
= 0.795
Calculate the percentage of trucks and buses in the flow of traffic stream.
[tex]f_{HV} = \dfrac{1}{1+P_{\tau}(E_{\tau}-1) + P_R(E_R-1)}[/tex]
Take the values from the table "Passenger car equivalent for extended highway segments" referring to trucks and buses and rolling terrains for passenger car equivalent for trucks and buses and recreational vehicles. As a result, [tex]E_T[/tex] has a value of 2.5 and [tex]E_R[/tex] has a value of 2.0.
Since [tex]P_R[/tex] is zero and there is no recreational vehicle.
Then;
[tex]0.759 = \dfrac{1}{1+ P_T(2.5 -1) +0}[/tex]
[tex]P_T = 0.1719[/tex]
Finally, to estimate the maximum number of large trucks and buses; we have:
[tex]= V\times P_T = 1800 \times 0.1719[/tex]
Maximum number of large trucks and buses = 309
Find the surface area of the prism L=13 W=7 H=4
Answers
Answer:
342 units squared
Step-by-step explanation:
since this is a rectangular prism, all we have to do is multiply the values by one of the other values once and multiply that by 2
please help i am giving away brainliest
A swimming pool in the shape of a cylinder with a diameter of 10 m and a depth of 3 m is being filled with water. 27,535 L have been added so far. 1 m3 is equal to 1000 L. To the nearest liter, how much more water can the pool hold?
A. 236,000 L
B. 208,084 L
C. 236,616 L
D. 207,314 L
No dam links
Answers
Answer:
207,314
Step-by-step explanation:
V = πr2h =π · 52·3 ≈ 235.61945 m^3
because 1m^3 = 1000 L, (27,535 / 1000) = the amount of added water in m^3. As this is equal to 27.535, we can substract this from 235.62.
235.62 - 27.535 is about 208.085, or 207.314 because of rounding. As this is in m^3, we multiply by liters to arrive at the answer of 207,314, or option D.
What is the value of logg 8?
Answers
Answer:
The value of log 8 is 0.9030
Step-by-step explanation:
To find:
Value of log 8
Solution:
Let we take,
x=log8
x=log (2)^3
x=3log2
x=3*0.3010
x=0.9030
Hence, the value of log 8 is 0.90.
Simplify: (3^5)^2 / 3^-2
A) 3^10
B) 3^9
C) 3^12
D) 3^8
Answers
Answer:
3^12
Step-by-step explanation:
(3^5)^2 / 3 − ^2 = 243^2/3−^2 = 59049 / 3−^2 = 59049/ 1 / 9 = 531441
= 3*3*3*3*3*3*3*3*3*3*3*3 = 3^12
which is the largest interval over which the function shown in the table is increasing?
x y=-- x2 ?
-4
-8
-
-2
-2
(x, y)
(-4,-8)
(-2,-2)
(0,0)
(2.-2)
(4.-8)
0
NO
-2
4
-8
O
A. x < -2
O B. x<0
C. X>0
D. X> 2
Answers
Answer:
x < 0
Step-by-step explanation:
If you were to graph the function, you would get a parabola that opens down with the vertex at (0, 0). So, the graph is increasing from -∞ to 0.
PLEASEEEEE HELPPPPP!!!!!!
Answers
Answer:
RS=5.65
Step-by-step explanation:
Please gimme few minutes
Maria randomly selects a number from the list of numbers below.
56, 90, 88, 76, 12
What is the probability that she selects an even number?
Answers
Answer:
1:1 or 100% i don't know which you need
Step-by-step explanation:
Larson uses his credit card to purchase a new video game system for $519.82. He can pay off up to $225 per month. The card has an annual rate of 15.4% compounded monthly. How much total interest will he pay?
Answers
Answer Explanation: Math
The first step in determining the solution to the system of equations, y = –x2 – 4x – 3 and y = 2x + 5, algebraically is to set the two equations equal as –x2 – 4x – 3 = 2x + 5. What is the next step?
Set y = 0 in y = –x2 – 4x – 3.
Factor each side of the equation.
Use substitution to create a one-variable equation.
Combine like terms onto one side of the equation.
Answers
Answer:
Last one. Combine like terms onto side of the equation.
Step-by-step explanation:
The first step in determining the solution to the system of equations, [tex]y = -x^2 - 4x - 3[/tex] and [tex]y = 2x + 5[/tex] , algebraically is to set the two equations equal as [tex](-x^2 - 4x - 3) = 2x + 5[/tex], will be to set the equations equal to each other.
What is system of equations ?System of equations comprises of two or more equations of two or more variables and seeks common solutions to the equations.
We have,
[tex]y = -x^2 - 4x - 3[/tex]
[tex]y = 2x + 5[/tex]
So, to determine solution to these System of equations,
We have to
Set the equations equal to each other and solve for the value of [tex]x[/tex],
i.e.
[tex]-x^2 - 4x - 3=2x+5[/tex]
[tex]-x^2-6x-8=0[/tex]
[tex]x^2+6x+8=0[/tex]
[tex]x^2+4x+2x+8=0[/tex]
[tex]x(x+4)+2(x+4)=0[/tex]
[tex](x+2)(x+4)=0[/tex]
⇒ [tex]x+2=0[/tex]
[tex]x=-2[/tex]
[tex]x+4=0[/tex]
[tex]x=-4[/tex]
So, from the above solution we came to know that the first step in determining the solution to the given System of equations is to set the equations equal to each other.
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what is a square unit
Answers
Answer:
A square unit is a small area of a square used to find a total.
Step-by-step explanation:
Write the equation of the graph.
Answers
Answer:
it is the bottom answer or if it was labeled it would be D.
Is this correct? Pls help me
Answers
Answer:
Im pretty sure you are correct
Step-by-step explanation:
Belive in urself m8
Answer:
no I don't think this is correct
Step-by-step explanation:
(no btw)
what is the range of the following data set?
Answers
Answer: The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.