Answers
Answer:
See below ~
Step-by-step explanation:
Combination Rule
ⁿCₓ = n! / (n - x)! x!#1) ²²C₂₀
²²C₂₀ = 22! / 2! 20!22 x 21 x 20! / 2! x 20!22 x 21 / 211 x 21231#2) ¹²C₈
¹²C₈ = 12! / 4! 8!12 x 11 x 10 x 9 x 8! / 4! x 8!12 x 11 x 10 x 9 / 4 x 3 x 211 x 5 x 999 x 5495Answer:
[tex]\displaystyle ^{22}C_{20} =231[/tex]
[tex]\displaystyle ^{12}C_{8} =495[/tex]
Step-by-step explanation:
Binomial Coefficients
[tex]\displaystyle \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{(n-r)! \, r!}[/tex]
[tex]\begin{aligned}\displaystyle \implies ^{22}C_{20} & = \frac{22!}{(22-20)! \, 20!}\\\\ & =\frac{22!}{2! \, 20!}\\\\ & =\frac{22 \cdot 21 \cdot 20!}{2! \, 20!}\\\\ & =\frac{22 \cdot 21}{2 \cdot 1}\\\\ & =\frac{462}{2}\\\\ & =231\end{ailgned}[/tex]
[tex]\displaystyle \begin{aligned} \implies ^{12}C_{8} & = \frac{12!}{(12-8)! \, 8!}\\\\ & =\frac{12!}{4! \, 8!}\\\\ & =\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{4! \, 8!}\\\\ & =\frac{12 \cdot 11 \cdot 10 \cdot 9}{4 \cdot 3 \cdot 2 \cdot 1}\\\\ & =\frac{11880}{24}\\\\ & =495\end{aligned}[/tex]
Related Questions
Solve the following please:
Answers
Answer: 161
[3×2^5+13×(−2)]+7[8−(4−9)]
Calculate 2 to the power of 5 and get 32.
3×32+13(−2)+7(8−(4−9))
Multiply 3 and 32 to get 96.
96+13(−2)+7(8−(4−9))
Multiply 13 and −2 to get −26.
96−26+7(8−(4−9))
Subtract 26 from 96 to get 70.
70+7(8−(4−9))
Subtract 9 from 4 to get −5.
70+7(8−(−5))
The opposite of −5 is 5.
70+7(8+5)
Add 8 and 5 to get 13.
70+7×13
Multiply 7 and 13 to get 91.
70+91
Add 70 and 91 to get 161.
161
Answer:
Step-by-step explanation:
Use PEDMAS
[3 *2⁵ + 13*(-2) ] + 7[8-(4-9) ] = [3*2⁵ + 13*(-2)] +7[ 8 - (-5) ]
{calulate the inner most parentesis (4- 9 = -5)}
= [3*32 + 13*(-2) ] + 7* [ 8+5]
{Find the exponent 2⁵ = 32}
= [ 96 + (-26) ] + 7* 13
{Here 3 & 32 aree multiplied & 13 and (-2) are multiplied and 8 is added to 5}
= 70 + 91
= 161
the sum of 10 observation is 110 then the mean is
A)11
B)10
C)7
D)5
Answers
Answer:
11
Step-by-step explanation:
[tex]since \: mean = \frac{sum \: of \: observations}{number \: of \: observations} \\ mean = \frac{110}{10} = 11 \\ therefore \: the \: mean = 11[/tex]
what is (4,5) rotated 90 degrees clockwise?
(pls help)
Answers
Answer:
(5,-4)
Step-by-step explanation:
A cafeteria is in the shape of a rectangle. The length of the rectangle is four times its width. The area of the cafeteria is 14,800 square feet. What is the length of the cafeteria? Round to the nearest foot.
Answers
Answer:
243 feet
Step-by-step explanation:
Answer:
243 i think please
brainlist
Step-by-step explanation:
hi
Pls help with this I started it but I don't know what to do next
Answers
Answer:
There is nothing there lol, If you attach something i may be able to help :)
Step-by-step explanation:
Leo designs a stand for the new statue on display at the local library. The stand is in the shape of a right trapezoidal prism. The base of the prism has an area of 4 ft^2 and the prism stands 2.4 feet high. As Leo paints the stand, he calculates the surface area of the stand to be 32 ft^2.
(a) Leo is asked to purchase roping that will be used to close off the area around the statue. He purchases a length that is five times the perimeter of the stand in roping. How much roping does he purchase?
(b) Leo plans to add gold leaf to the sides of the stand but not to the two bases. What percent of the area of the stand will have gold leaf? Round your answer to the nearest whole number.
Answers
Answer:
See below ~
Step-by-step explanation:
(a)
Formula
Surface Area = (2 x Base Area) + (Perimeter x Height)Solving
32 = 2 x 4 + (P + 2.4)P + 2.4 = 4P = 1.6 ftLength of rope = 5P5 x 1.6Length of rope = 8 feet(b)
Slant height = √(2.4)² + (1)² = √5.76 + 1 = √6.76 = 2.6 feetArea of a side = slant height x lengthArea of a side = 2.6 x 2 = 5.2 square feetTotal area of sides = 5.2 x 2 = 10.4 square feet% (Area) = 10.4/32 = 0.32532.5%33%-345-234
Show how you worked it out
Answers
Answer:
-579
Step-by-step explanation:
-345-234-345-234=-579 subtract numbers= -579Which of the following represents an exponential relationship?
A
(1,5),(2,10),(3,15)(1,5),(2,10),(3,15)
B
(2,9),(3,27),(4,81)(2,9),(3,27),(4,81)
C
(2,4),(3,9),(4,16)(2,4),(3,9),(4,16)
D
(5,15),(6,18),(7,21)
Answers
Answer:
(C)
Step-by-step explanation:
2 power 2 = 4
3 power 2 = 9
4 power 2 = 16
Can someone help me please!!
Answers
Answer:
40°
Step-by-step explanation:
The red 75° curve means that both angles must sum up to 75°The question provides two angles 35° and n°Using math, you can do:n° + 35° = 75°Subtracting 35° from both sides of the equation:n° = 75° - 35° = 40°Answer:
40°
Step-by-step explanation:
if the measurement of the two angles combined is 75 and one of the angles is 35, we can subtract 35 from 75 to get 40, which should be the answer for n, and you can check it by adding 40 and 35 to get 75, the total of both angles
what is the vaule of x?
Answers
Answer:
98 degree
Step-by-step explanation:
x = 180 - FGH
but
FGH = 180- (53+45)
thus
FGH = 82
thus
x = 180-82
thus
x = 98
There are 1 blue ball pen, 1 red ball pen, and 1 green ball pen in Lily's bag while there are 1 blue ball pen and 1 red ball pen is Mandy's bag. A ball pen is randomly drawn from each bag. Find the probability that both ball pens drawn are green
Answers
Answer:
well its simple really.
Step-by-step explanation:
its a 1 percent chance however, by moving her hand around enough like around 20 seconds she'll get green.
(0, 5) and (1, 7) fall on a particular line. What is its equation in slope-intercept
Answers
Answer:
The answer is 2x+5.
Step-by-step explanation:
11
50
11 What is the solution to 8x - 3(2x - 4) = 3(x - 6)?
-
No solution
2
30
FO
EXTD 10:36
acer
Answers
x=30
Solution:First, use the distributive property:8x-3(2x-4)=3(x-6)8x-6x+12=3x-18Simplify:2x+12=3x-182x-3x=-12-18-x=-30x=30Hope it helps.
Do comment if you have any query.
Pls help me I need the answer with how u did it pls
and the quis Solve for x, then find the measure of the angle given
Answers
Answer:
Step-by-step explanation:
finding x°:
since 83° and x° are alternate angles:
x° = 83°
also angleABC is x°
need some help with the question in the image
Cheers
Answers
Answer: 1.45litres
Step-by-step explanation:
250ml = 0.25litres
1.2+0.25= 1.45
ans is 1.45litres
Which equation could be used to find the number of days, d, in h hours? A. 24+h=d B. 24h=d C. 24/h=d D. H/24=d
Answers
Answer:
h/24= d
if you have any questions do ask
Need help with this one
Answers
The unit rate of the cost of different weight of pistachios as shown on the graph is $1.25 per pounds.
What is unit rate?A unit rate is a rate where the second quantity is one unit . Therefore, the unit rate of the linear graph can be found as follows;
(2, 2.5)(4, 5)
unit rate = y₂ - y₁ / x₂ - x₁
x₁ = 2
x₂ = 4
y₁ = 2.5
y₂ = 5
unit rate = 5 - 2.5 / 4 - 2 = 2.5 / 2 = $1.25 per pounds
learn more on unit rate here: https://brainly.com/question/11258929
please help me i will give brainlest if the correct answer
Answers
Penny sells knitted scarves for $12 each. The cost of the supplies to make each scarf is x dollars.
How much profit will Penny make if she sells y scarves?
A. y(12 – x)
B. 12(x – y)
C. y(x – 12)
D. x(12 – y)
Answers
Answer:
A. y(12 – x)
Step-by-step explanation:
Mr. Davis took his car to the repair shop. His total bill was $253. He was charged $48 for parts, and $5 for shop materials.
The rest of the charge was for labor. If it took four hours to fix the car, how much does the shop charge per hour for labor?
Answers
Answer:
33.333333
Step-by-step explanation:
(253-(48+5))/6
(253-53)/6
200/6
33.333333
Events A and B are overlapping.
P(A) =4/11 ; P(B) =3/11 , P(A and B) = 2/11.
Find P(A or B).
7/11
5/11
8/11
9/11
Answers
5/11 is the final answer.
P(A) = 4/11P(B) = 3/11When events are overlapping
formula: P(A or B) = P(A) + P(B) - P(A and B)
=======
P(A or B) = 4/11 + 3/11 - 2/11
P(A or B) = 7/11 - 2/11
P(A or B) = 5/11
Answer:
5/11
Step-by-step explanation:
Given:
P(A) = 4/11P(B) = 3/11P(A ∩ B) = 2/11We can construct a Venn diagram to help answer this question (see attached).
Place 2/11 in the overlapping part. Then calculate the remaining probabilities:
P(A) - P(A ∩ B) = 4/11 - 2/11 = 2/11
P(B) - P(A ∩ B) = 3/11 - 2/11 = 1/11
P(A' ∩ B') = 1 - 5/11 = 6/11
So P(A ∪ B) = 2/11 + 2/11 + 1/11 = 5/11
In some countries, people believe that blood type has a strong impact on personality. For example, Type B blood is thought to be associated with passion and creativity. A statistics student at a large U. S. University decides to test this theory. Reasoning that people involved in the arts should be passionate and creative, she takes a simple random sample of students majoring or minoring in arts at her university and asks them for their blood type. Here are her results:
Observed number of performing arts majors with each blood type
Type A Type B Type AB Type 0 Total
50 23 10 67 150
Assume the distribution of blood type among all U. S. Residents is as follows:
Type A: 42%; Type B: 10%; Type AB: 4%; Type O: 44%.
(a) The student wants to carry out a test of significance to see if the distribution of blood types among arts majors or minors is different from the U. S. Distribution. State the null and alternative hypotheses for this test.
(b) Find the expected counts for each blood type under the assumption that the null hypothesis is true.
(c) Discuss whether the conditions for this test have been met.
(d) Find the value of the test statistic and the P-value of the test, and make the appropriate conclusion. Use α = 0. 5.
(e) Based on your answer to (d), which error is it possible that you have made, Type I or Type II? Describe that error in the context of the problem
Answers
The null hypothesis for the test regarding the blood type is that they distribution of blood types among art major is the same as the US distribution.
What is a null hypothesis?It should be noted that null hypothesis simply suggests that there is no statistical relationship.
Here, the null hypothesis for the test regarding the blood type is that the distribution of blood types among art major is the same as the US distribution and the alternative hypothesis is that the distribution of blood types among art major is different from the US distribution.
The conditions for this test have been met as all expected frequencies are greater than 5.
Since the test statistic is 9.63 and the p-value is 0.022, one can reject the null hypothesis. Therefore, it'll be concluded that the distribution of blood types among arts majors and minors is different from the U.S distribution.
Learn more about hypothesis on:
https://brainly.com/question/15980493
Find the volume of this prism
Answers
Answer:
324 cubic cm
Step-by-step explanation:
triangular prism
base*width*height/2
9x6x12/2
=9x6x6
=54x6
=324
Answer:
V = 324 cm³
Step-by-step explanation:
V = lwh/2
V = (6 · 12 · 9)/2
V = 648/2
V = 324 cm³
Hope this helps and God bless!
What are the solutions of -x2 + 4x = x - 4?
O-5 and 0
0-5 and -1
0-1 and 4
O and 4
Answers
Answer:
-1 and 4
Step-by-step explanation:
first you bring the terms on the right side to the left and you get:
-x^2 + 3x + 4 = 0
then you divide both sides of the quadratic by -1:
x^2 - 3x - 4 = 0
then you factor the equation:
(x + 1)(x - 4) = 0
for any product to be zero, one of the factors must be zero. hence, either x + 1 or x - 4 can be zero. so x can be -1 and//or 4.
have a great day <3
PLS HELP ME ASAP! IT IS 80 POINTS WORTH! Florida has 67 counties and Texas has 254 counties. The mean population for the state of Florida by county is 291,834 with a standard deviation of 467,012.03, and the median is 107,056. The mean population for the state of Texas by county is 104,127 with a standard deviation of 374,012.2261, and the median is 18,293.
Some of the data for both states is shown. A business is moving from Texas to Florida. As a result of the move 8,193 people move from the largest Texas county to the smallest Florida county, in terms of population. Mark the population statistics that will be affected with this population change found in the chart below with "check". Does the IQR for Florida increase, decrease or stay the same?
Does the Mean of Texas increase, decrease or stay the same?
Does the median of FL increase, decrease or stay the same?
Does the standard deviation of Texas increase, decrease or stay the same?
Answers
Answer:
The mean of texas will decrease. The median of FL will increase. The standered deviation will stay the same.
Step-by-step explanation:
Answer:
The mean of texas will decrease.
The median of FL will increase.
The standard deviation will stay the same.
IQR for Florida's is 310,349 and Texas's is 42,369.
Step-by-step explanation:
IQR iss Q3-Q1
When a bill is not paid by the due date, a late fee is added each month until the bill is paid. The values in the table represent the total amount due, in dollars, for each month that a payment remains overdue. Using x for the number of months overdue and y for the total amount due, in dollars, construct a linear function that describes the relationship between the number of months the bill is overdue and the total amount due. Enter the equation of the function in the box, and use paper to show your work
Answers
Bill + (Late fee x months) = Final bill
FunctionsGiven that when a bill is not paid by the due date, a late fee is added each month until the bill is paid, to construct a linear function that describes the relationship between the number of months the bill is overdue and the total amount due you must perform the following calculation:
Bill + (Late fee x months) = Final billThus, if the bill is $1000 and the late fee is $50 per month, and it takes 4 months to regularize the debt, the function would apply as follows:1000 + (50 x 4) = X1000 + 200 = X1200 = XLearn more about functions in https://brainly.com/question/12431044
Answer:Bill + (Late fee x months) = Final bill
Step-by-step explanation:
Find the perimeter of the isosceles triangle with points A (0,0); B (3,3); and C (6,0)
Answers
Answer:
use distance formula for the sides of the triangle
What's the domain of this function graph?
A)
[0,∞)
B)
(–∞, 0)
C)
[1,∞)
D)
(–∞,∞)
Answers
Answer:
A) [0,∞)
Step-by-step explanation:
The domain is the horizontal extent of the graph.
__
The given graph goes no farther left than x=0. It extends to infinity to the right (as signified by the arrow pointing right).
The domain is [0, ∞).
Answer:
/
Step-by-step explanation:
Solve the right triangle. Round your answers to the nearest tenth
Answers
B=40°
a=15.9
c=24.8
EXPLANATION:
B= 180°-(50°+90°) =40°
cosB=opposite/hypotenus
cos(40)=19/c
c=19/cos(40)
=24.8
a^2 + b^2 = c^2
a^2 + 19^2 = 24.8^2
a^2 = 24.8^2 - 19^2
= 615.04 - 361
= 254.04
a= redical(254.04) = 15.9
HOPE THIS HELPS :)
Help me please thanks
Answers
12v + 8
hope it helps...!!!