So I have to compute the following but i don't know what they mean any help?
Answers
Answer:
Step-by-step explanation:
This is a Combination (as in permutation vs combination) question the symbol (n r) refers to "n choose r". This is sometimes written as nCr
i.e the question is asking you to find how many combinations each will yield when you chose r items from n item without repetition and order does not matter.
I will only do the first question for you and you can just follow the same steps to solve the rest of the questions.
Recall that
[tex]nCr=\frac{n!}{(r!)(n-r)!}[/tex]
Consider question a) we are given (5 1) or ₅C₁
we can see that n = 5 and r = 1
If we substitute this into the formula:
₅C₁ = (5!) / [ (1!)(5- 1)!]
= (5!) / [ (5- 1)!]
= (5!) / (4!)
= (5·4·3·2·1) / (4·3·2·1)
= 5
hence ₅C₁ = 5
Answer:
(a) 5
(b) 10
(c) 35
(d) 28
(e) 9
(f) 21
Step-by-step explanation:
[tex](\frac{n}{k} )=\frac{n!}{k!(n-k)!}[/tex]
(a)
[tex](\frac{5}{1} )=\frac{5!}{1!(5-1)!} \\\\(\frac{5}{1} )=\frac{5*4*3*2*1}{1*4!} \\\\(\frac{5}{1} )=\frac{120}{1*4*3*2*1} \\\\(\frac{5}{1} )=\frac{120}{24} \\\\(\frac{5}{1} )=5[/tex]
(b)
[tex](\frac{5}{3} )=\frac{5!}{3!(5-3)!} \\\\(\frac{5}{3} )=\frac{5*4*3*2*1}{3*2*1*2!} \\\\(\frac{5}{3} )=\frac{120}{3*2*1*2*1}\\\\(\frac{5}{3} )=\frac{120}{12} \\\\(\frac{5}{3} )=10[/tex]
(c)
[tex](\frac{7}{4} )=\frac{7!}{4!(7-4)!} \\\\(\frac{7}{4} )=\frac{7*6*5*4*3*2*1}{4*3*2*1*3!} \\\\(\frac{7}{4} )=\frac{5040}{4*3*2*1*3*2*1} \\\\(\frac{7}{4} )=\frac{5040}{144} \\\\(\frac{7}{4} )=35[/tex]
(d)
[tex](\frac{8}{2}) =\frac{8!}{2!(8-2)!} \\\\(\frac{8}{2}) =\frac{8*7*6*5*4*3*2*1}{2*1*6!} \\\\(\frac{8}{2}) =\frac{40320}{2*1*6*5*4*3*2*1}\\\\(\frac{8}{2}) =\frac{40320}{1440} \\\\(\frac{8}{2}) =28[/tex]
(e)
[tex](\frac{9}{8} )=\frac{9!}{8!(9-8)!} \\\\(\frac{9}{8} )=\frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1} \\\\(\frac{9}{8} )=\frac{362880}{40320} \\\\(\frac{9}{8} )=9[/tex]
(f)
[tex](\frac{10}{4} )=\frac{10!}{4!(10-4)!} \\\\(\frac{10}{4} )=\frac{10*9*8*7*6*5*4*3*2*1}{4*3*2*1*6!} \\\\(\frac{10}{4} )=\frac{3628800}{24*6*5*4*3*2*1} \\\\(\frac{10}{4} )=\frac{362880}{17280} \\\\(\frac{10}{4} )=21[/tex]
Related Questions
Solve -2/3x > 8 or -2/3x -12 or x -6} 3. {x | -12 < x < -6}
Answers
10 ft
8 ft
8.9 ft
4 ft
Calculate the perimeter of this figure
to the nearest 10th
Answers
Answer:
40.9 ft.
Step-by-step explanation:
We know all the side lengths needed:
8 + (10*2) + 8.9 +4 = 40.9
So then you just add them!
15 / 80
a) Work out 4 1/7 + 1 1/2
Answers
Answer:
5 9/14
Step-by-step explanation:
4 1/7 + 1 1/2= 5+1/7+1/2= 5+ 2/14+7/14= 5+ 9/14= 5 9/14
first put them into improper fractions, makes it easier
29/7 + 3/2
make the denominator the same
58/14 + 21/14 = 79/14
put it into a mixed fraction
79/14 = 5 9/14
Hey, can you please help me out?
Very appreciate
Verified and certified by me
Answers
Answer:
d
Step-by-step explanation:
first two are to measure mass not area and third is too large of a measurement for a beach towel. Hope it helps!
Angela is following this recipe to make biscuits.
Angela uses 3.37 of syrup.
How much sugar is needed in kg?
Recipe: Makes 14 biscuits
120 g margarine
150 g sugar
275 ml syrup
200 g oats
60 g sultanas
Answers
Answer:
150 G sugar. ⬅️CORECT ANSWER
Please help! Correct answer only!
You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 1 to 20. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is even, you win $34. If the number the ball lands on is odd, you win nothing. If you play the game, what is the expected payoff?
Answers
Answer:
" Expected Payoff " - 17 Dollars ; Type in 17
Step-by-step explanation:
Consider the probability of landing in an odd section;
[tex]Sections of the Wheel - 20 Sections,\\Numbers Numbered On the Wheel - 1 To 20,\\\\Odd Numbers = Even Numbers,\\Odd Numbers = 20 / 2 = 10,\\Even Numbers = Odd Numbers = 10,\\\\Probability of Spinning Even - 10 / 20 = ( Simplified ) 1 / 2,\\Money Won = 34 Dollars,\\\\Proportionality - 1 / 2 = x / 34, Where, x = " Expected Payoff "\\1 / 2 = x / 34,\\2x = 34,\\x = 17 Dollars,\\\\Conclusion ; " Expected Payoff " = 17 Dollars[/tex]
Solution ; Provided Directly Above
During the last 5 basketball games, Javier scored 13 , 20, 13, 15, and 24 points.
What is the range of the data? *
Answers
Answer:
During the last 5 basketball games, Javier scored 13 , 20, 13, 15, and 24 points
Step-by-step explanation:
Answer:
11 points
Step-by-step explanation:
Range = Highest value - lowest value
Highest value = 24
Lowest value = 13
Range = 24 - 13
Range = 11
a rectangular inflatable swimming pool is 2 [tex]\frac{4}{5}[/tex] yards long, 2 yards wide, and [tex]\frac{3}{5}[/tex] yard tall. What is the volume of the pool? Round to the nearest tenth
Answers
Answer:
3.4 yd^3
Step-by-step explanation:
The volume is
V = l*w*h
V = 2 4/5 * 2 * 3/5
Changing the mixed number to an improper fraction
2 4/5 = ( 5*2+4)/5 = 14/5
V = 14/5 * 2 * 3/5
= 84/25
Changing back to a mixed number
3*25 = 75 with 9 left over
3 9/25
3.36 yd^3
To the nearest tenth
3.4 yd^3
Answer: 3.4 yards cubed, after rounding.
Step-by-step explanation:
To find the volume of a rectangular prism, use the following formula:
[tex]V = wlh[/tex], where w is the width, l is the length, and h is the height
Substitute the values given to you into the formula:
[tex]V = 2 * \frac{3}{5} * 2\frac{4}{5}[/tex]
Simplify the mixed number by multiplying both the numerator and denominator of 2/1 by 5 to get 10/5 and add it to the fraction to get 14/5.
[tex]V = \frac{2}{1} * \frac{3}{5} * \frac{14}{5}[/tex]
Now, multiply the numerators and denominators of the fractions and simplify:
[tex]V = \frac{2 * 3 * 14}{5 * 5}\\\\V = \frac{84}{25}\\\\\\V = 3.36[/tex]
The volume is 3.36 yards cubed. Round to the nearest tenth to get 3.4 yards cubed.
A bookstore has 60 books about math this is 0.05% of the total number of books on the shelves how many books are there in the bookstore that are not about math
Answers
Answer:
119,940 books are not about math.
What I did:
60x2000=120,000
120,000-60=119,940
Answer:
119940
Step-by-step explanation:
.05 % are about math
b= books
b * .05% = 60
Change to decimal form
b * .0005 = 60
Divide each side by .0005
b = 60/.0005
b =120000 books in the store
we want the ones not about math
120000-60
119940
PLEASE HELP. A Ferries wheel has a diameter of 100 ft. The center of the wheel is 60 feet off the ground. If it takes the Ferries wheel 12 seconds to make a full rotation, find the height of a rider 2 seconds after he passes position A, the right most point on the wheel.
Answer choices:
A. 103.30 ft
B. 80.34 ft
C. 74.40 ft
D. 101.96 ft
Answers
Answer:
lresaputa es la C
Step-by-step explanation:
For every 4 girls in mr hegarty class there are 5 boys. what is the ratio of boys to girls in the class? Give answer in simplest form.
Answers
Answer: 4:5
Step-by-step explanation:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
which of the following descriptions represents the transformation shown in the image?
Answers
Answer:
A
Step-by-step explanation:
It is a 90-degree rotation counterclockwise 2 units left and 3 units down.
what is the slope and y-intercept of the following equation 3x + 2y = -6
Answers
Answer:
The slope is -1.5x and the y-intercept is -3
Step-by-step explanation:
First person to give me Brainliest wins the official contest!!! Hurry!
Un cazador se encuentra en la parte mas alta de un arbol. Para averiguar a que altura se encuentra, deja caer una bola, observando que demora 4 segundos. Encuentra el alto del arbol (g=10m/s2)
Answers
Answer:
80 m
Step-by-step explanation:
La velocidad inicial de la pelota es 0 m/s.
La altura del árbol es s.
El tiempo necesario es de 4 segundos.
Podemos aplicar una de las ecuaciones de movimiento de Newton:
[tex]s = ut + \frac{1}{2}gt^2[/tex]
donde u = velocidad inicial
t = tiempo empleado
g = aceleración debido a la gravedad
Por lo tanto:
[tex]s = 0 * 4 + (1/2 * 10 * 4^2)\\\\s = 0 + 80 \\\\s = 80 m[/tex]
El árbol tiene 80 metros de altura.
Pls help!! ASAP!!!!
Figure ABCD is reflected about the y-axis to obtain figure A′B′C′D′:
A coordinate plane is shown. Figure ABCD has vertices A at 2 comma 5, B at 1 comma 2, C at 3 comma 1, and D at 4 comma 5. Figure A prime B prime C prime D prime has vertices A prime at negative 2 comma 5, B prime at negative 1 comma 2, C prime at negative 3 comma 1, and D prime at negative 4 comma 5.
Which statement best describes the relationship between the two figures? (4 points)
Figure ABCD is similar to figure A′B′C′D′.
Figure ABCD is bigger than figure A′B′C′D′.
The measure of angle D is equal to the measure of angle A′.
The measure of angle D is equal to the measure of angle B′.
Answers
Given right triangle ABC . To the nearest degree, find the measure of angle B. 20° 43° 47° 70°
Answers
Answer:
The answer is "70°"
Step-by-step explanation:
In the given question an attachment file is missing. so, the attachment file and its solution can be defined as follows:
Given:
ABC is the right triangle.
Find B=?
Solution:
[tex]\Rightarrow \sin \theta= \frac{p}{h}\\\\[/tex]
[tex]\Rightarrow \sin B^{\circ}=\frac{AB}{AC}= \frac{4.8}{5.1}\\\\[/tex]
[tex]\Rightarrow \sin B^{\circ}= .941[/tex]
[tex]\Rightarrow B^{\circ}= \sin^{-1} (0.941)\\\\\bold{\sin^{-1} (0.941) = 70.2^{\circ}}\\\\\therefore \ \ \ \ \bold{B^{\circ} = 70^{\circ}}[/tex]
Answer:
70
Step-by-step explanation:
what is the value of x?
Answers
Answer:
60
Step-by-step explanation:
60 times 2 is 120 plus 24 is 144
(2x+24)=144 (vertically opposite angles equal)
Continue to solve for x
2000 soldiers stand in a row. Beginning from the left, each soldier calls out a number, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, and so on. Beginning from the right, each soldier calls out a number 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, and so on. How many of these soldiers call out a number 3 when beginning from the left and right??
Answers
Answer:
The number of soldiers that call out a number 3 is 666 soldiers
Step-by-step explanation:
The parameters given are;
Number of soldiers = 2000
Soldiers calling from the left = 1, 2, 3,.....
Soldiers calling from the right = 1, 2, 3,.....
Therefore, since the number soldiers calling out the number 3 are 1 in 3 from the left and 1 in 3 from the right, we split the soldiers into 2 groups of 1000, with one group calling from left and the other group calling from the right;
The number of 3s in called out in the first group from the left is therefore;
1000/3 = 333.33 which is 333 soldiers or from the 3rd soldier to the 999th soldier
Similarly the number of 3s called out from the second group = 333
Hence the total number of soldiers that call out a number 3 = 333 + 333 = 666 soldiers.
4n − m + 3p + 2m − n − p
Answers
Answer:
3n+m+2p
Step-by-step explanation:
group all like terms and solve.
so,
4n-n = 3n
-m + 2m = m
3p - p = 2p
Then, group them together: 3n+m+2p
Which fraction is equivalent to StartFraction 2 Over 6 EndFraction? StartFraction 3 Over 7 EndFraction, because StartFraction 2 Over 6 EndFraction = StartFraction 2 + 1 Over 6 + 1 EndFraction = StartFraction 3 Over 7 EndFraction StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction StartFraction 3 Over 12 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 12 EndFraction StartFraction 3 Over 8 EndFraction, because StartFraction 2 Over 6 EndFraction = one-half = StartFraction 2 + 1 Over 6 + 2 EndFraction = StartFraction 3 Over 8 EndFraction
Answers
Question:
Which fraction is equivalent to [tex]\frac{2}{6}[/tex]?
- [tex]\frac{3}{7}[/tex] because [tex]\frac{2}{6}= \frac{2 + 1}{6 + 1}[/tex]
- [tex]\frac{3}{9}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
- [tex]\frac{3}{12}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
- [tex]\frac{3}{8}[/tex] because [tex]\frac{2}{6}= \frac{1}{2} = \frac{2+1}{6+2} = \frac{3}{8}[/tex]
Answer:
- [tex]\frac{3}{9}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
Step-by-step explanation:
Two fractions are said to be equal if and only if they give the same value when simplified.
The equivalent of [tex]\frac{2}{6}[/tex] is as explained in the selected option;
First, divide numerator and denominator by 2
[tex]\frac{2/2}{6/2}[/tex]
Then simplify
2/2 = 1 and 6/2 = 3; So;
[tex]\frac{2/2}{6/2} = \frac{1}{3}[/tex]
Multiply numerator and denominator by 3
[tex]\frac{1*3}{3*3} = \frac{3}{9}[/tex]
Hence, [tex]\frac{2}{6}[/tex] is equivalent to [tex]\frac{3}{9}[/tex]
Answer:
B
Step-by-step explanation:
StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction
You're making dessert but your recipe needs adjustment. Your chocolate chip cookie recipe makes 4 dozen cookies, but you need 3
1
dozen cookies. If the recipe requires 15 cups of butter, 5 teaspoons of baking powder, and 2 cups of pecans, how much of each of
these ingredients are necessary for 3 dozen cookies? Simplify your answer
Answers
Answer:
Butter = (3*15) / 4 = 45/4 = 11 1/4 tsp
Baking powder = (3*5) / 4 = 15/4
= 3 3/4 tsp
Pecans = (3 * 2) / 4 = 6/4
= 3/2 = 1.5 cups
Here, we are required to determine how much of each of these ingredients are necessary for 3 dozen cookies
The ingredients are;
11 and 1 quarter cups of butter is needed.3 and 3 quarters teaspoons of baking powder are needed.1 and a half cups of peacans are needed.Therefore, for 3 dozen cookies; 3 quarters of the requirements for 4 dozen cookies;
Cups of butter needed = (3/4) × 15 = 11.25Teaspoons of baking powder needed = (3/4)× 5 = 3.75Cups of peacans needed = (3/4)× 2 = 1.5Ultimately,
11 and 1 quarter cups of butter is needed.3 and 3 quarters teaspoons of baking powder are needed.1 and a half cups of peacans are needed.Read more:
https://brainly.com/question/19473677
Based on the equation 3x + 8y = 48, what is the missing value in the table?
Answers
Answer:
24x
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
I did the edu test hope this helps♡
Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it. If his body
processes 5% of the caffeine every hour, how much will be left in 8 hours?
Answers
The body uses 5%, so 95% of the previous amount is left every hour:
Total = start value x (1- %)^time
Total = 110 x(0.95)^8
Total left = 72.9762 milligrams
Round the answer as needed.
Tres pueblos A, B y C, situados en los lados de un triángulo, quieren construir una piscina común para sus habitantes, de forma que quede a la misma distancia de los tres. ¿En qué punto se construirá? ¿Cómo se llama ese punto?
Answers
Answer:
The name of the point is the circumcenter of the triangle
Step-by-step explanation:
The pool will be built at a point which is equidistant from the three points.
This means that the distance from that center point to point A equals the distance from that center point to point B which is equal to the distance from that center point to point C.
The name of this point is called the CIRCUMCENTER of the triangle
The circumcenter is equidistant from the three vertices of the triangle which are the points A , B and C in this case
there are 357 seniors in harris high school. The ratio of boys to girls is 7:10. How many girls are in the senior class?
Answers
You get x= 107.1
So there are 107 girls in the senior class
Need help thanks :) The question is down below
Answers
Answer:
n=63
x=117
r=63
p=117
w=117
m=117
k=117
Step-by-step explanation:
If you start with the given angle of 63 p would have to be 117 because 180-63 is 117. This would make r 63 because you would use the 117+63 to make a 180 degree angle. w will then be made 117 because it's vertical to p and vertical angles are congruent. we can find x by using corresponding angles. x= k because they are corresponding angles as well. n would be 63 because of k being 117 and because of vertical angles m is 117.
Hope this helps :)
k, m, p, w, x are all = 117 degrees
n, and r are both = 63 degrees
Because of angle laws, where opposite angles are equal to eachother, and alternate angles are equal to eachother and co-interior angles add up to 180 degrees; sorry, I would attach a photo but it is not allowing me to... keeps on saying, “Sorry, something went wrong.”
Hope this helps.
Katie went out for dinner with her friends and left a 17% tip. If B represents the bill, an expression that represents the total bill she will pay is 0.83b
Answers
Answer:
1.17B
Step-by-step explanation:
Katie and her friends will pay 17% of the bill, B.
Therefore, we have to add 17% of B to B to find how much they will pay:
17/100 * B = 0.17B
Therefore, the total bill will be:
Bill + tip
= B + 0.17B = 1.17B
The expression that represents the total bill they will pay is 1.17B
X2=
a. 48
b. 16
c. 12
Answers
Answer:
16
Step-by-step explanation:
x^2 = whole * part
x^2 = (6+2) * 2
x^2 = 8*2
x^2 = 16
Answer:
16
Step-by-step explanation:
Hope this helps.
If you find answers that say 48 for this same problem, they are incorrect. Please disregard them.
3 lines are shown. A line with points M, H, K intersects a line with points J, H, L at point H. A line extends from point H to point P between angle K H J. Angle M H L is 140 degrees and angle K H P is 20 degrees. What is mAnglePHJ? 100° 120° 140° 160°
Answers
Answer:
The answer is 120 degrees
Step-by-step explanation:
your welcome!!!!!!!!!!!!
Answer:
120
Step-by-step explanation:
edge 2022