[tex]Evaluating Combination Notation & Problem Solving[/tex]
Evaluate the following combinations. Write also your solutions.
![[tex]Evaluating Combination Notation & Problem Solving[/tex]Evaluate The Following Combinations.](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/mdlTNXO3TATsTc1MLGGfwfORAzywLbML.jpeg)
Answers
Answer:
Step-by-step explanation:
1. ⁷C₅ = ⁷C₂ = 7 x 6 / 2 = 21
2. ⁹C₈ = ⁹C₁ = 9
3. ¹²C₅ = 12 x 11 x 10 x 9 x 8 / 2 x 3 x 4 x 5
= 11 x 9 x 8 = 11 x 72 = 792
4. ²⁰C₁₇ = ²⁰C₃ = 20 x 19 x 18 / 2 x 3
= 19 x 3 = 57
5. ¹⁶C₁₃ = ¹⁶C₃ = 16 x 15 x 14 / 2 x 3
= 8 x 5 x 14 = 40 x 14 = 560
6. ⁷C₄ + ¹¹C₉ = ⁷C₃ + ¹¹C₂ = (7 x 6 x 5 / 2 x 3) + (11 x 10 / 2)
= 35 + 55 = 90
7. ⁷C₃ + ⁷C₄ + ⁷C₅ = 2(⁷C₃) + ⁷C₂ = (2 x 7 x 6 x 5 / 2 x 3) + (7 x 6 / 2)
= 70 + 21 = 91
Legit only this much I can do now.
Hope it is enough.
Related Questions
What are m and b in the linear equation 15 + 9x + 3 + 7x = y?
Answers
15 + 3 + 9x + 7x = y
18 + 16x = y
Recall
b + mx = y
m = 16
b = 18
What is a savings goal? PLS I NEED HELP QICK PLSSS nvm
Answers
Answer:
A goal for the amount of money being saved.
Step-by-step explanation:
Practice Translate Expressions
Write an algebraic expression that models the given word phrase.
1) 15 divided by d ________________________
2) seven fewer than a number n ________________________
3) two times the sum of a and b ________________________
4) nine less than 5 multiplied by the number p ________________________
5) the product of 15 and x ________________________
6) quotient of 4 more than the number z and the number y decreased by _________
Answers
2) n - 7
3) (a + b) x 2
4) 5p - 9
5) 15x
6) 4 + z / y
whats 1.07 x 30 in standard form
Answers
Answer:
The simple answer is 32.1
Step-by-step explanation:
It might look easier if you add 1 x 30 and 0.07 x 30.
Answer:
The correct answer is 32.1
Step-by-step explanation:
The standard deviation for u(90, 230)
Answers
Answer:
Standard deviation is 70
Step-by-step explanation:
square root of 4,900= 70 (solved using standard deviation formula)
Find the real-number root.
√1.44
1.2
no real roots
2.07
0.72
Answers
Answer: A. 1.2
Step-by-step explanation:
The principal, real, root of:
2^√1.44
=1.2
All roots:
1.2
−1.2
1.44 is not a perfect square
I need help please ASAP !!
Answers
Answer:
Step-by-step explanation:
5) ∠1
6) ∠2 and ∠3
7) ∠1
3. Suppose a serial number must consist of four different digits, followed by two
different letters. How many different serial numbers are possible?
Answers
Answer: 6,760,000 different possible serial numbers.
Step-by-step explanation: There are 10 digits numbered 0 to 9. There are also 26 letters in the alphabet. Using this, we can do 10*10*10*10*26*26 as there are four digits needed and two letters. This computes to approximately 6,760,000 different possible serial numbers, assuming no other factors are involved.
which expression has the greatest value?
1. 4 - 2^-2
2. 4 - 2^2
3. 4(-2)^2
4. -4(-2)^2
Answers
3nomber is right
Is it helpfui
I think its 3! ^w^
Sawarasenai kimi wa shoujo na no?~
A tree casts a shadow of 24 ft. At the same time, a 6 ft adult casts a shadow of 2 ft. what is the hight of the tree?
Answers
Answer: 8ft tall
Step-by-step explanation:
6/2=3
24/3=8
so the tree is 8ft tall
What are the coordinates of the vertex for f(x) = x2 + 4x + 10?
A- (−2, 2)
B- (2, 2)
C- (−2, 6)
D- (2, 6)
Answers
Answer:
I believe the answer is C (-2,6)
[tex]\\ \rm\rightarrowtail y=x^2+4x+10[/tex]
Add and subtract 4[tex]\\ \rm\rightarrowtail y=x^2+4x+4+10-4[/tex]
[tex]\\ \rm\rightarrowtail y=x^2+4x+2^2+6[/tex]
[tex]\\ \rm\rightarrowtail y=(x+2)^2+6[/tex]
Vertex form
y=a(x-h)^2+kVertex:-
(h,k)=(-2,6)What is the sum of -6 4/5 and -6 4/5
Answers
Answer:
i may be correct or not, i am not sure
Step-by-step explanation:
-34/5+-34/5 is -68/5 which is 13 3/5
Answer:
-13[tex]\frac{3}{5}[/tex]
Step-by-step explanation
[tex]-6\frac{4}{5} + -6\frac{4}{5}[/tex]
calculate
-13[tex]\frac{3}{5}[/tex]
Find the value of n.
3+ (2 + 8) = (3 + 2) + n
Answers
Answer: n=8
Step-by-step explanation: 3+2+8=13
3+2=5 so 13-5=8
Answer:
n=8
Step-by-step explanation:
PEMDAS:
Solve out each side then subtract 5 from the side with n.
Work:
3+(2+8)=(3+2)+n
3+10=5+n
13=5+n
8=n
if 8 times a number is added to twice the number, the result is 80.
Answers
Twice the number = x + x = 2x
8x + 2x = 80
10x = 80
Divide through by 10
x = 8
Where x is the number
I need help please due in a hour
Answers
Answer:
so easy ....dude
Step-by-step explanation:
you can do it..
The rod is made of A-36 steel and has a diameter of 0.22 in . If the rod is 4 ft long when the springs are compressed 0.7 in . and the temperature of the rod is T= 30 ∘F , determine the force in the rod when its temperature is T= 150 ∘F .
Answers
The force in the rod when the temperature is 150 °F is 718.72 pounds-force.
How to determine the resulting the resulting force due to mechanical and thermal deformationLet suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force ([tex]F[/tex]), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.
Given simmetry considerations, we derive an expression for the spring force ([tex]F[/tex]), in pounds-force, as a sum of mechanical and thermal effects by principle of superposition:
[tex]F = k\cdot (\Delta x + 0.5\cdot \Delta l)[/tex] (1)
Where:
[tex]k[/tex] - Spring constant, in pounds-force per inch.[tex]\Delta x[/tex] - Spring deformation, in inches.[tex]\Delta l[/tex] - Rod elongation, in inches.The rod elongation is described by the following thermal dilatation formula:
[tex]\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})[/tex] (2)
Where:
[tex]\alpha[/tex] - Coefficient of linear expansion, in [tex]\frac{1}{^{\circ}F}[/tex].[tex]L_{o}[/tex] - Initial length of the rod, in inches. [tex]T_{o}[/tex] - Initial temperature, in degrees Fahrenheit.[tex]T_{f}[/tex] - Final temperature, in degrees Fahrenheit.If we know [tex]k = 1000\,\frac{lb}{in}[/tex], [tex]\Delta x = 0.7\,in[/tex], [tex]\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}[/tex], [tex]L_{o} = 48\,in[/tex], [tex]T_{o} = 30\,^{\circ}F[/tex] and [tex]T_{f} = 150\,^{\circ}F[/tex], then the force in the rod at final temperature is:
[tex]F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right][/tex]
[tex]F = 718.72\,lbf[/tex]
The force in the rod when the temperature is 150 °F is 718.72 pounds-force. [tex]\blacksquare[/tex]
To learn more on deformations, we kindly invite to check this verified question: https://brainly.com/question/13774755
100points please help
Image attached
Find x
Answers
180 -190
PLEASE HELP
Write a story problem to go with the multiplication problem 5 x 3/4 . Then solve the problem.
Answers
Story:
John is baking a cake. He need to feed 5 people with the cake but the recipe is only designed for 1 serving. In the regular recipe, it required 3/4 cups of sugar. How much sugar does he need for the new recipe?
Answer:
3.75 or 3 3/4
Answer:
A store has 5 oranges then a customer buys 3/4 of them. How many is left
Step-by-step explanation:
5x3/4=3.75 if it was in decimal but in fraction it is 23/4
5x3/4=3.75
3/4 is 0.75
0.75 x 5=3.75
lf x = 4 and y = 7, evaluate the following expression:
3(x + y)
Answers
3(4+7)
Simplify
3(11)
Multiply
3 x 11 = 33
So, the answer is 33.
The ratio of dogs to cats at the veterinarian's office on Saturday. was 6 to 5. If there were 15 cats at the office, how many dogs and cats were there altogether?
Answers
Answer:
33 total cats and dogs
Step-by-step explanation:
15/5=3
3*6=18
18+15=33
hope this helps
Answer:
Dogs: 18Cats: 15In total: 33Step-by-step explanation:
Set up a proportion: [tex]\frac{6}{5} = \frac{x}{15}[/tex] Cross multiply, then divide: 15 × 6 = 90, 90 ÷ 5 = 18So, there are 18 dogs in total.Add the dogs and cats together: 18 + 15 = 33I hope this helps!
I need help doing this I don't pay attention in class now I'm lost
Answers
Answer:
i think the answer is 6498
Step-by-step explanation:
Answer:
6498
Step-by-step explanation:
Pay attention in class :)
Okay, so basically, you just need to replace x and y with the corresponding numbers.
So our equation would be:
9 * 2(5 * 7 - 8 * 2) squared
Now we solve with PEMDAS:
9 * 2(35 - 16)squared
9 * 2(19)squared
9 * 2(361)
18 * 361
6498
Let me know if I did something wrong!
could you pls help me i have the question in the picture ok
Answers
Step-by-step explanation:
the answer is 44 you have to multiply 3 and 11 and you'll get 8 then calculate 33-8 and then subtract and then you get 25 so you put 44
Have a good day !!!
Jack is 4 times as old as Lacy. 9 years from now the sum of their ages will be 63. How old are they now?
Jack is
years old while Lacy is
years old.
Answers
Answer:
jack is 54 and lacey is 13.5. I think
Step-by-step explanation:
Let Jack be J and Lacy be L.
First equation: J=4L
Second equation: (J+9)+(L+9)=63
Solving using substitution:
4L+9+L+9=63
5L+18=63
5L= 45
L = 9
L=9 and J=4L = 4*9 = 36
So Jack is 36 years old and Lacy is 9 years old.
what is alergbra about and why ?
Answers
Answer:
Simply put, algebra is about finding the unknown or putting real life variables into equations and then solving them. ... Algebra can include real numbers, complex numbers, matrices, vectors, and many more forms of mathematic representation
Step-by-step explanation:
71.6 less then or greater then 71.63
Answers
Answer:
less
Step-by-step explanation: 71.6 can also be seen as 71.60 therefore 71.63 is greater
Answer:
Less than.
Think of .6 as the tenths place to tens place.
.63 is 6 tenths and 3 hundredths, so 63.
Now ask yourself, "Is 63 greater than 60?"
And your answer is yes.
Please help ASAP marking brainly
Answers
Answer:
y = 2
Step-by-step explanation:
We are given the value of x (second equation). Let's substitute the value of x into the first equation to find y.
[tex]\rightarrow \dfrac{x}{y} = 6[/tex]
[tex]\rightarrow \dfrac{4(y + 1)}{y} = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[}x = 4(y + 1)]}[/tex]
Use cross multiplication.
[tex]\rightarrow 4(y + 1) = 6 \times y[/tex]
[tex]\rightarrow 4(y + 1) = 6 y[/tex]
Simplify the distributive property.
[tex]\rightarrow 4(y + 1) = 6 y[/tex]
[tex]\rightarrow 4y + 4 = 6 y[/tex]
Subtract 4y both sides.
[tex]\rightarrow 4y - 4y + 4 = 6 y - 4y[/tex]
[tex]\rightarrow 4 = 2y[/tex]
Divide both sides by 2.
[tex]\rightarrow \dfrac{4}{2} = \dfrac{2y}{2}[/tex]
[tex]\rightarrow 2 = y[/tex]
Thus, the value of y is 2.
Solve the following equations for x (5 points each). (a) -3x+10=34 and (b) 13x-4=11x+10-8
please show work
Answers
Answer:
A)x=-8 B)x=3
Step-by-step explanation:
A)-3x+10=34 -3x+10-10=34-10 -3x/-3=24/-3 x=-8
B) 13x-4=11x+10-8 13x-4+4=11x+10-8+4 13x-11x=11x-11x+6 2x/2=6/2 x=3
In this image, what is the value of C? Round your answer to the nearest tenth.
Answers
Answer:
C = 7.2
Step-by-step explanation:
What's Pythagorean Theorem?
Pythagorean Theorem is a theorem in which it states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. This can be represented as an equation of a² + b² = c².To find the value of C, we're going to use Pythagorean Theorem! We're given the legs as 4 and 6.
Step 1: Simplify.
[tex]4^2+6^2=c^2[/tex][tex]16+36=c^2[/tex] [tex]52=c^2[/tex]Step 2: Take square root of both sides.
[tex]\sqrt{c^2}=\sqrt{52}[/tex] C ≈ 7.2Therefore, the value of C is 7.2.
A rectangle has a length of 3x – 1 and a width of 2x + 4. Find the perimeter of this rectangle. Then find the area of the rectangle.
Answers
Answermmm
Step-by-step explanation:
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Answer:
Area:
(3x-1) * (2x+4) = 6x² + 10x - 4
Perimeter:
((3x-1)*2) + ((2x+4)*2) = 10x + 6
AHIJ has coordinates H(0, 0), I(-3, -1), and J-1, -2). Graph the triangle and its translation 3 units to the right and 2 units down. What are the coordinates of J'
Answers
The coordinates of the triangle is plotted on the graph and the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
Given data ,
Let the triangle be represented as ΔHIJ
Let the coordinates of the triangle be H(0, 0), I(-3, -1), and J(-1, -2)
Now , the translation rule is
The triangle is translated 3 units to the right and 2 units down
So , add 3 to the x-coordinates and subtract 2 from the y-coordinates of each point
So , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
Hence , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
To learn more about translations click :
https://brainly.com/question/19007400
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