one-third of the sum of a number and 4 in algebra

Using the combination formula, it is found that:

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The order in which the students are chosen is not important, which means that the combination formula is used to solve this question.

Combination formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

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Question a:

Twice as many ways to choose the teams of 3 than the teams of 2, thus:

[tex]C_{n,3} = 2C_{n,2}[/tex]

[tex]\frac{n!}{3!(n-3)!} = 2\frac{n!}{2!(n-2)!}[/tex]

We have to solve for n, thus:

[tex]2!n!(n-2)! = 2(3!)(n!)(n-3)![/tex]

[tex](n-2)! = 3!(n-3)![/tex]

From the factorial concept: [tex](n-2)! = (n-2)(n-3)![/tex], thus:

[tex](n-2)! = 3!(n-3)![/tex]

[tex](n-2)(n-3)! = 3!(n-3)![/tex]

[tex]n - 2 = 3![/tex]

[tex]n - 2 = 6[/tex]

[tex]n = 8[/tex]

There are 8 students in the group.

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Question b:

First we have to find the total number of students, using the same logic as item a.

[tex]C_{n,3} = 2C_{n,2}[/tex]

[tex]\frac{n!}{3!(n-3)!} = 3\frac{n!}{2!(n-2)!}[/tex]

[tex]2!n!(n-2)! = 3n!3!(n-3)![/tex]

[tex]2(n-2)(n-3)! = 18(n-3)![/tex]

[tex]n - 2 = 9[/tex]

[tex]n = 11[/tex]

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The number of teams of three is:

[tex]C_{11,3} = \frac{11!}{3!8!} = 165[/tex]

165 teams of three can be selected from this group.

A similar problem is given at https://brainly.com/question/23302762

Answer:

[tex] \sqrt{12} \times \sqrt{27} \\ = 2 \sqrt{3} \times 3 \sqrt{3} \\ 6 \sqrt{3 } \times \sqrt{3} \\ = 6 \times 3 \\ = 18 \\ thank \: u[/tex]

Answer:

18

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

its correct i solved it by paper im lazy typing it here lol, anyways 18 has to be the correct answer.

hope i helped

With some give information, we need to solve some algebraic problems that involve a change of units, lets see step by step how we do that:

A) First, we know that:

The bridge was constructed in 2.5 years

Knowing that 1 year =  12 months, we can rewrite:

2.5 years = (2.5)*(12 montsh) = 28 months

The two crews built, together, 12,513 ft of the bridge.

Now, we know that the South Padre Island crew built an average of 208.5 per month.

Then in the 28 months for the whole construction, they built 28 times that amount:

D = (28 months)*(208.5 per month)  = 5,838 ft

Then the rest was constructed by the Port Isabel Crew.

They constructed 12,513 ft -  5,838 ft = 6,675ft

So that crew constructed 6,675 ft in 28 months, then the average number of feet built per month (the quotient between the total amount built and the number of months in which that was built) is:

6,675 ft/28 months = 238.39 ft per month.

b)

South Padre Island crew constructed  5,838 ft

Port Isabel Crew constructed 6,675ft

Now we want to transform these to miles.

Remember that;

1 mille = 5280 ft.

Then to transform from ft to miles, we just need to divide our measures by 5280 ft

Then:

South Padre Island crew constructed  5,838 ft = (5,838ft/5280ft) mi = 1.11 mi

Port Isabel Crew constructed 6,675ft = (6,675ft/5280ft) mi = 1.26 mi

c) Is this answer reasonable?

Mathematically, yes, both crews constructed about the same in about the same time, with a small difference that may be related to the sizes of each crew or something like that.

We could conclude that this would not be reasonable if the monthly rates were dramatically different.

If you want to learn more, you can read:

https://brainly.com/question/15051367

Answer:

B) Associative Property of Multiplication

Step-by-step explanation:

The associative property states you can change where the parentheses (grouping terms) are in a multiplication statement, and you'll get the same product.

More generally:

(a * b) * c = a * (b * c)

Answer:

B) Associative Property Of Multiplication

Step-by-step explanation:

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

Therefore, changing the grouping of (8x3) or (3x4) does not change the product.

Answer:

Let the integers are p and q.

In case both integers are positive or negative, you add the numbers up and apply their sign to the sum.

Examples:

In case one of the integers is negative and one positive.

Use absolute value in this case.

Subtract the numbers and apply the sign of the number with the greater absolute value.

Examples:

Step-by-step explanation:

Let the numbers be x and y

If both are of same signs then

|x + y| = x + y

-|x + y| = -(x + y) = -x - y

If one is negative and one is positive

-|x + (-y)| = -|x - y| = -x + y

-|y + (-x)| = -|y - x| = -y + x

Answer:

the answer is on the computer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Stop doing it

Answer:

The height is 11/2

Step-by-step explanation:

We know SA = 30n

and r = 2

We are solving for h. So plug in our values

30n = 2n(2)^2 + 2n(2)h

Multiply and square on the right side terms

30n = 8n + 4nh

Divide everything by n

30 = 8 + 4h

Subtract 8 on both sides

22 = 4h

Divide by 4 on both sides

h = 22/4 = 11/2

Check:

30n = 2n(2)^2 + 2n(2)(11/2)

30n = 8n + 22n

30n = 30n

The answer would be 98/5

Answer:

gauth math

got it perfect answer

Answer:

x=30

Step-by-step explanation:

Subtract 5 from both sides of the equ

Answer:

c =2n

Step-by-step explanation:

cost c is given by cost of each person multiplied by number n of people

Answer:

none of these

Step-by-step explanation:

area of the triangle =height ×base and then divide by 2

Answer:

sandwich and drink only (no dessert)

so 4 x 6 = 24

you have 24 different combinations you can do

hope this helps

Step-by-step explanation:

Answer:

hope this helps you have a great

Answer:

[tex]x2+x+xy+y+zx+z \\ =x(x+1+y+y+z)+z \\ =x(x+2y+z+1)+z

[/tex]

Step-by-step explanation:

take like terms together..

x²+x+zx+xy+y+z

x(x+z+y)+y(x+y+z)

(x+y)(x+y+z)

hope it helps

Answer:

6v+16

Step-by-step explanation:

2(2v+13) + 2(v-5) > 4v+26+2v-10 > 6v+16

Answer:

Perimeter is 6v + 16

Step-by-step explanation:

Perimeter formular of rectangle:

[tex]{ \sf{perimeter = 2(length + width)}} \\ { \sf{p = 2(l + w)}}[/tex]

length is (2v + 13)

width is v - 5

[tex]{ \sf{p = 2 \{(2v + 13) + (v - 5) \}}} \\ { \sf{p = 2 \{(2v + v) + (13 - 5) \}}} \\ { \sf{p = 2(3v + 8)}} \\ { \sf{p = 6v + 16}}[/tex]

Answer:

Read explanation

Step-by-step explanation:

The two operations that you will get the same answer for no matter what order you do it is addition and multiplication.

Bonus: Technically, if you had something like 1-2-3 you could rewrite it as 1 + (-2) + (-3) and now it won't matter the order and for something like 1/2/3 you could rewrite as 1 * (1/2) * (1/3) and not it wont matter the order too!

This propetie is called the associative property of addition and multiplication.

In the second question since its addition the order you do it in does not matter.

Why: If you think of it logically adding in a diffrent order than the question does not matter since in the end your still adding the same ammount.

Remember: You can only swap the orders if everything is addition or multiplication and remember your order of operations when using this propety in the years to come.

Hoped this helped, Eddie K.W.

Answer:

I HOPE IT WILL HELP YOU.

Have a great day ahead.

Answer: 855 is the answer

Hi there!  

»»————-　★　————-««

I believe your answer is:  

15cm²

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Area of a rectangle is:}}\\\\A = l * w\\----------------\\\rightarrow L = 5; w = 3\\\\\rightarrow A = 5 * 3\\\\\rightarrow A = \boxed{15cm^2}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Hey there! I'm happy to help!

We see that all of our y-values go negative and our x-values stay the same. It isn't a rotation because then our x-values will switch, but they haven't switched in our problem, so A and D are incorrect.

Reflecting over the line y=x is just reflecting over a diagonal line, and that will switch the x-value as well.

The correct answer is B. reflect over the x-axis. All of the x-values stay the same here, but the y-values are all on the other side of the x-axis, so they are all negative now, and this matches the change we see with our points.

Have a wonderful day and keep on learning! :D

Step-by-step explanation:

[tex]sum \: of \: angles \: in \: a \: circle = 360 \\ so \\ 5a + 2a + 2a + 5a + 4a = 360 \\ 18a = 360 \\ a = \frac{360}{18} \\ a = 20 \\ thank \: you[/tex]

Answer:

120 + z = 180 (linear pair)

=> z = 180 - 120

=> z = 60

130 + y = 180 (linear pair)

=> y = 180 - 130

=> y = 50

50 + 60 + x = 180 (Angle sum property of a triangle = 180)

=> 110 + x = 180

=> x = 180 - 110

=> x = 70

Step-by-step explanation:

2f - 3(4f - 5g) + 5g +7fg

multiply the 3 in

2f - 12f - 15g + 5g + 7fg

add or subtract common terms

-10f -10g +7fg will be your final answer

Answer:

Step-by-step explanation:

As the question did not say how to 'solve the question', I would assume it will be to simplify the equation, as there is no way of solving an expression without an answer.

Simplify:

2f - 3(4f-5g) + 5g +7fg

Get rid of the parentheses

2f - 12f - 15g + 5g +7fg

Simplify similar expressions

-10f - 10g + 7fg

Therefore, 2f - 3(4f-5g) + 5g +7fg simplified is equal to -10f - 10g + 7fg.

Answer:

[tex]\frac{12}{3} - 5 +16 : 4 = 3[/tex]

Step-by-step explanation:

[tex]\sqrt{144} = 12\\\sqrt[5]{243} = 3\\\\\sqrt[3]{64}= 4[/tex]

Answer:

0

Step-by-step explanation:

Any nonzero number to 0 power results in 1.

This implies m is simply 0 since it would give

(x^8/yz^5)^0 which is 1.

Answer:

the value of "m" is 0

Step-by-step explanation:

the entire fraction is equal to 1, the fraction is raised to a power of 0, non-zero

raised to the power of 0 is always equal to 1 so then its  

(\frac{x^{8}}{yz^{5}})^0 =1

now then this gives us the value of "m" = 0

hope that helps>3