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3 years ago

(07.05)

Mathematics

2 answers:

Llana [10]3 years ago

5 0

Answer: n = -2

Step-by-step explanation:

3n +2(n + 2) = 9n + 12

(simplify 2(n + 2)) =

3n + 2n + 4 = 9n + 12

(subtract 9n from both sides)

3n + 2n - 9n + 4 = 12

-4n + 4 = 12

(subtract 4 from both sides)

-4n = 8

(divide -4 from both sides)

n = -2

Nikolay [14]3 years ago

5 0

Answer:

b. -2

Step-by-step explanation:

3n + 2 ( n + 2 ) = 9n + 12

[To simplify, multiply 2 with n and 2]

3n + 2n + 4 = 9n + 12

5n + 4 = 9n + 12

[Add 2n and 3n]

5n + 4 - 9n = 12

[Sign of 9n would change when it's moved from one side of the = to the other]

5n - 9n = 12 - 4

[Similarly, sign of 4 would change from + to -]

- 4n = 8

n = 8/-4

n = -2

Hope this helps :D

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The senior class at a very small high school has 25 students. Officers need to be elected for four positions: President, Vice-Pr

kirill115 [55]

Answer:

(a) The total number of ways to select 4 officers from from 25 students is 12,650.

(b) The total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.

Step-by-step explanation:

(a)

It is provided that there are a total of n = 25 students.

Officers need to be elected for four positions:

President, Vice-President, Secretary, and Treasurer.

k = 4

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!(n-k)!}$

Compute the number of ways to select 4 students from from 25 as follows:

${25\choose 4}=\frac{25!}{4!(25-4)!}$

$=\frac{25!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22\times 21!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22}{4\times 3\times 2\times 1}\\\\=12650$

Thus, the total number of ways to select 4 officers from from 25 students is 12,650.

(b)

It is provided that of the 25 students, there are 13 girls and 12 boys in the class.

For the post of President and Treasurer only girls are selected.

For the post of Vice-President and Secretary only boys are selected.

Compute the number of ways to select 2 girls for the post of President and Treasurer as follows:

${13\choose 2}=\frac{13!}{2!(13-2)!}$

$=\frac{13!}{2!\times 11!}\\\\=\frac{13\times 12\times 11!}{2!\times 11!}\\\\=\frac{13\times 12}{ 2\times 1}\\\\=78$

Compute the number of ways to select 2 boys for the post of Vice-President and Secretary as follows:

${12\choose 2}=\frac{12!}{2!(12-2)!}$

$=\frac{12!}{2!\times 10!}\\\\=\frac{12\times 11\times 10!}{2!\times 10!}\\\\=\frac{12\times 11}{ 2\times 1}\\\\=66$

The number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is:

${13\choose 2}\times {12\choose 2}=78\times 66=5148$

Thus, the total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.

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3 years ago

At a particular restaurant each mozzarella stick has 90 cal in each pizza roll has 80 cal. A combination meal with the mozzarell

serious [3.7K]

Answer:

The meal consist 11 mozzarella sticks and 6 pizza rolls.

Step-by-step explanation:

We are given the following in the question:

Calories in mozzarella stick = 90

Calories in pizza roll = 80

Let x be the number of a mozzarella stick and y be the number of pizza rolls.

Total calories in meal = 1470

Thus, we can write the equation:

$90x + 80y = 1470$

There are five more mozzarella sticks than pizza roll.

Thus, we can write the equation:

$x = y + 5\\x-y = 5$

Solving the two equations, we get,

$90x+80y+80x-80y = 1470 + 400\\170x = 1870\\x = 11\\y = 11-5 = 6$

Thus, the meal consist 11 mozzarella sticks and 6 pizza rolls.

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Answer:

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Step-by-step explanation:

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