RESTAURANT MANAGEMENT

Select all pairs of numbers that have a least common multiple of 30.

ddd [48]

5 and 6 and 3 and 10, the pairs of numbers that have a least common multiple of 30.

<u>Step-by-step explanation:</u>

Case 1: LCM (3, 6)

Prime factorization of 3: $1 \times 3$

Prime factorization of 6: $2 \times 3$

Using all prime numbers found as often as each occurs most often we take

$2 \times 3=6$

Therefore LCM (3, 6) = 6.

Case 2: LCM (5, 6)

Prime factorization of 5: $1 \times 5$

Prime factorization of 6: $2 \times 3$

Using all prime numbers found as often as each occurs most often we take

$5 \times 2 \times 3=30$

Therefore LCM (5, 6) = 30

Case 3: LCM (3, 10)

Prime factorization of 3: $1 \times 3$

Prime factorization of 10: $2 \times 5$

Using all prime numbers found as often as each occurs most often we take

$5 \times 2 \times 3=30$

Therefore LCM (3, 10) = 30

Case 4: LCM (5, 10)

Prime factorization of 5: $1 \times 5$

Prime factorization of 10: $2 \times 5$

Using all prime numbers found as often as each occurs most often we take

$5 \times 2=10$

Therefore LCM (5, 10) = 10

8 0

3 years ago

One half the sum of a number z and 3 1/2 is 4 1/2

solong [7]

4 1/2(2)=9. Multiply by 2 to get total
9- 3 1/2=z. Subtract 3 1/2 from total to get Z
5 1/2= Z

3 0

4 years ago

Which unit rate is the lowest price per ounce? Choice A: 6 ounces of raisins for $2.98 Choice B: 13 ounces of raisins for $7.18

nikitadnepr [17]

1.49/6=0.248 cents
3.59/13=0.276 cents

6 0

4 years ago

Read 2 more answers

1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating

elixir [45]

The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.

<h3>The equation of the theatre's income</h3>

The theatre charges $4.50 per student.

Assume the number of students is x, the equation of the theatre's income would be:

I(x) = 4.5x

<h3>The equation of the theatre's expenses</h3>

The theatre expense per student is $1.25, and the operating cost on the staff is $130

The equation of the theatre's expenses would be:

E(x) = 1.25x + 130

<h3>Complete the table</h3>

Using the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:

Students, x 0 10 20 30 40 50 60 70

Income, I 0 45 90 135 180 225 270 315

Expenses, E 130 142.5 155 167.5 180 192.5 205 217.5

<h3>The graph of the theatre's income and expenses</h3>

See attachment

<h3>The pattern by which theatre's income and expenses increase</h3>

The functions I(x) and E(x) are linear functions.

So, the pattern with which the functions increase is a linear pattern.

<h3>The number of students when the theatre's income and expenses are equal</h3>

This means that:

I(x) = E(x)

So, we have:

4.5x = 1.25x + 130

Subtract 1.25 from both sides

3.25x = 130

Divide both sides by 3.25

x = 40

Hence, the number of students is 40

<h3>The theatre profit</h3>

This is the difference between the theatre expenses and their income.

So, we have:

P(x) = E(x) - I(x)

This gives

P(x) = 1.25x + 130 - 4.5x

Simplify

P(x) = 130 - 3.25x

<h3>Solution to the inequalities</h3>

We have:

E(x) < 255

This gives

1.25x + 130 < 255

Subtract 130 from both sides and divide by 1.25

x < 100 students

Also, we have:

I(x) > 675

This gives

4.5x > 657

Solve for x

x > 146 students

Hence, the number of students for the inequalities are less than 100 and greater than 146

Read more about linear equations and inequalities at:

brainly.com/question/11234618

8 0

2 years ago

Can someone awnser this

Ostrovityanka [42]

It has a constant daily growth rate of 1.5

5 0

4 years ago