At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer. on monday 3,000 customers came to the theater. how many people received both free items?

20 people

Step-by-step explanation:

At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer.

On Monday, 3,000 customers came to the theater.

To find the number of people who got both free items, we will calculate the Least common Multiple (LCM) of 30 and 75.

LCM of 30, 75

= 5 × 3 × 5 × 2

= 150

Each 150th customer will receive both free items.

Total number of people who receive both free items = 3000 ÷ 150

                                                                                        = 20 people

On Monday 20 people will receive both free items.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it