MATHEMATICS HIGH SCHOOL

Miriam is picking out some movies to rent, and she is primarily interested in comedies and foreign films. She has narrowed down her selections to 10 comedies and 15 foreign films. How many different combinations of 3 movies can she rent if she wants at least two comedies?

Answers

Answer 1

Answer:

Answer:

There are 795 combinations.

Step-by-step explanation:

The number of ways or combinations in which we can select k element from a group of n elements is given by:

$nCk=(n!)/(k!(n-k)!)$

So, if Miriam want to choose 3 movies with at least two comedies, she have two options: Choose 2 comedies and 1 foreign film or choose 3 comedies.

Then, the number of combinations for every case are:

1. Choose 2 Comedies from the 10 and choose 1 foreign film from 15. This is calculated as:

$10C2*15C1=(10!)/(2!(10-8)!)*(15)/(1!(15-14)!)$

$10C2*15C1=675$

2. Choose 3 Comedies from the 10. This is calculated as:

$10C3=(10!)/(3!(10-3)!)=120$

Therefore, there are 795 combinations and it is calculated as:

675 + 120 = 795

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Completing Proofs Involving Linear PairsGiven: m ZELG = 124°

Prove: x = 28

Statements

Reasons

1. m ZELG = 124

1. given

2. m ZELD = 2x

2. given

H

L

3. ZELG and ZELD are

a linear pair

3. definition of a linear pair

(2x)

G

4. m ZELD + m ZELG = 180

4.

Ε

• F.

5. 2x + 124 = 180

5. substitution

Complete the steps in the two-column proof.

6.

6. subtraction property

7. x = 28

7. division property

Intro

Done

vity

Answers

The corresponding angles of the lines solved and the value of x = 28°

What are angles in parallel lines?

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Given data ,

Let the measure of ∠ELG = 124°

The measure of ∠ELD = 2x

∠ELG and ∠ELD are a linear pairs of angles

So , the measure of ∠ELG + ∠ELD = 180°

On simplifying , we get

2x + 124° = 180°

Subtracting 124° on both sides , we get

2x = 56°

Divide by 2 on both sides , we get

x = 28°

Therefore , the value of x is 28°

Hence , the angle is x = 28°

To learn more about angles in parallel lines click :

brainly.com/question/27400033

#SPJ7

Answer:

1. angle addition post

2. 2x=56

I need help finding the solution (x,y) of4x - y = 2
8x + 5y = -3
[Multiply the first equation by 5.]

Answers

Answer:

x = 1/4

Step-by-step explanation:

20x - 5y = 10

8x + 5y = -3

28x = 7

x = 1/4

The length of one side of an equilateral triangle is 6 square root 3 meters. Find the length of one altitude of the triangle.

Answers

The altitude of the equilateral triangle with sides 6√3 meters is 9 meters.

Properties of equilateral triangle

All the sides are equal
All the angles are equal(60 degree each)

The length of the sides are 6√3 meters each. Recall triangles has three sides.

Therefore, the altitude or height of the triangle can be found as follows:

Using Pythagoras theorem,

c² = a² + b²

where

c = hypotenuse

a and b are the other 2 legs.

Therefore,

h² = (6√3)² - (1 /2 (6√3))²

h² = 108 - 27

h = √81

h = 9 meters

Therefore, the altitude of the triangle is 9 meters.

learn more on triangle here: brainly.com/question/8224697?referrer=searchResults

Answer:

9 m

Step-by-step explanation:

The formula of an altitude of an equilateral traingle with side a:

$h=(a\sqrt3)/(2)$

We have $a=6\sqrt3$

Substitute:

$h=(6\sqrt3\cdot\sqrt3)/(2)=((6)(\sqrt3)^2)/(2)$

Use $\left(√(a)\right)^2=a$

$h=((6)(3))/(2)=(18)/(2)=9$

The state university reported 1183 cases of flu in their student body for the month of January. If this was a 350% increase above the number of flu cases in the month of December, how many students had flu in December?

Answers

Let us assume the number of students having flu in December = x
Number of students having flu in the month of January = 1183
Percentage increase in the number of people having flu from the month of December to the month of January = 350%
Then we can write the equation as
350x/100 = 1183
350x = 1183 * 100
350x = 118300
x = 118300/350
= 11830/35
= 338
So the number of students that were affected by flu in the month of December was 338. This is the easiest way to get to the required answer.

Answer:

338

Step-by-step explanation:

1183/350%

= 338 people

type it in your calculator just like my equation and you'll get the answer.

Rewrite in simplest terms (10x−2y)−(x+3y)

Answers

Answer:

The simplified expression is 9x - 5y.

To simplify the expression we can distribute the negative sign to the parenthesis. We can also get rid of the parenthesis of both terms once we have distributed.

$(10x-2y)-x-3y$

$10x-2y-x-3y$

We can now combine like terms:

$9x-5y$

So, our simplified expression is 9x - 5y.

Suzanne wants to put a fence around Her Square Garden. If the garden covers an area of 121m2, how many meters of fencing does she need? Please help thank you!

Answers

So, since it is square, we are going to take the square root of 121 which is 11. And since fencing goes around something, that means we have to find the perimeter. So since all four sides are the same length, we can just multiply 11 by 4 to get 44 meters of fencing

Answer:

Step-by-step explanation:

$\sqrt121 = 11$

and there is 4 sides to a square so you multiply 11 * 4

resulting 44

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