All categories

3 years ago

This is my my second to last one, thanks for helping me

Mathematics

1 answer:

icang [17]3 years ago

3 0

9514 1404 393

Answer:

$9
Option 4

Step-by-step explanation:

The equations need to match the problem statements. If we let C and S represent the costs of Cherry and Sweet potato pies, respectively, then the revenue from each sale can be expressed as an equation.

1 cherry and 7 sweet potato for $114 ⇒ C +7S = 114

14 sweet potato and 11 cherry for $309 ⇒ 11C +14S = 309

Note that we have used C and S in the second equation in the same order as they appeared in the first equation, even though the problem statement has that order reversed. This facilitates solving the equations using elimination or Cramer's rule.

These equations match Option 4.

The cost of a cherry pie can be found by eliminating S from the equations. We can do that by subtracting twice the first equation from the second:

(11C +14S) -2(C +7S) = (309) -2(114)

9C = 81 . . . . . simplify

C = 9 . . . . . . . divide by 9

The cost of each cherry pie is $9.

You might be interested in

Find the value of x. <br> (6x + 1)<br> (9x - 23)

shtirl [24]

Answer:

Step-by-step explanation:

(6x+1)(9x-23)= 6x(9x-23)+1(9x-23)

= 54x²-138+9x-23

= 54x²+9x-161

3 0

2 years ago

DJ Titus is making a playlist for a radio show; he is trying to decide what 10 songs to play and in what order they should be pl

Dominik [7]

Answer:

Different playlists possible = 18287141644800

Step-by-step explanation:

Given - DJ Titus is making a playlist for a radio show; he is trying to

decide what 10 songs to play and in what order they should be

played.

Step 1 of 2 : If he has his choices narrowed down to 7 blues,

7 disco, 5 pop, and 7 reggae songs.

To find - He wants to play no more than 4 reggae songs.

How many different playlists are possible ?

Proof -

Given that he wants to play no more that 4 reggae songs.

So the possibility of choice of reggae song is 0, 1, 2, 3, 4

Now,

Case I -

If 0 reggae song is selected

⇒All 10 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₁₀ ₓ ⁷C₀ = 92,378

Case II -

If 1 reggae song is selected

⇒All 9 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₉ ₓ ⁷C₁ = 646,646

Case III -

If 2 reggae song is selected

⇒All 8 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₈ ₓ ⁷C₂ = 1,587,222

Case IV -

If 3 reggae song is selected

⇒All 7 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₇ ₓ ⁷C₃ = 1,763,580

Case V -

If 4 reggae song is selected

⇒All 6 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₆ ₓ ⁷C₄ = 949,620

So,

Total possible ways = 92,378+ 646,646+ 1,587,222+ 1,763,580+ 949,620

= 5,039,446

⇒Total possible ways = 5,039,446

Now,

Also the 10 songs selected can arranged themselves in 10! ways. ( because order of song played does not matter )

∴ we get

Different playlists possible = 10! × 5,039,446

= 18287141644800

⇒Different playlists possible = 18287141644800

6 0

3 years ago

which of the following sets could be the sides of a right triangle? {2,3, square root 13} {5,5,2 square root 10} {5,12,15}

anastassius [24]

All of these sets meet the requirements of the triangle inequality. The sum of any two numbers in the set is greater than the third one. (You really only need to check that the sum of the smallest two is greater than the largest.)

It can help to resolve the numbers that are only indicated as to value.

√13 ≈ 3.606

2√10 ≈ 6.325

_____

Your comparisons can be ...

2 + 3 = 5 > 3.606 . . . is a triangle

5 + 5 = 10 > 6.325 . . . . . . is a triangle

5 + 12 = 17 > 15 . . . . . . . . is a triangle

8 0

3 years ago

Orbet used 24 square tiles to make a rectangle. The perimeter of the rectangle is 20 units. What would be the perimeters of the

Dmitriy789 [7]

Answer:

The perimeter of other rectangles are 50, 28, 22 units

The area of all possible rectangles are same and equals to 24 unit²

Step-by-step explanation:

Given - Orbet used 24 square tiles to make a rectangle. The perimeter of the rectangle is 20 units.

To find - What would be the perimeters of the other rectangles Orbet could make using only these 24 tiles? How do the areas of the rectangles compare?

Proof -

We know that

Are of Rectangle = Length × Breadth

And Perimeter of Rectangle = 2 (Length + Breadth )

Now,

Given that,

Orbet used 24 square tiles

And perimeter of the rectangle made = 20

So,

Possible Length of rectangle = 6

Possible breadth of Rectangle = 4

Or Vice-versa.

Total number of Rectangles possible = 4

Possibilities are - 1 × 24, 2 × 12, 3 × 8, 4 × 6

Case I :

Length of rectangle = 1

Breadth of rectangle = 24

∴ Perimeter of rectangle = 2(1 + 24) = 2(25) = 50 units

Area of rectangle = 1 × 24 = 24 unit²

Case II :

Length of rectangle = 2

Breadth of rectangle = 12

∴ Perimeter of rectangle = 2(2 + 12) = 2(14) = 28 units

Area of rectangle = 2 × 12 = 24 unit²

Case III :

Length of rectangle = 3

Breadth of rectangle = 8

∴ Perimeter of rectangle = 2(3 + 8) = 2(11) = 22 units

Area of rectangle = 3 × 8 = 24 unit²

Case IV :

Length of rectangle = 4

Breadth of rectangle = 6

∴ Perimeter of rectangle = 2(4 + 6) = 2(10) = 20 units

Area of rectangle = 4 × 6 = 24 unit²

∴ we get

The perimeter of other rectangles are 50, 28, 22 units

The area of all possible rectangles are same and equals to 24 unit²

5 0

3 years ago

HELP!!<br>What is the surface area of this shape?

Hunter-Best [27]

2 triangular faces

1/2bh

10x15=150

2x150= 300

‘back’ face

7x20=140

‘front’ face

7x25= 175

‘bottom’ face

7x15= 105

total: 585m^2

6 0

3 years ago