Your friend's final bowling score is 105. Your final bowling score is 14 pins less than your friend's final score. Write and sol

Answer:

y = x - 3

Step-by-step explanation:

4x - 5 = 7 + 4y  subtracting 7 from each side

4x - 12 = 4y

 then dividing every term by 4

x - 3 = y

Step One

Deduct 32 from both sides.

F - 32 = \frac{9}{5}(k - 273.15)

Step Two

Multiply each side by \frac{5}{9}.

\frac{5}{9}(F - 32) = \frac{5}{9} \times \frac{9}{5}(k - 273.15)

\frac{5}{9}(F - 32) = k - 273.15

Step Three

Add 273.15 to both sides.

\frac{5}{9}(F - 32) + 273.15 = k

Problem B

F = 180

Solve for k

k = \frac{5}{9}(F - 32) + 273.15

k = \frac{5}{9}(180 - 32) + 273.15

k = \frac{5}{9} \times 148 + 273.15

k = 82.2222 + 273.15

k = 355.3722

k = 355.4  <<< Answer

Answer:

The detailed work and solution can be found in the attachment

Step-by-step explanation:

Answer:

The universal formula applicable for determining the necessary combinations of n ice cream flavors.

For 10 flavors of ice cream

Step-by-step explanation:

Let's denote V = Vanilla, C = Chocolate, S = Strawberry, P = Pineapple, B = Berry

For 2 flavors of ice cream:

V, C

{V/V, V/C, C/C}

3 possible combinations

For 3 flavors of ice cream:

V, C, S

{V/V, V/C, V/S, C/S, C/C, S/S}

6 possible combinations

For 4 flavors of ice cream:

V, C, S, P

{V/V, V/C, V/S, V/P, C/S, C/P, S/P, C/C, S/S, P/P}

10 possible combinations

For 5 flavors of ice cream:

V, C, S, P, B

{V/V, V/C, V/S, V/P, V/B, C/S, C/P, C/B, S/P, S/B, P/B, C/C, S/S, P/P, B/B }

15 possible combinations

Thus, we derive a sequence of

3, 6, 10, 15...

This sequence is recognized as the Triangular number series

1 + 2 = 3

1 + 2 + 3 = 6

1 + 2 + 3 + 4 = 10

1 + 2 + 3 + 4 + 5 = 15

The general formula for this sequence is

Utilizing this formula allows us to predict the number of 2-scoop combinations from 10 flavors.

Consequently, there are 55 varying combinations for a 2-scoop cone when selecting from 10 flavors.