Which sequences are geometric? Check all that apply. –2, –4, –6, –8, –10, … 16, –8, 4, –2, 1 –15, –18, –21.6, –25.92, –31.104, …

<span>5.7 liters of a 5% solution combined with 4.3 liters of a 40% solution. To begin, define the problem with formulas. x Represents the liters of the 5% solution utilized. 10-x Represents the liters of the 40% solution used. This forms an equation: 5% of x plus 40% of (10-x) equals 20% of 10. 0.05x + 0.40(10-x) = 0.20 * 10 Now, distribute the 0.40 coefficient. 0.05x + 4.0 - 0.40x = 0.20 * 10 Next, combine the terms. 4.0 - 0.35x = 2.0 Add 0.35x to each side. 4.0 = 2.0 + 0.35x Subtract 2 from both sides. 2.0 = 0.35x Lastly, divide both sides by 0.35. 5.7 = x Thus, 5.7 liters of a 5% solution is required. To determine the volume of the 40% solution, subtract from 10. 10.0 - 5.7 = 4.3</span>

Answer:

Step-by-step solution:

Leon’s older brother’s height is feet

feet

Because Leon is 1/3 foot shorter than his brother,

Leon’s height =

Convert to like fractions by multiplying numerator and denominator: multiply 3 for the first fraction and 4 for the second.

So, Leon’s height =

feet

Therefore, Leon’s height is feet.

4 pounds cost $1.96
1.96 / 4 gives $0.49 per pound. 

96 soldiers will remain unassigned and the arrangement will consist of 52 rows.

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.