Alison is saving for retirement. Her company matches what she puts into her 401K in a ratio of 2:3. If she puts in $400 each mon

Answer:

Step-by-step explanation:

The total count of laptops, N = 20

Defective laptops, n = 3

The school is purchasing 2 laptops

Case 1:

Both purchased laptops are non-defective

Probability of selecting 2 non-defective laptops

The count of non-defective laptops equals 20 - 3 = 17

Overall laptop count = 20

Probability, P = 17/20 = 0.85

Case 2:

One laptop is found defective

The probability of choosing 1 defective and 1 non-defective laptop

P' = 3/20 x 17/19 = 0.134

Case 3:

Both laptops are defective

Choosing 2 laptops from 3 = 3 C 2 = 3

Selecting 2 from 20 = 20 C 2 = 190

The probability of selecting two defective laptops equals 3 / 190 = 0.0158

P'' =

(10x)^(-3)
= 1/[(10x)^3]
= 1/[10^3 * x^3]
= 1/(1000x^3)

The final result is 1/(1000x^3), and none of the given choices seem correct. (Option C would be correct if it used round brackets.)

Hope this helps~

Answer:

a) The first inequality is 100 + 55x > 150 + 51x;

b) The final inequality results in x > 12.5

c) Sal's mother will need to use the second phone for at least 13 months.

Step-by-step explanation:

a) Let x represent the number of months.

1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.

2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.

3. For the second phone to be cheaper, we set up the inequality:

150 + 51x < 100 + 55x

which simplifies to

100 + 55x > 150 + 51x

b) Now solve this:

55x - 51x > 150 - 100

4x > 50

so x > 12.5

c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).

The math equation to solve is 36 + 34 + 25, and the sum is 95.

The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.