The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4→10x − 5y = −20 3x

Response:

1. Closure

2. Distributive

3. Closure

Detailed explanation:

In this scenario, we are examining the properties that each equation demonstrates.

The first equation shows the closure property.

This indicates that whether we add in one direction or the other, the result remains unchanged. Therefore, we conclude that addition conforms to the closure property in this case.

The third equation also shows the closure property. Regardless of how we approach the addition for this equation, the outcome remains consistent.

The second equation displays the distributive property.

Each element within the parentheses is multiplied by the negative sign before we proceed with further calculations.

Answer:

To inspect a batch consisting of 20 semiconductor chips, a sample of 3 is selected. Out of these, 10 chips fail to meet customer specifications.

a) Total distinct samples possible = 20C3 =   =1140

b) For exactly 2 good chips and 1 bad chip

Total samples = 10C2 * 10C1 = 45 * 10 =450

c) Combinations of 2 good 1 bad, 1 good 2 bad, and 3 bad chips

Total samples = 10C2 * 10C1 + 10C1 * 10C2 + 10C3

=

Answer: 0.1289

Step-by-step explanation:

Given: The proportion of students absent on Mondays at a large university.:

Sample size:

Mean:

Standard deviation =

Let x represent a binomial variable.

Referencing the standard normal distribution table,

(1)

Z score for normal distribution:-

For x=4

For x=3

Thus, from (1)

Consequently, the likelihood of four students being absent =

Answer: The most significant angle created during his journey appears at the mall, between his house and the library.

Step-by-step explanation:

Hi, since this scenario forms a right triangle (refer to the attached image), the angle between his house and the library measures 90°.

For a right triangle, the total of its internal angles equals 180°, making the right angle (90°) the largest among them.

Thus, the angle at the mall, between his house and the library, is indeed the largest angle formed during his trip.

If you need further clarification or have questions, feel free to ask!