All categories

3 years ago

Prove that the value of the expression a^2–a is divisible by 2 for any whole value of a.

1 answer:

8 0

Note that $a^2-a=a(a-1)$ , so that $a^2-a$ is the product of two consecutive integers. This means one of them must be even, and the other is odd. The product of an odd number and an even number is itself an even number, so $2\mid a^2-a$ for any integer $a$ .

You might be interested in

For an outdoor concert by the city orchestra, concert organizers estimate that 10,000 people will attend if it's not raining. If

Vlada [557]

Answer:

The number of expected people at the concert is 8,500 people

Step-by-step explanation:

In this question, we are asked to determine the expected number of people that will attend a concert if we are given the probabilities that it will rain and it will not rain.

We proceed as follows;

The probability that it will rain is 30% or 0:3

The probability that it will not rain would be 1 -0.3 = 0.7

Now, we proceed to calculate the number of people that will attend by multiplying the probabilities by the expected number of people when it rains and when it does not rain.

Mathematically this is;

Number of expected guests = (probability of not raining * number of expected guests when it does not rain) + (probability of raining * number of expected guests when it rains)

Let’s plug values;

Number of expected guests = (0.3 * 5,000) + (0.7 * 10,000) = 1,500 + 7,000 = 8,500 people

4 0

3 years ago

What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0 with th

shusha [124]

22.6sin[39.0]= 21.78

3 0

3 years ago

A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point.

Gwar [14]

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> the number of solved puzzles

y -----> the number of solved riddles

we know that

$2x+y \geq 4$

The solution of the inequality is the shaded area above the solid line $2x+y=4$

The slope of the solid line is negative $m=-2$

The y-intercept of the solid line is the point (0,4)

The x-intercept of the solid line is the point (2,0)

therefore

The graph in the attached figure

3 0

3 years ago

Read 2 more answers

Dr. Hilton uses the graph to determine if a patient has a

seropon [69]

Answer:

At least 100 degrees

Step-by-step explanation:

Here, we want to make an inequality assertion from the graph drawn by Dr Hilton.

The correct conclusion here is that a person has a fever once his/her temperature is greater than or equal to 100 degrees.

How do we know this from the graph? from the graph, we can see a yellow circular mark placed on 100. This indicates that we are starting our consideration from the point 100 degrees. What we don not know is if our answer is less than, greater than, less than or equal to or greater than or equal to.

The correct answer is however greater than or equal to. Firstly we check the fill of the yellow circular mark. Once it is filled and not left blank, then it indicates an equal to relationship, meaning 100 degrees itself is included in the range.

finally we then consider the direction it faces and from here we can conclude that it is greater than or equal to

6 0

3 years ago

Read 2 more answers

19. (9+2) X 6 -5=<br> Help

Nata [24]

Answer:

Step-by-step explanation:

Use PEMDAS (Parenthesis first, Exponents second, Division/Multiplication third, Addition/Subtraction last)

(9+2) x 6 - 5

11 x 6 - 5

66 - 5