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1 year ago

How many ways can you select a committee of 4 students out of 10 students?

Mathematics

1 answer:

Aleks04 [339]1 year ago

3 0

$\binom{10}{4}=\frac{10!}{6!4!}=\frac{10(9)(8)(7)}{24}=10(3)(7)=\boxed{210}$

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Doug, a student in this class, knows how to write programs in JAVA. Everyone who knows how to write programs in JAVA can get a h

In-s [12.5K]

Missing Part of Question

Explain which rules of inference are used in the above

Answer:

Universal instantiation, Modus ponens and Existential generalization

Step-by-step explanation:

Splitting the Statement into two, we have

"Doug knows how to write program is Java"

and

"Doug can get a high paying job"

Represent Doug with x. Then the statements is rewritten as

P(x) = "x knows how to write program is Java"

and

Q(x) = "x can get a high paying job"

In logic, A premise is a statement in an argument that provides reason or support for the conclusion.

So, Statement 1 can be written as

1. P(x) ---- Premise

Then, we have

2. Vx(P(x) --> Q(x)) -- Premise. This mean that P(x) for all values in the domain.

The universal instantiation of (2) leads to

3. P(Doug) --> Q(Doug)

The modus ponens of the above gives

4. Q(Doug)

The existential generalisation from above gives

5. ƎxQ(x)

Which means someone in this class can get a high paying job.

PS:

Universal Instantiation is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class; it is represented by VxP(x).

Existential Generalisation is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition.

It is represented as ƎxP(x)

4 0

3 years ago

What is the volume of a cone when the radius is 6 and the height is 13

lidiya [134]

Answer:

<h2>489.84 units³</h2>

Step-by-step explanation:

Given,

Radius ( r ) = 6

Height ( h ) = 13

Volume of cone = ?

Now, Let's find the volume of cone:

$= \pi \: {r}^{2} \frac{h}{3}$

plug the values

$= 3.14 \times {6}^{2} \times \frac{13}{3}$

Evaluate the power

$= 3.14 \times 36 \times \frac{13}{3}$

Calculate

$489.84$ units³

Hope this helps..

Best regards!!

6 0

3 years ago

PLZ HELP ASAP FOR BRAINLIEST

kykrilka [37]

Answer:

1/4

Step-by-step explanation:

You can set up ratios or fractions for the matching sides.

A/B

1/4 = 1/4

1.1/ 4/4= 1/4

1.5/6 = 1/4

5 0

3 years ago

Read 2 more answers

The Sum of twice a number and 5 is at most 15. What are the possible values for the number?

NISA [10]

Let's call that number x, twice the number will be 2x, sum of it and 5 is, 2x+5. So if this expression is at most 15, it means, it can be only less than 15 and equal to 15. Let's show this as an inequality.

$2x+5\le 15$

Let's solve.

$2x+5\le 15\\ \\ 2x\le 15-5\\ \\ 2x\le 10\\ \\ x\le \frac { 10 }{ 2 } \\ \\ x\le 5$

$x\quad \in \quad \left[ -\infty ,5 \right]$

If the number is a natural number. The values it can take is, $x\quad \in \quad \left[ 0,1,2,3,4,5 \right]$

6 0

3 years ago

Read 2 more answers

In which number is the digit 9 one-tenth as much than it is in the number 75,974

sertanlavr [38]

Answer:

In the number 36,521 the digit 5 is in one position lower than it is in the provided number, which means it's value is 1/10th of the original digit.

Step-by-step explanation:

7 0

3 years ago