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3 years ago

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Find the value of n(A) if n(B) = 38, n(ANB) = 17, and n(AUB) = 59. n(A)- (Type a whole number.) W More More T V

1 answer:

victus00 [196]3 years ago

5 0

Answer:

$n(A)=38$

Step-by-step explanation:

In sets theory n(A) represents the number of elements in set A.This number is the cardinal number of the set A.

For n(AUB) there is an equation that relates n(A),n(B) and n(A∩B) :

n(AUB) = n(A) + n(B) - n(A∩B)

In our exercise :

n(AUB) = n(A) + n(B) - n(A∩B)

$59 = n(A) +38-17\\n(A) = 59-38+17\\\\n(A)= 38$

Another important equation for maths is similar to this one :

P(AUB) = P(A) + P(B) - P(A∩B)

Where ''P'' is the event probability.This equation is used in probability and statistics.

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Find the value of x² - x+1 when x=√3 -1, in the form a+b√3 where a and b are integers

lidiya [134]

Answer:

$6-3\sqrt{3}$

If you compare this to $a+b\sqrt{3}$ , then $a=6$ and $b=-3$ .

Step-by-step explanation:

We are given $x=\sqrt{3}-1$ and we are asked to find the value of $x^2-x+1$ .

So we will need to find $x^2$ .

$x=\sqrt{3}-1$

Square both sides:

$x^2=(\sqrt{3}-1)^2$

Expand using identity: $(x-a)^2=x^2-2ax+a^2$ .

$x^2=(\sqrt{3})^2-2(\sqrt{3})(1)+1^2$

$x^2=3-2\sqrt{3}+1$

$x^2=4-2\sqrt{3}$

Let's go back to the full $x^2-x+1$ .

$x^2-x+1$

$(4-2\sqrt{3})-(\sqrt{3}-1)+1$

$4-2\sqrt{3}-\sqrt{3}+1+1$

$6-3\sqrt{3}$

If you compare this to $a+b\sqrt{3}$ , then $a=6$ and $b=-3$ .

5 0

3 years ago

Compute the following radical.<br> sq root 144

lara31 [8.8K]

we are given

$\sqrt{144}$

Firstly, we will find all possible factors of 144

$144=2\times 2\times 2\times 2\times 3\times 3$

we can also write as

$144=(2\times 2)^2\times (3)^2$

now, we can put exponent to over entire term

$144=(2\times 2\times 3)^2$

now, we can replace 144

$\sqrt{144}=\sqrt{(2\times 2\times 3)^2}$

now, sqrt will get cancelled with square

and we get

$\sqrt{144}=(2\times 2\times 3)$

now, we can simplify it

$\sqrt{144}=(4\times 3)$

$\sqrt{144}=12$ .............Answer

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3 years ago

Read 2 more answers

What is the value of r in the equation? Negative 1. 5 (4 minus r) = negative 12 –6 –4 4 6.

Debora [2.8K]

Answer:

-458

Step-by-step explanation:

-1.5(4 - r) = -12 - 6 -446

-6 + r = -464

r = -458

5 0

2 years ago