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3 years ago

A single card is drawn at random from a standard 52 card deck. Work out in its simplest form: p(3)= P(not 3)=

Mathematics

1 answer:

photoshop1234 [79]3 years ago

4 0

Answer:

1/13 and 12/13

Step-by-step explanation:

To answer this question, we need to know the number of cards that are 3 .

Each suite has a single 3 and there are 4 suites.

This means we have 4 cards that are 3

Now, the probability of 3; P(3) would be 4/52 = 1/13

P(of not 3) = 1- probability of 3 = 1-1/13 = 12/13

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Write as a product of two polynomials. a(b–c)+d(c–b)

Natasha2012 [34]

The product of two polynomial is (b - c)(a - d)

Step-by-step explanation:

Let us explain the meaning of polynomial

A polynomial is an expression consisting of:

Variables

Coefficients
Involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables

∵ a(b - c) + d(c - b)

∵ We need to write it as a product of two polynomials

- That means factorize it to have two brackets multiplied by

each other and each one has 2 terms

∵ The bracket (c - b) can be written as (-b + c)

- Take (-1) as a common factor from the bracket (-b + c)

∵ -b ÷ (-1) = b

∵ c ÷ (-1) = -c

∴ (-b + c) = - (b - c)

- Substitute it in the expression above

∴ a(b - c) + d(c - b) = a(b - c) + d(-1)(b - c)

∵ d(-1) = -d

∴ a(b - c) + d(c - b) = a(b - c) - d(b - c)

Let us factorize the expression a(b - c) - d(b - c)

The bracket (b - c) is a common factor of the two terms

∵ (b - c) is a common factor of the two terms of the expression

∵ a(b - c) ÷ (b - c) = a

∵ - d(b - c) ÷ (b - c) = - d

∴ a(b - c) - d(b - c) = (b - c)(a - d) ⇒ product of 2 polynomial

The product of two polynomial is (b - c)(a - d)

Learn more:

You can learn more about factorization in brainly.com/question/7932185

#LearnwithBrainly

4 0

4 years ago

What is the reciprocal of 3/4? How can you be sure it is the reciprocal?

inysia [295]

To find the reciprocal of a fraction, just fill it over. Therefore, the reciprocal of 3/4= 4/3. We can be sure that this is the reciprocal because any number multiplied by its reciprocal gives the product of 1:
$\frac{3}{4} \times \frac{4}{3} = 1$

3 0

3 years ago

Read 2 more answers

Radical functions. please help me!

Sphinxa [80]

These are 8 questions and 8 answers:

1) Quesion 1:

9+√2
---------
4 - √7

Answer: the third option:

36 + 9√7 + 4√2 + √14
-----------------------------
9

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator.

The conjugate of 4 - √7 = 4 + √7

=>

$\frac{9+ \sqrt{2} }{4- \sqrt{7} } . \frac{4+ \sqrt{7} }{4+ \sqrt{7} } = \frac{(9)(4)+9 \sqrt{7}+4 \sqrt{2} + \sqrt{2} . \sqrt{7} }{(4)^2-( \sqrt{7})^2 } =$

$= \frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{16-7}$

2) Question 2: sum

$5x (\sqrt[3]{x^2y})+2( \sqrt[3]{x^5y})$

Answer: fourth option

$7x( \sqrt[3]{x^2y} )$

Explanation:

Take x^5 out of the second radical which will result in a like term of the first radical:

$5x( \sqrt[3]{x^2y} )+2( \sqrt[3]{x^5y}) =5x( \sqrt[3]{x^2y} )+2x( \sqrt[3]{x^2y})=7x( \sqrt[3]{x^2y})$

which is the fourth option

3) Question 3. Which expression is equivalent to:

$\frac{ \sqrt{10} }{ \sqrt[4]{8} }$

Answer: the first option

Explanation

$\frac{ \sqrt{10} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{10^2} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{100} }{ \sqrt[4]{8} } . \frac{ \sqrt[4]{8^3} }{ \sqrt[4]{8^3} } = \frac{ \sqrt[4]{(100)(512)} }{8} = \frac{ \sqrt[4]{51200} }{8} = \frac{4 \sqrt[4]{200} }{8} = \frac{ \sqrt[4]{200} }{2}$

4) Question 4 What is the simplest form?

Answer: the second option

Explanation:

$\sqrt[4]{81x^8y^5}=x^2 y\sqrt[4]{3^4y} =3x^2y \sqrt[4]{y}$

5) Question 5 Product

Answer: the fourth option:

$104x^4+16x^4 \sqrt{30} [/tex]\\Explanation:\\Use the square of a binomial product: (a + b)^2 = a^2 + 2ab + b^2\\[tex](4x \sqrt{5x^2} )^2+2(4x \sqrt{5x^2})(2x^2 \sqrt{6}) +(2x^2 \sqrt{6} )^2=$

$=16x^2(5x^2)+16x^4( \sqrt{30} )+4x^4(6)=80x^4+16x^4 \sqrt{30} +24x^4=$

$=104x^4+16x^4 \sqrt{30}$

which is the fourth option.

6) Question 6 Product

Answer: fourth option

Explanation:

$\sqrt[3]{16x^7} . \sqrt[3]{12x^9} = \sqrt[3]{2^4.2^2.3x^7x^9} = \sqrt[3]{2^6.3.x^{16}}=2^2 x^5 \sqrt[3]{3x} =4 x^5\sqrt[3]{3x}$

which is the fourth option.

7) Question 7. Simplified form of 2√18 + 3√2 + √162

Answer: 18√2

Explanation:

$2 \sqrt{18}+3 \sqrt{2} + \sqrt{162}=2(3) \sqrt{2} + 3 \sqrt{2} +9 \sqrt{2} =18 \sqrt{2}$

which is the second option.

8) Question 8 which function is undefined for x = 0.

Answer: second option y = √ (x - 2)

Explanation.

The square root function is not defined for negative values.

When x = 0, x - 2 = -2, whose square root is not defined.

Therefore, the square root of x - 2 is not defined for x = 0.

5 0

3 years ago

Help I've been working on this for 2 hours simplify all should contain only positive exponents

Doss [256]

The answers to the questions

6 0

3 years ago

What is the value of x in the equation 3x – 4y = 65, when y = 4? <br> the answer is x=27

Olenka [21]

What is the value of x in the equation 3x-4y=65 when y=4?

Simple...plug n chug..

3x-4(4)=65

3x-16=65

Now, isolate the variable, x....

3x-16=65
+16 +16

3x=81

Now, divide,

$\frac{3x}{3} = \frac{81}{3}$

x=27.

Thus, your answer.

7 0

3 years ago