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tekilochka [14]

2 years ago

7

Q 1.) Expand using identities:i. (a+2b)²ii. (5x-3y)²iii. (3a+4)(3a-4)(9a²+16)

1 answer:

Ganezh [65]2 years ago

4 0

Step-by-step explanation:

#1.

(a + 2b)²

<em>Using identity (x + y)² = x² + 2xy + y², we get:</em>

= (a)² + (2b)² + 2 × (a) × (2b)

= a² + 4b² + 4ab

= a² + 4ab + 4b² Ans.

#2.

(5x - 3y)²

<em>Using identity (a - b)² = a² - 2ab + b², we get:</em>

= (5x)² + (3y)² - 2 × (5x) × (3y)

= 25x² + 9y² - 30xy

= 25x² - 30xy + 9y² Ans.

#3.

(3a + 4)(3a - 4)(9a² + 16)

<em>Using identity (x + y)(x - y) = x² - y², we get:</em>

= [(3a)² - (4)²][9a² + 16]

= (9a² - 16)(9a² + 16)

= (9a²)² - (16)²

= 81a⁴ - 256 Ans.

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A student takes an exam containing 1414 multiple choice questions. The probability of choosing a correct answer by knowledgeable

Readme [11.4K]

Answer:

0.0082 = 0.82% probability that he will pass

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the students guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 14, p = 0.3$ .

If the student makes knowledgeable guesses, what is the probability that he will pass?

He needs to guess at least 9 answers correctly. So

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{14,9}.(0.3)^{9}.(0.7)^{5} = 0.0066$

$P(X = 10) = C_{14,10}.(0.3)^{10}.(0.7)^{4} = 0.0014$

$P(X = 11) = C_{14,11}.(0.3)^{11}.(0.7)^{3} = 0.0002$

$P(X = 12) = C_{14,12}.(0.3)^{12}.(0.7)^{2} = 0.000024$

$P(X = 13) = C_{14,13}.(0.3)^{13}.(0.7)^{1} = 0.000002$

$P(X = 14) = C_{14,14}.(0.3)^{14}.(0.7)^{0} \cong 0$

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0066 + 0.0014 + 0.0002 + 0.000024 + 0.000002 = 0.0082$

0.0082 = 0.82% probability that he will pass

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2 years ago

Multiple choice please answer please

faust18 [17]

Answer:

15/17

Step-by-step explanation:

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3 years ago

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The volume of a cube is given by the expression 3 and its surface area is given by the expression 62, where s is the length of t

Zigmanuir [339]

V=s³
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3 years ago

What numbers are greater than 20 that has 9 as a factor

OLga [1]

Any of 9's multiples besides 9 and 18 will work.

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2 years ago

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The owners of a golf course hired a company to determine how many squirrels were living on their property. First, the company pu

muminat

Answer:

Squirrel population is 440 squirrels.

Step-by-step explanation:

It is given that there are 22 squirrels are marked.

Later the company returned and counted a total of 220 squirrels of which are marked were 11.

So, we can set up proportional equation to find the squirrel population.

Let squirrel population is x.

We can set up proportional equation as

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Cross multiply

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Divide both sides by 11

x=440

Best estimate is 440.

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3 years ago