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3 years ago

Prove the polynomial identity.

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

7 0

Explanation:

Since we have given that

$(2x+1)^2-2(2x+1)$

Now, we have to prove it as

$(2x+1)(2x-1)$

Now, start the iterations:

$(2x+1)^2-2(2x+1)\\\\=4x^2+1+4x-4x-2\\\\=4x^2+1-2\\\\=4x^2-1\\\\=(2x)^2-1\\\\=(2x+1)(2x-1)$

So, first blank will be filled with

$4x^2+4x+1$

Second blank will be filled with

$4x^2-1$

Hence proved.

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What is x for y=mx+b

Hoochie [10]

Y and x are the variables

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3 years ago

63% of US adults opposed to taxes on junk food and soda. You randomly select 10 US adults. Find the probability that the number

WARRIOR [948]

Answer:

a) 0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.

b) 0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.

c) 0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they are opposed to taxes on junk food and soda, or they are not. Each adult is independent of other adults, which means that the binomial probability distribution is used to solve the 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.

63% of US adults opposed to taxes on junk food and soda.

This means that $p = 0.63$

You randomly select 10 US adults.

This means that $n = 10$

(a) exactly one

This is $P(X = 1)$ . So

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

$P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008$

0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.

(b) at least four

This is

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{10,0}.(0.63)^{0}.(0.37)^{10} \approx 0$

$P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008$

$P(X = 2) = C_{10,2}.(0.63)^{2}.(0.37)^{8} = 0.0063$

$P(X = 3) = C_{10,3}.(0.63)^{3}.(0.37)^{7} = 0.0285$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0008 + 0.0063 + 0.0285 = 0.0356$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0356 = 0.9644$

0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.

(c) less than eight

This is

$P(X < 8) = 1 - P(X \geq 8)$

In which

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 8) = C_{10,8}.(0.63)^{8}.(0.37)^{2} = 0.1529$

$P(X = 9) = C_{10,1}.(0.63)^{9}.(0.37)^{1} = 0.0578$

$P(X = 10) = C_{10,2}.(0.63)^{10}.(0.37)^{0} = 0.0098$

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1529 + 0.0578 + 0.0098 = 0.2205$

$P(X < 8) = 1 - P(X \geq 8) = 1 - 0.2205 = 0.7795$

0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.

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4 years ago

Hola please help i’ll give brainliest but please answer correctly

Sergeu [11.5K]

Answer:

Step-by-step explanation: 1) 14.5 bc

We have the equation:

43.5 ÷ 3 = 14.500

Calculated to 3 decimal places.

2) They are all the same because they are the same numbers but in different places.

i hope this helps! =3

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3 years ago

X= <br> (-6x+125) (11x + 6)

artcher [175]

9514 1404 393

Answer:

x = 7

Step-by-step explanation:

The base angles of an isosceles triangle are congruent, so ...

11x +6 = -6x +125

17x = 119 . . . . . . . . . add 6x-6 to both sides

x = 7 . . . . . . . . divide by 17

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3 years ago

At a pizza shop, 75% of the customers order pizza, 20% of the customers order salad, and 15% of the customers order a pizza and

Vladimir79 [104]

Better probability of them getting pizza

3 0

4 years ago

Read 2 more answers