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Art [367]
3 years ago
11

How to solve which number completes the square of the expression belo? 2x^2-3x+ 1. 9/8 2. 9 3. -9/2 4. 9/16

Mathematics
1 answer:
choli [55]3 years ago
7 0

Answer:  1. \dfrac{9}{8} .

Step-by-step explanation:

The given expression  2x^2-3x+1

Using completing the square method.

First, we divide the entire expression by 2 and write in the form of x^2+bx=c , we get

x^2-\dfrac{3}{2}x+\dfrac{1}{2}

Such that b=\dfrac{3}{2}\ \ \ , c=\dfrac{1}{2}

Now add and subtract (\dfrac{b}{2})^2 on both sides.

(\dfrac{b}{2})^2=(\dfrac{\dfrac{3}{2}}{2})^2\\\\=(\dfrac{3}{2\times2})^2\\\\=(\dfrac{3^2}{4^2})\\\\=\dfrac{9}{8}

Here, we add and subtract \dfrac{9}{8} .

Hence, the correct answer is  1. \dfrac{9}{8} .

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The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deduction
Len [333]

Answer:

(a) <em>                             </em><em>n</em> :      20           50          100         500

P (-200 < <em>X</em> - <em>μ </em>< 200) : 0.2886    0.4444    0.5954    0.9376

(b) The correct option is (b).

Step-by-step explanation:

Let the random variable <em>X</em> represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.

The mean amount of deductions is, <em>μ</em> = $16,642 and standard deviation is, <em>σ</em> = $2,400.

Assuming that the random variable <em>X </em>follows a normal distribution.

(a)

Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:

  • For a sample size of <em>n</em> = 20

P(\mu-200

                                           =P(-0.37

  • For a sample size of <em>n</em> = 50

P(\mu-200

                                           =P(-0.59

  • For a sample size of <em>n</em> = 100

P(\mu-200

                                           =P(-0.83

  • For a sample size of <em>n</em> = 500

P(\mu-200

                                           =P(-1.86

<em>                                  n</em> :      20           50          100         500

P (-200 < <em>X</em> - <em>μ </em>< 200) : 0.2886    0.4444    0.5954    0.9376

(b)

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample (\bar x) approaches the whole population mean (\mu_{x}).

Consider the probabilities computed in part (a).

As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.

So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

Thus, the correct option is (b).

8 0
3 years ago
A box of chocolate is divided among Jim, Jack and David. David gets 2/5 of the box and Jack gets 1/5 of David's share and the re
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Answer:

200

Step-by-step explanation:

Jack share = 2/5 x 1/5 = 2/25

amount left over = 1 - (2/25 + 2/5) = 13/25

13/25 x t = 260

t = total amount of chocolate

t = (260 x 25) / 13 = 500

Davids share = 2/5 x 500 = 200

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