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2 years ago

Solve 5x^2-4x-2=0 by completing the square

Mathematics

1 answer:

konstantin123 [22]2 years ago

5 0

Answer:

Hello

Here's the answer:

2x^2 + 5x + 2 = 0\\
2x^2+4x+x+2=0\\
2x(x+2)+1(x+2)=0\\
(2x+1)(x+2)=0\\
x=-\frac{1}{2} \vee x=-2

x^2-4x+1=0\\
x^2-4x+4-3=0\\
(x-2)^2=3\\
x-2 =\sqrt3 \vee x-2=-\sqrt3\\
x=2+\sqrt3 \vee x=2-\sqrt3

Step-by-step explanation:

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The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50, with a standard deviation of $5.00. Assu

m_a_m_a [10]

Answer: 0.0170

Step-by-step explanation:

Given : The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50, with a standard deviation of $5.00.

i.e. $\mu=23.50$

$\sigma=5$

We assume the distribution of amounts purchased follows the normal distribution.

Sample size : n=50

Let $\overline{x}$ be the sample mean.

Formula : $z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Then, the probability that the sample mean is at least $25.00 will be :-

$P(\overline{x}\geq\25.00)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\geq\dfrac{25-23.50}{\dfrac{5}{\sqrt{50}}})\\\\=P(z\geq2.12)\\\\=1-P(z$

Hence, the likelihood the sample mean is at least $25.00= 0.0170

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2 years ago

The average time an individual reads online national news reports is 49 minutes. Assume the standard deviation is 16 minutes and

Olin [163]

Answer:

0.118 is the probability someone will spend no more than 30 minutes reading online national news reports.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 49 minutes

Standard Deviation, σ = 16 minutes

We are given that the distribution of time an individual reads is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(no more than 30 minutes)

$P( x \leq 610) = P( z \leq \displaystyle\frac{30 - 49}{16}) = P(z \leq -1.1875)$

Calculation the value from standard normal z table, we have,

$P(x \leq 30) = 0.118 = 11.8\%$

0.118 is the probability someone will spend no more than 30 minutes reading online national news reports.

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2 years ago

What property is 5+0=5

jok3333 [9.3K]

5+0=5 is the property of zero
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2 years ago

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soldi70 [24.7K]

Answer:

50.27

Step-by-step explanation:

area of a circle: pi X r^2

r= radius

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2 years ago

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Rt=R1 R2__, determined Rt when R1=100 and R2 =200?<br>R1+R2 (electronics)

zloy xaker [14]

Answer:

$R_t=300\ \Omega$

Step-by-step explanation:

Given that,

R₁ = 100 ohms

R₂ = 200 ohms

We need to find the equivalent resistance of the circuit. So,

$R_t=R_1+R_2\\\\R_t=100+200\\\\R_t=300\ \Omega$

So, the equivalent resistance is $300\ \Omega$ .

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2 years ago