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2 years ago

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

2 answers:

7 0

X² + mx + m A perfect square trinomial is where:x² - is the square of the first term binomialmx - is twice the product of the binomials first and last termm - is the square of the last term binomial
x² + mx + m = (x + 1)²
(x + 1)² ⇒ (x+1)(x+1) = x(x+1) +1(x+1) ⇒ x² + x + x +1 = x² + 2x + 1

kiruha [24]2 years ago

3 0

X^2+mx+m= (x+1)^2 is your answer

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A website reports that 70% of its users are from outside a certain country, and 60% of its users logon the website every day. Su

JulijaS [17]

Answer:

The value is $P (I | L ) = 0.63$

The probability has increased

Step-by-step explanation:

From the question we are told that

The percentage that are from outside the country is $P(O) = 0.70$

The percentage that logs on everyday is $P(L) = 0.60$

The percentage that logs on everyday that are from the inside the country is $P(L | I) = 0.80$

Generally using Bayes' Rule the probability that a person is from the country given that he logs on the website every day is mathematically represented as

$P (I | L ) = \frac{P(I)* P(L|I)}{ P(O) *P(L|O) + P(I) *P(L|I) }$

Where $P(I)$ is the percentage that are from inside that country which is mathematically represented as

$P(I) = 1 - P(O)$

$P(I) = 1 - 0.70$

$P(I) = 0.30$

And $P(L| O)$ is percentage that logs on everyday that are from the outside the country which is evaluated as

$P(L| O) = 1- P(L| I)$

$P(L| O) = 1- 0.80$

$P(L| O) = 0.20$

$P (I | L ) = \frac{ 0.3* 0.80 }{ 0.7 *0.20 + 0.3 * 0.8 }$

$P (I | L ) = 0.63$

Given that the percentage that are from inside that country is $P(I) = 0.30$

and that the probability that a person is from the country given that he logs on the website every day is $P (I | L ) = 0.63$

We see that the additional information increased the probability

5 0

1 year ago

The area of a rectangle is (27x5 + 9x4 - 18x3) square feet. The width of the rectangle is 9x2 feet. What is the length of the re

Yuliya22 [10]

If the width is 9x², then the length is 27x^5+9x^4-18x^3/9x², which equals 3x³+x²+2x. ☺☺☺☺

8 0

1 year ago

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There are 500 employees in a firm, 45% are female. a sample of 60 employees is selected randomly. the probability that the sampl

beks73 [17]

Let X be the number of female employee. Let n be the sample size, p be the probability that selected employee is female.

It is given that 45% employee are female it mean p=0.45

Sample size n=60

From given information X follows Binomial distribution with n=50 and p=0.45

For large value of n the Binomial distribution approximates to Normal distribution.

Let p be the proportion of female employee in the given sample.

Then distribution of proportion P is normal with parameters

mean =p and standard deviation = $\sqrt{\frac{p(1-p)}{n}}$

Here we have p=0.45

So mean = p = 0.45 and

standard deviation = $\sqrt{\frac{0.45(1-0.45)}{60}}$

standard deviation = 0.0642

Now probability that sample proportions of female lies between 0.40 and 0.55 is

P(0.40 < P < 0.45) = $P(\frac{0.40 - 0.45}{0.0642} < \frac{P-mean}{standard deviation} < \frac{0.55- 0.45}{0.0642} )$

= P(-0.7788 < Z < 1.5576)

= P(Z < 1.5576) - P(Z < -0.7788)

= P(Z < 1.56) - P(Z < -0.78)

= 0.9406 - 0.2177

= 0.7229

The probability that the sample proportion of females is between 0.40 and 0.55 is 0.7229

6 0

1 year ago

A storage tank is a right-circular cylinder 20 ft long and 8 ft in diameter with its axis horizontal. If 3 the tank is half full

Arada [10]

Answer:

Step-by-step explanation:

The step by step calculation is as shown in the attached file.

3 0

1 year ago

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1. Hope's employer deposits her paycheck directly into her checking account. How much would her employer have

nadya68 [22]

Answer:

$284.79

Step-by-step explanation:

Hope has $284.79 deposited into his account. Hope's will receive a paycheck every two weeks.

7 0

2 years ago

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