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adoni [48]
3 years ago
10

Find the value of the lesser root of x2 - 7x + 12 = 0. A) -3 B) -1 C) 1 D) 3

Mathematics
2 answers:
kvv77 [185]3 years ago
8 0
The answer to your question is D) 3
icang [17]3 years ago
6 0

Answer:

x_1 = \frac{-(-7) - \sqrt{(-7)^2 -4(1)(12)}}{2(1)}= \frac{7-1}{2}= 3

x_2 = \frac{-(-7) + \sqrt{(-7)^2 -4(1)(12)}}{2(1)}= \frac{7+1}{2}= 4

So then since we want the lesser root the correct answer on this case is:

D) 3

Step-by-step explanation:

For this case we have the followin expression:

x^2 -7x +12=0

For this case we can use the quadratic formula in order to solve it, given by:

x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}

And on this case a = 1, b = -7, c = 12. And if we replace we got:

x_1 = \frac{-(-7) - \sqrt{(-7)^2 -4(1)(12)}}{2(1)}= \frac{7-1}{2}= 3

x_2 = \frac{-(-7) + \sqrt{(-7)^2 -4(1)(12)}}{2(1)}= \frac{7+1}{2}= 4

So then since we want the lesser root the correct answer on this case is:

D) 3

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The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime
Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334

X[bar] ± Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }

174.5 ± 2.334* \frac{6.9}{\sqrt{50} }

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0
3 years ago
A easy question help.
Citrus2011 [14]

Answer:

170ft

Step-by-step explanation:

7 0
2 years ago
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0.23w = 2.07

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w = 9 ounces

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3 years ago
The polygons are similar. Solve for x.<br><br> scale factor from A to B = 3:5
Sonbull [250]

Answer:

9

Step-by-step explanation:

if scale factor is 3/5, then

(x+12):35=3:5, ⇒

\frac{x+12}{35} =\frac{3}{5}; x=21-12; x=9

3 0
3 years ago
Simplify: (x + 3)(+ 2)
Alinara [238K]

Answer:

<h2><u><em>2x + 6</em></u></h2>

Step-by-step explanation:

Simplify: (x + 3)*(+ 2)

(x + 3)*(+ 2) =

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4 0
2 years ago
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